Daily Papers

We focus on the problem of species distribution modeling using global-scale presence-only data. Most previous studies have mapped the range of a given species using geographical and environmental features alone. To capture a stronger implicit relationship between species, we encode the taxonomic hierarchy of species using a large language model. This enables range mapping for any taxonomic rank and unseen species without additional supervision. Further, we propose a novel proximity-aware evaluation metric that enables evaluating species distribution models using any pixel-level representation of ground-truth species range map. The proposed metric penalizes the predictions of a model based on its proximity to the ground truth. We describe the effectiveness of our model by systematically evaluating on the task of species range prediction, zero-shot prediction and geo-feature regression against the state-of-the-art. Results show our model outperforms the strong baselines when trained with a variety of multi-label learning losses.

Vision-and-language reasoning requires an understanding of visual concepts, language semantics, and, most importantly, the alignment and relationships between these two modalities. We thus propose the LXMERT (Learning Cross-Modality Encoder Representations from Transformers) framework to learn these vision-and-language connections. In LXMERT, we build a large-scale Transformer model that consists of three encoders: an object relationship encoder, a language encoder, and a cross-modality encoder. Next, to endow our model with the capability of connecting vision and language semantics, we pre-train the model with large amounts of image-and-sentence pairs, via five diverse representative pre-training tasks: masked language modeling, masked object prediction (feature regression and label classification), cross-modality matching, and image question answering. These tasks help in learning both intra-modality and cross-modality relationships. After fine-tuning from our pre-trained parameters, our model achieves the state-of-the-art results on two visual question answering datasets (i.e., VQA and GQA). We also show the generalizability of our pre-trained cross-modality model by adapting it to a challenging visual-reasoning task, NLVR2, and improve the previous best result by 22% absolute (54% to 76%). Lastly, we demonstrate detailed ablation studies to prove that both our novel model components and pre-training strategies significantly contribute to our strong results; and also present several attention visualizations for the different encoders. Code and pre-trained models publicly available at: https://github.com/airsplay/lxmert

Research related to automatically detecting Alzheimer's disease (AD) is important, given the high prevalence of AD and the high cost of traditional methods. Since AD significantly affects the content and acoustics of spontaneous speech, natural language processing and machine learning provide promising techniques for reliably detecting AD. We compare and contrast the performance of two such approaches for AD detection on the recent ADReSS challenge dataset: 1) using domain knowledge-based hand-crafted features that capture linguistic and acoustic phenomena, and 2) fine-tuning Bidirectional Encoder Representations from Transformer (BERT)-based sequence classification models. We also compare multiple feature-based regression models for a neuropsychological score task in the challenge. We observe that fine-tuned BERT models, given the relative importance of linguistics in cognitive impairment detection, outperform feature-based approaches on the AD detection task.

In our era of enormous neural networks, empirical progress has been driven by the philosophy that more is better. Recent deep learning practice has found repeatedly that larger model size, more data, and more computation (resulting in lower training loss) improves performance. In this paper, we give theoretical backing to these empirical observations by showing that these three properties hold in random feature (RF) regression, a class of models equivalent to shallow networks with only the last layer trained. Concretely, we first show that the test risk of RF regression decreases monotonically with both the number of features and the number of samples, provided the ridge penalty is tuned optimally. In particular, this implies that infinite width RF architectures are preferable to those of any finite width. We then proceed to demonstrate that, for a large class of tasks characterized by powerlaw eigenstructure, training to near-zero training loss is obligatory: near-optimal performance can only be achieved when the training error is much smaller than the test error. Grounding our theory in real-world data, we find empirically that standard computer vision tasks with convolutional neural tangent kernels clearly fall into this class. Taken together, our results tell a simple, testable story of the benefits of overparameterization, overfitting, and more data in random feature models.

Absolute Pose Regression (APR) methods use deep neural networks to directly regress camera poses from RGB images. However, the predominant APR architectures only rely on 2D operations during inference, resulting in limited accuracy of pose estimation due to the lack of 3D geometry constraints or priors. In this work, we propose a test-time refinement pipeline that leverages implicit geometric constraints using a robust feature field to enhance the ability of APR methods to use 3D information during inference. We also introduce a novel Neural Feature Synthesizer (NeFeS) model, which encodes 3D geometric features during training and directly renders dense novel view features at test time to refine APR methods. To enhance the robustness of our model, we introduce a feature fusion module and a progressive training strategy. Our proposed method achieves state-of-the-art single-image APR accuracy on indoor and outdoor datasets.

In this work, we explore the use of a novel neural network architecture, the Kolmogorov-Arnold Networks (KANs) as feature extractors for sensor-based (specifically IMU) Human Activity Recognition (HAR). Where conventional networks perform a parameterized weighted sum of the inputs at each node and then feed the result into a statically defined nonlinearity, KANs perform non-linear computations represented by B-SPLINES on the edges leading to each node and then just sum up the inputs at the node. Instead of learning weights, the system learns the spline parameters. In the original work, such networks have been shown to be able to more efficiently and exactly learn sophisticated real valued functions e.g. in regression or PDE solution. We hypothesize that such an ability is also advantageous for computing low-level features for IMU-based HAR. To this end, we have implemented KAN as the feature extraction architecture for IMU-based human activity recognition tasks, including four architecture variations. We present an initial performance investigation of the KAN feature extractor on four public HAR datasets. It shows that the KAN-based feature extractor outperforms CNN-based extractors on all datasets while being more parameter efficient.

With the rise of large language models (LLMs) for flexibly processing information as strings, a natural application is regression, specifically by preprocessing string representations into LLM embeddings as downstream features for metric prediction. In this paper, we provide one of the first comprehensive investigations into embedding-based regression and demonstrate that LLM embeddings as features can be better for high-dimensional regression tasks than using traditional feature engineering. This regression performance can be explained in part due to LLM embeddings over numeric data inherently preserving Lipschitz continuity over the feature space. Furthermore, we quantify the contribution of different model effects, most notably model size and language understanding, which we find surprisingly do not always improve regression performance.

Feature selection is the problem of selecting a subset of features for a machine learning model that maximizes model quality subject to a budget constraint. For neural networks, prior methods, including those based on ell_1 regularization, attention, and other techniques, typically select the entire feature subset in one evaluation round, ignoring the residual value of features during selection, i.e., the marginal contribution of a feature given that other features have already been selected. We propose a feature selection algorithm called Sequential Attention that achieves state-of-the-art empirical results for neural networks. This algorithm is based on an efficient one-pass implementation of greedy forward selection and uses attention weights at each step as a proxy for feature importance. We give theoretical insights into our algorithm for linear regression by showing that an adaptation to this setting is equivalent to the classical Orthogonal Matching Pursuit (OMP) algorithm, and thus inherits all of its provable guarantees. Our theoretical and empirical analyses offer new explanations towards the effectiveness of attention and its connections to overparameterization, which may be of independent interest.

In representation learning, uniformity refers to the uniform feature distribution in the latent space (i.e., unit hypersphere). Previous work has shown that improving uniformity contributes to the learning of under-represented classes. However, most of the previous work focused on classification; the representation space of imbalanced regression remains unexplored. Classification-based methods are not suitable for regression tasks because they cluster features into distinct groups without considering the continuous and ordered nature essential for regression. In a geometric aspect, we uniquely focus on ensuring uniformity in the latent space for imbalanced regression through two key losses: enveloping and homogeneity. The enveloping loss encourages the induced trace to uniformly occupy the surface of a hypersphere, while the homogeneity loss ensures smoothness, with representations evenly spaced at consistent intervals. Our method integrates these geometric principles into the data representations via a Surrogate-driven Representation Learning (SRL) framework. Experiments with real-world regression and operator learning tasks highlight the importance of uniformity in imbalanced regression and validate the efficacy of our geometry-based loss functions.

We introduce Random Feature Representation Boosting (RFRBoost), a novel method for constructing deep residual random feature neural networks (RFNNs) using boosting theory. RFRBoost uses random features at each layer to learn the functional gradient of the network representation, enhancing performance while preserving the convex optimization benefits of RFNNs. In the case of MSE loss, we obtain closed-form solutions to greedy layer-wise boosting with random features. For general loss functions, we show that fitting random feature residual blocks reduces to solving a quadratically constrained least squares problem. We demonstrate, through numerical experiments on 91 tabular datasets for regression and classification, that RFRBoost significantly outperforms traditional RFNNs and end-to-end trained MLP ResNets, while offering substantial computational advantages and theoretical guarantees stemming from boosting theory.

By leveraging temporal dependency in video sequences, multi-frame human pose estimation algorithms have demonstrated remarkable results in complicated situations, such as occlusion, motion blur, and video defocus. These algorithms are predominantly based on heatmaps, resulting in high computation and storage requirements per frame, which limits their flexibility and real-time application in video scenarios, particularly on edge devices. In this paper, we develop an efficient and effective video-based human pose regression method, which bypasses intermediate representations such as heatmaps and instead directly maps the input to the output joint coordinates. Despite the inherent spatial correlation among adjacent joints of the human pose, the temporal trajectory of each individual joint exhibits relative independence. In light of this, we propose a novel Decoupled Space-Time Aggregation network (DSTA) to separately capture the spatial contexts between adjacent joints and the temporal cues of each individual joint, thereby avoiding the conflation of spatiotemporal dimensions. Concretely, DSTA learns a dedicated feature token for each joint to facilitate the modeling of their spatiotemporal dependencies. With the proposed joint-wise local-awareness attention mechanism, our method is capable of efficiently and flexibly utilizing the spatial dependency of adjacent joints and the temporal dependency of each joint itself. Extensive experiments demonstrate the superiority of our method. Compared to previous regression-based single-frame human pose estimation methods, DSTA significantly enhances performance, achieving an 8.9 mAP improvement on PoseTrack2017. Furthermore, our approach either surpasses or is on par with the state-of-the-art heatmap-based multi-frame human pose estimation methods. Project page: https://github.com/zgspose/DSTA.

Imbalanced distributions are ubiquitous in real-world data. They create constraints on Deep Neural Networks to represent the minority labels and avoid bias towards majority labels. The extensive body of imbalanced approaches address categorical label spaces but fail to effectively extend to regression problems where the label space is continuous. Local and global correlations among continuous labels provide valuable insights towards effectively modelling relationships in feature space. In this work, we propose ConR, a contrastive regularizer that models global and local label similarities in feature space and prevents the features of minority samples from being collapsed into their majority neighbours. ConR discerns the disagreements between the label space and feature space and imposes a penalty on these disagreements. ConR addresses the continuous nature of label space with two main strategies in a contrastive manner: incorrect proximities are penalized proportionate to the label similarities and the correct ones are encouraged to model local similarities. ConR consolidates essential considerations into a generic, easy-to-integrate, and efficient method that effectively addresses deep imbalanced regression. Moreover, ConR is orthogonal to existing approaches and smoothly extends to uni- and multi-dimensional label spaces. Our comprehensive experiments show that ConR significantly boosts the performance of all the state-of-the-art methods on four large-scale deep imbalanced regression benchmarks. Our code is publicly available in https://github.com/BorealisAI/ConR.

We present PyMAF-X, a regression-based approach to recovering parametric full-body models from monocular images. This task is very challenging since minor parametric deviation may lead to noticeable misalignment between the estimated mesh and the input image. Moreover, when integrating part-specific estimations into the full-body model, existing solutions tend to either degrade the alignment or produce unnatural wrist poses. To address these issues, we propose a Pyramidal Mesh Alignment Feedback (PyMAF) loop in our regression network for well-aligned human mesh recovery and extend it as PyMAF-X for the recovery of expressive full-body models. The core idea of PyMAF is to leverage a feature pyramid and rectify the predicted parameters explicitly based on the mesh-image alignment status. Specifically, given the currently predicted parameters, mesh-aligned evidence will be extracted from finer-resolution features accordingly and fed back for parameter rectification. To enhance the alignment perception, an auxiliary dense supervision is employed to provide mesh-image correspondence guidance while spatial alignment attention is introduced to enable the awareness of the global contexts for our network. When extending PyMAF for full-body mesh recovery, an adaptive integration strategy is proposed in PyMAF-X to produce natural wrist poses while maintaining the well-aligned performance of the part-specific estimations. The efficacy of our approach is validated on several benchmark datasets for body, hand, face, and full-body mesh recovery, where PyMAF and PyMAF-X effectively improve the mesh-image alignment and achieve new state-of-the-art results. The project page with code and video results can be found at https://www.liuyebin.com/pymaf-x.

Classification algorithms have recently found applications in computational physics for the selection of numerical methods or models adapted to the environment and the state of the physical system. For such classification tasks, labeled training data come from numerical simulations and generally correspond to physical fields discretized on a mesh. Three challenging difficulties arise: the lack of training data, their high dimensionality, and the non-applicability of common data augmentation techniques to physics data. This article introduces two algorithms to address these issues, one for dimensionality reduction via feature selection, and one for data augmentation. These algorithms are combined with a wide variety of classifiers for their evaluation. When combined with a stacking ensemble made of six multilayer perceptrons and a ridge logistic regression, they enable reaching an accuracy of 90% on our classification problem for nonlinear structural mechanics.

In this paper, we evaluate the different features sets, feature types, and classifiers on both song and speech emotion recognition. Three feature sets: GeMAPS, pyAudioAnalysis, and LibROSA; two feature types: low-level descriptors and high-level statistical functions; and four classifiers: multilayer perceptron, LSTM, GRU, and convolution neural networks are examined on both song and speech data with the same parameter values. The results show no remarkable difference between song and speech data using the same method. In addition, high-level statistical functions of acoustic features gained higher performance scores than low-level descriptors in this classification task. This result strengthens the previous finding on the regression task which reported the advantage use of high-level features.

With the advent of deep learning for computer vision tasks, the need for accurately labeled data in large volumes is vital for any application. The increasingly available large amounts of solar image data generated by the Solar Dynamic Observatory (SDO) mission make this domain particularly interesting for the development and testing of deep learning systems. The currently available labeled solar data is generated by the SDO mission's Feature Finding Team's (FFT) specialized detection modules. The major drawback of these modules is that detection and labeling is performed with a cadence of every 4 to 12 hours, depending on the module. Since SDO image data products are created every 10 seconds, there is a considerable gap between labeled observations and the continuous data stream. In order to address this shortcoming, we trained a deep regression network to track the movement of two solar phenomena: Active Region and Coronal Hole events. To the best of our knowledge, this is the first attempt of solar event tracking using a deep learning approach. Since it is impossible to fully evaluate the performance of the suggested event tracks with the original data (only partial ground truth is available), we demonstrate with several metrics the effectiveness of our approach. With the purpose of generating continuously labeled solar image data, we present this feasibility analysis showing the great promise of deep regression networks for this task.

Language models have recently been shown capable of performing regression tasks wherein numeric predictions are represented as decoded strings. In this work, we provide theoretical grounds for this capability and furthermore investigate the utility of causal auto-regressive sequence models when they are applied to any feature representation. We find that, despite being trained in the usual way - for next-token prediction via cross-entropy loss - decoding-based regression is as performant as traditional approaches for tabular regression tasks, while being flexible enough to capture arbitrary distributions, such as in the task of density estimation.

Dense feature matching is an important computer vision task that involves estimating all correspondences between two images of a 3D scene. In this paper, we revisit robust losses for matching from a Markov chain perspective, yielding theoretical insights and large gains in performance. We begin by constructing a unifying formulation of matching as a Markov chain, based on which we identify two key stages which we argue should be decoupled for matching. The first is the coarse stage, where the estimated result needs to be globally consistent. The second is the refinement stage, where the model needs precise localization capabilities. Inspired by the insight that these stages concern distinct issues, we propose a coarse matcher following the regression-by-classification paradigm that provides excellent globally consistent, albeit not exactly localized, matches. This is followed by a local feature refinement stage using well-motivated robust regression losses, yielding extremely precise matches. Our proposed approach, which we call RoMa, achieves significant improvements compared to the state-of-the-art. Code is available at https://github.com/Parskatt/RoMa

Single-frame infrared small target detection is considered to be a challenging task, due to the extreme imbalance between target and background, bounding box regression is extremely sensitive to infrared small targets, and small target information is easy to lose in the high-level semantic layer. In this paper, we propose an enhancing feature learning network (EFLNet) based on YOLOv7 framework to solve these problems. First, we notice that there is an extremely imbalance between the target and the background in the infrared image, which makes the model pay more attention to the background features, resulting in missed detection. To address this problem, we propose a new adaptive threshold focal loss function that adjusts the loss weight automatically, compelling the model to allocate greater attention to target features. Second, we introduce the normalized Gaussian Wasserstein distance to alleviate the difficulty of model convergence caused by the extreme sensitivity of the bounding box regression to infrared small targets. Finally, we incorporate a dynamic head mechanism into the network to enable adaptive learning of the relative importance of each semantic layer. Experimental results demonstrate our method can achieve better performance in the detection performance of infrared small targets compared to state-of-the-art deep-learning based methods.

Improving the generalization of deep networks is an important open challenge, particularly in domains without plentiful data. The mixup algorithm improves generalization by linearly interpolating a pair of examples and their corresponding labels. These interpolated examples augment the original training set. Mixup has shown promising results in various classification tasks, but systematic analysis of mixup in regression remains underexplored. Using mixup directly on regression labels can result in arbitrarily incorrect labels. In this paper, we propose a simple yet powerful algorithm, C-Mixup, to improve generalization on regression tasks. In contrast with vanilla mixup, which picks training examples for mixing with uniform probability, C-Mixup adjusts the sampling probability based on the similarity of the labels. Our theoretical analysis confirms that C-Mixup with label similarity obtains a smaller mean square error in supervised regression and meta-regression than vanilla mixup and using feature similarity. Another benefit of C-Mixup is that it can improve out-of-distribution robustness, where the test distribution is different from the training distribution. By selectively interpolating examples with similar labels, it mitigates the effects of domain-associated information and yields domain-invariant representations. We evaluate C-Mixup on eleven datasets, ranging from tabular to video data. Compared to the best prior approach, C-Mixup achieves 6.56%, 4.76%, 5.82% improvements in in-distribution generalization, task generalization, and out-of-distribution robustness, respectively. Code is released at https://github.com/huaxiuyao/C-Mixup.

Regression-based methods have recently shown promising results in reconstructing human meshes from monocular images. By directly mapping raw pixels to model parameters, these methods can produce parametric models in a feed-forward manner via neural networks. However, minor deviation in parameters may lead to noticeable misalignment between the estimated meshes and image evidences. To address this issue, we propose a Pyramidal Mesh Alignment Feedback (PyMAF) loop to leverage a feature pyramid and rectify the predicted parameters explicitly based on the mesh-image alignment status in our deep regressor. In PyMAF, given the currently predicted parameters, mesh-aligned evidences will be extracted from finer-resolution features accordingly and fed back for parameter rectification. To reduce noise and enhance the reliability of these evidences, an auxiliary pixel-wise supervision is imposed on the feature encoder, which provides mesh-image correspondence guidance for our network to preserve the most related information in spatial features. The efficacy of our approach is validated on several benchmarks, including Human3.6M, 3DPW, LSP, and COCO, where experimental results show that our approach consistently improves the mesh-image alignment of the reconstruction. The project page with code and video results can be found at https://hongwenzhang.github.io/pymaf.

Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost estimates, and revenue predictions all benefit from being able to quantify the range of possible values accurately. As such, many models have been developed for this problem over many years of research in statistics, machine learning, and related fields. Rather than proposing yet another (new) algorithm for quantile regression we adopt a meta viewpoint: we investigate methods for aggregating any number of conditional quantile models, in order to improve accuracy and robustness. We consider weighted ensembles where weights may vary over not only individual models, but also over quantile levels, and feature values. All of the models we consider in this paper can be fit using modern deep learning toolkits, and hence are widely accessible (from an implementation point of view) and scalable. To improve the accuracy of the predicted quantiles (or equivalently, prediction intervals), we develop tools for ensuring that quantiles remain monotonically ordered, and apply conformal calibration methods. These can be used without any modification of the original library of base models. We also review some basic theory surrounding quantile aggregation and related scoring rules, and contribute a few new results to this literature (for example, the fact that post sorting or post isotonic regression can only improve the weighted interval score). Finally, we provide an extensive suite of empirical comparisons across 34 data sets from two different benchmark repositories.

Overparametrization often helps improve the generalization performance. This paper proposes a dual view of overparametrization suggesting that downsampling may also help generalize. Motivated by this dual view, we characterize two out-of-sample prediction risks of the sketched ridgeless least square estimator in the proportional regime masymp n asymp p, where m is the sketching size, n the sample size, and p the feature dimensionality. Our results reveal the statistical role of downsampling. Specifically, downsampling does not always hurt the generalization performance, and may actually help improve it in some cases. We identify the optimal sketching sizes that minimize the out-of-sample prediction risks, and find that the optimally sketched estimator has stabler risk curves that eliminates the peaks of those for the full-sample estimator. We then propose a practical procedure to empirically identify the optimal sketching size. Finally, we extend our results to cover central limit theorems and misspecified models. Numerical studies strongly support our theory.

The origin of adversarial examples is still inexplicable in research fields, and it arouses arguments from various viewpoints, albeit comprehensive investigations. In this paper, we propose a way of delving into the unexpected vulnerability in adversarially trained networks from a causal perspective, namely adversarial instrumental variable (IV) regression. By deploying it, we estimate the causal relation of adversarial prediction under an unbiased environment dissociated from unknown confounders. Our approach aims to demystify inherent causal features on adversarial examples by leveraging a zero-sum optimization game between a casual feature estimator (i.e., hypothesis model) and worst-case counterfactuals (i.e., test function) disturbing to find causal features. Through extensive analyses, we demonstrate that the estimated causal features are highly related to the correct prediction for adversarial robustness, and the counterfactuals exhibit extreme features significantly deviating from the correct prediction. In addition, we present how to effectively inoculate CAusal FEatures (CAFE) into defense networks for improving adversarial robustness.

As the field of automated machine learning (AutoML) advances, it becomes increasingly important to incorporate domain knowledge into these systems. We present an approach for doing so by harnessing the power of large language models (LLMs). Specifically, we introduce Context-Aware Automated Feature Engineering (CAAFE), a feature engineering method for tabular datasets that utilizes an LLM to iteratively generate additional semantically meaningful features for tabular datasets based on the description of the dataset. The method produces both Python code for creating new features and explanations for the utility of the generated features. Despite being methodologically simple, CAAFE improves performance on 11 out of 14 datasets -- boosting mean ROC AUC performance from 0.798 to 0.822 across all dataset - similar to the improvement achieved by using a random forest instead of logistic regression on our datasets. Furthermore, CAAFE is interpretable by providing a textual explanation for each generated feature. CAAFE paves the way for more extensive semi-automation in data science tasks and emphasizes the significance of context-aware solutions that can extend the scope of AutoML systems to semantic AutoML. We release our https://github.com/automl/CAAFE{code}, a simple https://colab.research.google.com/drive/1mCA8xOAJZ4MaB_alZvyARTMjhl6RZf0a{demo} and a https://pypi.org/project/caafe/{python package}.

This paper extends the classic theory of convex optimization to the minimization of functions that are equal to the negated logarithm of what we term as a sum-log-concave function, i.e., a sum of log-concave functions. In particular, we show that such functions are in general not convex but still satisfy generalized convexity inequalities. These inequalities unveil the key importance of a certain vector that we call the cross-gradient and that is, in general, distinct from the usual gradient. Thus, we propose the Cross Gradient Descent (XGD) algorithm moving in the opposite direction of the cross-gradient and derive a convergence analysis. As an application of our sum-log-concave framework, we introduce the so-called checkered regression method relying on a sum-log-concave function. This classifier extends (multiclass) logistic regression to non-linearly separable problems since it is capable of tessellating the feature space by using any given number of hyperplanes, creating a checkerboard-like pattern of decision regions.

Recently, polar-based representation has shown promising properties in perceptual tasks. In addition to Cartesian-based approaches, which separate point clouds unevenly, representing point clouds as polar grids has been recognized as an alternative due to (1) its advantage in robust performance under different resolutions and (2) its superiority in streaming-based approaches. However, state-of-the-art polar-based detection methods inevitably suffer from the feature distortion problem because of the non-uniform division of polar representation, resulting in a non-negligible performance gap compared to Cartesian-based approaches. To tackle this issue, we present PARTNER, a novel 3D object detector in the polar coordinate. PARTNER alleviates the dilemma of feature distortion with global representation re-alignment and facilitates the regression by introducing instance-level geometric information into the detection head. Extensive experiments show overwhelming advantages in streaming-based detection and different resolutions. Furthermore, our method outperforms the previous polar-based works with remarkable margins of 3.68% and 9.15% on Waymo and ONCE validation set, thus achieving competitive results over the state-of-the-art methods.

This paper presents an end-to-end neural mapping method for camera localization, dubbed NeuMap, encoding a whole scene into a grid of latent codes, with which a Transformer-based auto-decoder regresses 3D coordinates of query pixels. State-of-the-art feature matching methods require each scene to be stored as a 3D point cloud with per-point features, consuming several gigabytes of storage per scene. While compression is possible, performance drops significantly at high compression rates. Conversely, coordinate regression methods achieve high compression by storing scene information in a neural network but suffer from reduced robustness. NeuMap combines the advantages of both approaches by utilizing 1) learnable latent codes for efficient scene representation and 2) a scene-agnostic Transformer-based auto-decoder to infer coordinates for query pixels. This scene-agnostic network design learns robust matching priors from large-scale data and enables rapid optimization of codes for new scenes while keeping the network weights fixed. Extensive evaluations on five benchmarks show that NeuMap significantly outperforms other coordinate regression methods and achieves comparable performance to feature matching methods while requiring a much smaller scene representation size. For example, NeuMap achieves 39.1% accuracy in the Aachen night benchmark with only 6MB of data, whereas alternative methods require 100MB or several gigabytes and fail completely under high compression settings. The codes are available at https://github.com/Tangshitao/NeuMap

The fusion of LiDARs and cameras has been increasingly adopted in autonomous driving for perception tasks. The performance of such fusion-based algorithms largely depends on the accuracy of sensor calibration, which is challenging due to the difficulty of identifying common features across different data modalities. Previously, many calibration methods involved specific targets and/or manual intervention, which has proven to be cumbersome and costly. Learning-based online calibration methods have been proposed, but their performance is barely satisfactory in most cases. These methods usually suffer from issues such as sparse feature maps, unreliable cross-modality association, inaccurate calibration parameter regression, etc. In this paper, to address these issues, we propose CalibFormer, an end-to-end network for automatic LiDAR-camera calibration. We aggregate multiple layers of camera and LiDAR image features to achieve high-resolution representations. A multi-head correlation module is utilized to identify correlations between features more accurately. Lastly, we employ transformer architectures to estimate accurate calibration parameters from the correlation information. Our method achieved a mean translation error of 0.8751 cm and a mean rotation error of 0.0562 ^{circ} on the KITTI dataset, surpassing existing state-of-the-art methods and demonstrating strong robustness, accuracy, and generalization capabilities.

Can we relocalize in a scene represented by a single reference image? Standard visual relocalization requires hundreds of images and scale calibration to build a scene-specific 3D map. In contrast, we propose Map-free Relocalization, i.e., using only one photo of a scene to enable instant, metric scaled relocalization. Existing datasets are not suitable to benchmark map-free relocalization, due to their focus on large scenes or their limited variability. Thus, we have constructed a new dataset of 655 small places of interest, such as sculptures, murals and fountains, collected worldwide. Each place comes with a reference image to serve as a relocalization anchor, and dozens of query images with known, metric camera poses. The dataset features changing conditions, stark viewpoint changes, high variability across places, and queries with low to no visual overlap with the reference image. We identify two viable families of existing methods to provide baseline results: relative pose regression, and feature matching combined with single-image depth prediction. While these methods show reasonable performance on some favorable scenes in our dataset, map-free relocalization proves to be a challenge that requires new, innovative solutions.

Images of heavily occluded objects in cluttered scenes, such as fruit clusters in trees, are hard to segment. To further retrieve the 3D size and 6D pose of each individual object in such cases, bounding boxes are not reliable from multiple views since only a little portion of the object's geometry is captured. We introduce the first CNN-based ellipse detector, called Ellipse R-CNN, to represent and infer occluded objects as ellipses. We first propose a robust and compact ellipse regression based on the Mask R-CNN architecture for elliptical object detection. Our method can infer the parameters of multiple elliptical objects even they are occluded by other neighboring objects. For better occlusion handling, we exploit refined feature regions for the regression stage, and integrate the U-Net structure for learning different occlusion patterns to compute the final detection score. The correctness of ellipse regression is validated through experiments performed on synthetic data of clustered ellipses. We further quantitatively and qualitatively demonstrate that our approach outperforms the state-of-the-art model (i.e., Mask R-CNN followed by ellipse fitting) and its three variants on both synthetic and real datasets of occluded and clustered elliptical objects.

Dataset distillation methods have achieved remarkable success in distilling a large dataset into a small set of representative samples. However, they are not designed to produce a distilled dataset that can be effectively used for facilitating self-supervised pre-training. To this end, we propose a novel problem of distilling an unlabeled dataset into a set of small synthetic samples for efficient self-supervised learning (SSL). We first prove that a gradient of synthetic samples with respect to a SSL objective in naive bilevel optimization is biased due to the randomness originating from data augmentations or masking. To address this issue, we propose to minimize the mean squared error (MSE) between a model's representations of the synthetic examples and their corresponding learnable target feature representations for the inner objective, which does not introduce any randomness. Our primary motivation is that the model obtained by the proposed inner optimization can mimic the self-supervised target model. To achieve this, we also introduce the MSE between representations of the inner model and the self-supervised target model on the original full dataset for outer optimization. Lastly, assuming that a feature extractor is fixed, we only optimize a linear head on top of the feature extractor, which allows us to reduce the computational cost and obtain a closed-form solution of the head with kernel ridge regression. We empirically validate the effectiveness of our method on various applications involving transfer learning.

Regardless of the selected asset class and the level of model complexity (Transformer versus LSTM versus Perceptron/RNN), the GMADL loss function produces superior results than standard MSE-type loss functions and has better numerical properties in the context of optimization than MADL. Better results mean the possibility of achieving a higher risk-weighted return based on buy and sell signals built on forecasts generated by a given theoretical model estimated using the GMADL versus MSE or MADL function. In practice, GMADL solves the problem of selecting the most preferable feature in both classification and regression problems, improving the performance of each estimation. What is important is that, through additional parameterization, GMADL also solves the problem of optimizing investment systems on high-frequency data in such a way that they focus on strategy variants that contain fewer transactions so that transaction costs do not reduce the effectiveness of a given strategy to zero. Moreover, the implementation leverages state-of-the-art machine learning tools, including frameworks for hyperparameter tuning, architecture testing, and walk-forward optimization, ensuring robust and scalable solutions for real-world algorithmic trading.

Pulmonary Hypertension (PH) is a severe disease characterized by an elevated pulmonary artery pressure. The gold standard for PH diagnosis is measurement of mean Pulmonary Artery Pressure (mPAP) during an invasive Right Heart Catheterization. In this paper, we investigate noninvasive approach to PH detection utilizing Magnetic Resonance Imaging, Computer Models and Machine Learning. We show using the ablation study, that physics-informed feature engineering based on models of blood circulation increases the performance of Gradient Boosting Decision Trees-based algorithms for classification of PH and regression of values of mPAP. We compare results of regression (with thresholding of estimated mPAP) and classification and demonstrate that metrics achieved in both experiments are comparable. The predicted mPAP values are more informative to the physicians than the probability of PH returned by classification models. They provide the intuitive explanation of the outcome of the machine learning model (clinicians are accustomed to the mPAP metric, contrary to the PH probability).

Cross-validation is the de facto standard for predictive model evaluation and selection. In proper use, it provides an unbiased estimate of a model's predictive performance. However, data sets often undergo various forms of data-dependent preprocessing, such as mean-centering, rescaling, dimensionality reduction, and outlier removal. It is often believed that such preprocessing stages, if done in an unsupervised manner (that does not incorporate the class labels or response values) are generally safe to do prior to cross-validation. In this paper, we study three commonly-practiced preprocessing procedures prior to a regression analysis: (i) variance-based feature selection; (ii) grouping of rare categorical features; and (iii) feature rescaling. We demonstrate that unsupervised preprocessing can, in fact, introduce a substantial bias into cross-validation estimates and potentially hurt model selection. This bias may be either positive or negative and its exact magnitude depends on all the parameters of the problem in an intricate manner. Further research is needed to understand the real-world impact of this bias across different application domains, particularly when dealing with small sample sizes and high-dimensional data.

Recent advancements in autonomous driving, augmented reality, robotics, and embodied intelligence have necessitated 3D perception algorithms. However, current 3D perception methods, particularly small models, struggle with processing logical reasoning, question-answering, and handling open scenario categories. On the other hand, generative multimodal large language models (MLLMs) excel in general capacity but underperform in 3D tasks, due to weak spatial and local object perception, poor text-based geometric numerical output, and inability to handle camera focal variations. To address these challenges, we propose the following solutions: Spatial-Enhanced Local Feature Mining for better spatial feature extraction, 3D Query Token-Derived Info Decoding for precise geometric regression, and Geometry Projection-Based 3D Reasoning for handling camera focal length variations. We employ parameter-efficient fine-tuning for a pre-trained MLLM and develop LLMI3D, a powerful 3D perception MLLM. Additionally, we have constructed the IG3D dataset, which provides fine-grained descriptions and question-answer annotations. Extensive experiments demonstrate that our LLMI3D achieves state-of-the-art performance, significantly outperforming existing methods.

This article investigates signal estimation in wireless transmission (i.e., receive beamforming) from the perspective of statistical machine learning, where the transmit signals may be from an integrated sensing and communication system; that is, 1) signals may be not only discrete constellation points but also arbitrary complex values; 2) signals may be spatially correlated. Particular attention is paid to handling various uncertainties such as the uncertainty of the transmit signal covariance, the uncertainty of the channel matrix, the uncertainty of the channel noise covariance, the existence of channel impulse noises, and the limited sample size of pilots. To proceed, a distributionally robust machine learning framework that is insensitive to the above uncertainties is proposed, which reveals that channel estimation is not a necessary operation. For optimal linear estimation, the proposed framework includes several existing beamformers as special cases such as diagonal loading and eigenvalue thresholding. For optimal nonlinear estimation, estimators are limited in reproducing kernel Hilbert spaces and neural network function spaces, and corresponding uncertainty-aware solutions (e.g., kernelized diagonal loading) are derived. In addition, we prove that the ridge and kernel ridge regression methods in machine learning are distributionally robust against diagonal perturbation in feature covariance.

Purpose: Hard-to-interpret Black-box Machine Learning (ML) were often used for early Alzheimer's Disease (AD) detection. Methods: To interpret eXtreme Gradient Boosting (XGBoost), Random Forest (RF), and Support Vector Machine (SVM) black-box models a workflow based on Shapley values was developed. All models were trained on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset and evaluated for an independent ADNI test set, as well as the external Australian Imaging and Lifestyle flagship study of Ageing (AIBL), and Open Access Series of Imaging Studies (OASIS) datasets. Shapley values were compared to intuitively interpretable Decision Trees (DTs), and Logistic Regression (LR), as well as natural and permutation feature importances. To avoid the reduction of the explanation validity caused by correlated features, forward selection and aspect consolidation were implemented. Results: Some black-box models outperformed DTs and LR. The forward-selected features correspond to brain areas previously associated with AD. Shapley values identified biologically plausible associations with moderate to strong correlations with feature importances. The most important RF features to predict AD conversion were the volume of the amygdalae, and a cognitive test score. Good cognitive test performances and large brain volumes decreased the AD risk. The models trained using cognitive test scores significantly outperformed brain volumetric models (p<0.05). Cognitive Normal (CN) vs. AD models were successfully transferred to external datasets. Conclusion: In comparison to previous work, improved performances for ADNI and AIBL were achieved for CN vs. Mild Cognitive Impairment (MCI) classification using brain volumes. The Shapley values and the feature importances showed moderate to strong correlations.

Learning-based optical flow estimation has been dominated with the pipeline of cost volume with convolutions for flow regression, which is inherently limited to local correlations and thus is hard to address the long-standing challenge of large displacements. To alleviate this, the state-of-the-art framework RAFT gradually improves its prediction quality by using a large number of iterative refinements, achieving remarkable performance but introducing linearly increasing inference time. To enable both high accuracy and efficiency, we completely revamp the dominant flow regression pipeline by reformulating optical flow as a global matching problem, which identifies the correspondences by directly comparing feature similarities. Specifically, we propose a GMFlow framework, which consists of three main components: a customized Transformer for feature enhancement, a correlation and softmax layer for global feature matching, and a self-attention layer for flow propagation. We further introduce a refinement step that reuses GMFlow at higher feature resolution for residual flow prediction. Our new framework outperforms 31-refinements RAFT on the challenging Sintel benchmark, while using only one refinement and running faster, suggesting a new paradigm for accurate and efficient optical flow estimation. Code is available at https://github.com/haofeixu/gmflow.

We propose that the grokking phenomenon, where the train loss of a neural network decreases much earlier than its test loss, can arise due to a neural network transitioning from lazy training dynamics to a rich, feature learning regime. To illustrate this mechanism, we study the simple setting of vanilla gradient descent on a polynomial regression problem with a two layer neural network which exhibits grokking without regularization in a way that cannot be explained by existing theories. We identify sufficient statistics for the test loss of such a network, and tracking these over training reveals that grokking arises in this setting when the network first attempts to fit a kernel regression solution with its initial features, followed by late-time feature learning where a generalizing solution is identified after train loss is already low. We provide an asymptotic theoretical description of the grokking dynamics in this model using dynamical mean field theory (DMFT) for high dimensional data. We find that the key determinants of grokking are the rate of feature learning -- which can be controlled precisely by parameters that scale the network output -- and the alignment of the initial features with the target function y(x). We argue this delayed generalization arises when (1) the top eigenvectors of the initial neural tangent kernel and the task labels y(x) are misaligned, but (2) the dataset size is large enough so that it is possible for the network to generalize eventually, but not so large that train loss perfectly tracks test loss at all epochs, and (3) the network begins training in the lazy regime so does not learn features immediately. We conclude with evidence that this transition from lazy (linear model) to rich training (feature learning) can control grokking in more general settings, like on MNIST, one-layer Transformers, and student-teacher networks.

A large-scale deep model pre-trained on massive labeled or unlabeled data transfers well to downstream tasks. Linear evaluation freezes parameters in the pre-trained model and trains a linear classifier separately, which is efficient and attractive for transfer. However, little work has investigated the classifier in linear evaluation except for the default logistic regression. Inspired by the statistical efficiency of naive Bayes, the paper revisits the classical topic on discriminative vs. generative classifiers. Theoretically, the paper considers the surrogate loss instead of the zero-one loss in analyses and generalizes the classical results from binary cases to multiclass ones. We show that, under mild assumptions, multiclass naive Bayes requires O(log n) samples to approach its asymptotic error while the corresponding multiclass logistic regression requires O(n) samples, where n is the feature dimension. To establish it, we present a multiclass H-consistency bound framework and an explicit bound for logistic loss, which are of independent interests. Simulation results on a mixture of Gaussian validate our theoretical findings. Experiments on various pre-trained deep vision models show that naive Bayes consistently converges faster as the number of data increases. Besides, naive Bayes shows promise in few-shot cases and we observe the "two regimes" phenomenon in pre-trained supervised models. Our code is available at https://github.com/ML-GSAI/Revisiting-Dis-vs-Gen-Classifiers.

With the rapidly increasing demand for oriented object detection (OOD), recent research involving weakly-supervised detectors for learning rotated box (RBox) from the horizontal box (HBox) has attracted more and more attention. In this paper, we explore a more challenging yet label-efficient setting, namely single point-supervised OOD, and present our approach called Point2RBox. Specifically, we propose to leverage two principles: 1) Synthetic pattern knowledge combination: By sampling around each labeled point on the image, we spread the object feature to synthetic visual patterns with known boxes to provide the knowledge for box regression. 2) Transform self-supervision: With a transformed input image (e.g. scaled/rotated), the output RBoxes are trained to follow the same transformation so that the network can perceive the relative size/rotation between objects. The detector is further enhanced by a few devised techniques to cope with peripheral issues, e.g. the anchor/layer assignment as the size of the object is not available in our point supervision setting. To our best knowledge, Point2RBox is the first end-to-end solution for point-supervised OOD. In particular, our method uses a lightweight paradigm, yet it achieves a competitive performance among point-supervised alternatives, 41.05%/27.62%/80.01% on DOTA/DIOR/HRSC datasets.

Review websites, such as TripAdvisor and Yelp, allow users to post online reviews for various businesses, products and services, and have been recently shown to have a significant influence on consumer shopping behaviour. An online review typically consists of free-form text and a star rating out of 5. The problem of predicting a user's star rating for a product, given the user's text review for that product, is called Review Rating Prediction and has lately become a popular, albeit hard, problem in machine learning. In this paper, we treat Review Rating Prediction as a multi-class classification problem, and build sixteen different prediction models by combining four feature extraction methods, (i) unigrams, (ii) bigrams, (iii) trigrams and (iv) Latent Semantic Indexing, with four machine learning algorithms, (i) logistic regression, (ii) Naive Bayes classification, (iii) perceptrons, and (iv) linear Support Vector Classification. We analyse the performance of each of these sixteen models to come up with the best model for predicting the ratings from reviews. We use the dataset provided by Yelp for training and testing the models.

This paper proposes a method for the automatic creation of variables (in the case of regression) that complement the information contained in the initial input vector. The method works as a pre-processing step in which the continuous values of the variable to be regressed are discretized into a set of intervals which are then used to define value thresholds. Then classifiers are trained to predict whether the value to be regressed is less than or equal to each of these thresholds. The different outputs of the classifiers are then concatenated in the form of an additional vector of variables that enriches the initial vector of the regression problem. The implemented system can thus be considered as a generic pre-processing tool. We tested the proposed enrichment method with 5 types of regressors and evaluated it in 33 regression datasets. Our experimental results confirm the interest of the approach.

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

Evaluating the performance of machine learning models under distribution shift is challenging, especially when we only have unlabeled data from the shifted (target) domain, along with labeled data from the original (source) domain. Recent work suggests that the notion of disagreement, the degree to which two models trained with different randomness differ on the same input, is a key to tackle this problem. Experimentally, disagreement and prediction error have been shown to be strongly connected, which has been used to estimate model performance. Experiments have led to the discovery of the disagreement-on-the-line phenomenon, whereby the classification error under the target domain is often a linear function of the classification error under the source domain; and whenever this property holds, disagreement under the source and target domain follow the same linear relation. In this work, we develop a theoretical foundation for analyzing disagreement in high-dimensional random features regression; and study under what conditions the disagreement-on-the-line phenomenon occurs in our setting. Experiments on CIFAR-10-C, Tiny ImageNet-C, and Camelyon17 are consistent with our theory and support the universality of the theoretical findings.

We introduce the concept of programmable feature engineering for time series modeling and propose a feature programming framework. This framework generates large amounts of predictive features for noisy multivariate time series while allowing users to incorporate their inductive bias with minimal effort. The key motivation of our framework is to view any multivariate time series as a cumulative sum of fine-grained trajectory increments, with each increment governed by a novel spin-gas dynamical Ising model. This fine-grained perspective motivates the development of a parsimonious set of operators that summarize multivariate time series in an abstract fashion, serving as the foundation for large-scale automated feature engineering. Numerically, we validate the efficacy of our method on several synthetic and real-world noisy time series datasets.

Machine learning models, such as neural networks, decision trees, random forests, and gradient boosting machines, accept a feature vector, and provide a prediction. These models learn in a supervised fashion where we provide feature vectors mapped to the expected output. It is common practice to engineer new features from the provided feature set. Such engineered features will either augment or replace portions of the existing feature vector. These engineered features are essentially calculated fields based on the values of the other features. Engineering such features is primarily a manual, time-consuming task. Additionally, each type of model will respond differently to different kinds of engineered features. This paper reports empirical research to demonstrate what kinds of engineered features are best suited to various machine learning model types. We provide this recommendation by generating several datasets that we designed to benefit from a particular type of engineered feature. The experiment demonstrates to what degree the machine learning model can synthesize the needed feature on its own. If a model can synthesize a planned feature, it is not necessary to provide that feature. The research demonstrated that the studied models do indeed perform differently with various types of engineered features.

Within the field of causal inference, we consider the problem of estimating heterogeneous treatment effects from data. We propose and validate a novel approach for learning feature representations to aid the estimation of the conditional average treatment effect or CATE. Our method focuses on an intermediate layer in a neural network trained to predict the outcome from the features. In contrast to previous approaches that encourage the distribution of representations to be treatment-invariant, we leverage a genetic algorithm that optimizes over representations useful for predicting the outcome to select those less useful for predicting the treatment. This allows us to retain information within the features useful for predicting outcome even if that information may be related to treatment assignment. We validate our method on synthetic examples and illustrate its use on a real life dataset.

We propose a deep learning methodology for multivariate regression that is based on pattern recognition that triggers fast learning over sensor data. We used a conversion of sensors-to-image which enables us to take advantage of Computer Vision architectures and training processes. In addition to this data preparation methodology, we explore the use of state-of-the-art architectures to generate regression outputs to predict agricultural crop continuous yield information. Finally, we compare with some of the top models reported in MLCAS2021. We found that using a straightforward training process, we were able to accomplish an MAE of 4.394, RMSE of 5.945, and R^2 of 0.861.

The presence of distribution shifts poses a significant challenge for deploying modern machine learning models in real-world applications. This work focuses on the target shift problem in a regression setting (Zhang et al., 2013; Nguyen et al., 2016). More specifically, the target variable y (also known as the response variable), which is continuous, has different marginal distributions in the training source and testing domain, while the conditional distribution of features x given y remains the same. While most literature focuses on classification tasks with finite target space, the regression problem has an infinite dimensional target space, which makes many of the existing methods inapplicable. In this work, we show that the continuous target shift problem can be addressed by estimating the importance weight function from an ill-posed integral equation. We propose a nonparametric regularized approach named ReTaSA to solve the ill-posed integral equation and provide theoretical justification for the estimated importance weight function. The effectiveness of the proposed method has been demonstrated with extensive numerical studies on synthetic and real-world datasets.

Representation learning has been a critical topic in machine learning. In Click-through Rate Prediction, most features are represented as embedding vectors and learned simultaneously with other parameters in the model. With the development of CTR models, feature representation learning has become a trending topic and has been extensively studied by both industrial and academic researchers in recent years. This survey aims at summarizing the feature representation learning in a broader picture and pave the way for future research. To achieve such a goal, we first present a taxonomy of current research methods on feature representation learning following two main issues: (i) which feature to represent and (ii) how to represent these features. Then we give a detailed description of each method regarding these two issues. Finally, the review concludes with a discussion on the future directions of this field.

Image-level regression is an important task in Earth observation, where visual domain and label shifts are a core challenge hampering generalization. However, cross-domain regression within remote sensing data remains understudied due to the absence of suited datasets. We introduce a new dataset with aerial and satellite imagery in five countries with three forest-related regression tasks. To match real-world applicative interests, we compare methods through a restrictive setup where no prior on the target domain is available during training, and models are adapted with limited information during testing. Building on the assumption that ordered relationships generalize better, we propose manifold diffusion for regression as a strong baseline for transduction in low-data regimes. Our comparison highlights the comparative advantages of inductive and transductive methods in cross-domain regression.

Feature engineering has become one of the most important steps to improve model prediction performance, and to produce quality datasets. However, this process requires non-trivial domain-knowledge which involves a time-consuming process. Thereby, automating such process has become an active area of research and of interest in industrial applications. In this paper, a novel method, called Meta-learning and Causality Based Feature Engineering (MACFE), is proposed; our method is based on the use of meta-learning, feature distribution encoding, and causality feature selection. In MACFE, meta-learning is used to find the best transformations, then the search is accelerated by pre-selecting "original" features given their causal relevance. Experimental evaluations on popular classification datasets show that MACFE can improve the prediction performance across eight classifiers, outperforms the current state-of-the-art methods in average by at least 6.54%, and obtains an improvement of 2.71% over the best previous works.

In this paper, we introduce the idea of decomposing the residuals of regression with respect to the data instances instead of features. This allows us to determine the effects of each individual instance on the model and each other, and in doing so makes for a model-agnostic method of identifying instances of interest. In doing so, we can also determine the appropriateness of the model and data in the wider context of a given study. The paper focuses on the possible applications that such a framework brings to the relatively unexplored field of instance analysis in the context of Explainable AI tasks.

The goal of automated feature generation is to liberate machine learning experts from the laborious task of manual feature generation, which is crucial for improving the learning performance of tabular data. The major challenge in automated feature generation is to efficiently and accurately identify effective features from a vast pool of candidate features. In this paper, we present OpenFE, an automated feature generation tool that provides competitive results against machine learning experts. OpenFE achieves high efficiency and accuracy with two components: 1) a novel feature boosting method for accurately evaluating the incremental performance of candidate features and 2) a two-stage pruning algorithm that performs feature pruning in a coarse-to-fine manner. Extensive experiments on ten benchmark datasets show that OpenFE outperforms existing baseline methods by a large margin. We further evaluate OpenFE in two Kaggle competitions with thousands of data science teams participating. In the two competitions, features generated by OpenFE with a simple baseline model can beat 99.3% and 99.6% data science teams respectively. In addition to the empirical results, we provide a theoretical perspective to show that feature generation can be beneficial in a simple yet representative setting. The code is available at https://github.com/ZhangTP1996/OpenFE.

We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the response that has a unimodal distribution. Existing multiple-output quantile regression approaches are effective in such cases, so we apply them on the learned representation, and then transform the solution to the original space of the response. This process results in a flexible and informative region that can have an arbitrary shape, a property that existing methods lack. Second, we propose an extension of conformal prediction to the multivariate response setting that modifies any method to return sets with a pre-specified coverage level. The desired coverage is theoretically guaranteed in the finite-sample case for any distribution. Experiments conducted on both real and synthetic data show that our method constructs regions that are significantly smaller compared to existing techniques.

Conformal prediction (CP) for regression can be challenging, especially when the output distribution is heteroscedastic, multimodal, or skewed. Some of the issues can be addressed by estimating a distribution over the output, but in reality, such approaches can be sensitive to estimation error and yield unstable intervals.~Here, we circumvent the challenges by converting regression to a classification problem and then use CP for classification to obtain CP sets for regression.~To preserve the ordering of the continuous-output space, we design a new loss function and make necessary modifications to the CP classification techniques.~Empirical results on many benchmarks shows that this simple approach gives surprisingly good results on many practical problems.

Feature engineering has demonstrated substantial utility for many machine learning workflows, such as in the small data regime or when distribution shifts are severe. Thus automating this capability can relieve much manual effort and improve model performance. Towards this, we propose AutoMAN, or Automated Mask-based Feature Engineering, an automated feature engineering framework that achieves high accuracy, low latency, and can be extended to heterogeneous and time-varying data. AutoMAN is based on effectively exploring the candidate transforms space, without explicitly manifesting transformed features. This is achieved by learning feature importance masks, which can be extended to support other modalities such as time series. AutoMAN learns feature transform importance end-to-end, incorporating a dataset's task target directly into feature engineering, resulting in state-of-the-art performance with significantly lower latency compared to alternatives.

The paper studies the linear model for Bitcoin price which includes regression features based on Bitcoin currency statistics, mining processes, Google search trends, Wikipedia pages visits. The pattern of deviation of regression model prediction from real prices is simpler comparing to price time series. It is assumed that this pattern can be predicted by an experienced expert. In such a way, using the combination of the regression model and expert correction, one can receive better results than with either regression model or expert opinion only. It is shown that Bayesian approach makes it possible to utilize the probabilistic approach using distributions with fat tails and take into account the outliers in Bitcoin price time series.

In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a multi-task optimization problem as a regularization technique to enable single-task models to leverage multi-task learning information. We derive a closed-form solution for multi-task optimization in the context of linear models. Our analysis provides valuable insights by linking the multi-task learning performance to various model statistics such as raw data covariances, signal-generating hyperplanes, noise levels, as well as the size and number of datasets. We finally propose a consistent estimation of training and testing errors, thereby offering a robust foundation for hyperparameter optimization in multi-task regression scenarios. Experimental validations on both synthetic and real-world datasets in regression and multivariate time series forecasting demonstrate improvements on univariate models, incorporating our method into the training loss and thus leveraging multivariate information.

In this paper we introduce Feature Gradients, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e., in mini-batches) and in linear time and space with respect to both the number of features D and the sample size N . This, along with a discrete-to-continuous relaxation of the search domain, allows for an efficient, gradient-based search algorithm among feature subsets for very large datasets. Crucially, our algorithm is capable of finding higher-order correlations between features and targets for both the N > D and N < D regimes, as opposed to approaches that do not consider such interactions and/or only consider one regime. We provide experimental demonstration of the algorithm in small and large sample-and feature-size settings.

Click-through prediction (CTR) models transform features into latent vectors and enumerate possible feature interactions to improve performance based on the input feature set. Therefore, when selecting an optimal feature set, we should consider the influence of both feature and its interaction. However, most previous works focus on either feature field selection or only select feature interaction based on the fixed feature set to produce the feature set. The former restricts search space to the feature field, which is too coarse to determine subtle features. They also do not filter useless feature interactions, leading to higher computation costs and degraded model performance. The latter identifies useful feature interaction from all available features, resulting in many redundant features in the feature set. In this paper, we propose a novel method named OptFS to address these problems. To unify the selection of feature and its interaction, we decompose the selection of each feature interaction into the selection of two correlated features. Such a decomposition makes the model end-to-end trainable given various feature interaction operations. By adopting feature-level search space, we set a learnable gate to determine whether each feature should be within the feature set. Because of the large-scale search space, we develop a learning-by-continuation training scheme to learn such gates. Hence, OptFS generates the feature set only containing features which improve the final prediction results. Experimentally, we evaluate OptFS on three public datasets, demonstrating OptFS can optimize feature sets which enhance the model performance and further reduce both the storage and computational cost.

Feature shaping refers to a family of methods that exhibit state-of-the-art performance for out-of-distribution (OOD) detection. These approaches manipulate the feature representation, typically from the penultimate layer of a pre-trained deep learning model, so as to better differentiate between in-distribution (ID) and OOD samples. However, existing feature-shaping methods usually employ rules manually designed for specific model architectures and OOD datasets, which consequently limit their generalization ability. To address this gap, we first formulate an abstract optimization framework for studying feature-shaping methods. We then propose a concrete reduction of the framework with a simple piecewise constant shaping function and show that existing feature-shaping methods approximate the optimal solution to the concrete optimization problem. Further, assuming that OOD data is inaccessible, we propose a formulation that yields a closed-form solution for the piecewise constant shaping function, utilizing solely the ID data. Through extensive experiments, we show that the feature-shaping function optimized by our method improves the generalization ability of OOD detection across a large variety of datasets and model architectures.

Dynamic feature selection, where we sequentially query features to make accurate predictions with a minimal budget, is a promising paradigm to reduce feature acquisition costs and provide transparency into a model's predictions. The problem is challenging, however, as it requires both predicting with arbitrary feature sets and learning a policy to identify valuable selections. Here, we take an information-theoretic perspective and prioritize features based on their mutual information with the response variable. The main challenge is implementing this policy, and we design a new approach that estimates the mutual information in a discriminative rather than generative fashion. Building on our approach, we then introduce several further improvements: allowing variable feature budgets across samples, enabling non-uniform feature costs, incorporating prior information, and exploring modern architectures to handle partial inputs. Our experiments show that our method provides consistent gains over recent methods across a variety of datasets.

We present 3DRegNet, a novel deep learning architecture for the registration of 3D scans. Given a set of 3D point correspondences, we build a deep neural network to address the following two challenges: (i) classification of the point correspondences into inliers/outliers, and (ii) regression of the motion parameters that align the scans into a common reference frame. With regard to regression, we present two alternative approaches: (i) a Deep Neural Network (DNN) registration and (ii) a Procrustes approach using SVD to estimate the transformation. Our correspondence-based approach achieves a higher speedup compared to competing baselines. We further propose the use of a refinement network, which consists of a smaller 3DRegNet as a refinement to improve the accuracy of the registration. Extensive experiments on two challenging datasets demonstrate that we outperform other methods and achieve state-of-the-art results. The code is available.

With the introduction of data protection and privacy regulations, it has become crucial to remove the lineage of data on demand from a machine learning (ML) model. In the last few years, there have been notable developments in machine unlearning to remove the information of certain training data efficiently and effectively from ML models. In this work, we explore unlearning for the regression problem, particularly in deep learning models. Unlearning in classification and simple linear regression has been considerably investigated. However, unlearning in deep regression models largely remains an untouched problem till now. In this work, we introduce deep regression unlearning methods that generalize well and are robust to privacy attacks. We propose the Blindspot unlearning method which uses a novel weight optimization process. A randomly initialized model, partially exposed to the retain samples and a copy of the original model are used together to selectively imprint knowledge about the data that we wish to keep and scrub off the information of the data we wish to forget. We also propose a Gaussian fine tuning method for regression unlearning. The existing unlearning metrics for classification are not directly applicable to regression unlearning. Therefore, we adapt these metrics for the regression setting. We conduct regression unlearning experiments for computer vision, natural language processing and forecasting applications. Our methods show excellent performance for all these datasets across all the metrics. Source code: https://github.com/ayu987/deep-regression-unlearning

We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect Y can be written as a function of the cause X and a noise source N independent of X, which may be scaled by a positive function g over the cause, i.e., Y = f(X) + g(X)N. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of Y given X as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

Nowadays, it is possible to scan faces and automatically register them with high quality. However, the resulting face meshes often need further processing: we need to stabilize them to remove unwanted head movement. Stabilization is important for tasks like game development or movie making which require facial expressions to be cleanly separated from rigid head motion. Since manual stabilization is labor-intensive, there have been attempts to automate it. However, previous methods remain impractical: they either still require some manual input, produce imprecise alignments, rely on dubious heuristics and slow optimization, or assume a temporally ordered input. Instead, we present a new learning-based approach that is simple and fully automatic. We treat stabilization as a regression problem: given two face meshes, our network directly predicts the rigid transform between them that brings their skulls into alignment. We generate synthetic training data using a 3D Morphable Model (3DMM), exploiting the fact that 3DMM parameters separate skull motion from facial skin motion. Through extensive experiments we show that our approach outperforms the state-of-the-art both quantitatively and qualitatively on the tasks of stabilizing discrete sets of facial expressions as well as dynamic facial performances. Furthermore, we provide an ablation study detailing the design choices and best practices to help others adopt our approach for their own uses. Supplementary videos can be found on the project webpage syntec-research.github.io/FaceStab.

In symbolic regression, the goal is to find an analytical expression that accurately fits experimental data with the minimal use of mathematical symbols such as operators, variables, and constants. However, the combinatorial space of possible expressions can make it challenging for traditional evolutionary algorithms to find the correct expression in a reasonable amount of time. To address this issue, Neural Symbolic Regression (NSR) algorithms have been developed that can quickly identify patterns in the data and generate analytical expressions. However, these methods, in their current form, lack the capability to incorporate user-defined prior knowledge, which is often required in natural sciences and engineering fields. To overcome this limitation, we propose a novel neural symbolic regression method, named Neural Symbolic Regression with Hypothesis (NSRwH) that enables the explicit incorporation of assumptions about the expected structure of the ground-truth expression into the prediction process. Our experiments demonstrate that the proposed conditioned deep learning model outperforms its unconditioned counterparts in terms of accuracy while also providing control over the predicted expression structure.

In this work we propose for the first time a transformer-based framework for unsupervised representation learning of multivariate time series. Pre-trained models can be potentially used for downstream tasks such as regression and classification, forecasting and missing value imputation. By evaluating our models on several benchmark datasets for multivariate time series regression and classification, we show that not only does our modeling approach represent the most successful method employing unsupervised learning of multivariate time series presented to date, but also that it exceeds the current state-of-the-art performance of supervised methods; it does so even when the number of training samples is very limited, while offering computational efficiency. Finally, we demonstrate that unsupervised pre-training of our transformer models offers a substantial performance benefit over fully supervised learning, even without leveraging additional unlabeled data, i.e., by reusing the same data samples through the unsupervised objective.

Automated model selection is often proposed to users to choose which machine learning model (or method) to apply to a given regression task. In this paper, we show that combining different regression models can yield better results than selecting a single ('best') regression model, and outline an efficient method that obtains optimally weighted convex linear combination from a heterogeneous set of regression models. More specifically, in this paper, a heuristic weight optimization, used in a preceding conference paper, is replaced by an exact optimization algorithm using convex quadratic programming. We prove convexity of the quadratic programming formulation for the straightforward formulation and for a formulation with weighted data points. The novel weight optimization is not only (more) exact but also more efficient. The methods we develop in this paper are implemented and made available via github-open source. They can be executed on commonly available hardware and offer a transparent and easy to interpret interface. The results indicate that the approach outperforms model selection methods on a range of data sets, including data sets with mixed variable type from drug discovery applications.

Choosing which properties of the data to use as input to multivariate decision algorithms -- a.k.a. feature selection -- is an important step in solving any problem with machine learning. While there is a clear trend towards training sophisticated deep networks on large numbers of relatively unprocessed inputs (so-called automated feature engineering), for many tasks in physics, sets of theoretically well-motivated and well-understood features already exist. Working with such features can bring many benefits, including greater interpretability, reduced training and run time, and enhanced stability and robustness. We develop a new feature selection method based on Distance Correlation (DisCo), and demonstrate its effectiveness on the tasks of boosted top- and W-tagging. Using our method to select features from a set of over 7,000 energy flow polynomials, we show that we can match the performance of much deeper architectures, by using only ten features and two orders-of-magnitude fewer model parameters.

Symbolic regression (SR) is a powerful technique for discovering the underlying mathematical expressions from observed data. Inspired by the success of deep learning, recent efforts have focused on two categories for SR methods. One is using a neural network or genetic programming to search the expression tree directly. Although this has shown promising results, the large search space poses difficulties in learning constant factors and processing high-dimensional problems. Another approach is leveraging a transformer-based model training on synthetic data and offers advantages in inference speed. However, this method is limited to fixed small numbers of dimensions and may encounter inference problems when given data is out-of-distribution compared to the synthetic data. In this work, we propose DySymNet, a novel neural-guided Dynamic Symbolic Network for SR. Instead of searching for expressions within a large search space, we explore DySymNet with various structures and optimize them to identify expressions that better-fitting the data. With a topology structure like neural networks, DySymNet not only tackles the challenge of high-dimensional problems but also proves effective in optimizing constants. Based on extensive numerical experiments using low-dimensional public standard benchmarks and the well-known SRBench with more variables, our method achieves state-of-the-art performance in terms of fitting accuracy and robustness to noise.

Neural field methods have seen great progress in various long-standing tasks in computer vision and computer graphics, including novel view synthesis and geometry reconstruction. As existing neural field methods try to predict some coordinate-based continuous target values, such as RGB for Neural Radiance Field (NeRF), all of these methods are regression models and are optimized by some regression loss. However, are regression models really better than classification models for neural field methods? In this work, we try to visit this very fundamental but overlooked question for neural fields from a machine learning perspective. We successfully propose a novel Neural Field Classifier (NFC) framework which formulates existing neural field methods as classification tasks rather than regression tasks. The proposed NFC can easily transform arbitrary Neural Field Regressor (NFR) into its classification variant via employing a novel Target Encoding module and optimizing a classification loss. By encoding a continuous regression target into a high-dimensional discrete encoding, we naturally formulate a multi-label classification task. Extensive experiments demonstrate the impressive effectiveness of NFC at the nearly free extra computational costs. Moreover, NFC also shows robustness to sparse inputs, corrupted images, and dynamic scenes.

Cricket, "a Gentleman's Game", is a prominent sport rising worldwide. Due to the rising competitiveness of the sport, players and team management have become more professional with their approach. Prior studies predicted individual performance or chose the best team but did not highlight the batter's potential. On the other hand, our research aims to evaluate a player's impact while considering his control in various circumstances. This paper seeks to understand the conundrum behind this impactful performance by determining how much control a player has over the circumstances and generating the "Effective Runs",a new measure we propose. We first gathered the fundamental cricket data from open-source datasets; however, variables like pitch, weather, and control were not readily available for all matches. As a result, we compiled our corpus data by analyzing the commentary of the match summaries. This gave us an insight into the particular game's weather and pitch conditions. Furthermore, ball-by-ball inspection from the commentary led us to determine the control of the shots played by the batter. We collected data for the entire One Day International career, up to February 2022, of 3 prominent cricket players: Rohit G Sharma, David A Warner, and Kane S Williamson. Lastly, to prepare the dataset, we encoded, scaled, and split the dataset to train and test Machine Learning Algorithms. We used Multiple Linear Regression (MLR), Polynomial Regression, Support Vector Regression (SVR), Decision Tree Regression, and Random Forest Regression on each player's data individually to train them and predict the Impact the player will have on the game. Multiple Linear Regression and Random Forest give the best predictions accuracy of 90.16 percent and 87.12 percent, respectively.

Interactions among features are central to understanding the behavior of machine learning models. Recent research has made significant strides in detecting and quantifying feature interactions in single predictive models. However, we argue that the feature interactions extracted from a single pre-specified model may not be trustworthy since: a well-trained predictive model may not preserve the true feature interactions and there exist multiple well-performing predictive models that differ in feature interaction strengths. Thus, we recommend exploring feature interaction strengths in a model class of approximately equally accurate predictive models. In this work, we introduce the feature interaction score (FIS) in the context of a Rashomon set, representing a collection of models that achieve similar accuracy on a given task. We propose a general and practical algorithm to calculate the FIS in the model class. We demonstrate the properties of the FIS via synthetic data and draw connections to other areas of statistics. Additionally, we introduce a Halo plot for visualizing the feature interaction variance in high-dimensional space and a swarm plot for analyzing FIS in a Rashomon set. Experiments with recidivism prediction and image classification illustrate how feature interactions can vary dramatically in importance for similarly accurate predictive models. Our results suggest that the proposed FIS can provide valuable insights into the nature of feature interactions in machine learning models.

We introduce a novel machine learning model for credit risk by combining tree-boosting with a latent spatio-temporal Gaussian process model accounting for frailty correlation. This allows for modeling non-linearities and interactions among predictor variables in a flexible data-driven manner and for accounting for spatio-temporal variation that is not explained by observable predictor variables. We also show how estimation and prediction can be done in a computationally efficient manner. In an application to a large U.S. mortgage credit risk data set, we find that both predictive default probabilities for individual loans and predictive loan portfolio loss distributions obtained with our novel approach are more accurate compared to conventional independent linear hazard models and also linear spatio-temporal models. Using interpretability tools for machine learning models, we find that the likely reasons for this outperformance are strong interaction and non-linear effects in the predictor variables and the presence of large spatio-temporal frailty effects.

Given a matrix Ain R^{ntimes d} and a vector bin R^n, we consider the regression problem with ell_infty guarantees: finding a vector x'in R^d such that |x'-x^*|_infty leq epsilon{d}cdot |Ax^*-b|_2cdot |A^dagger| where x^*=argmin_{xin R^d}|Ax-b|_2. One popular approach for solving such ell_2 regression problem is via sketching: picking a structured random matrix Sin R^{mtimes n} with mll n and SA can be quickly computed, solve the ``sketched'' regression problem argmin_{xin R^d} |SAx-Sb|_2. In this paper, we show that in order to obtain such ell_infty guarantee for ell_2 regression, one has to use sketching matrices that are dense. To the best of our knowledge, this is the first user case in which dense sketching matrices are necessary. On the algorithmic side, we prove that there exists a distribution of dense sketching matrices with m=epsilon^{-2}dlog^3(n/delta) such that solving the sketched regression problem gives the ell_infty guarantee, with probability at least 1-delta. Moreover, the matrix SA can be computed in time O(ndlog n). Our row count is nearly-optimal up to logarithmic factors, and significantly improves the result in [Price, Song and Woodruff, ICALP'17], in which a super-linear in d rows, m=Omega(epsilon^{-2}d^{1+gamma}) for gamma=Theta(frac{loglog n{log d}}) is required. We also develop a novel analytical framework for ell_infty guarantee regression that utilizes the Oblivious Coordinate-wise Embedding (OCE) property introduced in [Song and Yu, ICML'21]. Our analysis is arguably much simpler and more general than [Price, Song and Woodruff, ICALP'17], and it extends to dense sketches for tensor product of vectors.

In this study, we propose Feature-aligned N-BEATS as a domain generalization model for univariate time series forecasting problems. The proposed model is an extension of the doubly residual stacking architecture of N-BEATS (Oreshkin et al. [34]) into a representation learning framework. The model is a new structure that involves marginal feature probability measures (i.e., pushforward measures of multiple source domains) induced by the intricate composition of residual operators of N-BEATS in each stack and aligns them stack-wise via an entropic regularized Wasserstein distance referred to as the Sinkhorn divergence (Genevay et al. [14]). The loss function consists of a typical forecasting loss for multiple source domains and an alignment loss calculated with the Sinkhorn divergence, which allows the model to learn invariant features stack-wise across multiple source data sequences while retaining N-BEATS's interpretable design. We conduct a comprehensive experimental evaluation of the proposed approach and the results demonstrate the model's forecasting and generalization capabilities in comparison with methods based on the original N-BEATS.

Mixture models arise in many regression problems, but most methods have seen limited adoption partly due to these algorithms' highly-tailored and model-specific nature. On the other hand, transformers are flexible, neural sequence models that present the intriguing possibility of providing general-purpose prediction methods, even in this mixture setting. In this work, we investigate the hypothesis that transformers can learn an optimal predictor for mixtures of regressions. We construct a generative process for a mixture of linear regressions for which the decision-theoretic optimal procedure is given by data-driven exponential weights on a finite set of parameters. We observe that transformers achieve low mean-squared error on data generated via this process. By probing the transformer's output at inference time, we also show that transformers typically make predictions that are close to the optimal predictor. Our experiments also demonstrate that transformers can learn mixtures of regressions in a sample-efficient fashion and are somewhat robust to distribution shifts. We complement our experimental observations by proving constructively that the decision-theoretic optimal procedure is indeed implementable by a transformer.

A number of computer vision deep regression approaches report improved results when adding a classification loss to the regression loss. Here, we explore why this is useful in practice and when it is beneficial. To do so, we start from precisely controlled dataset variations and data samplings and find that the effect of adding a classification loss is the most pronounced for regression with imbalanced data. We explain these empirical findings by formalizing the relation between the balanced and imbalanced regression losses. Finally, we show that our findings hold on two real imbalanced image datasets for depth estimation (NYUD2-DIR), and age estimation (IMDB-WIKI-DIR), and on the problem of imbalanced video progress prediction (Breakfast). Our main takeaway is: for a regression task, if the data sampling is imbalanced, then add a classification loss.

Air pollution constitutes a global problem of paramount importance that affects not only human health, but also the environment. The existence of spatial and temporal data regarding the concentrations of pollutants is crucial for performing air pollution studies and monitor emissions. However, although observation data presents great temporal coverage, the number of stations is very limited and they are usually built in more populated areas. The main objective of this work is to create models capable of inferring pollutant concentrations in locations where no observation data exists. A machine learning model, more specifically the random forest model, was developed for predicting concentrations in the Iberian Peninsula in 2019 for five selected pollutants: NO_2, O_3 SO_2, PM10, and PM2.5. Model features include satellite measurements, meteorological variables, land use classification, temporal variables (month, day of year), and spatial variables (latitude, longitude, altitude). The models were evaluated using various methods, including station 10-fold cross-validation, in which in each fold observations from 10\% of the stations are used as testing data and the rest as training data. The R^2, RMSE and mean bias were determined for each model. The NO_2 and O_3 models presented good values of R^2, 0.5524 and 0.7462, respectively. However, the SO_2, PM10, and PM2.5 models performed very poorly in this regard, with R^2 values of -0.0231, 0.3722, and 0.3303, respectively. All models slightly overestimated the ground concentrations, except the O_3 model. All models presented acceptable cross-validation RMSE, except the O_3 and PM10 models where the mean value was a little higher (12.5934 mu g/m^3 and 10.4737 mu g/m^3, respectively).

In representation learning, regression has traditionally received less attention than classification. Directly applying representation learning techniques designed for classification to regression often results in fragmented representations in the latent space, yielding sub-optimal performance. In this paper, we argue that the potential of contrastive learning for regression has been overshadowed due to the neglect of two crucial aspects: ordinality-awareness and hardness. To address these challenges, we advocate "mixup your own contrastive pairs for supervised contrastive regression", instead of relying solely on real/augmented samples. Specifically, we propose Supervised Contrastive Learning for Regression with Mixup (SupReMix). It takes anchor-inclusive mixtures (mixup of the anchor and a distinct negative sample) as hard negative pairs and anchor-exclusive mixtures (mixup of two distinct negative samples) as hard positive pairs at the embedding level. This strategy formulates harder contrastive pairs by integrating richer ordinal information. Through extensive experiments on six regression datasets including 2D images, volumetric images, text, tabular data, and time-series signals, coupled with theoretical analysis, we demonstrate that SupReMix pre-training fosters continuous ordered representations of regression data, resulting in significant improvement in regression performance. Furthermore, SupReMix is superior to other approaches in a range of regression challenges including transfer learning, imbalanced training data, and scenarios with fewer training samples.

Small sample sizes are common in many disciplines, which necessitates pooling roughly similar datasets across multiple institutions to study weak but relevant associations between images and disease outcomes. Such data often manifest shift/imbalance in covariates (i.e., secondary non-imaging data). Controlling for such nuisance variables is common within standard statistical analysis, but the ideas do not directly apply to overparameterized models. Consequently, recent work has shown how strategies from invariant representation learning provides a meaningful starting point, but the current repertoire of methods is limited to accounting for shifts/imbalances in just a couple of covariates at a time. In this paper, we show how viewing this problem from the perspective of Category theory provides a simple and effective solution that completely avoids elaborate multi-stage training pipelines that would otherwise be needed. We show the effectiveness of this approach via extensive experiments on real datasets. Further, we discuss how this style of formulation offers a unified perspective on at least 5+ distinct problem settings, from self-supervised learning to matching problems in 3D reconstruction.

Pre-trained foundation models (FMs) have shown exceptional performance in univariate time series forecasting tasks. However, several practical challenges persist, including managing intricate dependencies among features and quantifying uncertainty in predictions. This study aims to tackle these critical limitations by introducing adapters; feature-space transformations that facilitate the effective use of pre-trained univariate time series FMs for multivariate tasks. Adapters operate by projecting multivariate inputs into a suitable latent space and applying the FM independently to each dimension. Inspired by the literature on representation learning and partially stochastic Bayesian neural networks, we present a range of adapters and optimization/inference strategies. Experiments conducted on both synthetic and real-world datasets confirm the efficacy of adapters, demonstrating substantial enhancements in forecasting accuracy and uncertainty quantification compared to baseline methods. Our framework, AdaPTS, positions adapters as a modular, scalable, and effective solution for leveraging time series FMs in multivariate contexts, thereby promoting their wider adoption in real-world applications. We release the code at https://github.com/abenechehab/AdaPTS.

Feature-based methods are commonly used to explain model predictions, but these methods often implicitly assume that interpretable features are readily available. However, this is often not the case for high-dimensional data, and it can be hard even for domain experts to mathematically specify which features are important. Can we instead automatically extract collections or groups of features that are aligned with expert knowledge? To address this gap, we present FIX (Features Interpretable to eXperts), a benchmark for measuring how well a collection of features aligns with expert knowledge. In collaboration with domain experts, we propose FIXScore, a unified expert alignment measure applicable to diverse real-world settings across cosmology, psychology, and medicine domains in vision, language and time series data modalities. With FIXScore, we find that popular feature-based explanation methods have poor alignment with expert-specified knowledge, highlighting the need for new methods that can better identify features interpretable to experts.

Data-based and learning-based sound source localization (SSL) has shown promising results in challenging conditions, and is commonly set as a classification or a regression problem. Regression-based approaches have certain advantages over classification-based, such as continuous direction-of-arrival estimation of static and moving sources. However, multi-source scenarios require multiple regressors without a clear training strategy up-to-date, that does not rely on auxiliary information such as simultaneous sound classification. We investigate end-to-end training of such methods with a technique recently proposed for video object detectors, adapted to the SSL setting. A differentiable network is constructed that can be plugged to the output of the localizer to solve the optimal assignment between predictions and references, optimizing directly the popular CLEAR-MOT tracking metrics. Results indicate large improvements over directly optimizing mean squared errors, in terms of localization error, detection metrics, and tracking capabilities.

Time Series Forecasting has been an active area of research due to its many applications ranging from network usage prediction, resource allocation, anomaly detection, and predictive maintenance. Numerous publications published in the last five years have proposed diverse sets of objective loss functions to address cases such as biased data, long-term forecasting, multicollinear features, etc. In this paper, we have summarized 14 well-known regression loss functions commonly used for time series forecasting and listed out the circumstances where their application can aid in faster and better model convergence. We have also demonstrated how certain categories of loss functions perform well across all data sets and can be considered as a baseline objective function in circumstances where the distribution of the data is unknown. Our code is available at GitHub: https://github.com/aryan-jadon/Regression-Loss-Functions-in-Time-Series-Forecasting-Tensorflow.

Major complications arise from the recent increase in the amount of high-dimensional data, including high computational costs and memory requirements. Feature selection, which identifies the most relevant and informative attributes of a dataset, has been introduced as a solution to this problem. Most of the existing feature selection methods are computationally inefficient; inefficient algorithms lead to high energy consumption, which is not desirable for devices with limited computational and energy resources. In this paper, a novel and flexible method for unsupervised feature selection is proposed. This method, named QuickSelection, introduces the strength of the neuron in sparse neural networks as a criterion to measure the feature importance. This criterion, blended with sparsely connected denoising autoencoders trained with the sparse evolutionary training procedure, derives the importance of all input features simultaneously. We implement QuickSelection in a purely sparse manner as opposed to the typical approach of using a binary mask over connections to simulate sparsity. It results in a considerable speed increase and memory reduction. When tested on several benchmark datasets, including five low-dimensional and three high-dimensional datasets, the proposed method is able to achieve the best trade-off of classification and clustering accuracy, running time, and maximum memory usage, among widely used approaches for feature selection. Besides, our proposed method requires the least amount of energy among the state-of-the-art autoencoder-based feature selection methods.

Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed strategies that do not improve with experience. In this paper, we introduce the first symbolic regression method that leverages large scale pre-training. We procedurally generate an unbounded set of equations, and simultaneously pre-train a Transformer to predict the symbolic equation from a corresponding set of input-output-pairs. At test time, we query the model on a new set of points and use its output to guide the search for the equation. We show empirically that this approach can re-discover a set of well-known physical equations, and that it improves over time with more data and compute.

Feature selection helps reduce data acquisition costs in ML, but the standard approach is to train models with static feature subsets. Here, we consider the dynamic feature selection (DFS) problem where a model sequentially queries features based on the presently available information. DFS is often addressed with reinforcement learning, but we explore a simpler approach of greedily selecting features based on their conditional mutual information. This method is theoretically appealing but requires oracle access to the data distribution, so we develop a learning approach based on amortized optimization. The proposed method is shown to recover the greedy policy when trained to optimality, and it outperforms numerous existing feature selection methods in our experiments, thus validating it as a simple but powerful approach for this problem.

Model-based human pose estimation is currently approached through two different paradigms. Optimization-based methods fit a parametric body model to 2D observations in an iterative manner, leading to accurate image-model alignments, but are often slow and sensitive to the initialization. In contrast, regression-based methods, that use a deep network to directly estimate the model parameters from pixels, tend to provide reasonable, but not pixel accurate, results while requiring huge amounts of supervision. In this work, instead of investigating which approach is better, our key insight is that the two paradigms can form a strong collaboration. A reasonable, directly regressed estimate from the network can initialize the iterative optimization making the fitting faster and more accurate. Similarly, a pixel accurate fit from iterative optimization can act as strong supervision for the network. This is the core of our proposed approach SPIN (SMPL oPtimization IN the loop). The deep network initializes an iterative optimization routine that fits the body model to 2D joints within the training loop, and the fitted estimate is subsequently used to supervise the network. Our approach is self-improving by nature, since better network estimates can lead the optimization to better solutions, while more accurate optimization fits provide better supervision for the network. We demonstrate the effectiveness of our approach in different settings, where 3D ground truth is scarce, or not available, and we consistently outperform the state-of-the-art model-based pose estimation approaches by significant margins. The project website with videos, results, and code can be found at https://seas.upenn.edu/~nkolot/projects/spin.

A feature-based model explanation denotes how much each input feature contributes to a model's output for a given data point. As the number of proposed explanation functions grows, we lack quantitative evaluation criteria to help practitioners know when to use which explanation function. This paper proposes quantitative evaluation criteria for feature-based explanations: low sensitivity, high faithfulness, and low complexity. We devise a framework for aggregating explanation functions. We develop a procedure for learning an aggregate explanation function with lower complexity and then derive a new aggregate Shapley value explanation function that minimizes sensitivity.

Deep-learning models can extract a rich assortment of features from data. Which features a model uses depends not only on predictivity-how reliably a feature indicates train-set labels-but also on availability-how easily the feature can be extracted, or leveraged, from inputs. The literature on shortcut learning has noted examples in which models privilege one feature over another, for example texture over shape and image backgrounds over foreground objects. Here, we test hypotheses about which input properties are more available to a model, and systematically study how predictivity and availability interact to shape models' feature use. We construct a minimal, explicit generative framework for synthesizing classification datasets with two latent features that vary in predictivity and in factors we hypothesize to relate to availability, and quantify a model's shortcut bias-its over-reliance on the shortcut (more available, less predictive) feature at the expense of the core (less available, more predictive) feature. We find that linear models are relatively unbiased, but introducing a single hidden layer with ReLU or Tanh units yields a bias. Our empirical findings are consistent with a theoretical account based on Neural Tangent Kernels. Finally, we study how models used in practice trade off predictivity and availability in naturalistic datasets, discovering availability manipulations which increase models' degree of shortcut bias. Taken together, these findings suggest that the propensity to learn shortcut features is a fundamental characteristic of deep nonlinear architectures warranting systematic study given its role in shaping how models solve tasks.

Prediction of future movement of stock prices has always been a challenging task for the researchers. While the advocates of the efficient market hypothesis (EMH) believe that it is impossible to design any predictive framework that can accurately predict the movement of stock prices, there are seminal work in the literature that have clearly demonstrated that the seemingly random movement patterns in the time series of a stock price can be predicted with a high level of accuracy. Design of such predictive models requires choice of appropriate variables, right transformation methods of the variables, and tuning of the parameters of the models. In this work, we present a very robust and accurate framework of stock price prediction that consists of an agglomeration of statistical, machine learning and deep learning models. We use the daily stock price data, collected at five minutes interval of time, of a very well known company that is listed in the National Stock Exchange (NSE) of India. The granular data is aggregated into three slots in a day, and the aggregated data is used for building and training the forecasting models. We contend that the agglomerative approach of model building that uses a combination of statistical, machine learning, and deep learning approaches, can very effectively learn from the volatile and random movement patterns in a stock price data. We build eight classification and eight regression models based on statistical and machine learning approaches. In addition to these models, a deep learning regression model using a long-and-short-term memory (LSTM) network is also built. Extensive results have been presented on the performance of these models, and the results are critically analyzed.

Symbolic regression plays a crucial role in modern scientific research thanks to its capability of discovering concise and interpretable mathematical expressions from data. A grand challenge lies in the arduous search for parsimonious and generalizable mathematical formulas, in an infinite search space, while intending to fit the training data. Existing algorithms have faced a critical bottleneck of accuracy and efficiency over a decade when handling problems of complexity, which essentially hinders the pace of applying symbolic regression for scientific exploration across interdisciplinary domains. To this end, we introduce a parallelized tree search (PTS) model to efficiently distill generic mathematical expressions from limited data. Through a series of extensive experiments, we demonstrate the superior accuracy and efficiency of PTS for equation discovery, which greatly outperforms the state-of-the-art baseline models on over 80 synthetic and experimental datasets (e.g., lifting its performance by up to 99% accuracy improvement and one-order of magnitude speed up). PTS represents a key advance in accurate and efficient data-driven discovery of symbolic, interpretable models (e.g., underlying physical laws) and marks a pivotal transition towards scalable symbolic learning.

Knowing the features of a complex system that are highly relevant to a particular target variable is of fundamental interest in many areas of science. Existing approaches are often limited to linear settings, sometimes lack guarantees, and in most cases, do not scale to the problem at hand, in particular to images. We propose DRCFS, a doubly robust feature selection method for identifying the causal features even in nonlinear and high dimensional settings. We provide theoretical guarantees, illustrate necessary conditions for our assumptions, and perform extensive experiments across a wide range of simulated and semi-synthetic datasets. DRCFS significantly outperforms existing state-of-the-art methods, selecting robust features even in challenging highly non-linear and high-dimensional problems.

A variety of recent papers discuss the application of Shapley values, a concept for explaining coalitional games, for feature attribution in machine learning. However, the correct way to connect a machine learning model to a coalitional game has been a source of controversy. The two main approaches that have been proposed differ in the way that they condition on known features, using either (1) an interventional or (2) an observational conditional expectation. While previous work has argued that one of the two approaches is preferable in general, we argue that the choice is application dependent. Furthermore, we argue that the choice comes down to whether it is desirable to be true to the model or true to the data. We use linear models to investigate this choice. After deriving an efficient method for calculating observational conditional expectation Shapley values for linear models, we investigate how correlation in simulated data impacts the convergence of observational conditional expectation Shapley values. Finally, we present two real data examples that we consider to be representative of possible use cases for feature attribution -- (1) credit risk modeling and (2) biological discovery. We show how a different choice of value function performs better in each scenario, and how possible attributions are impacted by modeling choices.

Recent advancements in visual localization and mapping have demonstrated considerable success in integrating point and line features. However, expanding the localization framework to include additional mapping components frequently results in increased demand for memory and computational resources dedicated to matching tasks. In this study, we show how a lightweight neural network can learn to represent both 3D point and line features, and exhibit leading pose accuracy by harnessing the power of multiple learned mappings. Specifically, we utilize a single transformer block to encode line features, effectively transforming them into distinctive point-like descriptors. Subsequently, we treat these point and line descriptor sets as distinct yet interconnected feature sets. Through the integration of self- and cross-attention within several graph layers, our method effectively refines each feature before regressing 3D maps using two simple MLPs. In comprehensive experiments, our indoor localization findings surpass those of Hloc and Limap across both point-based and line-assisted configurations. Moreover, in outdoor scenarios, our method secures a significant lead, marking the most considerable enhancement over state-of-the-art learning-based methodologies. The source code and demo videos of this work are publicly available at: https://thpjp.github.io/pl2map/

Multivariate time series forecasting is an important machine learning problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. Temporal data arise in these real-world applications often involves a mixture of long-term and short-term patterns, for which traditional approaches such as Autoregressive models and Gaussian Process may fail. In this paper, we proposed a novel deep learning framework, namely Long- and Short-term Time-series network (LSTNet), to address this open challenge. LSTNet uses the Convolution Neural Network (CNN) and the Recurrent Neural Network (RNN) to extract short-term local dependency patterns among variables and to discover long-term patterns for time series trends. Furthermore, we leverage traditional autoregressive model to tackle the scale insensitive problem of the neural network model. In our evaluation on real-world data with complex mixtures of repetitive patterns, LSTNet achieved significant performance improvements over that of several state-of-the-art baseline methods. All the data and experiment codes are available online.

This paper addresses a regression problem in which output label values are the results of sensing the magnitude of a phenomenon. A low value of such labels can mean either that the actual magnitude of the phenomenon was low or that the sensor made an incomplete observation. This leads to a bias toward lower values in labels and the resultant learning because labels may have lower values due to incomplete observations, even if the actual magnitude of the phenomenon was high. Moreover, because an incomplete observation does not provide any tags indicating incompleteness, we cannot eliminate or impute them. To address this issue, we propose a learning algorithm that explicitly models incomplete observations corrupted with an asymmetric noise that always has a negative value. We show that our algorithm is unbiased as if it were learned from uncorrupted data that does not involve incomplete observations. We demonstrate the advantages of our algorithm through numerical experiments.

Similarity metrics such as representational similarity analysis (RSA) and centered kernel alignment (CKA) have been used to compare layer-wise representations between neural networks. However, these metrics are confounded by the population structure of data items in the input space, leading to spuriously high similarity for even completely random neural networks and inconsistent domain relations in transfer learning. We introduce a simple and generally applicable fix to adjust for the confounder with covariate adjustment regression, which retains the intuitive invariance properties of the original similarity measures. We show that deconfounding the similarity metrics increases the resolution of detecting semantically similar neural networks. Moreover, in real-world applications, deconfounding improves the consistency of representation similarities with domain similarities in transfer learning, and increases correlation with out-of-distribution accuracy.

We study regressions with multiple treatments and a set of controls that is flexible enough to purge omitted variable bias. We show that these regressions generally fail to estimate convex averages of heterogeneous treatment effects -- instead, estimates of each treatment's effect are contaminated by non-convex averages of the effects of other treatments. We discuss three estimation approaches that avoid such contamination bias, including the targeting of easiest-to-estimate weighted average effects. A re-analysis of nine empirical applications finds economically and statistically meaningful contamination bias in observational studies; contamination bias in experimental studies is more limited due to smaller variability in propensity scores.

We study the problem of single-image zero-shot 3D shape reconstruction. Recent works learn zero-shot shape reconstruction through generative modeling of 3D assets, but these models are computationally expensive at train and inference time. In contrast, the traditional approach to this problem is regression-based, where deterministic models are trained to directly regress the object shape. Such regression methods possess much higher computational efficiency than generative methods. This raises a natural question: is generative modeling necessary for high performance, or conversely, are regression-based approaches still competitive? To answer this, we design a strong regression-based model, called ZeroShape, based on the converging findings in this field and a novel insight. We also curate a large real-world evaluation benchmark, with objects from three different real-world 3D datasets. This evaluation benchmark is more diverse and an order of magnitude larger than what prior works use to quantitatively evaluate their models, aiming at reducing the evaluation variance in our field. We show that ZeroShape not only achieves superior performance over state-of-the-art methods, but also demonstrates significantly higher computational and data efficiency.

Learning features from data is one of the defining characteristics of deep learning, but our theoretical understanding of the role features play in deep learning is still rudimentary. To address this gap, we introduce a new tool, the interaction tensor, for empirically analyzing the interaction between data and model through features. With the interaction tensor, we make several key observations about how features are distributed in data and how models with different random seeds learn different features. Based on these observations, we propose a conceptual framework for feature learning. Under this framework, the expected accuracy for a single hypothesis and agreement for a pair of hypotheses can both be derived in closed-form. We demonstrate that the proposed framework can explain empirically observed phenomena, including the recently discovered Generalization Disagreement Equality (GDE) that allows for estimating the generalization error with only unlabeled data. Further, our theory also provides explicit construction of natural data distributions that break the GDE. Thus, we believe this work provides valuable new insight into our understanding of feature learning.

Symbolic regression (SR) is the problem of learning a symbolic expression from numerical data. Recently, deep neural models trained on procedurally-generated synthetic datasets showed competitive performance compared to more classical Genetic Programming (GP) algorithms. Unlike their GP counterparts, these neural approaches are trained to generate expressions from datasets given as context. This allows them to produce accurate expressions in a single forward pass at test time. However, they usually do not benefit from search abilities, which result in low performance compared to GP on out-of-distribution datasets. In this paper, we propose a novel method which provides the best of both worlds, based on a Monte-Carlo Tree Search procedure using a context-aware neural mutation model, which is initially pre-trained to learn promising mutations, and further refined from successful experiences in an online fashion. The approach demonstrates state-of-the-art performance on the well-known SRBench benchmark.

Learning feature representations of geographical space is vital for any machine learning model that integrates geolocated data, spanning application domains such as remote sensing, ecology, or epidemiology. Recent work mostly embeds coordinates using sine and cosine projections based on Double Fourier Sphere (DFS) features -- these embeddings assume a rectangular data domain even on global data, which can lead to artifacts, especially at the poles. At the same time, relatively little attention has been paid to the exact design of the neural network architectures these functional embeddings are combined with. This work proposes a novel location encoder for globally distributed geographic data that combines spherical harmonic basis functions, natively defined on spherical surfaces, with sinusoidal representation networks (SirenNets) that can be interpreted as learned Double Fourier Sphere embedding. We systematically evaluate the cross-product of positional embeddings and neural network architectures across various classification and regression benchmarks and synthetic evaluation datasets. In contrast to previous approaches that require the combination of both positional encoding and neural networks to learn meaningful representations, we show that both spherical harmonics and sinusoidal representation networks are competitive on their own but set state-of-the-art performances across tasks when combined. We provide source code at www.github.com/marccoru/locationencoder

We propose a game-based formulation for learning dimensionality-reducing representations of feature vectors, when only a prior knowledge on future prediction tasks is available. In this game, the first player chooses a representation, and then the second player adversarially chooses a prediction task from a given class, representing the prior knowledge. The first player aims is to minimize, and the second player to maximize, the regret: The minimal prediction loss using the representation, compared to the same loss using the original features. For the canonical setting in which the representation, the response to predict and the predictors are all linear functions, and under the mean squared error loss function, we derive the theoretically optimal representation in pure strategies, which shows the effectiveness of the prior knowledge, and the optimal regret in mixed strategies, which shows the usefulness of randomizing the representation. For general representations and loss functions, we propose an efficient algorithm to optimize a randomized representation. The algorithm only requires the gradients of the loss function, and is based on incrementally adding a representation rule to a mixture of such rules.

This paper presents a computationally efficient variant of gradient boosting for multi-class classification and multi-output regression tasks. Standard gradient boosting uses a 1-vs-all strategy for classifications tasks with more than two classes. This strategy translates in that one tree per class and iteration has to be trained. In this work, we propose the use of multi-output regressors as base models to handle the multi-class problem as a single task. In addition, the proposed modification allows the model to learn multi-output regression problems. An extensive comparison with other multi-ouptut based gradient boosting methods is carried out in terms of generalization and computational efficiency. The proposed method showed the best trade-off between generalization ability and training and predictions speeds.

The Invariant Risk Minimization (IRM) principle was first proposed by Arjovsky et al. [2019] to address the domain generalization problem by leveraging data heterogeneity from differing experimental conditions. Specifically, IRM seeks to find a data representation under which an optimal classifier remains invariant across all domains. Despite the conceptual appeal of IRM, the effectiveness of the originally proposed invariance penalty has recently been brought into question. In particular, there exists counterexamples for which that invariance penalty can be arbitrarily small for non-invariant data representations. We propose an alternative invariance penalty by revisiting the Gramian matrix of the data representation. We discuss the role of its eigenvalues in the relationship between the risk and the invariance penalty, and demonstrate that it is ill-conditioned for said counterexamples. The proposed approach is guaranteed to recover an invariant representation for linear settings under mild non-degeneracy conditions. Its effectiveness is substantiated by experiments on DomainBed and InvarianceUnitTest, two extensive test beds for domain generalization.

Machine learning for time-series forecasting remains a key area of research. Despite successful application of many machine learning techniques, relating computational efficiency to forecast error remains an under-explored domain. This paper addresses this topic through a series of real-time experiments to quantify the relationship between computational cost and forecast error using meteorological nowcasting as an example use-case. We employ a variety of popular regression techniques (XGBoost, FC-MLP, Transformer, and LSTM) for multi-horizon, short-term forecasting of three variables (temperature, wind speed, and cloud cover) for multiple locations. During a 5-day live experiment, 4000 data sources were streamed for training and inferencing 144 models per hour. These models were parameterized to explore forecast error for two computational cost minimization methods: a novel auto-adaptive data reduction technique (Variance Horizon) and a performance-based concept drift-detection mechanism. Forecast error of all model variations were benchmarked in real-time against a state-of-the-art numerical weather prediction model. Performance was assessed using classical and novel evaluation metrics. Results indicate that using the Variance Horizon reduced computational usage by more than 50\%, while increasing between 0-15\% in error. Meanwhile, performance-based retraining reduced computational usage by up to 90\% while also improving forecast error by up to 10\%. Finally, the combination of both the Variance Horizon and performance-based retraining outperformed other model configurations by up to 99.7\% when considering error normalized to computational usage.

Efficiently and flexibly estimating treatment effect heterogeneity is an important task in a wide variety of settings ranging from medicine to marketing, and there are a considerable number of promising conditional average treatment effect estimators currently available. These, however, typically rely on the assumption that the measured covariates are enough to justify conditional exchangeability. We propose the P-learner, motivated by the R- and DR-learner, a tailored two-stage loss function for learning heterogeneous treatment effects in settings where exchangeability given observed covariates is an implausible assumption, and we wish to rely on proxy variables for causal inference. Our proposed estimator can be implemented by off-the-shelf loss-minimizing machine learning methods, which in the case of kernel regression satisfies an oracle bound on the estimated error as long as the nuisance components are estimated reasonably well.

Feature selection is playing an increasingly significant role with respect to many computer vision applications spanning from object recognition to visual object tracking. However, most of the recent solutions in feature selection are not robust across different and heterogeneous set of data. In this paper, we address this issue proposing a robust probabilistic latent graph-based feature selection algorithm that performs the ranking step while considering all the possible subsets of features, as paths on a graph, bypassing the combinatorial problem analytically. An appealing characteristic of the approach is that it aims to discover an abstraction behind low-level sensory data, that is, relevancy. Relevancy is modelled as a latent variable in a PLSA-inspired generative process that allows the investigation of the importance of a feature when injected into an arbitrary set of cues. The proposed method has been tested on ten diverse benchmarks, and compared against eleven state of the art feature selection methods. Results show that the proposed approach attains the highest performance levels across many different scenarios and difficulties, thereby confirming its strong robustness while setting a new state of the art in feature selection domain.

A primary cost driver for training large models is wall-clock training time. We show that popular time estimates based on FLOPs are poor estimates, and construct a more accurate proxy based on memory copies. We show that with some simple accounting, we can estimate the training speed of a transformer model from its hyperparameters. Combined with a scaling law curve like Chinchilla, this lets us estimate the final loss of the model. We fit our estimate to real data with a linear regression, and apply the result to rewrite Chinchilla in terms of a model's estimated training time as opposed to the amount of training data. This gives an expression for the loss in terms of the model's hyperparameters alone. We show that this expression is accurate across a wide range of model hyperparameter values, enabling us to analytically make architectural decisions and train models more efficiently.

Many learning algorithms have invariances: when their training data is transformed in certain ways, the function they learn transforms in a predictable manner. Here we formalize this notion using concepts from the mathematical field of category theory. The invariances that a supervised learning algorithm possesses are formalized by categories of predictor and target spaces, whose morphisms represent the algorithm's invariances, and an index category whose morphisms represent permutations of the training examples. An invariant learning algorithm is a natural transformation between two functors from the product of these categories to the category of sets, representing training datasets and learned functions respectively. We illustrate the framework by characterizing and contrasting the invariances of linear regression and ridge regression.

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate dimension reduction, typically achieved via basis expansions. Currently, these bases are chosen a priori without the information for the task at hand and thus may not be effective for the designated task. We instead propose to adaptively learn these bases in an end-to-end fashion. We introduce neural networks that employ a new Basis Layer whose hidden units are each basis functions themselves implemented as a micro neural network. Our architecture learns to apply parsimonious dimension reduction to functional inputs that focuses only on information relevant to the target rather than irrelevant variation in the input function. Across numerous classification/regression tasks with functional data, our method empirically outperforms other types of neural networks, and we prove that our approach is statistically consistent with low generalization error. Code is available at: https://github.com/jwyyy/AdaFNN.

We present a simple picture of the training process of joint embedding self-supervised learning methods. We find that these methods learn their high-dimensional embeddings one dimension at a time in a sequence of discrete, well-separated steps. We arrive at this conclusion via the study of a linearized model of Barlow Twins applicable to the case in which the trained network is infinitely wide. We solve the training dynamics of this model from small initialization, finding that the model learns the top eigenmodes of a certain contrastive kernel in a stepwise fashion, and obtain a closed-form expression for the final learned representations. Remarkably, we then see the same stepwise learning phenomenon when training deep ResNets using the Barlow Twins, SimCLR, and VICReg losses. Our theory suggests that, just as kernel regression can be thought of as a model of supervised learning, kernel PCA may serve as a useful model of self-supervised learning.

Many businesses and industries nowadays rely on large quantities of time series data making time series forecasting an important research area. Global forecasting models that are trained across sets of time series have shown a huge potential in providing accurate forecasts compared with the traditional univariate forecasting models that work on isolated series. However, there are currently no comprehensive time series archives for forecasting that contain datasets of time series from similar sources available for the research community to evaluate the performance of new global forecasting algorithms over a wide variety of datasets. In this paper, we present such a comprehensive time series forecasting archive containing 20 publicly available time series datasets from varied domains, with different characteristics in terms of frequency, series lengths, and inclusion of missing values. We also characterise the datasets, and identify similarities and differences among them, by conducting a feature analysis. Furthermore, we present the performance of a set of standard baseline forecasting methods over all datasets across eight error metrics, for the benefit of researchers using the archive to benchmark their forecasting algorithms.

Pixel-wise regression is probably the most common problem in fine-grained computer vision tasks, such as estimating keypoint heatmaps and segmentation masks. These regression problems are very challenging particularly because they require, at low computation overheads, modeling long-range dependencies on high-resolution inputs/outputs to estimate the highly nonlinear pixel-wise semantics. While attention mechanisms in Deep Convolutional Neural Networks(DCNNs) has become popular for boosting long-range dependencies, element-specific attention, such as Nonlocal blocks, is highly complex and noise-sensitive to learn, and most of simplified attention hybrids try to reach the best compromise among multiple types of tasks. In this paper, we present the Polarized Self-Attention(PSA) block that incorporates two critical designs towards high-quality pixel-wise regression: (1) Polarized filtering: keeping high internal resolution in both channel and spatial attention computation while completely collapsing input tensors along their counterpart dimensions. (2) Enhancement: composing non-linearity that directly fits the output distribution of typical fine-grained regression, such as the 2D Gaussian distribution (keypoint heatmaps), or the 2D Binormial distribution (binary segmentation masks). PSA appears to have exhausted the representation capacity within its channel-only and spatial-only branches, such that there is only marginal metric differences between its sequential and parallel layouts. Experimental results show that PSA boosts standard baselines by 2-4 points, and boosts state-of-the-arts by 1-2 points on 2D pose estimation and semantic segmentation benchmarks.

A directed acyclic graph (DAG) provides valuable prior knowledge that is often discarded in regression tasks in machine learning. We show that the independences arising from the presence of collider structures in DAGs provide meaningful inductive biases, which constrain the regression hypothesis space and improve predictive performance. We introduce collider regression, a framework to incorporate probabilistic causal knowledge from a collider in a regression problem. When the hypothesis space is a reproducing kernel Hilbert space, we prove a strictly positive generalisation benefit under mild assumptions and provide closed-form estimators of the empirical risk minimiser. Experiments on synthetic and climate model data demonstrate performance gains of the proposed methodology.

Aiming to generalize the label knowledge from a source domain with continuous outputs to an unlabeled target domain, Domain Adaptation Regression (DAR) is developed for complex practical learning problems. However, due to the continuity problem in regression, existing conditional distribution alignment theory and methods with discrete prior, which are proven to be effective in classification settings, are no longer applicable. In this work, focusing on the feasibility problems in DAR, we establish the sufficiency theory for the regression model, which shows the generalization error can be sufficiently dominated by the cross-domain conditional discrepancy. Further, to characterize conditional discrepancy with continuous conditioning variable, a novel Conditional Operator Discrepancy (COD) is proposed, which admits the metric property on conditional distributions via the kernel embedding theory. Finally, to minimize the discrepancy, a COD-based conditional invariant representation learning model is proposed, and the reformulation is derived to show that reasonable modifications on moment statistics can further improve the discriminability of the adaptation model. Extensive experiments on standard DAR datasets verify the validity of theoretical results and the superiority over SOTA DAR methods.

We present Natural Gradient Boosting (NGBoost), an algorithm for generic probabilistic prediction via gradient boosting. Typical regression models return a point estimate, conditional on covariates, but probabilistic regression models output a full probability distribution over the outcome space, conditional on the covariates. This allows for predictive uncertainty estimation -- crucial in applications like healthcare and weather forecasting. NGBoost generalizes gradient boosting to probabilistic regression by treating the parameters of the conditional distribution as targets for a multiparameter boosting algorithm. Furthermore, we show how the Natural Gradient is required to correct the training dynamics of our multiparameter boosting approach. NGBoost can be used with any base learner, any family of distributions with continuous parameters, and any scoring rule. NGBoost matches or exceeds the performance of existing methods for probabilistic prediction while offering additional benefits in flexibility, scalability, and usability. An open-source implementation is available at github.com/stanfordmlgroup/ngboost.

Data augmentation is becoming essential for improving regression performance in critical applications including manufacturing, climate prediction, and finance. Existing techniques for data augmentation largely focus on classification tasks and do not readily apply to regression tasks. In particular, the recent Mixup techniques for classification have succeeded in improving the model performance, which is reasonable due to the characteristics of the classification task, but has limitations in regression. We show that mixing examples that have large data distances using linear interpolations may have increasingly-negative effects on model performance. Our key idea is thus to limit the distances between examples that are mixed. We propose RegMix, a data augmentation framework for regression that learns for each example how many nearest neighbors it should be mixed with for the best model performance using a validation set. Our experiments conducted both on synthetic and real datasets show that RegMix outperforms state-of-the-art data augmentation baselines applicable to regression.

This study introduces PV-RNN, a novel variational RNN inspired by the predictive-coding ideas. The model learns to extract the probabilistic structures hidden in fluctuating temporal patterns by dynamically changing the stochasticity of its latent states. Its architecture attempts to address two major concerns of variational Bayes RNNs: how can latent variables learn meaningful representations and how can the inference model transfer future observations to the latent variables. PV-RNN does both by introducing adaptive vectors mirroring the training data, whose values can then be adapted differently during evaluation. Moreover, prediction errors during backpropagation, rather than external inputs during the forward computation, are used to convey information to the network about the external data. For testing, we introduce error regression for predicting unseen sequences as inspired by predictive coding that leverages those mechanisms. The model introduces a weighting parameter, the meta-prior, to balance the optimization pressure placed on two terms of a lower bound on the marginal likelihood of the sequential data. We test the model on two datasets with probabilistic structures and show that with high values of the meta-prior the network develops deterministic chaos through which the data's randomness is imitated. For low values, the model behaves as a random process. The network performs best on intermediate values, and is able to capture the latent probabilistic structure with good generalization. Analyzing the meta-prior's impact on the network allows to precisely study the theoretical value and practical benefits of incorporating stochastic dynamics in our model. We demonstrate better prediction performance on a robot imitation task with our model using error regression compared to a standard variational Bayes model lacking such a procedure.

Recognizing that traditional forecasting models often rely solely on historical demand, this work investigates the potential of data-driven techniques to automatically select and integrate market indicators for improving customer demand predictions. By adopting an exploratory methodology, we integrate macroeconomic time series, such as national GDP growth, from the Eurostat database into Neural Prophet and SARIMAX forecasting models. Suitable time series are automatically identified through different state-of-the-art feature selection methods and applied to sales data from our industrial partner. It could be shown that forecasts can be significantly enhanced by incorporating external information. Notably, the potential of feature selection methods stands out, especially due to their capability for automation without expert knowledge and manual selection effort. In particular, the Forward Feature Selection technique consistently yielded superior forecasting accuracy for both SARIMAX and Neural Prophet across different company sales datasets. In the comparative analysis of the errors of the selected forecasting models, namely Neural Prophet and SARIMAX, it is observed that neither model demonstrates a significant superiority over the other.

The design of modern recommender systems relies on understanding which parts of the feature space are relevant for solving a given recommendation task. However, real-world data sets in this domain are often characterized by their large size, sparsity, and noise, making it challenging to identify meaningful signals. Feature ranking represents an efficient branch of algorithms that can help address these challenges by identifying the most informative features and facilitating the automated search for more compact and better-performing models (AutoML). We introduce OutRank, a system for versatile feature ranking and data quality-related anomaly detection. OutRank was built with categorical data in mind, utilizing a variant of mutual information that is normalized with regard to the noise produced by features of the same cardinality. We further extend the similarity measure by incorporating information on feature similarity and combined relevance. The proposed approach's feasibility is demonstrated by speeding up the state-of-the-art AutoML system on a synthetic data set with no performance loss. Furthermore, we considered a real-life click-through-rate prediction data set where it outperformed strong baselines such as random forest-based approaches. The proposed approach enables exploration of up to 300% larger feature spaces compared to AutoML-only approaches, enabling faster search for better models on off-the-shelf hardware.

The information bottleneck (IB) approach is popular to improve the generalization, robustness and explainability of deep neural networks. Essentially, it aims to find a minimum sufficient representation t by striking a trade-off between a compression term I(x;t) and a prediction term I(y;t), where I(cdot;cdot) refers to the mutual information (MI). MI is for the IB for the most part expressed in terms of the Kullback-Leibler (KL) divergence, which in the regression case corresponds to prediction based on mean squared error (MSE) loss with Gaussian assumption and compression approximated by variational inference. In this paper, we study the IB principle for the regression problem and develop a new way to parameterize the IB with deep neural networks by exploiting favorable properties of the Cauchy-Schwarz (CS) divergence. By doing so, we move away from MSE-based regression and ease estimation by avoiding variational approximations or distributional assumptions. We investigate the improved generalization ability of our proposed CS-IB and demonstrate strong adversarial robustness guarantees. We demonstrate its superior performance on six real-world regression tasks over other popular deep IB approaches. We additionally observe that the solutions discovered by CS-IB always achieve the best trade-off between prediction accuracy and compression ratio in the information plane. The code is available at https://github.com/SJYuCNEL/Cauchy-Schwarz-Information-Bottleneck.

Backward compatibility of model predictions is a desired property when updating a machine learning driven application. It allows to seamlessly improve the underlying model without introducing regression bugs. In classification tasks these bugs occur in the form of negative flips. This means an instance that was correctly classified by the old model is now classified incorrectly by the updated model. This has direct negative impact on the user experience of such systems e.g. a frequently used voice assistant query is suddenly misclassified. A common reason to update the model is when new training data becomes available and needs to be incorporated. Simply retraining the model with the updated data introduces the unwanted negative flips. We study the problem of regression during data updates and propose Backward Compatible Weight Interpolation (BCWI). This method interpolates between the weights of the old and new model and we show in extensive experiments that it reduces negative flips without sacrificing the improved accuracy of the new model. BCWI is straight forward to implement and does not increase inference cost. We also explore the use of importance weighting during interpolation and averaging the weights of multiple new models in order to further reduce negative flips.

Most existing debiasing methods for multimodal models, including causal intervention and inference methods, utilize approximate heuristics to represent the biases, such as shallow features from early stages of training or unimodal features for multimodal tasks like VQA, etc., which may not be accurate. In this paper, we study bias arising from confounders in a causal graph for multimodal data and examine a novel approach that leverages causally-motivated information minimization to learn the confounder representations. Robust predictive features contain diverse information that helps a model generalize to out-of-distribution data. Hence, minimizing the information content of features obtained from a pretrained biased model helps learn the simplest predictive features that capture the underlying data distribution. We treat these features as confounder representations and use them via methods motivated by causal theory to remove bias from models. We find that the learned confounder representations indeed capture dataset biases, and the proposed debiasing methods improve out-of-distribution (OOD) performance on multiple multimodal datasets without sacrificing in-distribution performance. Additionally, we introduce a novel metric to quantify the sufficiency of spurious features in models' predictions that further demonstrates the effectiveness of our proposed methods. Our code is available at: https://github.com/Vaidehi99/CausalInfoMin

The recent boom of linear forecasting models questions the ongoing passion for architectural modifications of Transformer-based forecasters. These forecasters leverage Transformers to model the global dependencies over temporal tokens of time series, with each token formed by multiple variates of the same timestamp. However, Transformers are challenged in forecasting series with larger lookback windows due to performance degradation and computation explosion. Besides, the embedding for each temporal token fuses multiple variates that represent potential delayed events and distinct physical measurements, which may fail in learning variate-centric representations and result in meaningless attention maps. In this work, we reflect on the competent duties of Transformer components and repurpose the Transformer architecture without any modification to the basic components. We propose iTransformer that simply applies the attention and feed-forward network on the inverted dimensions. Specifically, the time points of individual series are embedded into variate tokens which are utilized by the attention mechanism to capture multivariate correlations; meanwhile, the feed-forward network is applied for each variate token to learn nonlinear representations. The iTransformer model achieves state-of-the-art on challenging real-world datasets, which further empowers the Transformer family with promoted performance, generalization ability across different variates, and better utilization of arbitrary lookback windows, making it a nice alternative as the fundamental backbone of time series forecasting. Code is available at this repository: https://github.com/thuml/iTransformer.

Learning high-quality feature embeddings efficiently and effectively is critical for the performance of web-scale machine learning systems. A typical model ingests hundreds of features with vocabularies on the order of millions to billions of tokens. The standard approach is to represent each feature value as a d-dimensional embedding, introducing hundreds of billions of parameters for extremely high-cardinality features. This bottleneck has led to substantial progress in alternative embedding algorithms. Many of these methods, however, make the assumption that each feature uses an independent embedding table. This work introduces a simple yet highly effective framework, Feature Multiplexing, where one single representation space is used across many different categorical features. Our theoretical and empirical analysis reveals that multiplexed embeddings can be decomposed into components from each constituent feature, allowing models to distinguish between features. We show that multiplexed representations lead to Pareto-optimal parameter-accuracy tradeoffs for three public benchmark datasets. Further, we propose a highly practical approach called Unified Embedding with three major benefits: simplified feature configuration, strong adaptation to dynamic data distributions, and compatibility with modern hardware. Unified embedding gives significant improvements in offline and online metrics compared to highly competitive baselines across five web-scale search, ads, and recommender systems, where it serves billions of users across the world in industry-leading products.

Much of the world's most valued data is stored in relational databases and data warehouses, where the data is organized into many tables connected by primary-foreign key relations. However, building machine learning models using this data is both challenging and time consuming. The core problem is that no machine learning method is capable of learning on multiple tables interconnected by primary-foreign key relations. Current methods can only learn from a single table, so the data must first be manually joined and aggregated into a single training table, the process known as feature engineering. Feature engineering is slow, error prone and leads to suboptimal models. Here we introduce an end-to-end deep representation learning approach to directly learn on data laid out across multiple tables. We name our approach Relational Deep Learning (RDL). The core idea is to view relational databases as a temporal, heterogeneous graph, with a node for each row in each table, and edges specified by primary-foreign key links. Message Passing Graph Neural Networks can then automatically learn across the graph to extract representations that leverage all input data, without any manual feature engineering. Relational Deep Learning leads to more accurate models that can be built much faster. To facilitate research in this area, we develop RelBench, a set of benchmark datasets and an implementation of Relational Deep Learning. The data covers a wide spectrum, from discussions on Stack Exchange to book reviews on the Amazon Product Catalog. Overall, we define a new research area that generalizes graph machine learning and broadens its applicability to a wide set of AI use cases.

Air pollution remains a leading global health risk, exacerbated by rapid industrialization and urbanization, contributing significantly to morbidity and mortality rates. In this paper, we introduce AirCast, a novel multi-variable air pollution forecasting model, by combining weather and air quality variables. AirCast employs a multi-task head architecture that simultaneously forecasts atmospheric conditions and pollutant concentrations, improving its understanding of how weather patterns affect air quality. Predicting extreme pollution events is challenging due to their rare occurrence in historic data, resulting in a heavy-tailed distribution of pollution levels. To address this, we propose a novel Frequency-weighted Mean Absolute Error (fMAE) loss, adapted from the class-balanced loss for regression tasks. Informed from domain knowledge, we investigate the selection of key variables known to influence pollution levels. Additionally, we align existing weather and chemical datasets across spatial and temporal dimensions. AirCast's integrated approach, combining multi-task learning, frequency weighted loss and domain informed variable selection, enables more accurate pollution forecasts. Our source code and models are made public here (https://github.com/vishalned/AirCast.git)

Despite the success of neural networks (NNs), there is still a concern among many over their "black box" nature. Why do they work? Here we present a simple analytic argument that NNs are in fact essentially polynomial regression models. This view will have various implications for NNs, e.g. providing an explanation for why convergence problems arise in NNs, and it gives rough guidance on avoiding overfitting. In addition, we use this phenomenon to predict and confirm a multicollinearity property of NNs not previously reported in the literature. Most importantly, given this loose correspondence, one may choose to routinely use polynomial models instead of NNs, thus avoiding some major problems of the latter, such as having to set many tuning parameters and dealing with convergence issues. We present a number of empirical results; in each case, the accuracy of the polynomial approach matches or exceeds that of NN approaches. A many-featured, open-source software package, polyreg, is available.

We propose a penalized nonparametric approach to estimating the quantile regression process (QRP) in a nonseparable model using rectifier quadratic unit (ReQU) activated deep neural networks and introduce a novel penalty function to enforce non-crossing of quantile regression curves. We establish the non-asymptotic excess risk bounds for the estimated QRP and derive the mean integrated squared error for the estimated QRP under mild smoothness and regularity conditions. To establish these non-asymptotic risk and estimation error bounds, we also develop a new error bound for approximating C^s smooth functions with s >0 and their derivatives using ReQU activated neural networks. This is a new approximation result for ReQU networks and is of independent interest and may be useful in other problems. Our numerical experiments demonstrate that the proposed method is competitive with or outperforms two existing methods, including methods using reproducing kernels and random forests, for nonparametric quantile regression.

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning.

Due to the rise of privacy concerns, in many practical applications the training data is aggregated before being shared with the learner, in order to protect privacy of users' sensitive responses. In an aggregate learning framework, the dataset is grouped into bags of samples, where each bag is available only with an aggregate response, providing a summary of individuals' responses in that bag. In this paper, we study two natural loss functions for learning from aggregate responses: bag-level loss and the instance-level loss. In the former, the model is learnt by minimizing a loss between aggregate responses and aggregate model predictions, while in the latter the model aims to fit individual predictions to the aggregate responses. In this work, we show that the instance-level loss can be perceived as a regularized form of the bag-level loss. This observation lets us compare the two approaches with respect to bias and variance of the resulting estimators, and introduce a novel interpolating estimator which combines the two approaches. For linear regression tasks, we provide a precise characterization of the risk of the interpolating estimator in an asymptotic regime where the size of the training set grows in proportion to the features dimension. Our analysis allows us to theoretically understand the effect of different factors, such as bag size on the model prediction risk. In addition, we propose a mechanism for differentially private learning from aggregate responses and derive the optimal bag size in terms of prediction risk-privacy trade-off. We also carry out thorough experiments to corroborate our theory and show the efficacy of the interpolating estimator.

Latent factor models are the driving forces of the state-of-the-art recommender systems, with an important insight of vectorizing raw input features into dense embeddings. The dimensions of different feature embeddings are often set to a same value empirically, which limits the predictive performance of latent factor models. Existing works have proposed heuristic or reinforcement learning-based methods to search for mixed feature embedding dimensions. For efficiency concern, these methods typically choose embedding dimensions from a restricted set of candidate dimensions. However, this restriction will hurt the flexibility of dimension selection, leading to suboptimal performance of search results. In this paper, we propose Differentiable Neural Input Search (DNIS), a method that searches for mixed feature embedding dimensions in a more flexible space through continuous relaxation and differentiable optimization. The key idea is to introduce a soft selection layer that controls the significance of each embedding dimension, and optimize this layer according to model's validation performance. DNIS is model-agnostic and thus can be seamlessly incorporated with existing latent factor models for recommendation. We conduct experiments with various architectures of latent factor models on three public real-world datasets for rating prediction, Click-Through-Rate (CTR) prediction, and top-k item recommendation. The results demonstrate that our method achieves the best predictive performance compared with existing neural input search approaches with fewer embedding parameters and less time cost.

Noise plagues many numerical datasets, where the recorded values in the data may fail to match the true underlying values due to reasons including: erroneous sensors, data entry/processing mistakes, or imperfect human estimates. We consider general regression settings with covariates and a potentially corrupted response whose observed values may contain errors. By accounting for various uncertainties, we introduced veracity scores that distinguish between genuine errors and natural data fluctuations, conditioned on the available covariate information in the dataset. We propose a simple yet efficient filtering procedure for eliminating potential errors, and establish theoretical guarantees for our method. We also contribute a new error detection benchmark involving 5 regression datasets with real-world numerical errors (for which the true values are also known). In this benchmark and additional simulation studies, our method identifies incorrect values with better precision/recall than other approaches.

Numerous deep learning applications benefit from multi-task learning with multiple regression and classification objectives. In this paper we make the observation that the performance of such systems is strongly dependent on the relative weighting between each task's loss. Tuning these weights by hand is a difficult and expensive process, making multi-task learning prohibitive in practice. We propose a principled approach to multi-task deep learning which weighs multiple loss functions by considering the homoscedastic uncertainty of each task. This allows us to simultaneously learn various quantities with different units or scales in both classification and regression settings. We demonstrate our model learning per-pixel depth regression, semantic and instance segmentation from a monocular input image. Perhaps surprisingly, we show our model can learn multi-task weightings and outperform separate models trained individually on each task.

Our motivation is to shed light the performance of the widely popular "R-Learner." Like many other methods for estimating conditional average treatment effects (CATEs), R-Learning can be expressed as a weighted pseudo-outcome regression (POR). Previous comparisons of POR techniques have paid careful attention to the choice of pseudo-outcome transformation. However, we argue that the dominant driver of performance is actually the choice of weights. Specifically, we argue that R-Learning implicitly performs an inverse-variance weighted form of POR. These weights stabilize the regression and allow for convenient simplifications of bias terms.

Sparse Autoencoders (SAEs) have shown promise in improving the interpretability of neural network activations, but can learn features that are not features of the input, limiting their effectiveness. We propose Mutual Feature Regularization (MFR), a regularization technique for improving feature learning by encouraging SAEs trained in parallel to learn similar features. We motivate MFR by showing that features learned by multiple SAEs are more likely to correlate with features of the input. By training on synthetic data with known features of the input, we show that MFR can help SAEs learn those features, as we can directly compare the features learned by the SAE with the input features for the synthetic data. We then scale MFR to SAEs that are trained to denoise electroencephalography (EEG) data and SAEs that are trained to reconstruct GPT-2 Small activations. We show that MFR can improve the reconstruction loss of SAEs by up to 21.21\% on GPT-2 Small, and 6.67\% on EEG data. Our results suggest that the similarity between features learned by different SAEs can be leveraged to improve SAE training, thereby enhancing performance and the usefulness of SAEs for model interpretability.

Recent works have empirically analyzed in-context learning and shown that transformers trained on synthetic linear regression tasks can learn to implement ridge regression, which is the Bayes-optimal predictor, given sufficient capacity [Aky\"urek et al., 2023], while one-layer transformers with linear self-attention and no MLP layer will learn to implement one step of gradient descent (GD) on a least-squares linear regression objective [von Oswald et al., 2022]. However, the theory behind these observations remains poorly understood. We theoretically study transformers with a single layer of linear self-attention, trained on synthetic noisy linear regression data. First, we mathematically show that when the covariates are drawn from a standard Gaussian distribution, the one-layer transformer which minimizes the pre-training loss will implement a single step of GD on the least-squares linear regression objective. Then, we find that changing the distribution of the covariates and weight vector to a non-isotropic Gaussian distribution has a strong impact on the learned algorithm: the global minimizer of the pre-training loss now implements a single step of pre-conditioned GD. However, if only the distribution of the responses is changed, then this does not have a large effect on the learned algorithm: even when the response comes from a more general family of nonlinear functions, the global minimizer of the pre-training loss still implements a single step of GD on a least-squares linear regression objective.

Observational studies require adjustment for confounding factors that are correlated with both the treatment and outcome. In the setting where the observed variables are tabular quantities such as average income in a neighborhood, tools have been developed for addressing such confounding. However, in many parts of the developing world, features about local communities may be scarce. In this context, satellite imagery can play an important role, serving as a proxy for the confounding variables otherwise unobserved. In this paper, we study confounder adjustment in this non-tabular setting, where patterns or objects found in satellite images contribute to the confounder bias. Using the evaluation of anti-poverty aid programs in Africa as our running example, we formalize the challenge of performing causal adjustment with such unstructured data -- what conditions are sufficient to identify causal effects, how to perform estimation, and how to quantify the ways in which certain aspects of the unstructured image object are most predictive of the treatment decision. Via simulation, we also explore the sensitivity of satellite image-based observational inference to image resolution and to misspecification of the image-associated confounder. Finally, we apply these tools in estimating the effect of anti-poverty interventions in African communities from satellite imagery.

Ordinal regression refers to classifying object instances into ordinal categories. It has been widely studied in many scenarios, such as medical disease grading, movie rating, etc. Known methods focused only on learning inter-class ordinal relationships, but still incur limitations in distinguishing adjacent categories thus far. In this paper, we propose a simple sequence prediction framework for ordinal regression called Ord2Seq, which, for the first time, transforms each ordinal category label into a special label sequence and thus regards an ordinal regression task as a sequence prediction process. In this way, we decompose an ordinal regression task into a series of recursive binary classification steps, so as to subtly distinguish adjacent categories. Comprehensive experiments show the effectiveness of distinguishing adjacent categories for performance improvement and our new approach exceeds state-of-the-art performances in four different scenarios. Codes are available at https://github.com/wjh892521292/Ord2Seq.

Recent studies of gradient descent with large step sizes have shown that there is often a regime with an initial increase in the largest eigenvalue of the loss Hessian (progressive sharpening), followed by a stabilization of the eigenvalue near the maximum value which allows convergence (edge of stability). These phenomena are intrinsically non-linear and do not happen for models in the constant Neural Tangent Kernel (NTK) regime, for which the predictive function is approximately linear in the parameters. As such, we consider the next simplest class of predictive models, namely those that are quadratic in the parameters, which we call second-order regression models. For quadratic objectives in two dimensions, we prove that this second-order regression model exhibits progressive sharpening of the NTK eigenvalue towards a value that differs slightly from the edge of stability, which we explicitly compute. In higher dimensions, the model generically shows similar behavior, even without the specific structure of a neural network, suggesting that progressive sharpening and edge-of-stability behavior aren't unique features of neural networks, and could be a more general property of discrete learning algorithms in high-dimensional non-linear models.

In the era of proliferation of large language and image generation models, the phenomenon of "model collapse" refers to the situation whereby as a model is trained recursively on data generated from previous generations of itself over time, its performance degrades until the model eventually becomes completely useless, i.e the model collapses. In this work, we study this phenomenon in the setting of high-dimensional regression and obtain analytic formulae which quantitatively outline this phenomenon in a broad range of regimes. In the special case of polynomial decaying spectral and source conditions, we obtain modified scaling laws which exhibit new crossover phenomena from fast to slow rates. We also propose a simple strategy based on adaptive regularization to mitigate model collapse. Our theoretical results are validated with experiments.

We propose an approach to estimate the number of samples required for a model to reach a target performance. We find that the power law, the de facto principle to estimate model performance, leads to large error when using a small dataset (e.g., 5 samples per class) for extrapolation. This is because the log-performance error against the log-dataset size follows a nonlinear progression in the few-shot regime followed by a linear progression in the high-shot regime. We introduce a novel piecewise power law (PPL) that handles the two data regimes differently. To estimate the parameters of the PPL, we introduce a random forest regressor trained via meta learning that generalizes across classification/detection tasks, ResNet/ViT based architectures, and random/pre-trained initializations. The PPL improves the performance estimation on average by 37% across 16 classification and 33% across 10 detection datasets, compared to the power law. We further extend the PPL to provide a confidence bound and use it to limit the prediction horizon that reduces over-estimation of data by 76% on classification and 91% on detection datasets.

Training classifiers is difficult with severe class imbalance, but many rare events are the culmination of a sequence with much more common intermediate outcomes. For example, in online marketing a user first sees an ad, then may click on it, and finally may make a purchase; estimating the probability of purchases is difficult because of their rarity. We show both theoretically and through data experiments that the more abundant data in earlier steps may be leveraged to improve estimation of probabilities of rare events. We present PRESTO, a relaxation of the proportional odds model for ordinal regression. Instead of estimating weights for one separating hyperplane that is shifted by separate intercepts for each of the estimated Bayes decision boundaries between adjacent pairs of categorical responses, we estimate separate weights for each of these transitions. We impose an L1 penalty on the differences between weights for the same feature in adjacent weight vectors in order to shrink towards the proportional odds model. We prove that PRESTO consistently estimates the decision boundary weights under a sparsity assumption. Synthetic and real data experiments show that our method can estimate rare probabilities in this setting better than both logistic regression on the rare category, which fails to borrow strength from more abundant categories, and the proportional odds model, which is too inflexible.

Understanding why a model makes a certain prediction can be as crucial as the prediction's accuracy in many applications. However, the highest accuracy for large modern datasets is often achieved by complex models that even experts struggle to interpret, such as ensemble or deep learning models, creating a tension between accuracy and interpretability. In response, various methods have recently been proposed to help users interpret the predictions of complex models, but it is often unclear how these methods are related and when one method is preferable over another. To address this problem, we present a unified framework for interpreting predictions, SHAP (SHapley Additive exPlanations). SHAP assigns each feature an importance value for a particular prediction. Its novel components include: (1) the identification of a new class of additive feature importance measures, and (2) theoretical results showing there is a unique solution in this class with a set of desirable properties. The new class unifies six existing methods, notable because several recent methods in the class lack the proposed desirable properties. Based on insights from this unification, we present new methods that show improved computational performance and/or better consistency with human intuition than previous approaches.

When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often involve the absence of shape parametrization during the inference stage, leaving us with only mesh discretizations as available data. Learning simulations from such mesh-based representations poses significant challenges, with recent advances relying heavily on deep graph neural networks to overcome the limitations of conventional machine learning approaches. Despite their promising results, graph neural networks exhibit certain drawbacks, including their dependency on extensive datasets and limitations in providing built-in predictive uncertainties or handling large meshes. In this work, we propose a machine learning method that do not rely on graph neural networks. Complex geometrical shapes and variations with fixed topology are dealt with using well-known mesh morphing onto a common support, combined with classical dimensionality reduction techniques and Gaussian processes. The proposed methodology can easily deal with large meshes without the need for explicit shape parameterization and provides crucial predictive uncertainties, which are essential for informed decision-making. In the considered numerical experiments, the proposed method is competitive with respect to existing graph neural networks, regarding training efficiency and accuracy of the predictions.

This paper addresses unsupervised representation learning on tabular data containing multiple views generated by distinct sources of measurement. Traditional methods, which tackle this problem using the multi-view framework, are constrained by predefined assumptions that assume feature sets share the same information and representations should learn globally shared factors. However, this assumption is not always valid for real-world tabular datasets with complex dependencies between feature sets, resulting in localized information that is harder to learn. To overcome this limitation, we propose a data-driven approach that learns feature set dependencies by representing feature sets as graph nodes and their relationships as learnable edges. Furthermore, we introduce LEGATO, a novel hierarchical graph autoencoder that learns a smaller, latent graph to aggregate information from multiple views dynamically. This approach results in latent graph components that specialize in capturing localized information from different regions of the input, leading to superior downstream performance.

A key goal of current mechanistic interpretability research in NLP is to find linear features (also called "feature vectors") for transformers: directions in activation space corresponding to concepts that are used by a given model in its computation. Present state-of-the-art methods for finding linear features require large amounts of labelled data -- both laborious to acquire and computationally expensive to utilize. In this work, we introduce a novel method, called "observable propagation" (in short: ObsProp), for finding linear features used by transformer language models in computing a given task -- using almost no data. Our paradigm centers on the concept of observables, linear functionals corresponding to given tasks. We then introduce a mathematical theory for the analysis of feature vectors: we provide theoretical motivation for why LayerNorm nonlinearities do not affect the direction of feature vectors; we also introduce a similarity metric between feature vectors called the coupling coefficient which estimates the degree to which one feature's output correlates with another's. We use ObsProp to perform extensive qualitative investigations into several tasks, including gendered occupational bias, political party prediction, and programming language detection. Our results suggest that ObsProp surpasses traditional approaches for finding feature vectors in the low-data regime, and that ObsProp can be used to better understand the mechanisms responsible for bias in large language models. Code for experiments can be found at github.com/jacobdunefsky/ObservablePropagation.

One of the primary challenges in brain tumor segmentation arises from the uncertainty of voxels close to tumor boundaries. However, the conventional process of generating ground truth segmentation masks fails to treat such uncertainties properly. Those "hard labels" with 0s and 1s conceptually influenced the majority of prior studies on brain image segmentation. As a result, tumor segmentation is often solved through voxel classification. In this work, we instead view this problem as a voxel-level regression, where the ground truth represents a certainty mapping from any pixel to the border of the tumor. We propose a novel ground truth label transformation, which is based on a signed geodesic transform, to capture the uncertainty in brain tumors' vicinity. We combine this idea with a Focal-like regression L1-loss that enables effective regression learning in high-dimensional output space by appropriately weighting voxels according to their difficulty. We thoroughly conduct an experimental evaluation to validate the components of our proposed method, compare it to a diverse array of state-of-the-art segmentation models, and show that it is architecture-agnostic. The code of our method is made publicly available (https://github.com/Oulu-IMEDS/SiNGR/).

The acquisition of labels for supervised learning can be expensive. To improve the sample efficiency of neural network regression, we study active learning methods that adaptively select batches of unlabeled data for labeling. We present a framework for constructing such methods out of (network-dependent) base kernels, kernel transformations, and selection methods. Our framework encompasses many existing Bayesian methods based on Gaussian process approximations of neural networks as well as non-Bayesian methods. Additionally, we propose to replace the commonly used last-layer features with sketched finite-width neural tangent kernels and to combine them with a novel clustering method. To evaluate different methods, we introduce an open-source benchmark consisting of 15 large tabular regression data sets. Our proposed method outperforms the state-of-the-art on our benchmark, scales to large data sets, and works out-of-the-box without adjusting the network architecture or training code. We provide open-source code that includes efficient implementations of all kernels, kernel transformations, and selection methods, and can be used for reproducing our results.

Testing and evaluation is a critical step in the development and deployment of connected and automated vehicles (CAVs). Due to the black-box property and various types of CAVs, how to test and evaluate CAVs adaptively remains a major challenge. Many approaches have been proposed to adaptively generate testing scenarios during the testing process. However, most existing approaches cannot be applied to complex scenarios, where the variables needed to define such scenarios are high dimensional. Towards filling this gap, the adaptive testing with sparse control variates method is proposed in this paper. Instead of adaptively generating testing scenarios, our approach evaluates CAVs' performances by adaptively utilizing the testing results. Specifically, each testing result is adjusted using multiple linear regression techniques based on control variates. As the regression coefficients can be adaptively optimized for the CAV under test, using the adjusted results can reduce the estimation variance, compared with using the testing results directly. To overcome the high dimensionality challenge, sparse control variates are utilized only for the critical variables of testing scenarios. To validate the proposed method, the high-dimensional overtaking scenarios are investigated, and the results demonstrate that our approach can further accelerate the evaluation process by about 30 times.

This paper studies the prediction of a target z from a pair of random variables (x,y), where the ground-truth predictor is additive E[z mid x,y] = f_star(x) +g_{star}(y). We study the performance of empirical risk minimization (ERM) over functions f+g, f in F and g in G, fit on a given training distribution, but evaluated on a test distribution which exhibits covariate shift. We show that, when the class F is "simpler" than G (measured, e.g., in terms of its metric entropy), our predictor is more resilient to heterogenous covariate shifts in which the shift in x is much greater than that in y. These results rely on a novel H\"older style inequality for the Dudley integral which may be of independent interest. Moreover, we corroborate our theoretical findings with experiments demonstrating improved resilience to shifts in "simpler" features across numerous domains.

We study the connection between multicalibration and boosting for squared error regression. First we prove a useful characterization of multicalibration in terms of a ``swap regret'' like condition on squared error. Using this characterization, we give an exceedingly simple algorithm that can be analyzed both as a boosting algorithm for regression and as a multicalibration algorithm for a class H that makes use only of a standard squared error regression oracle for H. We give a weak learning assumption on H that ensures convergence to Bayes optimality without the need to make any realizability assumptions -- giving us an agnostic boosting algorithm for regression. We then show that our weak learning assumption on H is both necessary and sufficient for multicalibration with respect to H to imply Bayes optimality. We also show that if H satisfies our weak learning condition relative to another class C then multicalibration with respect to H implies multicalibration with respect to C. Finally we investigate the empirical performance of our algorithm experimentally using an open source implementation that we make available. Our code repository can be found at https://github.com/Declancharrison/Level-Set-Boosting.

We present TraDE, a self-attention-based architecture for auto-regressive density estimation with continuous and discrete valued data. Our model is trained using a penalized maximum likelihood objective, which ensures that samples from the density estimate resemble the training data distribution. The use of self-attention means that the model need not retain conditional sufficient statistics during the auto-regressive process beyond what is needed for each covariate. On standard tabular and image data benchmarks, TraDE produces significantly better density estimates than existing approaches such as normalizing flow estimators and recurrent auto-regressive models. However log-likelihood on held-out data only partially reflects how useful these estimates are in real-world applications. In order to systematically evaluate density estimators, we present a suite of tasks such as regression using generated samples, out-of-distribution detection, and robustness to noise in the training data and demonstrate that TraDE works well in these scenarios.

We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard function (constant, increasing, decreasing, up-then-down, down-then-up), various common survival distributions (log-logistic, Burr type XII, Weibull, Gompertz), and includes defective distributions (i.e., cure models). This generality is achieved using four basic distributional parameters: two scale-type parameters and two shape parameters. Generalising to covariate dependence, the scale-type regression components correspond to accelerated failure time (AFT) and proportional hazards (PH) models. Therefore, this general formulation unifies the most popular survival models which allows us to consider the practical value of possible modelling choices for survival data. Furthermore, in line with our proposed flexible baseline distribution, we advocate the use of multi-parameter regression in which more than one distributional parameter depends on covariates - rather than the usual convention of having a single covariate-dependent (scale) parameter. While many choices are available, we suggest introducing covariates through just one or other of the two scale parameters, which covers AFT and PH models, in combination with a `power' shape parameter, which allows for more complex non-AFT/non-PH effects, while the other shape parameter remains covariate-independent, and handles automatic selection of the baseline distribution. We explore inferential issues in simulations, both with and without a covariate, with particular focus on evidence concerning the need, or otherwise, to include both AFT and PH parameters. We illustrate the efficacy of our modelling framework by investigating differences between treatment groups using data from a lung cancer study and a melanoma study. Censoring is accommodated throughout.

Modeling multivariate time series is a well-established problem with a wide range of applications from healthcare to financial markets. Traditional State Space Models (SSMs) are classical approaches for univariate time series modeling due to their simplicity and expressive power to represent linear dependencies. They, however, have fundamentally limited expressive power to capture non-linear dependencies, are slow in practice, and fail to model the inter-variate information flow. Despite recent attempts to improve the expressive power of SSMs by using deep structured SSMs, the existing methods are either limited to univariate time series, fail to model complex patterns (e.g., seasonal patterns), fail to dynamically model the dependencies of variate and time dimensions, and/or are input-independent. We present Chimera that uses two input-dependent 2-D SSM heads with different discretization processes to learn long-term progression and seasonal patterns. To improve the efficiency of complex 2D recurrence, we present a fast training using a new 2-dimensional parallel selective scan. We further present and discuss 2-dimensional Mamba and Mamba-2 as the spacial cases of our 2D SSM. Our experimental evaluation shows the superior performance of Chimera on extensive and diverse benchmarks, including ECG and speech time series classification, long-term and short-term time series forecasting, and time series anomaly detection.

Transfer learning with a small amount of target data is an effective and common approach to adapting a pre-trained model to distribution shifts. In some situations, target data labels may be expensive to obtain, so we may only have access to a limited number of target data points. To make the most of a very small target dataset, we propose a lightweight, sample-efficient approach that learns a diverse set of features and adapts to a target distribution by interpolating these features. Our approach, Project and Probe (Pro^2), first learns a linear projection that maps a pre-trained embedding onto orthogonal directions while being predictive of labels in the source dataset. The goal of this step is to learn a variety of predictive features, so that at least some of them remain useful after distribution shift. Pro^2 then learns a linear classifier on top of these projected features using a small target dataset. Theoretically, we find that Pro^2 results in more sample-efficient generalization by inducing a favorable bias-variance tradeoff. Our experiments on four datasets, with multiple distribution shift settings for each, show that Pro^2 improves performance by 5-15% when given limited target data compared to prior methods such as standard linear probing.

Forecasting on sparse multivariate time series (MTS) aims to model the predictors of future values of time series given their incomplete past, which is important for many emerging applications. However, most existing methods process MTS's individually, and do not leverage the dynamic distributions underlying the MTS's, leading to sub-optimal results when the sparsity is high. To address this challenge, we propose a novel generative model, which tracks the transition of latent clusters, instead of isolated feature representations, to achieve robust modeling. It is characterized by a newly designed dynamic Gaussian mixture distribution, which captures the dynamics of clustering structures, and is used for emitting timeseries. The generative model is parameterized by neural networks. A structured inference network is also designed for enabling inductive analysis. A gating mechanism is further introduced to dynamically tune the Gaussian mixture distributions. Extensive experimental results on a variety of real-life datasets demonstrate the effectiveness of our method.

Conventional supervised learning typically assumes that the learning task can be solved by learning a single function since the data is sampled from a fixed distribution. However, this assumption is invalid in open-ended environments where no task-level data partitioning is available. In this paper, we present a novel supervised learning framework of learning from open-ended data, which is modeled as data implicitly sampled from multiple domains with the data in each domain obeying a domain-specific target function. Since different domains may possess distinct target functions, open-ended data inherently requires multiple functions to capture all its input-output relations, rendering training a single global model problematic. To address this issue, we devise an Open-ended Supervised Learning (OSL) framework, of which the key component is a subjective function that allocates the data among multiple candidate models to resolve the "conflict" between the data from different domains, exhibiting a natural hierarchy. We theoretically analyze the learnability and the generalization error of OSL, and empirically validate its efficacy in both open-ended regression and classification tasks.

This paper presents a Bayesian nonparametric latent feature model specially suitable for exploratory analysis of high-dimensional count data. We perform a non-negative doubly sparse matrix factorization that has two main advantages: not only we are able to better approximate the row input distributions, but the inferred topics are also easier to interpret. By combining the three-parameter and restricted Indian buffet processes into a single prior, we increase the model flexibility, allowing for a full spectrum of sparse solutions in the latent space. We demonstrate the usefulness of our approach in the analysis of countries' economic structure. Compared to other approaches, empirical results show our model's ability to give easy-to-interpret information and better capture the underlying sparsity structure of data.

Standard infinite-width limits of neural networks sacrifice the ability for intermediate layers to learn representations from data. Recent work (A theory of representation learning gives a deep generalisation of kernel methods, Yang et al. 2023) modified the Neural Network Gaussian Process (NNGP) limit of Bayesian neural networks so that representation learning is retained. Furthermore, they found that applying this modified limit to a deep Gaussian process gives a practical learning algorithm which they dubbed the deep kernel machine (DKM). However, they only considered the simplest possible setting: regression in small, fully connected networks with e.g. 10 input features. Here, we introduce convolutional deep kernel machines. This required us to develop a novel inter-domain inducing point approximation, as well as introducing and experimentally assessing a number of techniques not previously seen in DKMs, including analogues to batch normalisation, different likelihoods, and different types of top-layer. The resulting model trains in roughly 77 GPU hours, achieving around 99% test accuracy on MNIST, 72% on CIFAR-100, and 92.7% on CIFAR-10, which is SOTA for kernel methods.

Supervised dictionary learning (SDL) is a classical machine learning method that simultaneously seeks feature extraction and classification tasks, which are not necessarily a priori aligned objectives. The goal of SDL is to learn a class-discriminative dictionary, which is a set of latent feature vectors that can well-explain both the features as well as labels of observed data. In this paper, we provide a systematic study of SDL, including the theory, algorithm, and applications of SDL. First, we provide a novel framework that `lifts' SDL as a convex problem in a combined factor space and propose a low-rank projected gradient descent algorithm that converges exponentially to the global minimizer of the objective. We also formulate generative models of SDL and provide global estimation guarantees of the true parameters depending on the hyperparameter regime. Second, viewed as a nonconvex constrained optimization problem, we provided an efficient block coordinate descent algorithm for SDL that is guaranteed to find an varepsilon-stationary point of the objective in O(varepsilon^{-1}(log varepsilon^{-1})^{2}) iterations. For the corresponding generative model, we establish a novel non-asymptotic local consistency result for constrained and regularized maximum likelihood estimation problems, which may be of independent interest. Third, we apply SDL for imbalanced document classification by supervised topic modeling and also for pneumonia detection from chest X-ray images. We also provide simulation studies to demonstrate that SDL becomes more effective when there is a discrepancy between the best reconstructive and the best discriminative dictionaries.

Time-series forecasting is one of the most active research topics in artificial intelligence. Applications in real-world time series should consider two factors for achieving reliable predictions: modeling dynamic dependencies among multiple variables and adjusting the model's intrinsic hyperparameters. A still open gap in that literature is that statistical and ensemble learning approaches systematically present lower predictive performance than deep learning methods. They generally disregard the data sequence aspect entangled with multivariate data represented in more than one time series. Conversely, this work presents a novel neural network architecture for time-series forecasting that combines the power of graph evolution with deep recurrent learning on distinct data distributions; we named our method Recurrent Graph Evolution Neural Network (ReGENN). The idea is to infer multiple multivariate relationships between co-occurring time-series by assuming that the temporal data depends not only on inner variables and intra-temporal relationships (i.e., observations from itself) but also on outer variables and inter-temporal relationships (i.e., observations from other-selves). An extensive set of experiments was conducted comparing ReGENN with dozens of ensemble methods and classical statistical ones, showing sound improvement of up to 64.87% over the competing algorithms. Furthermore, we present an analysis of the intermediate weights arising from ReGENN, showing that by looking at inter and intra-temporal relationships simultaneously, time-series forecasting is majorly improved if paying attention to how multiple multivariate data synchronously evolve.

Long-term time series forecasting (LTSF) is important for various domains but is confronted by challenges in handling the complex temporal-contextual relationships. As multivariate input models underperforming some recent univariate counterparts, we posit that the issue lies in the inefficiency of existing multivariate LTSF Transformers to model series-wise relationships: the characteristic differences between series are often captured incorrectly. To address this, we introduce ARM: a multivariate temporal-contextual adaptive learning method, which is an enhanced architecture specifically designed for multivariate LTSF modelling. ARM employs Adaptive Univariate Effect Learning (AUEL), Random Dropping (RD) training strategy, and Multi-kernel Local Smoothing (MKLS), to better handle individual series temporal patterns and correctly learn inter-series dependencies. ARM demonstrates superior performance on multiple benchmarks without significantly increasing computational costs compared to vanilla Transformer, thereby advancing the state-of-the-art in LTSF. ARM is also generally applicable to other LTSF architecture beyond vanilla Transformer.

We consider the problem of linear estimation, and establish an extension of the Gauss-Markov theorem, in which the bias operator is allowed to be non-zero but bounded with respect to a matrix norm of Schatten type. We derive simple and explicit formulas for the optimal estimator in the cases of Nuclear and Spectral norms (with the Frobenius case recovering ridge regression). Additionally, we analytically derive the generalization error in multiple random matrix ensembles, and compare with Ridge regression. Finally, we conduct an extensive simulation study, in which we show that the cross-validated Nuclear and Spectral regressors can outperform Ridge in several circumstances.

In this paper, we propose a speed-up approach for subclass discriminant analysis and formulate a novel efficient multi-view solution to it. The speed-up approach is developed based on graph embedding and spectral regression approaches that involve eigendecomposition of the corresponding Laplacian matrix and regression to its eigenvectors. We show that by exploiting the structure of the between-class Laplacian matrix, the eigendecomposition step can be substituted with a much faster process. Furthermore, we formulate a novel criterion for multi-view subclass discriminant analysis and show that an efficient solution for it can be obtained in a similar to the single-view manner. We evaluate the proposed methods on nine single-view and nine multi-view datasets and compare them with related existing approaches. Experimental results show that the proposed solutions achieve competitive performance, often outperforming the existing methods. At the same time, they significantly decrease the training time.

Time series research has gathered lots of interests in the last decade, especially for Time Series Classification (TSC) and Time Series Forecasting (TSF). Research in TSC has greatly benefited from the University of California Riverside and University of East Anglia (UCR/UEA) Time Series Archives. On the other hand, the advancement in Time Series Forecasting relies on time series forecasting competitions such as the Makridakis competitions, NN3 and NN5 Neural Network competitions, and a few Kaggle competitions. Each year, thousands of papers proposing new algorithms for TSC and TSF have utilized these benchmarking archives. These algorithms are designed for these specific problems, but may not be useful for tasks such as predicting the heart rate of a person using photoplethysmogram (PPG) and accelerometer data. We refer to this problem as Time Series Extrinsic Regression (TSER), where we are interested in a more general methodology of predicting a single continuous value, from univariate or multivariate time series. This prediction can be from the same time series or not directly related to the predictor time series and does not necessarily need to be a future value or depend heavily on recent values. To the best of our knowledge, research into TSER has received much less attention in the time series research community and there are no models developed for general time series extrinsic regression problems. Most models are developed for a specific problem. Therefore, we aim to motivate and support the research into TSER by introducing the first TSER benchmarking archive. This archive contains 19 datasets from different domains, with varying number of dimensions, unequal length dimensions, and missing values. In this paper, we introduce the datasets in this archive and did an initial benchmark on existing models.

We study the data selection problem, whose aim is to select a small representative subset of data that can be used to efficiently train a machine learning model. We present a new data selection approach based on k-means clustering and sensitivity sampling. Assuming access to an embedding representation of the data with respect to which the model loss is H\"older continuous, our approach provably allows selecting a set of ``typical'' k + 1/varepsilon^2 elements whose average loss corresponds to the average loss of the whole dataset, up to a multiplicative (1pmvarepsilon) factor and an additive varepsilon lambda Phi_k, where Phi_k represents the k-means cost for the input embeddings and lambda is the H\"older constant. We furthermore demonstrate the performance and scalability of our approach on fine-tuning foundation models and show that it outperforms state-of-the-art methods. We also show how it can be applied on linear regression, leading to a new sampling strategy that surprisingly matches the performances of leverage score sampling, while being conceptually simpler and more scalable.

Anomaly detection in supercomputers is a very difficult problem due to the big scale of the systems and the high number of components. The current state of the art for automated anomaly detection employs Machine Learning methods or statistical regression models in a supervised fashion, meaning that the detection tool is trained to distinguish among a fixed set of behaviour classes (healthy and unhealthy states). We propose a novel approach for anomaly detection in High Performance Computing systems based on a Machine (Deep) Learning technique, namely a type of neural network called autoencoder. The key idea is to train a set of autoencoders to learn the normal (healthy) behaviour of the supercomputer nodes and, after training, use them to identify abnormal conditions. This is different from previous approaches which where based on learning the abnormal condition, for which there are much smaller datasets (since it is very hard to identify them to begin with). We test our approach on a real supercomputer equipped with a fine-grained, scalable monitoring infrastructure that can provide large amount of data to characterize the system behaviour. The results are extremely promising: after the training phase to learn the normal system behaviour, our method is capable of detecting anomalies that have never been seen before with a very good accuracy (values ranging between 88% and 96%).

Invariance learning methods aim to learn invariant features in the hope that they generalize under distributional shifts. Although many tasks are naturally characterized by continuous domains, current invariance learning techniques generally assume categorically indexed domains. For example, auto-scaling in cloud computing often needs a CPU utilization prediction model that generalizes across different times (e.g., time of a day and date of a year), where `time' is a continuous domain index. In this paper, we start by theoretically showing that existing invariance learning methods can fail for continuous domain problems. Specifically, the naive solution of splitting continuous domains into discrete ones ignores the underlying relationship among domains, and therefore potentially leads to suboptimal performance. To address this challenge, we then propose Continuous Invariance Learning (CIL), which extracts invariant features across continuously indexed domains. CIL is a novel adversarial procedure that measures and controls the conditional independence between the labels and continuous domain indices given the extracted features. Our theoretical analysis demonstrates the superiority of CIL over existing invariance learning methods. Empirical results on both synthetic and real-world datasets (including data collected from production systems) show that CIL consistently outperforms strong baselines among all the tasks.

Machine learning models are often trained to predict the outcome resulting from a human decision. For example, if a doctor decides to test a patient for disease, will the patient test positive? A challenge is that historical decision-making determines whether the outcome is observed: we only observe test outcomes for patients doctors historically tested. Untested patients, for whom outcomes are unobserved, may differ from tested patients along observed and unobserved dimensions. We propose a Bayesian model class which captures this setting. The purpose of the model is to accurately estimate risk for both tested and untested patients. Estimating this model is challenging due to the wide range of possibilities for untested patients. To address this, we propose two domain constraints which are plausible in health settings: a prevalence constraint, where the overall disease prevalence is known, and an expertise constraint, where the human decision-maker deviates from purely risk-based decision-making only along a constrained feature set. We show theoretically and on synthetic data that domain constraints improve parameter inference. We apply our model to a case study of cancer risk prediction, showing that the model's inferred risk predicts cancer diagnoses, its inferred testing policy captures known public health policies, and it can identify suboptimalities in test allocation. Though our case study is in healthcare, our analysis reveals a general class of domain constraints which can improve model estimation in many settings.

Supervised learning can be viewed as distilling relevant information from input data into feature representations. This process becomes difficult when supervision is noisy as the distilled information might not be relevant. In fact, recent research shows that networks can easily overfit all labels including those that are corrupted, and hence can hardly generalize to clean datasets. In this paper, we focus on the problem of learning with noisy labels and introduce compression inductive bias to network architectures to alleviate this over-fitting problem. More precisely, we revisit one classical regularization named Dropout and its variant Nested Dropout. Dropout can serve as a compression constraint for its feature dropping mechanism, while Nested Dropout further learns ordered feature representations w.r.t. feature importance. Moreover, the trained models with compression regularization are further combined with Co-teaching for performance boost. Theoretically, we conduct bias-variance decomposition of the objective function under compression regularization. We analyze it for both single model and Co-teaching. This decomposition provides three insights: (i) it shows that over-fitting is indeed an issue for learning with noisy labels; (ii) through an information bottleneck formulation, it explains why the proposed feature compression helps in combating label noise; (iii) it gives explanations on the performance boost brought by incorporating compression regularization into Co-teaching. Experiments show that our simple approach can have comparable or even better performance than the state-of-the-art methods on benchmarks with real-world label noise including Clothing1M and ANIMAL-10N. Our implementation is available at https://yingyichen-cyy.github.io/CompressFeatNoisyLabels/.

Interpretability is becoming an active research topic as machine learning (ML) models are more widely used to make critical decisions. Tabular data is one of the most commonly used modes of data in diverse applications such as healthcare and finance. Much of the existing interpretability methods used for tabular data only report feature-importance scores -- either locally (per example) or globally (per model) -- but they do not provide interpretation or visualization of how the features interact. We address this limitation by introducing Feature Vectors, a new global interpretability method designed for tabular datasets. In addition to providing feature-importance, Feature Vectors discovers the inherent semantic relationship among features via an intuitive feature visualization technique. Our systematic experiments demonstrate the empirical utility of this new method by applying it to several real-world datasets. We further provide an easy-to-use Python package for Feature Vectors.

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

Machine learning models will often fail when deployed in an environment with a data distribution that is different than the training distribution. When multiple environments are available during training, many methods exist that learn representations which are invariant across the different distributions, with the hope that these representations will be transportable to unseen domains. In this work, we present a nonparametric strategy for learning invariant representations based on the recently-proposed Nadaraya-Watson (NW) head. The NW head makes a prediction by comparing the learned representations of the query to the elements of a support set that consists of labeled data. We demonstrate that by manipulating the support set, one can encode different causal assumptions. In particular, restricting the support set to a single environment encourages the model to learn invariant features that do not depend on the environment. We present a causally-motivated setup for our modeling and training strategy and validate on three challenging real-world domain generalization tasks in computer vision.

Although deep neural networks have achieved reasonable accuracy in solving face alignment, it is still a challenging task, specifically when we deal with facial images, under occlusion, or extreme head poses. Heatmap-based Regression (HBR) and Coordinate-based Regression (CBR) are among the two mainly used methods for face alignment. CBR methods require less computer memory, though their performance is less than HBR methods. In this paper, we propose an Adaptive Coordinate-based Regression (ACR) loss to improve the accuracy of CBR for face alignment. Inspired by the Active Shape Model (ASM), we generate Smooth-Face objects, a set of facial landmark points with less variations compared to the ground truth landmark points. We then introduce a method to estimate the level of difficulty in predicting each landmark point for the network by comparing the distribution of the ground truth landmark points and the corresponding Smooth-Face objects. Our proposed ACR Loss can adaptively modify its curvature and the influence of the loss based on the difficulty level of predicting each landmark point in a face. Accordingly, the ACR Loss guides the network toward challenging points than easier points, which improves the accuracy of the face alignment task. Our extensive evaluation shows the capabilities of the proposed ACR Loss in predicting facial landmark points in various facial images.

The premise of identifiable and causal representation learning is to improve the current representation learning paradigm in terms of generalizability or robustness. Despite recent progress in questions of identifiability, more theoretical results demonstrating concrete advantages of these methods for downstream tasks are needed. In this paper, we consider the task of intervention extrapolation: predicting how interventions affect an outcome, even when those interventions are not observed at training time, and show that identifiable representations can provide an effective solution to this task even if the interventions affect the outcome non-linearly. Our setup includes an outcome Y, observed features X, which are generated as a non-linear transformation of latent features Z, and exogenous action variables A, which influence Z. The objective of intervention extrapolation is to predict how interventions on A that lie outside the training support of A affect Y. Here, extrapolation becomes possible if the effect of A on Z is linear and the residual when regressing Z on A has full support. As Z is latent, we combine the task of intervention extrapolation with identifiable representation learning, which we call Rep4Ex: we aim to map the observed features X into a subspace that allows for non-linear extrapolation in A. We show that the hidden representation is identifiable up to an affine transformation in Z-space, which is sufficient for intervention extrapolation. The identifiability is characterized by a novel constraint describing the linearity assumption of A on Z. Based on this insight, we propose a method that enforces the linear invariance constraint and can be combined with any type of autoencoder. We validate our theoretical findings through synthetic experiments and show that our approach succeeds in predicting the effects of unseen interventions.

Nonlinear sufficient dimension reductionlibing_generalSDR, which constructs nonlinear low-dimensional representations to summarize essential features of high-dimensional data, is an important branch of representation learning. However, most existing methods are not applicable when the response variables are complex non-Euclidean random objects, which are frequently encountered in many recent statistical applications. In this paper, we introduce a new statistical dependence measure termed Fr\'echet Cumulative Covariance (FCCov) and develop a novel nonlinear SDR framework based on FCCov. Our approach is not only applicable to complex non-Euclidean data, but also exhibits robustness against outliers. We further incorporate Feedforward Neural Networks (FNNs) and Convolutional Neural Networks (CNNs) to estimate nonlinear sufficient directions in the sample level. Theoretically, we prove that our method with squared Frobenius norm regularization achieves unbiasedness at the sigma-field level. Furthermore, we establish non-asymptotic convergence rates for our estimators based on FNNs and ResNet-type CNNs, which match the minimax rate of nonparametric regression up to logarithmic factors. Intensive simulation studies verify the performance of our methods in both Euclidean and non-Euclidean settings. We apply our method to facial expression recognition datasets and the results underscore more realistic and broader applicability of our proposal.

Mixture of experts (MoE) are a popular class of statistical and machine learning models that have gained attention over the years due to their flexibility and efficiency. In this work, we consider Gaussian-gated localized MoE (GLoME) and block-diagonal covariance localized MoE (BLoME) regression models to present nonlinear relationships in heterogeneous data with potential hidden graph-structured interactions between high-dimensional predictors. These models pose difficult statistical estimation and model selection questions, both from a computational and theoretical perspective. This paper is devoted to the study of the problem of model selection among a collection of GLoME or BLoME models characterized by the number of mixture components, the complexity of Gaussian mean experts, and the hidden block-diagonal structures of the covariance matrices, in a penalized maximum likelihood estimation framework. In particular, we establish non-asymptotic risk bounds that take the form of weak oracle inequalities, provided that lower bounds for the penalties hold. The good empirical behavior of our models is then demonstrated on synthetic and real datasets.

Unlabeled data is a key component of modern machine learning. In general, the role of unlabeled data is to impose a form of smoothness, usually from the similarity information encoded in a base kernel, such as the epsilon-neighbor kernel or the adjacency matrix of a graph. This work revisits the classical idea of spectrally transformed kernel regression (STKR), and provides a new class of general and scalable STKR estimators able to leverage unlabeled data. Intuitively, via spectral transformation, STKR exploits the data distribution for which unlabeled data can provide additional information. First, we show that STKR is a principled and general approach, by characterizing a universal type of "target smoothness", and proving that any sufficiently smooth function can be learned by STKR. Second, we provide scalable STKR implementations for the inductive setting and a general transformation function, while prior work is mostly limited to the transductive setting. Third, we derive statistical guarantees for two scenarios: STKR with a known polynomial transformation, and STKR with kernel PCA when the transformation is unknown. Overall, we believe that this work helps deepen our understanding of how to work with unlabeled data, and its generality makes it easier to inspire new methods.

We propose a novel interpretation technique to explain the behavior of structured output models, which learn mappings between an input vector to a set of output variables simultaneously. Because of the complex relationship between the computational path of output variables in structured models, a feature can affect the value of output through other ones. We focus on one of the outputs as the target and try to find the most important features utilized by the structured model to decide on the target in each locality of the input space. In this paper, we assume an arbitrary structured output model is available as a black box and argue how considering the correlations between output variables can improve the explanation performance. The goal is to train a function as an interpreter for the target output variable over the input space. We introduce an energy-based training process for the interpreter function, which effectively considers the structural information incorporated into the model to be explained. The effectiveness of the proposed method is confirmed using a variety of simulated and real data sets.

We introduce methods for discovering and applying sparse feature circuits. These are causally implicated subnetworks of human-interpretable features for explaining language model behaviors. Circuits identified in prior work consist of polysemantic and difficult-to-interpret units like attention heads or neurons, rendering them unsuitable for many downstream applications. In contrast, sparse feature circuits enable detailed understanding of unanticipated mechanisms. Because they are based on fine-grained units, sparse feature circuits are useful for downstream tasks: We introduce SHIFT, where we improve the generalization of a classifier by ablating features that a human judges to be task-irrelevant. Finally, we demonstrate an entirely unsupervised and scalable interpretability pipeline by discovering thousands of sparse feature circuits for automatically discovered model behaviors.

Recently, efficient fine-tuning of large-scale pre-trained models has attracted increasing research interests, where linear probing (LP) as a fundamental module is involved in exploiting the final representations for task-dependent classification. However, most of the existing methods focus on how to effectively introduce a few of learnable parameters, and little work pays attention to the commonly used LP module. In this paper, we propose a novel Moment Probing (MP) method to further explore the potential of LP. Distinguished from LP which builds a linear classification head based on the mean of final features (e.g., word tokens for ViT) or classification tokens, our MP performs a linear classifier on feature distribution, which provides the stronger representation ability by exploiting richer statistical information inherent in features. Specifically, we represent feature distribution by its characteristic function, which is efficiently approximated by using first- and second-order moments of features. Furthermore, we propose a multi-head convolutional cross-covariance (MHC^3) to compute second-order moments in an efficient and effective manner. By considering that MP could affect feature learning, we introduce a partially shared module to learn two recalibrating parameters (PSRP) for backbones based on MP, namely MP_{+}. Extensive experiments on ten benchmarks using various models show that our MP significantly outperforms LP and is competitive with counterparts at less training cost, while our MP_{+} achieves state-of-the-art performance.

State-of-the-art methods for conditional average treatment effect (CATE) estimation make widespread use of representation learning. Here, the idea is to reduce the variance of the low-sample CATE estimation by a (potentially constrained) low-dimensional representation. However, low-dimensional representations can lose information about the observed confounders and thus lead to bias, because of which the validity of representation learning for CATE estimation is typically violated. In this paper, we propose a new, representation-agnostic framework for estimating bounds on the representation-induced confounding bias that comes from dimensionality reduction (or other constraints on the representations) in CATE estimation. First, we establish theoretically under which conditions CATEs are non-identifiable given low-dimensional (constrained) representations. Second, as our remedy, we propose to perform partial identification of CATEs or, equivalently, aim at estimating of lower and upper bounds of the representation-induced confounding bias. We demonstrate the effectiveness of our bounds in a series of experiments. In sum, our framework is of direct relevance in practice where the validity of CATE estimation is of importance.

We develop a fast, tractable technique called Net-Trim for simplifying a trained neural network. The method is a convex post-processing module, which prunes (sparsifies) a trained network layer by layer, while preserving the internal responses. We present a comprehensive analysis of Net-Trim from both the algorithmic and sample complexity standpoints, centered on a fast, scalable convex optimization program. Our analysis includes consistency results between the initial and retrained models before and after Net-Trim application and guarantees on the number of training samples needed to discover a network that can be expressed using a certain number of nonzero terms. Specifically, if there is a set of weights that uses at most s terms that can re-create the layer outputs from the layer inputs, we can find these weights from O(slog N/s) samples, where N is the input size. These theoretical results are similar to those for sparse regression using the Lasso, and our analysis uses some of the same recently-developed tools (namely recent results on the concentration of measure and convex analysis). Finally, we propose an algorithmic framework based on the alternating direction method of multipliers (ADMM), which allows a fast and simple implementation of Net-Trim for network pruning and compression.

The Feature Selection Library (FSLib) introduces a comprehensive suite of feature selection (FS) algorithms for MATLAB, aimed at improving machine learning and data mining tasks. FSLib encompasses filter, embedded, and wrapper methods to cater to diverse FS requirements. Filter methods focus on the inherent characteristics of features, embedded methods incorporate FS within model training, and wrapper methods assess features through model performance metrics. By enabling effective feature selection, FSLib addresses the curse of dimensionality, reduces computational load, and enhances model generalizability. The elimination of redundant features through FSLib streamlines the training process, improving efficiency and scalability. This facilitates faster model development and boosts key performance indicators such as accuracy, precision, and recall by focusing on vital features. Moreover, FSLib contributes to data interpretability by revealing important features, aiding in pattern recognition and understanding. Overall, FSLib provides a versatile framework that not only simplifies feature selection but also significantly benefits the machine learning and data mining ecosystem by offering a wide range of algorithms, reducing dimensionality, accelerating model training, improving model outcomes, and enhancing data insights.

The behavior of neural networks still remains opaque, and a recently widely noted phenomenon is that networks often achieve similar performance when initialized with different random parameters. This phenomenon has attracted significant attention in measuring the similarity between features learned by distinct networks. However, feature similarity could be vague in describing the same feature since equivalent features hardly exist. In this paper, we expand the concept of equivalent feature and provide the definition of what we call functionally equivalent features. These features produce equivalent output under certain transformations. Using this definition, we aim to derive a more intrinsic metric for the so-called feature complexity regarding the redundancy of features learned by a neural network at each layer. We offer a formal interpretation of our approach through the lens of category theory, a well-developed area in mathematics. To quantify the feature complexity, we further propose an efficient algorithm named Iterative Feature Merging. Our experimental results validate our ideas and theories from various perspectives. We empirically demonstrate that the functionally equivalence widely exists among different features learned by the same neural network and we could reduce the number of parameters of the network without affecting the performance.The IFM shows great potential as a data-agnostic model prune method. We have also drawn several interesting empirical findings regarding the defined feature complexity.

In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get masked by scale differences. To rectify this problem, several modifications of these classifiers have been proposed in the literature. However, existing methods are confined to location and scale differences only, and often fail to discriminate among populations differing outside of the first two moments. In this article, we propose some simple transformations of these classifiers resulting into improved performance even when the underlying populations have the same location and scale. We further propose a generalization of these classifiers based on the idea of grouping of variables. The high-dimensional behavior of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated examples as well as an extensive analysis of real data sets exhibit advantages of the proposed methods.

A multivariate time series refers to observations of two or more variables taken from a device or a system simultaneously over time. There is an increasing need to monitor multivariate time series and detect anomalies in real time to ensure proper system operation and good service quality. It is also highly desirable to have a lightweight anomaly detection system that considers correlations between different variables, adapts to changes in the pattern of the multivariate time series, offers immediate responses, and provides supportive information regarding detection results based on unsupervised learning and online model training. In the past decade, many multivariate time series anomaly detection approaches have been introduced. However, they are unable to offer all the above-mentioned features. In this paper, we propose RoLA, a real-time online lightweight anomaly detection system for multivariate time series based on a divide-and-conquer strategy, parallel processing, and the majority rule. RoLA employs multiple lightweight anomaly detectors to monitor multivariate time series in parallel, determine the correlations between variables dynamically on the fly, and then jointly detect anomalies based on the majority rule in real time. To demonstrate the performance of RoLA, we conducted an experiment based on a public dataset provided by the FerryBox of the One Ocean Expedition. The results show that RoLA provides satisfactory detection accuracy and lightweight performance.

Objective: To transform heterogeneous clinical data from electronic health records into clinically meaningful constructed features using data driven method that rely, in part, on temporal relations among data. Materials and Methods: The clinically meaningful representations of medical concepts and patients are the key for health analytic applications. Most of existing approaches directly construct features mapped to raw data (e.g., ICD or CPT codes), or utilize some ontology mapping such as SNOMED codes. However, none of the existing approaches leverage EHR data directly for learning such concept representation. We propose a new way to represent heterogeneous medical concepts (e.g., diagnoses, medications and procedures) based on co-occurrence patterns in longitudinal electronic health records. The intuition behind the method is to map medical concepts that are co-occuring closely in time to similar concept vectors so that their distance will be small. We also derive a simple method to construct patient vectors from the related medical concept vectors. Results: For qualitative evaluation, we study similar medical concepts across diagnosis, medication and procedure. In quantitative evaluation, our proposed representation significantly improves the predictive modeling performance for onset of heart failure (HF), where classification methods (e.g. logistic regression, neural network, support vector machine and K-nearest neighbors) achieve up to 23% improvement in area under the ROC curve (AUC) using this proposed representation. Conclusion: We proposed an effective method for patient and medical concept representation learning. The resulting representation can map relevant concepts together and also improves predictive modeling performance.

Sparse Autoencoders (SAEs) are a promising approach for extracting neural network representations by learning a sparse and overcomplete decomposition of the network's internal activations. However, SAEs are traditionally trained considering only activation values and not the effect those activations have on downstream computations. This limits the information available to learn features, and biases the autoencoder towards neglecting features which are represented with small activation values but strongly influence model outputs. To address this, we introduce Gradient SAEs (g-SAEs), which modify the k-sparse autoencoder architecture by augmenting the TopK activation function to rely on the gradients of the input activation when selecting the k elements. For a given sparsity level, g-SAEs produce reconstructions that are more faithful to original network performance when propagated through the network. Additionally, we find evidence that g-SAEs learn latents that are on average more effective at steering models in arbitrary contexts. By considering the downstream effects of activations, our approach leverages the dual nature of neural network features as both representations, retrospectively, and actions, prospectively. While previous methods have approached the problem of feature discovery primarily focused on the former aspect, g-SAEs represent a step towards accounting for the latter as well.

Prediction of stock prices has been an important area of research for a long time. While supporters of the efficient market hypothesis believe that it is impossible to predict stock prices accurately, there are formal propositions demonstrating that accurate modeling and designing of appropriate variables may lead to models using which stock prices and stock price movement patterns can be very accurately predicted. In this work, we propose an approach of hybrid modeling for stock price prediction building different machine learning and deep learning-based models. For the purpose of our study, we have used NIFTY 50 index values of the National Stock Exchange (NSE) of India, during the period December 29, 2014 till July 31, 2020. We have built eight regression models using the training data that consisted of NIFTY 50 index records during December 29, 2014 till December 28, 2018. Using these regression models, we predicted the open values of NIFTY 50 for the period December 31, 2018 till July 31, 2020. We, then, augment the predictive power of our forecasting framework by building four deep learning-based regression models using long-and short-term memory (LSTM) networks with a novel approach of walk-forward validation. We exploit the power of LSTM regression models in forecasting the future NIFTY 50 open values using four different models that differ in their architecture and in the structure of their input data. Extensive results are presented on various metrics for the all the regression models. The results clearly indicate that the LSTM-based univariate model that uses one-week prior data as input for predicting the next week open value of the NIFTY 50 time series is the most accurate model.

In discriminative settings such as regression and classification there are two random variables at play, the inputs X and the targets Y. Here, we demonstrate that the Variational Information Bottleneck can be viewed as a compromise between fully empirical and fully Bayesian objectives, attempting to minimize the risks due to finite sampling of Y only. We argue that this approach provides some of the benefits of Bayes while requiring only some of the work.

We study the cost of overfitting in noisy kernel ridge regression (KRR), which we define as the ratio between the test error of the interpolating ridgeless model and the test error of the optimally-tuned model. We take an "agnostic" view in the following sense: we consider the cost as a function of sample size for any target function, even if the sample size is not large enough for consistency or the target is outside the RKHS. We analyze the cost of overfitting under a Gaussian universality ansatz using recently derived (non-rigorous) risk estimates in terms of the task eigenstructure. Our analysis provides a more refined characterization of benign, tempered and catastrophic overfitting (cf. Mallinar et al. 2022).

Machine learning (ML) holds great potential for accurately forecasting treatment outcomes over time, which could ultimately enable the adoption of more individualized treatment strategies in many practical applications. However, a significant challenge that has been largely overlooked by the ML literature on this topic is the presence of informative sampling in observational data. When instances are observed irregularly over time, sampling times are typically not random, but rather informative -- depending on the instance's characteristics, past outcomes, and administered treatments. In this work, we formalize informative sampling as a covariate shift problem and show that it can prohibit accurate estimation of treatment outcomes if not properly accounted for. To overcome this challenge, we present a general framework for learning treatment outcomes in the presence of informative sampling using inverse intensity-weighting, and propose a novel method, TESAR-CDE, that instantiates this framework using Neural CDEs. Using a simulation environment based on a clinical use case, we demonstrate the effectiveness of our approach in learning under informative sampling.

We employ random matrix theory to establish consistency of generalized cross validation (GCV) for estimating prediction risks of sketched ridge regression ensembles, enabling efficient and consistent tuning of regularization and sketching parameters. Our results hold for a broad class of asymptotically free sketches under very mild data assumptions. For squared prediction risk, we provide a decomposition into an unsketched equivalent implicit ridge bias and a sketching-based variance, and prove that the risk can be globally optimized by only tuning sketch size in infinite ensembles. For general subquadratic prediction risk functionals, we extend GCV to construct consistent risk estimators, and thereby obtain distributional convergence of the GCV-corrected predictions in Wasserstein-2 metric. This in particular allows construction of prediction intervals with asymptotically correct coverage conditional on the training data. We also propose an "ensemble trick" whereby the risk for unsketched ridge regression can be efficiently estimated via GCV using small sketched ridge ensembles. We empirically validate our theoretical results using both synthetic and real large-scale datasets with practical sketches including CountSketch and subsampled randomized discrete cosine transforms.

Calibrated uncertainty estimates in machine learning are crucial to many fields such as autonomous vehicles, medicine, and weather and climate forecasting. While there is extensive literature on uncertainty calibration for classification, the classification findings do not always translate to regression. As a result, modern models for predicting uncertainty in regression settings typically produce uncalibrated and overconfident estimates. To address these gaps, we present a calibration method for regression settings that does not assume a particular uncertainty distribution over the error: Calibrating Regression Uncertainty Distributions Empirically (CRUDE). CRUDE makes the weaker assumption that error distributions have a constant arbitrary shape across the output space, shifted by predicted mean and scaled by predicted standard deviation. We detail a theoretical connection between CRUDE and conformal inference. Across an extensive set of regression tasks, CRUDE demonstrates consistently sharper, better calibrated, and more accurate uncertainty estimates than state-of-the-art techniques.

When a large feedforward neural network is trained on a small training set, it typically performs poorly on held-out test data. This "overfitting" is greatly reduced by randomly omitting half of the feature detectors on each training case. This prevents complex co-adaptations in which a feature detector is only helpful in the context of several other specific feature detectors. Instead, each neuron learns to detect a feature that is generally helpful for producing the correct answer given the combinatorially large variety of internal contexts in which it must operate. Random "dropout" gives big improvements on many benchmark tasks and sets new records for speech and object recognition.

We study the optimisation problem associated with Gaussian process regression using squared loss. The most common approach to this problem is to apply an exact solver, such as conjugate gradient descent, either directly, or to a reduced-order version of the problem. Recently, driven by successes in deep learning, stochastic gradient descent has gained traction as an alternative. In this paper, we show that when done rightx2014by which we mean using specific insights from the optimisation and kernel communitiesx2014this approach is highly effective. We thus introduce a particular stochastic dual gradient descent algorithm, that may be implemented with a few lines of code using any deep learning framework. We explain our design decisions by illustrating their advantage against alternatives with ablation studies and show that the new method is highly competitive. Our evaluations on standard regression benchmarks and a Bayesian optimisation task set our approach apart from preconditioned conjugate gradients, variational Gaussian process approximations, and a previous version of stochastic gradient descent for Gaussian processes. On a molecular binding affinity prediction task, our method places Gaussian process regression on par in terms of performance with state-of-the-art graph neural networks.

Feature attribution methods identify which features of an input most influence a model's output. Most widely-used feature attribution methods (such as SHAP, LIME, and Grad-CAM) are "class-dependent" methods in that they generate a feature attribution vector as a function of class. In this work, we demonstrate that class-dependent methods can "leak" information about the selected class, making that class appear more likely than it is. Thus, an end user runs the risk of drawing false conclusions when interpreting an explanation generated by a class-dependent method. In contrast, we introduce "distribution-aware" methods, which favor explanations that keep the label's distribution close to its distribution given all features of the input. We introduce SHAP-KL and FastSHAP-KL, two baseline distribution-aware methods that compute Shapley values. Finally, we perform a comprehensive evaluation of seven class-dependent and three distribution-aware methods on three clinical datasets of different high-dimensional data types: images, biosignals, and text.

This paper introduces WeatherFormer, a transformer encoder-based model designed to learn robust weather features from minimal observations. It addresses the challenge of modeling complex weather dynamics from small datasets, a bottleneck for many prediction tasks in agriculture, epidemiology, and climate science. WeatherFormer was pretrained on a large pretraining dataset comprised of 39 years of satellite measurements across the Americas. With a novel pretraining task and fine-tuning, WeatherFormer achieves state-of-the-art performance in county-level soybean yield prediction and influenza forecasting. Technical innovations include a unique spatiotemporal encoding that captures geographical, annual, and seasonal variations, adapting the transformer architecture to continuous weather data, and a pretraining strategy to learn representations that are robust to missing weather features. This paper for the first time demonstrates the effectiveness of pretraining large transformer encoder models for weather-dependent applications across multiple domains.

Symbolic regression (SR) is an area of interpretable machine learning that aims to identify mathematical expressions, often composed of simple functions, that best fit in a given set of covariates X and response y. In recent years, deep symbolic regression (DSR) has emerged as a popular method in the field by leveraging deep reinforcement learning to solve the complicated combinatorial search problem. In this work, we propose an alternative framework (GFN-SR) to approach SR with deep learning. We model the construction of an expression tree as traversing through a directed acyclic graph (DAG) so that GFlowNet can learn a stochastic policy to generate such trees sequentially. Enhanced with an adaptive reward baseline, our method is capable of generating a diverse set of best-fitting expressions. Notably, we observe that GFN-SR outperforms other SR algorithms in noisy data regimes, owing to its ability to learn a distribution of rewards over a space of candidate solutions.

Conventional supervised learning methods typically assume i.i.d samples and are found to be sensitive to out-of-distribution (OOD) data. We propose Generative Causal Representation Learning (GCRL) which leverages causality to facilitate knowledge transfer under distribution shifts. While we evaluate the effectiveness of our proposed method in human trajectory prediction models, GCRL can be applied to other domains as well. First, we propose a novel causal model that explains the generative factors in motion forecasting datasets using features that are common across all environments and with features that are specific to each environment. Selection variables are used to determine which parts of the model can be directly transferred to a new environment without fine-tuning. Second, we propose an end-to-end variational learning paradigm to learn the causal mechanisms that generate observations from features. GCRL is supported by strong theoretical results that imply identifiability of the causal model under certain assumptions. Experimental results on synthetic and real-world motion forecasting datasets show the robustness and effectiveness of our proposed method for knowledge transfer under zero-shot and low-shot settings by substantially outperforming the prior motion forecasting models on out-of-distribution prediction. Our code is available at https://github.com/sshirahmad/GCRL.

Several studies have shown that speech and language features, automatically extracted from clinical interviews or spontaneous discourse, have diagnostic value for mental disorders such as schizophrenia and bipolar disorder. They typically make use of a large feature set to train a classifier for distinguishing between two groups of interest, i.e. a clinical and control group. However, a purely data-driven approach runs the risk of overfitting to a particular data set, especially when sample sizes are limited. Here, we first down-select the set of language features to a small subset that is related to a well-validated test of functional ability, the Social Skills Performance Assessment (SSPA). This helps establish the concurrent validity of the selected features. We use only these features to train a simple classifier to distinguish between groups of interest. Linear regression reveals that a subset of language features can effectively model the SSPA, with a correlation coefficient of 0.75. Furthermore, the same feature set can be used to build a strong binary classifier to distinguish between healthy controls and a clinical group (AUC = 0.96) and also between patients within the clinical group with schizophrenia and bipolar I disorder (AUC = 0.83).

Click-through rate (CTR) prediction, which aims to predict the probability of a user clicking on an ad or an item, is critical to many online applications such as online advertising and recommender systems. The problem is very challenging since (1) the input features (e.g., the user id, user age, item id, item category) are usually sparse and high-dimensional, and (2) an effective prediction relies on high-order combinatorial features (a.k.a. cross features), which are very time-consuming to hand-craft by domain experts and are impossible to be enumerated. Therefore, there have been efforts in finding low-dimensional representations of the sparse and high-dimensional raw features and their meaningful combinations. In this paper, we propose an effective and efficient method called the AutoInt to automatically learn the high-order feature interactions of input features. Our proposed algorithm is very general, which can be applied to both numerical and categorical input features. Specifically, we map both the numerical and categorical features into the same low-dimensional space. Afterwards, a multi-head self-attentive neural network with residual connections is proposed to explicitly model the feature interactions in the low-dimensional space. With different layers of the multi-head self-attentive neural networks, different orders of feature combinations of input features can be modeled. The whole model can be efficiently fit on large-scale raw data in an end-to-end fashion. Experimental results on four real-world datasets show that our proposed approach not only outperforms existing state-of-the-art approaches for prediction but also offers good explainability. Code is available at: https://github.com/DeepGraphLearning/RecommenderSystems.

When users can benefit from certain predictive outcomes, they may be prone to act to achieve those outcome, e.g., by strategically modifying their features. The goal in strategic classification is therefore to train predictive models that are robust to such behavior. However, the conventional framework assumes that changing features does not change actual outcomes, which depicts users as "gaming" the system. Here we remove this assumption, and study learning in a causal strategic setting where true outcomes do change. Focusing on accuracy as our primary objective, we show how strategic behavior and causal effects underlie two complementing forms of distribution shift. We characterize these shifts, and propose a learning algorithm that balances between these two forces and over time, and permits end-to-end training. Experiments on synthetic and semi-synthetic data demonstrate the utility of our approach.

Learning representations that generalize under distribution shifts is critical for building robust machine learning models. However, despite significant efforts in recent years, algorithmic advances in this direction have been limited. In this work, we seek to understand the fundamental difficulty of out-of-distribution generalization with deep neural networks. We first empirically show that perhaps surprisingly, even allowing a neural network to explicitly fit the representations obtained from a teacher network that can generalize out-of-distribution is insufficient for the generalization of the student network. Then, by a theoretical study of two-layer ReLU networks optimized by stochastic gradient descent (SGD) under a structured feature model, we identify a fundamental yet unexplored feature learning proclivity of neural networks, feature contamination: neural networks can learn uncorrelated features together with predictive features, resulting in generalization failure under distribution shifts. Notably, this mechanism essentially differs from the prevailing narrative in the literature that attributes the generalization failure to spurious correlations. Overall, our results offer new insights into the non-linear feature learning dynamics of neural networks and highlight the necessity of considering inductive biases in out-of-distribution generalization.

Machine learning has opened up new tools for financial fraud detection. Using a sample of annotated transactions, a machine learning classification algorithm learns to detect frauds. With growing credit card transaction volumes and rising fraud percentages there is growing interest in finding appropriate machine learning classifiers for detection. However, fraud data sets are diverse and exhibit inconsistent characteristics. As a result, a model effective on a given data set is not guaranteed to perform on another. Further, the possibility of temporal drift in data patterns and characteristics over time is high. Additionally, fraud data has massive and varying imbalance. In this work, we evaluate sampling methods as a viable pre-processing mechanism to handle imbalance and propose a data-driven classifier selection strategy for characteristic highly imbalanced fraud detection data sets. The model derived based on our selection strategy surpasses peer models, whilst working in more realistic conditions, establishing the effectiveness of the strategy.

The asymptotically precise estimation of the generalization of kernel methods has recently received attention due to the parallels between neural networks and their associated kernels. However, prior works derive such estimates for training by kernel ridge regression (KRR), whereas neural networks are typically trained with gradient descent (GD). In the present work, we consider the training of kernels with a family of spectral algorithms specified by profile h(lambda), and including KRR and GD as special cases. Then, we derive the generalization error as a functional of learning profile h(lambda) for two data models: high-dimensional Gaussian and low-dimensional translation-invariant model. Under power-law assumptions on the spectrum of the kernel and target, we use our framework to (i) give full loss asymptotics for both noisy and noiseless observations (ii) show that the loss localizes on certain spectral scales, giving a new perspective on the KRR saturation phenomenon (iii) conjecture, and demonstrate for the considered data models, the universality of the loss w.r.t. non-spectral details of the problem, but only in case of noisy observation.

Prior-data fitted networks (PFNs) were recently proposed as a new paradigm for machine learning. Instead of training the network to an observed training set, a fixed model is pre-trained offline on small, simulated training sets from a variety of tasks. The pre-trained model is then used to infer class probabilities in-context on fresh training sets with arbitrary size and distribution. Empirically, PFNs achieve state-of-the-art performance on tasks with similar size to the ones used in pre-training. Surprisingly, their accuracy further improves when passed larger data sets during inference. This article establishes a theoretical foundation for PFNs and illuminates the statistical mechanisms governing their behavior. While PFNs are motivated by Bayesian ideas, a purely frequentistic interpretation of PFNs as pre-tuned, but untrained predictors explains their behavior. A predictor's variance vanishes if its sensitivity to individual training samples does and the bias vanishes only if it is appropriately localized around the test feature. The transformer architecture used in current PFN implementations ensures only the former. These findings shall prove useful for designing architectures with favorable empirical behavior.

The Shapley value is one of the most widely used measures of feature importance partly as it measures a feature's average effect on a model's prediction. We introduce joint Shapley values, which directly extend Shapley's axioms and intuitions: joint Shapley values measure a set of features' average contribution to a model's prediction. We prove the uniqueness of joint Shapley values, for any order of explanation. Results for games show that joint Shapley values present different insights from existing interaction indices, which assess the effect of a feature within a set of features. The joint Shapley values provide intuitive results in ML attribution problems. With binary features, we present a presence-adjusted global value that is more consistent with local intuitions than the usual approach.

In this study, we examine the efficacy of post-hoc local attribution methods in identifying features with predictive power from irrelevant ones in domains characterized by a low signal-to-noise ratio (SNR), a common scenario in real-world machine learning applications. We developed synthetic datasets encompassing symbolic functional, image, and audio data, incorporating a benchmark on the {\it (Model \(\times\) Attribution\(\times\) Noise Condition)} triplet. By rigorously testing various classic models trained from scratch, we gained valuable insights into the performance of these attribution methods in multiple conditions. Based on these findings, we introduce a novel extension to the notable recursive feature elimination (RFE) algorithm, enhancing its applicability for neural networks. Our experiments highlight its strengths in prediction and feature selection, alongside limitations in scalability. Further details and additional minor findings are included in the appendix, with extensive discussions. The codes and resources are available at https://github.com/geshijoker/ChaosMining/{URL}.

This manuscript considers the problem of learning a random Gaussian network function using a fully connected network with frozen intermediate layers and trainable readout layer. This problem can be seen as a natural generalization of the widely studied random features model to deeper architectures. First, we prove Gaussian universality of the test error in a ridge regression setting where the learner and target networks share the same intermediate layers, and provide a sharp asymptotic formula for it. Establishing this result requires proving a deterministic equivalent for traces of the deep random features sample covariance matrices which can be of independent interest. Second, we conjecture the asymptotic Gaussian universality of the test error in the more general setting of arbitrary convex losses and generic learner/target architectures. We provide extensive numerical evidence for this conjecture, which requires the derivation of closed-form expressions for the layer-wise post-activation population covariances. In light of our results, we investigate the interplay between architecture design and implicit regularization.

In the realm of time series forecasting (TSF), it is imperative for models to adeptly discern and distill hidden patterns within historical time series data to forecast future states. Transformer-based models exhibit formidable efficacy in TSF, primarily attributed to their advantage in apprehending these patterns. However, the quadratic complexity of the Transformer leads to low computational efficiency and high costs, which somewhat hinders the deployment of the TSF model in real-world scenarios. Recently, Mamba, a selective state space model, has gained traction due to its ability to process dependencies in sequences while maintaining near-linear complexity. For TSF tasks, these characteristics enable Mamba to comprehend hidden patterns as the Transformer and reduce computational overhead compared to the Transformer. Therefore, we propose a Mamba-based model named Simple-Mamba (S-Mamba) for TSF. Specifically, we tokenize the time points of each variate autonomously via a linear layer. A bidirectional Mamba layer is utilized to extract inter-variate correlations and a Feed-Forward Network is set to learn temporal dependencies. Finally, the generation of forecast outcomes through a linear mapping layer. Experiments on thirteen public datasets prove that S-Mamba maintains low computational overhead and achieves leading performance. Furthermore, we conduct extensive experiments to explore Mamba's potential in TSF tasks. Our code is available at https://github.com/wzhwzhwzh0921/S-D-Mamba.