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cs.LG cs.CV

10.1631/jzus.A0720058

0910.1650

http://arxiv.org/abs/0910.1650v1

2009-10-09T04:55:41Z

2009-10-09T04:55:41Z

Local and global approaches of affinity propagation clustering for large scale data

Recently a new clustering algorithm called 'affinity propagation' (AP) has been proposed, which efficiently clustered sparsely related data by passing messages between data points. However, we want to cluster large scale data where the similarities are not sparse in many cases. This paper presents two variants of AP for grouping large scale data with a dense similarity matrix. The local approach is partition affinity propagation (PAP) and the global method is landmark affinity propagation (LAP). PAP passes messages in the subsets of data first and then merges them as the number of initial step of iterations; it can effectively reduce the number of iterations of clustering. LAP passes messages between the landmark data points first and then clusters non-landmark data points; it is a large global approximation method to speed up clustering. Experiments are conducted on many datasets, such as random data points, manifold subspaces, images of faces and Chinese calligraphy, and the results demonstrate that the two approaches are feasible and practicable.

stat.AP cs.LG

10.1214/10-AOAS359

0910.2034

http://arxiv.org/abs/0910.2034v2

2010-11-10T09:02:00Z

2009-10-11T19:36:16Z

Strategies for online inference of model-based clustering in large and growing networks

In this paper we adapt online estimation strategies to perform model-based clustering on large networks. Our work focuses on two algorithms, the first based on the SAEM algorithm, and the second on variational methods. These two strategies are compared with existing approaches on simulated and real data. We use the method to decipher the connexion structure of the political websphere during the US political campaign in 2008. We show that our online EM-based algorithms offer a good trade-off between precision and speed, when estimating parameters for mixture distributions in the context of random graphs.

math.OC cs.LG math.PR

10.1109/TSP.2010.2062509

0910.2065

http://arxiv.org/abs/0910.2065v3

2010-06-07T18:04:14Z

2009-10-12T00:50:19Z

Distributed Learning in Multi-Armed Bandit with Multiple Players

We formulate and study a decentralized multi-armed bandit (MAB) problem. There are M distributed players competing for N independent arms. Each arm, when played, offers i.i.d. reward according to a distribution with an unknown parameter. At each time, each player chooses one arm to play without exchanging observations or any information with other players. Players choosing the same arm collide, and, depending on the collision model, either no one receives reward or the colliding players share the reward in an arbitrary way. We show that the minimum system regret of the decentralized MAB grows with time at the same logarithmic order as in the centralized counterpart where players act collectively as a single entity by exchanging observations and making decisions jointly. A decentralized policy is constructed to achieve this optimal order while ensuring fairness among players and without assuming any pre-agreement or information exchange among players. Based on a Time Division Fair Sharing (TDFS) of the M best arms, the proposed policy is constructed and its order optimality is proven under a general reward model. Furthermore, the basic structure of the TDFS policy can be used with any order-optimal single-player policy to achieve order optimality in the decentralized setting. We also establish a lower bound on the system regret growth rate for a general class of decentralized polices, to which the proposed policy belongs. This problem finds potential applications in cognitive radio networks, multi-channel communication systems, multi-agent systems, web search and advertising, and social networks.

cs.IT cs.LG math.IT math.OC

0910.2240

http://arxiv.org/pdf/0910.2240v1

2009-10-12T20:16:16Z

2009-10-12T20:16:16Z

Repeated Auctions with Learning for Spectrum Access in Cognitive Radio Networks

In this paper, spectrum access in cognitive radio networks is modeled as a repeated auction game subject to monitoring and entry costs. For secondary users, sensing costs are incurred as the result of primary users' activity. Furthermore, each secondary user pays the cost of transmissions upon successful bidding for a channel. Knowledge regarding other secondary users' activity is limited due to the distributed nature of the network. The resulting formulation is thus a dynamic game with incomplete information. In this paper, an efficient bidding learning algorithm is proposed based on the outcome of past transactions. As demonstrated through extensive simulations, the proposed distributed scheme outperforms a myopic one-stage algorithm, and can achieve a good balance between efficiency and fairness.

cs.CV cs.LG

0910.2279

http://arxiv.org/pdf/0910.2279v1

2009-10-13T00:54:31Z

2009-10-13T00:54:31Z

Positive Semidefinite Metric Learning with Boosting

The learning of appropriate distance metrics is a critical problem in image classification and retrieval. In this work, we propose a boosting-based technique, termed \BoostMetric, for learning a Mahalanobis distance metric. One of the primary difficulties in learning such a metric is to ensure that the Mahalanobis matrix remains positive semidefinite. Semidefinite programming is sometimes used to enforce this constraint, but does not scale well. \BoostMetric is instead based on a key observation that any positive semidefinite matrix can be decomposed into a linear positive combination of trace-one rank-one matrices. \BoostMetric thus uses rank-one positive semidefinite matrices as weak learners within an efficient and scalable boosting-based learning process. The resulting method is easy to implement, does not require tuning, and can accommodate various types of constraints. Experiments on various datasets show that the proposed algorithm compares favorably to those state-of-the-art methods in terms of classification accuracy and running time.

cs.LG

0910.2540

http://arxiv.org/pdf/0910.2540v1

2009-10-14T07:43:03Z

2009-10-14T07:43:03Z

Effectiveness and Limitations of Statistical Spam Filters

In this paper we discuss the techniques involved in the design of the famous statistical spam filters that include Naive Bayes, Term Frequency-Inverse Document Frequency, K-Nearest Neighbor, Support Vector Machine, and Bayes Additive Regression Tree. We compare these techniques with each other in terms of accuracy, recall, precision, etc. Further, we discuss the effectiveness and limitations of statistical filters in filtering out various types of spam from legitimate e-mails.

quant-ph cs.LG

0910.3713

http://arxiv.org/pdf/0910.3713v1

2009-10-19T21:55:11Z

2009-10-19T21:55:11Z

On Learning Finite-State Quantum Sources

We examine the complexity of learning the distributions produced by finite-state quantum sources. We show how prior techniques for learning hidden Markov models can be adapted to the quantum generator model to find that the analogous state of affairs holds: information-theoretically, a polynomial number of samples suffice to approximately identify the distribution, but computationally, the problem is as hard as learning parities with noise, a notorious open question in computational learning theory.

cs.LG math.ST stat.TH

0910.4627

http://arxiv.org/pdf/0910.4627v1

2009-10-24T07:10:24Z

2009-10-24T07:10:24Z

Self-concordant analysis for logistic regression

Most of the non-asymptotic theoretical work in regression is carried out for the square loss, where estimators can be obtained through closed-form expressions. In this paper, we use and extend tools from the convex optimization literature, namely self-concordant functions, to provide simple extensions of theoretical results for the square loss to the logistic loss. We apply the extension techniques to logistic regression with regularization by the $\ell_2$-norm and regularization by the $\ell_1$-norm, showing that new results for binary classification through logistic regression can be easily derived from corresponding results for least-squares regression.

cs.LG

0910.4683

http://arxiv.org/pdf/0910.4683v2

2010-05-10T23:01:30Z

2009-10-24T22:40:40Z

Competing with Gaussian linear experts

We study the problem of online regression. We prove a theoretical bound on the square loss of Ridge Regression. We do not make any assumptions about input vectors or outcomes. We also show that Bayesian Ridge Regression can be thought of as an online algorithm competing with all the Gaussian linear experts.

cs.NA cs.LG

10.1016/j.trc.2012.12.007

0910.5260

http://arxiv.org/abs/0910.5260v2

2009-11-03T23:35:13Z

2009-10-27T22:19:31Z

A Gradient Descent Algorithm on the Grassman Manifold for Matrix Completion

We consider the problem of reconstructing a low-rank matrix from a small subset of its entries. In this paper, we describe the implementation of an efficient algorithm called OptSpace, based on singular value decomposition followed by local manifold optimization, for solving the low-rank matrix completion problem. It has been shown that if the number of revealed entries is large enough, the output of singular value decomposition gives a good estimate for the original matrix, so that local optimization reconstructs the correct matrix with high probability. We present numerical results which show that this algorithm can reconstruct the low rank matrix exactly from a very small subset of its entries. We further study the robustness of the algorithm with respect to noise, and its performance on actual collaborative filtering datasets.

cs.CV astro-ph.EP astro-ph.IM cs.LG stat.ML

10.1017/S1473550409990358

0910.5454

http://arxiv.org/abs/0910.5454v1

2009-10-28T18:26:39Z

2009-10-28T18:26:39Z

The Cyborg Astrobiologist: Testing a Novelty-Detection Algorithm on Two Mobile Exploration Systems at Rivas Vaciamadrid in Spain and at the Mars Desert Research Station in Utah

(ABRIDGED) In previous work, two platforms have been developed for testing computer-vision algorithms for robotic planetary exploration (McGuire et al. 2004b,2005; Bartolo et al. 2007). The wearable-computer platform has been tested at geological and astrobiological field sites in Spain (Rivas Vaciamadrid and Riba de Santiuste), and the phone-camera has been tested at a geological field site in Malta. In this work, we (i) apply a Hopfield neural-network algorithm for novelty detection based upon color, (ii) integrate a field-capable digital microscope on the wearable computer platform, (iii) test this novelty detection with the digital microscope at Rivas Vaciamadrid, (iv) develop a Bluetooth communication mode for the phone-camera platform, in order to allow access to a mobile processing computer at the field sites, and (v) test the novelty detection on the Bluetooth-enabled phone-camera connected to a netbook computer at the Mars Desert Research Station in Utah. This systems engineering and field testing have together allowed us to develop a real-time computer-vision system that is capable, for example, of identifying lichens as novel within a series of images acquired in semi-arid desert environments. We acquired sequences of images of geologic outcrops in Utah and Spain consisting of various rock types and colors to test this algorithm. The algorithm robustly recognized previously-observed units by their color, while requiring only a single image or a few images to learn colors as familiar, demonstrating its fast learning capability.

cs.LG

0910.5461

http://arxiv.org/pdf/0910.5461v1

2009-10-28T18:46:41Z

2009-10-28T18:46:41Z

Anomaly Detection with Score functions based on Nearest Neighbor Graphs

We propose a novel non-parametric adaptive anomaly detection algorithm for high dimensional data based on score functions derived from nearest neighbor graphs on $n$-point nominal data. Anomalies are declared whenever the score of a test sample falls below $\alpha$, which is supposed to be the desired false alarm level. The resulting anomaly detector is shown to be asymptotically optimal in that it is uniformly most powerful for the specified false alarm level, $\alpha$, for the case when the anomaly density is a mixture of the nominal and a known density. Our algorithm is computationally efficient, being linear in dimension and quadratic in data size. It does not require choosing complicated tuning parameters or function approximation classes and it can adapt to local structure such as local change in dimensionality. We demonstrate the algorithm on both artificial and real data sets in high dimensional feature spaces.

stat.ML cond-mat.stat-mech cs.LG

0910.5761

http://arxiv.org/pdf/0910.5761v1

2009-10-30T01:10:44Z

2009-10-30T01:10:44Z

Which graphical models are difficult to learn?

We consider the problem of learning the structure of Ising models (pairwise binary Markov random fields) from i.i.d. samples. While several methods have been proposed to accomplish this task, their relative merits and limitations remain somewhat obscure. By analyzing a number of concrete examples, we show that low-complexity algorithms systematically fail when the Markov random field develops long-range correlations. More precisely, this phenomenon appears to be related to the Ising model phase transition (although it does not coincide with it).

cs.LG cs.CV cs.IR

0910.5932

http://arxiv.org/pdf/0910.5932v1

2009-10-30T18:19:03Z

2009-10-30T18:19:03Z

Metric and Kernel Learning using a Linear Transformation

Metric and kernel learning are important in several machine learning applications. However, most existing metric learning algorithms are limited to learning metrics over low-dimensional data, while existing kernel learning algorithms are often limited to the transductive setting and do not generalize to new data points. In this paper, we study metric learning as a problem of learning a linear transformation of the input data. We show that for high-dimensional data, a particular framework for learning a linear transformation of the data based on the LogDet divergence can be efficiently kernelized to learn a metric (or equivalently, a kernel function) over an arbitrarily high dimensional space. We further demonstrate that a wide class of convex loss functions for learning linear transformations can similarly be kernelized, thereby considerably expanding the potential applications of metric learning. We demonstrate our learning approach by applying it to large-scale real world problems in computer vision and text mining.

cs.LG stat.ML

0911.0054

http://arxiv.org/pdf/0911.0054v2

2015-05-16T22:45:35Z

2009-10-31T02:56:18Z

Learning Exponential Families in High-Dimensions: Strong Convexity and Sparsity

The versatility of exponential families, along with their attendant convexity properties, make them a popular and effective statistical model. A central issue is learning these models in high-dimensions, such as when there is some sparsity pattern of the optimal parameter. This work characterizes a certain strong convexity property of general exponential families, which allow their generalization ability to be quantified. In particular, we show how this property can be used to analyze generic exponential families under L_1 regularization.

cs.LG

0911.0225

http://arxiv.org/pdf/0911.0225v1

2009-11-02T19:53:01Z

2009-11-02T19:53:01Z

A Mirroring Theorem and its Application to a New Method of Unsupervised Hierarchical Pattern Classification

In this paper, we prove a crucial theorem called Mirroring Theorem which affirms that given a collection of samples with enough information in it such that it can be classified into classes and subclasses then (i) There exists a mapping which classifies and subclassifies these samples (ii) There exists a hierarchical classifier which can be constructed by using Mirroring Neural Networks (MNNs) in combination with a clustering algorithm that can approximate this mapping. Thus, the proof of the Mirroring theorem provides a theoretical basis for the existence and a practical feasibility of constructing hierarchical classifiers, given the maps. Our proposed Mirroring Theorem can also be considered as an extension to Kolmogrovs theorem in providing a realistic solution for unsupervised classification. The techniques we develop, are general in nature and have led to the construction of learning machines which are (i) tree like in structure, (ii) modular (iii) with each module running on a common algorithm (tandem algorithm) and (iv) selfsupervised. We have actually built the architecture, developed the tandem algorithm of such a hierarchical classifier and demonstrated it on an example problem.

cs.LG cs.AI

0911.0460

http://arxiv.org/pdf/0911.0460v2

2009-11-04T08:55:28Z

2009-11-03T08:17:05Z

Feature-Weighted Linear Stacking

Ensemble methods, such as stacking, are designed to boost predictive accuracy by blending the predictions of multiple machine learning models. Recent work has shown that the use of meta-features, additional inputs describing each example in a dataset, can boost the performance of ensemble methods, but the greatest reported gains have come from nonlinear procedures requiring significant tuning and training time. Here, we present a linear technique, Feature-Weighted Linear Stacking (FWLS), that incorporates meta-features for improved accuracy while retaining the well-known virtues of linear regression regarding speed, stability, and interpretability. FWLS combines model predictions linearly using coefficients that are themselves linear functions of meta-features. This technique was a key facet of the solution of the second place team in the recently concluded Netflix Prize competition. Significant increases in accuracy over standard linear stacking are demonstrated on the Netflix Prize collaborative filtering dataset.

cs.LG physics.data-an quant-ph

10.1016/j.nuclphysbps.2010.02.009

0911.0462

http://arxiv.org/abs/0911.0462v1

2009-11-03T00:27:36Z

2009-11-03T00:27:36Z

Strange Bedfellows: Quantum Mechanics and Data Mining

Last year, in 2008, I gave a talk titled {\it Quantum Calisthenics}. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.

cs.NE cs.LG

0911.0485

http://arxiv.org/pdf/0911.0485v1

2009-11-03T04:07:19Z

2009-11-03T04:07:19Z

Novel Intrusion Detection using Probabilistic Neural Network and Adaptive Boosting

This article applies Machine Learning techniques to solve Intrusion Detection problems within computer networks. Due to complex and dynamic nature of computer networks and hacking techniques, detecting malicious activities remains a challenging task for security experts, that is, currently available defense systems suffer from low detection capability and high number of false alarms. To overcome such performance limitations, we propose a novel Machine Learning algorithm, namely Boosted Subspace Probabilistic Neural Network (BSPNN), which integrates an adaptive boosting technique and a semi parametric neural network to obtain good tradeoff between accuracy and generality. As the result, learning bias and generalization variance can be significantly minimized. Substantial experiments on KDD 99 intrusion benchmark indicate that our model outperforms other state of the art learning algorithms, with significantly improved detection accuracy, minimal false alarms and relatively small computational complexity.

q-bio.PE cs.LG q-bio.QM

0911.0645

http://arxiv.org/pdf/0911.0645v2

2009-11-22T00:09:42Z

2009-11-03T18:43:43Z

Bayes estimators for phylogenetic reconstruction

Tree reconstruction methods are often judged by their accuracy, measured by how close they get to the true tree. Yet most reconstruction methods like ML do not explicitly maximize this accuracy. To address this problem, we propose a Bayesian solution. Given tree samples, we propose finding the tree estimate which is closest on average to the samples. This ``median'' tree is known as the Bayes estimator (BE). The BE literally maximizes posterior expected accuracy, measured in terms of closeness (distance) to the true tree. We discuss a unified framework of BE trees, focusing especially on tree distances which are expressible as squared euclidean distances. Notable examples include Robinson--Foulds distance, quartet distance, and squared path difference. Using simulated data, we show Bayes estimators can be efficiently computed in practice by hill climbing. We also show that Bayes estimators achieve higher accuracy, compared to maximum likelihood and neighbor joining.

cs.DS cs.LG

0911.1174

http://arxiv.org/pdf/0911.1174v1

2009-11-06T03:52:56Z

2009-11-06T03:52:56Z

Sharp Dichotomies for Regret Minimization in Metric Spaces

The Lipschitz multi-armed bandit (MAB) problem generalizes the classical multi-armed bandit problem by assuming one is given side information consisting of a priori upper bounds on the difference in expected payoff between certain pairs of strategies. Classical results of (Lai and Robbins 1985) and (Auer et al. 2002) imply a logarithmic regret bound for the Lipschitz MAB problem on finite metric spaces. Recent results on continuum-armed bandit problems and their generalizations imply lower bounds of $\sqrt{t}$, or stronger, for many infinite metric spaces such as the unit interval. Is this dichotomy universal? We prove that the answer is yes: for every metric space, the optimal regret of a Lipschitz MAB algorithm is either bounded above by any $f\in \omega(\log t)$, or bounded below by any $g\in o(\sqrt{t})$. Perhaps surprisingly, this dichotomy does not coincide with the distinction between finite and infinite metric spaces; instead it depends on whether the completion of the metric space is compact and countable. Our proof connects upper and lower bound techniques in online learning with classical topological notions such as perfect sets and the Cantor-Bendixson theorem. Among many other results, we show a similar dichotomy for the "full-feedback" (a.k.a., "best-expert") version.

cs.AI cs.LG

0911.1386

http://arxiv.org/pdf/0911.1386v1

2009-11-07T02:52:53Z

2009-11-07T02:52:53Z

Machine Learning: When and Where the Horses Went Astray?

Machine Learning is usually defined as a subfield of AI, which is busy with information extraction from raw data sets. Despite of its common acceptance and widespread recognition, this definition is wrong and groundless. Meaningful information does not belong to the data that bear it. It belongs to the observers of the data and it is a shared agreement and a convention among them. Therefore, this private information cannot be extracted from the data by any means. Therefore, all further attempts of Machine Learning apologists to justify their funny business are inappropriate.

cs.DS cond-mat.stat-mech cs.DM cs.LG cs.NA math.OC

10.1088/1751-8113/43/24/242002

0911.1419

http://arxiv.org/abs/0911.1419v2

2010-05-02T15:58:46Z

2009-11-08T04:15:01Z

Belief Propagation and Loop Calculus for the Permanent of a Non-Negative Matrix

We consider computation of permanent of a positive $(N\times N)$ non-negative matrix, $P=(P_i^j|i,j=1,\cdots,N)$, or equivalently the problem of weighted counting of the perfect matchings over the complete bipartite graph $K_{N,N}$. The problem is known to be of likely exponential complexity. Stated as the partition function $Z$ of a graphical model, the problem allows exact Loop Calculus representation [Chertkov, Chernyak '06] in terms of an interior minimum of the Bethe Free Energy functional over non-integer doubly stochastic matrix of marginal beliefs, $\beta=(\beta_i^j|i,j=1,\cdots,N)$, also correspondent to a fixed point of the iterative message-passing algorithm of the Belief Propagation (BP) type. Our main result is an explicit expression of the exact partition function (permanent) in terms of the matrix of BP marginals, $\beta$, as $Z=\mbox{Perm}(P)=Z_{BP} \mbox{Perm}(\beta_i^j(1-\beta_i^j))/\prod_{i,j}(1-\beta_i^j)$, where $Z_{BP}$ is the BP expression for the permanent stated explicitly in terms if $\beta$. We give two derivations of the formula, a direct one based on the Bethe Free Energy and an alternative one combining the Ihara graph-$\zeta$ function and the Loop Calculus approaches. Assuming that the matrix $\beta$ of the Belief Propagation marginals is calculated, we provide two lower bounds and one upper-bound to estimate the multiplicative term. Two complementary lower bounds are based on the Gurvits-van der Waerden theorem and on a relation between the modified permanent and determinant respectively.

physics.data-an cond-mat.stat-mech cs.LG nlin.CD stat.ME

0911.2381

http://arxiv.org/pdf/0911.2381v1

2009-11-12T13:08:20Z

2009-11-12T13:08:20Z

Analytical Determination of Fractal Structure in Stochastic Time Series

Current methods for determining whether a time series exhibits fractal structure (FS) rely on subjective assessments on estimators of the Hurst exponent (H). Here, I introduce the Bayesian Assessment of Scaling, an analytical framework for drawing objective and accurate inferences on the FS of time series. The technique exploits the scaling property of the diffusion associated to a time series. The resulting criterion is simple to compute and represents an accurate characterization of the evidence supporting different hypotheses on the scaling regime of a time series. Additionally, a closed-form Maximum Likelihood estimator of H is derived from the criterion, and this estimator outperforms the best available estimators.

cs.LG

10.1109/TIT.2012.2201375

0911.2904

http://arxiv.org/abs/0911.2904v4

2012-03-13T16:11:21Z

2009-11-15T18:43:10Z

Sequential anomaly detection in the presence of noise and limited feedback

This paper describes a methodology for detecting anomalies from sequentially observed and potentially noisy data. The proposed approach consists of two main elements: (1) {\em filtering}, or assigning a belief or likelihood to each successive measurement based upon our ability to predict it from previous noisy observations, and (2) {\em hedging}, or flagging potential anomalies by comparing the current belief against a time-varying and data-adaptive threshold. The threshold is adjusted based on the available feedback from an end user. Our algorithms, which combine universal prediction with recent work on online convex programming, do not require computing posterior distributions given all current observations and involve simple primal-dual parameter updates. At the heart of the proposed approach lie exponential-family models which can be used in a wide variety of contexts and applications, and which yield methods that achieve sublinear per-round regret against both static and slowly varying product distributions with marginals drawn from the same exponential family. Moreover, the regret against static distributions coincides with the minimax value of the corresponding online strongly convex game. We also prove bounds on the number of mistakes made during the hedging step relative to the best offline choice of the threshold with access to all estimated beliefs and feedback signals. We validate the theory on synthetic data drawn from a time-varying distribution over binary vectors of high dimensionality, as well as on the Enron email dataset.

cs.DS cs.LG

0911.2974

http://arxiv.org/pdf/0911.2974v3

2014-04-09T03:44:37Z

2009-11-16T16:39:33Z

A Dynamic Near-Optimal Algorithm for Online Linear Programming

A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding objective coefficient. In such a model, a decision variable has to be set each time a column is revealed without observing the future inputs and the goal is to maximize the overall objective function. In this paper, we provide a near-optimal algorithm for this general class of online problems under the assumption of random order of arrival and some mild conditions on the size of the LP right-hand-side input. Specifically, our learning-based algorithm works by dynamically updating a threshold price vector at geometric time intervals, where the dual prices learned from the revealed columns in the previous period are used to determine the sequential decisions in the current period. Due to the feature of dynamic learning, the competitiveness of our algorithm improves over the past study of the same problem. We also present a worst-case example showing that the performance of our algorithm is near-optimal.

cs.NE cs.LG

0911.3298

http://arxiv.org/pdf/0911.3298v1

2009-11-17T13:17:05Z

2009-11-17T13:17:05Z

Understanding the Principles of Recursive Neural networks: A Generative Approach to Tackle Model Complexity

Recursive Neural Networks are non-linear adaptive models that are able to learn deep structured information. However, these models have not yet been broadly accepted. This fact is mainly due to its inherent complexity. In particular, not only for being extremely complex information processing models, but also because of a computational expensive learning phase. The most popular training method for these models is back-propagation through the structure. This algorithm has been revealed not to be the most appropriate for structured processing due to problems of convergence, while more sophisticated training methods enhance the speed of convergence at the expense of increasing significantly the computational cost. In this paper, we firstly perform an analysis of the underlying principles behind these models aimed at understanding their computational power. Secondly, we propose an approximate second order stochastic learning algorithm. The proposed algorithm dynamically adapts the learning rate throughout the training phase of the network without incurring excessively expensive computational effort. The algorithm operates in both on-line and batch modes. Furthermore, the resulting learning scheme is robust against the vanishing gradients problem. The advantages of the proposed algorithm are demonstrated with a real-world application example.

cs.LG

10.1109/CTS.2009.5067478

0911.3304

http://arxiv.org/abs/0911.3304v1

2009-11-17T13:35:40Z

2009-11-17T13:35:40Z

Keystroke Dynamics Authentication For Collaborative Systems

We present in this paper a study on the ability and the benefits of using a keystroke dynamics authentication method for collaborative systems. Authentication is a challenging issue in order to guarantee the security of use of collaborative systems during the access control step. Many solutions exist in the state of the art such as the use of one time passwords or smart-cards. We focus in this paper on biometric based solutions that do not necessitate any additional sensor. Keystroke dynamics is an interesting solution as it uses only the keyboard and is invisible for users. Many methods have been published in this field. We make a comparative study of many of them considering the operational constraints of use for collaborative systems.

cs.LG math.CO math.GT stat.ML

0911.3633

http://arxiv.org/pdf/0911.3633v1

2009-11-18T19:22:09Z

2009-11-18T19:22:09Z

A Geometric Approach to Sample Compression

The Sample Compression Conjecture of Littlestone & Warmuth has remained unsolved for over two decades. This paper presents a systematic geometric investigation of the compression of finite maximum concept classes. Simple arrangements of hyperplanes in Hyperbolic space, and Piecewise-Linear hyperplane arrangements, are shown to represent maximum classes, generalizing the corresponding Euclidean result. A main result is that PL arrangements can be swept by a moving hyperplane to unlabeled d-compress any finite maximum class, forming a peeling scheme as conjectured by Kuzmin & Warmuth. A corollary is that some d-maximal classes cannot be embedded into any maximum class of VC dimension d+k, for any constant k. The construction of the PL sweeping involves Pachner moves on the one-inclusion graph, corresponding to moves of a hyperplane across the intersection of d other hyperplanes. This extends the well known Pachner moves for triangulations to cubical complexes.

stat.ML cs.CL cs.LG stat.AP

10.1109/JSTSP.2010.2076050

0911.3944

http://arxiv.org/abs/0911.3944v1

2009-11-20T01:30:36Z

2009-11-20T01:30:36Z

Likelihood-based semi-supervised model selection with applications to speech processing

In conventional supervised pattern recognition tasks, model selection is typically accomplished by minimizing the classification error rate on a set of so-called development data, subject to ground-truth labeling by human experts or some other means. In the context of speech processing systems and other large-scale practical applications, however, such labeled development data are typically costly and difficult to obtain. This article proposes an alternative semi-supervised framework for likelihood-based model selection that leverages unlabeled data by using trained classifiers representing each model to automatically generate putative labels. The errors that result from this automatic labeling are shown to be amenable to results from robust statistics, which in turn provide for minimax-optimal censored likelihood ratio tests that recover the nonparametric sign test as a limiting case. This approach is then validated experimentally using a state-of-the-art automatic speech recognition system to select between candidate word pronunciations using unlabeled speech data that only potentially contain instances of the words under test. Results provide supporting evidence for the utility of this approach, and suggest that it may also find use in other applications of machine learning.

stat.ML cs.LG stat.ME

0911.4046

http://arxiv.org/pdf/0911.4046v3

2011-01-02T07:04:21Z

2009-11-20T13:44:28Z

Super-Linear Convergence of Dual Augmented-Lagrangian Algorithm for Sparsity Regularized Estimation

We analyze the convergence behaviour of a recently proposed algorithm for regularized estimation called Dual Augmented Lagrangian (DAL). Our analysis is based on a new interpretation of DAL as a proximal minimization algorithm. We theoretically show under some conditions that DAL converges super-linearly in a non-asymptotic and global sense. Due to a special modelling of sparse estimation problems in the context of machine learning, the assumptions we make are milder and more natural than those made in conventional analysis of augmented Lagrangian algorithms. In addition, the new interpretation enables us to generalize DAL to wide varieties of sparse estimation problems. We experimentally confirm our analysis in a large scale $\ell_1$-regularized logistic regression problem and extensively compare the efficiency of DAL algorithm to previously proposed algorithms on both synthetic and benchmark datasets.

cs.LG cs.HC

0911.4262

http://arxiv.org/pdf/0911.4262v1

2009-11-22T16:01:09Z

2009-11-22T16:01:09Z

Towards Industrialized Conception and Production of Serious Games

Serious Games (SGs) have experienced a tremendous outburst these last years. Video game companies have been producing fun, user-friendly SGs, but their educational value has yet to be proven. Meanwhile, cognition research scientist have been developing SGs in such a way as to guarantee an educational gain, but the fun and attractive characteristics featured often would not meet the public's expectations. The ideal SG must combine these two aspects while still being economically viable. In this article, we propose a production chain model to efficiently conceive and produce SGs that are certified for their educational gain and fun qualities. Each step of this chain will be described along with the human actors, the tools and the documents that intervene.

cs.LG

0911.4863

http://arxiv.org/pdf/0911.4863v2

2011-05-13T01:52:49Z

2009-11-25T14:26:54Z

Statistical exponential families: A digest with flash cards

This document describes concisely the ubiquitous class of exponential family distributions met in statistics. The first part recalls definitions and summarizes main properties and duality with Bregman divergences (all proofs are skipped). The second part lists decompositions and related formula of common exponential family distributions. We recall the Fisher-Rao-Riemannian geometries and the dual affine connection information geometries of statistical manifolds. It is intended to maintain and update this document and catalog by adding new distribution items.

cs.AI cs.LG

0911.5104

http://arxiv.org/pdf/0911.5104v2

2009-12-30T23:34:14Z

2009-11-26T15:52:33Z

A Bayesian Rule for Adaptive Control based on Causal Interventions

Explaining adaptive behavior is a central problem in artificial intelligence research. Here we formalize adaptive agents as mixture distributions over sequences of inputs and outputs (I/O). Each distribution of the mixture constitutes a `possible world', but the agent does not know which of the possible worlds it is actually facing. The problem is to adapt the I/O stream in a way that is compatible with the true world. A natural measure of adaptation can be obtained by the Kullback-Leibler (KL) divergence between the I/O distribution of the true world and the I/O distribution expected by the agent that is uncertain about possible worlds. In the case of pure input streams, the Bayesian mixture provides a well-known solution for this problem. We show, however, that in the case of I/O streams this solution breaks down, because outputs are issued by the agent itself and require a different probabilistic syntax as provided by intervention calculus. Based on this calculus, we obtain a Bayesian control rule that allows modeling adaptive behavior with mixture distributions over I/O streams. This rule might allow for a novel approach to adaptive control based on a minimum KL-principle.

cs.CV cs.AI cs.LG cs.NE

0911.5372

http://arxiv.org/pdf/0911.5372v1

2009-11-28T04:58:38Z

2009-11-28T04:58:38Z

Maximin affinity learning of image segmentation

Images can be segmented by first using a classifier to predict an affinity graph that reflects the degree to which image pixels must be grouped together and then partitioning the graph to yield a segmentation. Machine learning has been applied to the affinity classifier to produce affinity graphs that are good in the sense of minimizing edge misclassification rates. However, this error measure is only indirectly related to the quality of segmentations produced by ultimately partitioning the affinity graph. We present the first machine learning algorithm for training a classifier to produce affinity graphs that are good in the sense of producing segmentations that directly minimize the Rand index, a well known segmentation performance measure. The Rand index measures segmentation performance by quantifying the classification of the connectivity of image pixel pairs after segmentation. By using the simple graph partitioning algorithm of finding the connected components of the thresholded affinity graph, we are able to train an affinity classifier to directly minimize the Rand index of segmentations resulting from the graph partitioning. Our learning algorithm corresponds to the learning of maximin affinities between image pixel pairs, which are predictive of the pixel-pair connectivity.

cs.CL cs.LG

0911.5703

http://arxiv.org/pdf/0911.5703v1

2009-11-30T18:15:35Z

2009-11-30T18:15:35Z

Hierarchies in Dictionary Definition Space

A dictionary defines words in terms of other words. Definitions can tell you the meanings of words you don't know, but only if you know the meanings of the defining words. How many words do you need to know (and which ones) in order to be able to learn all the rest from definitions? We reduced dictionaries to their "grounding kernels" (GKs), about 10% of the dictionary, from which all the other words could be defined. The GK words turned out to have psycholinguistic correlates: they were learned at an earlier age and more concrete than the rest of the dictionary. But one can compress still more: the GK turns out to have internal structure, with a strongly connected "kernel core" (KC) and a surrounding layer, from which a hierarchy of definitional distances can be derived, all the way out to the periphery of the full dictionary. These definitional distances, too, are correlated with psycholinguistic variables (age of acquisition, concreteness, imageability, oral and written frequency) and hence perhaps with the "mental lexicon" in each of our heads.

cs.LG cs.CR cs.DB

0911.5708

http://arxiv.org/pdf/0911.5708v1

2009-11-30T20:34:45Z

2009-11-30T20:34:45Z

Learning in a Large Function Space: Privacy-Preserving Mechanisms for SVM Learning

Several recent studies in privacy-preserving learning have considered the trade-off between utility or risk and the level of differential privacy guaranteed by mechanisms for statistical query processing. In this paper we study this trade-off in private Support Vector Machine (SVM) learning. We present two efficient mechanisms, one for the case of finite-dimensional feature mappings and one for potentially infinite-dimensional feature mappings with translation-invariant kernels. For the case of translation-invariant kernels, the proposed mechanism minimizes regularized empirical risk in a random Reproducing Kernel Hilbert Space whose kernel uniformly approximates the desired kernel with high probability. This technique, borrowed from large-scale learning, allows the mechanism to respond with a finite encoding of the classifier, even when the function class is of infinite VC dimension. Differential privacy is established using a proof technique from algorithmic stability. Utility--the mechanism's response function is pointwise epsilon-close to non-private SVM with probability 1-delta--is proven by appealing to the smoothness of regularized empirical risk minimization with respect to small perturbations to the feature mapping. We conclude with a lower bound on the optimal differential privacy of the SVM. This negative result states that for any delta, no mechanism can be simultaneously (epsilon,delta)-useful and beta-differentially private for small epsilon and small beta.

cs.LG cs.AI cs.CR cs.DB

0912.0071

http://arxiv.org/pdf/0912.0071v5

2011-02-16T22:35:55Z

2009-12-01T04:35:44Z

Differentially Private Empirical Risk Minimization

Privacy-preserving machine learning algorithms are crucial for the increasingly common setting in which personal data, such as medical or financial records, are analyzed. We provide general techniques to produce privacy-preserving approximations of classifiers learned via (regularized) empirical risk minimization (ERM). These algorithms are private under the $\epsilon$-differential privacy definition due to Dwork et al. (2006). First we apply the output perturbation ideas of Dwork et al. (2006), to ERM classification. Then we propose a new method, objective perturbation, for privacy-preserving machine learning algorithm design. This method entails perturbing the objective function before optimizing over classifiers. If the loss and regularizer satisfy certain convexity and differentiability criteria, we prove theoretical results showing that our algorithms preserve privacy, and provide generalization bounds for linear and nonlinear kernels. We further present a privacy-preserving technique for tuning the parameters in general machine learning algorithms, thereby providing end-to-end privacy guarantees for the training process. We apply these results to produce privacy-preserving analogues of regularized logistic regression and support vector machines. We obtain encouraging results from evaluating their performance on real demographic and benchmark data sets. Our results show that both theoretically and empirically, objective perturbation is superior to the previous state-of-the-art, output perturbation, in managing the inherent tradeoff between privacy and learning performance.

cs.LG

0912.0086

http://arxiv.org/pdf/0912.0086v1

2009-12-01T19:10:46Z

2009-12-01T19:10:46Z

Learning Mixtures of Gaussians using the k-means Algorithm

One of the most popular algorithms for clustering in Euclidean space is the $k$-means algorithm; $k$-means is difficult to analyze mathematically, and few theoretical guarantees are known about it, particularly when the data is {\em well-clustered}. In this paper, we attempt to fill this gap in the literature by analyzing the behavior of $k$-means on well-clustered data. In particular, we study the case when each cluster is distributed as a different Gaussian -- or, in other words, when the input comes from a mixture of Gaussians. We analyze three aspects of the $k$-means algorithm under this assumption. First, we show that when the input comes from a mixture of two spherical Gaussians, a variant of the 2-means algorithm successfully isolates the subspace containing the means of the mixture components. Second, we show an exact expression for the convergence of our variant of the 2-means algorithm, when the input is a very large number of samples from a mixture of spherical Gaussians. Our analysis does not require any lower bound on the separation between the mixture components. Finally, we study the sample requirement of $k$-means; for a mixture of 2 spherical Gaussians, we show an upper bound on the number of samples required by a variant of 2-means to get close to the true solution. The sample requirement grows with increasing dimensionality of the data, and decreasing separation between the means of the Gaussians. To match our upper bound, we show an information-theoretic lower bound on any algorithm that learns mixtures of two spherical Gaussians; our lower bound indicates that in the case when the overlap between the probability masses of the two distributions is small, the sample requirement of $k$-means is {\em near-optimal}.

cs.LG cs.CV

0912.0572

http://arxiv.org/pdf/0912.0572v1

2009-12-03T03:05:59Z

2009-12-03T03:05:59Z

Isometric Multi-Manifolds Learning

Isometric feature mapping (Isomap) is a promising manifold learning method. However, Isomap fails to work on data which distribute on clusters in a single manifold or manifolds. Many works have been done on extending Isomap to multi-manifolds learning. In this paper, we first proposed a new multi-manifolds learning algorithm (M-Isomap) with help of a general procedure. The new algorithm preserves intra-manifold geodesics and multiple inter-manifolds edges precisely. Compared with previous methods, this algorithm can isometrically learn data distributed on several manifolds. Secondly, the original multi-cluster manifold learning algorithm first proposed in \cite{DCIsomap} and called D-C Isomap has been revised so that the revised D-C Isomap can learn multi-manifolds data. Finally, the features and effectiveness of the proposed multi-manifolds learning algorithms are demonstrated and compared through experiments.

quant-ph cs.LG

0912.0779

http://arxiv.org/pdf/0912.0779v1

2009-12-04T06:30:27Z

2009-12-04T06:30:27Z

Training a Large Scale Classifier with the Quantum Adiabatic Algorithm

In a previous publication we proposed discrete global optimization as a method to train a strong binary classifier constructed as a thresholded sum over weak classifiers. Our motivation was to cast the training of a classifier into a format amenable to solution by the quantum adiabatic algorithm. Applying adiabatic quantum computing (AQC) promises to yield solutions that are superior to those which can be achieved with classical heuristic solvers. Interestingly we found that by using heuristic solvers to obtain approximate solutions we could already gain an advantage over the standard method AdaBoost. In this communication we generalize the baseline method to large scale classifier training. By large scale we mean that either the cardinality of the dictionary of candidate weak classifiers or the number of weak learners used in the strong classifier exceed the number of variables that can be handled effectively in a single global optimization. For such situations we propose an iterative and piecewise approach in which a subset of weak classifiers is selected in each iteration via global optimization. The strong classifier is then constructed by concatenating the subsets of weak classifiers. We show in numerical studies that the generalized method again successfully competes with AdaBoost. We also provide theoretical arguments as to why the proposed optimization method, which does not only minimize the empirical loss but also adds L0-norm regularization, is superior to versions of boosting that only minimize the empirical loss. By conducting a Quantum Monte Carlo simulation we gather evidence that the quantum adiabatic algorithm is able to handle a generic training problem efficiently.

cs.LG cs.NE

0912.1007

http://arxiv.org/pdf/0912.1007v1

2009-12-05T12:41:40Z

2009-12-05T12:41:40Z

Designing Kernel Scheme for Classifiers Fusion

In this paper, we propose a special fusion method for combining ensembles of base classifiers utilizing new neural networks in order to improve overall efficiency of classification. While ensembles are designed such that each classifier is trained independently while the decision fusion is performed as a final procedure, in this method, we would be interested in making the fusion process more adaptive and efficient. This new combiner, called Neural Network Kernel Least Mean Square1, attempts to fuse outputs of the ensembles of classifiers. The proposed Neural Network has some special properties such as Kernel abilities,Least Mean Square features, easy learning over variants of patterns and traditional neuron capabilities. Neural Network Kernel Least Mean Square is a special neuron which is trained with Kernel Least Mean Square properties. This new neuron is used as a classifiers combiner to fuse outputs of base neural network classifiers. Performance of this method is analyzed and compared with other fusion methods. The analysis represents higher performance of our new method as opposed to others.

cs.CV cs.LG

0912.1009

http://arxiv.org/pdf/0912.1009v1

2009-12-05T12:54:24Z

2009-12-05T12:54:24Z

Biogeography based Satellite Image Classification

Biogeography is the study of the geographical distribution of biological organisms. The mindset of the engineer is that we can learn from nature. Biogeography Based Optimization is a burgeoning nature inspired technique to find the optimal solution of the problem. Satellite image classification is an important task because it is the only way we can know about the land cover map of inaccessible areas. Though satellite images have been classified in past by using various techniques, the researchers are always finding alternative strategies for satellite image classification so that they may be prepared to select the most appropriate technique for the feature extraction task in hand. This paper is focused on classification of the satellite image of a particular land cover using the theory of Biogeography based Optimization. The original BBO algorithm does not have the inbuilt property of clustering which is required during image classification. Hence modifications have been proposed to the original algorithm and the modified algorithm is used to classify the satellite image of a given region. The results indicate that highly accurate land cover features can be extracted effectively when the proposed algorithm is used.

cs.CR cs.LG

0912.1014

http://arxiv.org/pdf/0912.1014v1

2009-12-05T13:15:08Z

2009-12-05T13:15:08Z

An ensemble approach for feature selection of Cyber Attack Dataset

Feature selection is an indispensable preprocessing step when mining huge datasets that can significantly improve the overall system performance. Therefore in this paper we focus on a hybrid approach of feature selection. This method falls into two phases. The filter phase select the features with highest information gain and guides the initialization of search process for wrapper phase whose output the final feature subset. The final feature subsets are passed through the Knearest neighbor classifier for classification of attacks. The effectiveness of this algorithm is demonstrated on DARPA KDDCUP99 cyber attack dataset.

stat.ML cs.LG

0912.1128

http://arxiv.org/pdf/0912.1128v1

2009-12-06T19:29:04Z

2009-12-06T19:29:04Z

How to Explain Individual Classification Decisions

After building a classifier with modern tools of machine learning we typically have a black box at hand that is able to predict well for unseen data. Thus, we get an answer to the question what is the most likely label of a given unseen data point. However, most methods will provide no answer why the model predicted the particular label for a single instance and what features were most influential for that particular instance. The only method that is currently able to provide such explanations are decision trees. This paper proposes a procedure which (based on a set of assumptions) allows to explain the decisions of any classification method.

cs.CR cs.GT cs.LG

10.1007/978-3-642-14577-3_16

0912.1155

http://arxiv.org/abs/0912.1155v2

2009-12-22T04:36:44Z

2009-12-07T01:45:32Z

A Learning-Based Approach to Reactive Security

Despite the conventional wisdom that proactive security is superior to reactive security, we show that reactive security can be competitive with proactive security as long as the reactive defender learns from past attacks instead of myopically overreacting to the last attack. Our game-theoretic model follows common practice in the security literature by making worst-case assumptions about the attacker: we grant the attacker complete knowledge of the defender's strategy and do not require the attacker to act rationally. In this model, we bound the competitive ratio between a reactive defense algorithm (which is inspired by online learning theory) and the best fixed proactive defense. Additionally, we show that, unlike proactive defenses, this reactive strategy is robust to a lack of information about the attacker's incentives and knowledge.

cs.LG

0912.1198

http://arxiv.org/pdf/0912.1198v1

2009-12-07T10:35:56Z

2009-12-07T10:35:56Z

Delay-Optimal Power and Subcarrier Allocation for OFDMA Systems via Stochastic Approximation

In this paper, we consider delay-optimal power and subcarrier allocation design for OFDMA systems with $N_F$ subcarriers, $K$ mobiles and one base station. There are $K$ queues at the base station for the downlink traffic to the $K$ mobiles with heterogeneous packet arrivals and delay requirements. We shall model the problem as a $K$-dimensional infinite horizon average reward Markov Decision Problem (MDP) where the control actions are assumed to be a function of the instantaneous Channel State Information (CSI) as well as the joint Queue State Information (QSI). This problem is challenging because it corresponds to a stochastic Network Utility Maximization (NUM) problem where general solution is still unknown. We propose an {\em online stochastic value iteration} solution using {\em stochastic approximation}. The proposed power control algorithm, which is a function of both the CSI and the QSI, takes the form of multi-level water-filling. We prove that under two mild conditions in Theorem 1 (One is the stepsize condition. The other is the condition on accessibility of the Markov Chain, which can be easily satisfied in most of the cases we are interested.), the proposed solution converges to the optimal solution almost surely (with probability 1) and the proposed framework offers a possible solution to the general stochastic NUM problem. By exploiting the birth-death structure of the queue dynamics, we obtain a reduced complexity decomposed solution with linear $\mathcal{O}(KN_F)$ complexity and $\mathcal{O}(K)$ memory requirement.

cs.LG

0912.1822

http://arxiv.org/pdf/0912.1822v1

2009-12-09T18:11:11Z

2009-12-09T18:11:11Z

Association Rule Pruning based on Interestingness Measures with Clustering

Association rule mining plays vital part in knowledge mining. The difficult task is discovering knowledge or useful rules from the large number of rules generated for reduced support. For pruning or grouping rules, several techniques are used such as rule structure cover methods, informative cover methods, rule clustering, etc. Another way of selecting association rules is based on interestingness measures such as support, confidence, correlation, and so on. In this paper, we study how rule clusters of the pattern Xi - Y are distributed over different interestingness measures.

cs.CV cs.LG

0912.1830

http://arxiv.org/pdf/0912.1830v1

2009-12-09T18:41:49Z

2009-12-09T18:41:49Z

Gesture Recognition with a Focus on Important Actions by Using a Path Searching Method in Weighted Graph

This paper proposes a method of gesture recognition with a focus on important actions for distinguishing similar gestures. The method generates a partial action sequence by using optical flow images, expresses the sequence in the eigenspace, and checks the feature vector sequence by applying an optimum path-searching method of weighted graph to focus the important actions. Also presented are the results of an experiment on the recognition of similar sign language words.

cs.CV cs.LG

0912.2302

http://arxiv.org/pdf/0912.2302v1

2009-12-11T18:14:29Z

2009-12-11T18:14:29Z

Synthesis of supervised classification algorithm using intelligent and statistical tools

A fundamental task in detecting foreground objects in both static and dynamic scenes is to take the best choice of color system representation and the efficient technique for background modeling. We propose in this paper a non-parametric algorithm dedicated to segment and to detect objects in color images issued from a football sports meeting. Indeed segmentation by pixel concern many applications and revealed how the method is robust to detect objects, even in presence of strong shadows and highlights. In the other hand to refine their playing strategy such as in football, handball, volley ball, Rugby..., the coach need to have a maximum of technical-tactics information about the on-going of the game and the players. We propose in this paper a range of algorithms allowing the resolution of many problems appearing in the automated process of team identification, where each player is affected to his corresponding team relying on visual data. The developed system was tested on a match of the Tunisian national competition. This work is prominent for many next computer vision studies as it's detailed in this study.

cs.LG

0912.2314

http://arxiv.org/pdf/0912.2314v1

2009-12-11T18:50:46Z

2009-12-11T18:50:46Z

Early Detection of Breast Cancer using SVM Classifier Technique

This paper presents a tumor detection algorithm from mammogram. The proposed system focuses on the solution of two problems. One is how to detect tumors as suspicious regions with a very weak contrast to their background and another is how to extract features which categorize tumors. The tumor detection method follows the scheme of (a) mammogram enhancement. (b) The segmentation of the tumor area. (c) The extraction of features from the segmented tumor area. (d) The use of SVM classifier. The enhancement can be defined as conversion of the image quality to a better and more understandable level. The mammogram enhancement procedure includes filtering, top hat operation, DWT. Then the contrast stretching is used to increase the contrast of the image. The segmentation of mammogram images has been playing an important role to improve the detection and diagnosis of breast cancer. The most common segmentation method used is thresholding. The features are extracted from the segmented breast area. Next stage include, which classifies the regions using the SVM classifier. The method was tested on 75 mammographic images, from the mini-MIAS database. The methodology achieved a sensitivity of 88.75%.

cs.LG cs.AI

0912.2385

http://arxiv.org/pdf/0912.2385v1

2009-12-12T00:59:26Z

2009-12-12T00:59:26Z

Closing the Learning-Planning Loop with Predictive State Representations

A central problem in artificial intelligence is that of planning to maximize future reward under uncertainty in a partially observable environment. In this paper we propose and demonstrate a novel algorithm which accurately learns a model of such an environment directly from sequences of action-observation pairs. We then close the loop from observations to actions by planning in the learned model and recovering a policy which is near-optimal in the original environment. Specifically, we present an efficient and statistically consistent spectral algorithm for learning the parameters of a Predictive State Representation (PSR). We demonstrate the algorithm by learning a model of a simulated high-dimensional, vision-based mobile robot planning task, and then perform approximate point-based planning in the learned PSR. Analysis of our results shows that the algorithm learns a state space which efficiently captures the essential features of the environment. This representation allows accurate prediction with a small number of parameters, and enables successful and efficient planning.

cs.CC cs.LG

0912.2709

http://arxiv.org/pdf/0912.2709v1

2009-12-14T19:14:03Z

2009-12-14T19:14:03Z

The Gaussian Surface Area and Noise Sensitivity of Degree-$d$ Polynomials

We provide asymptotically sharp bounds for the Gaussian surface area and the Gaussian noise sensitivity of polynomial threshold functions. In particular we show that if $f$ is a degree-$d$ polynomial threshold function, then its Gaussian sensitivity at noise rate $\epsilon$ is less than some quantity asymptotic to $\frac{d\sqrt{2\epsilon}}{\pi}$ and the Gaussian surface area is at most $\frac{d}{\sqrt{2\pi}}$. Furthermore these bounds are asymptotically tight as $\epsilon\to 0$ and $f$ the threshold function of a product of $d$ distinct homogeneous linear functions.

cs.NE cs.CR cs.LG

0912.2843

http://arxiv.org/pdf/0912.2843v2

2010-05-30T09:00:50Z

2009-12-15T10:57:58Z

Intrusion Detection In Mobile Ad Hoc Networks Using GA Based Feature Selection

Mobile ad hoc networking (MANET) has become an exciting and important technology in recent years because of the rapid proliferation of wireless devices. MANETs are highly vulnerable to attacks due to the open medium, dynamically changing network topology and lack of centralized monitoring point. It is important to search new architecture and mechanisms to protect the wireless networks and mobile computing application. IDS analyze the network activities by means of audit data and use patterns of well-known attacks or normal profile to detect potential attacks. There are two methods to analyze: misuse detection and anomaly detection. Misuse detection is not effective against unknown attacks and therefore, anomaly detection method is used. In this approach, the audit data is collected from each mobile node after simulating the attack and compared with the normal behavior of the system. If there is any deviation from normal behavior then the event is considered as an attack. Some of the features of collected audit data may be redundant or contribute little to the detection process. So it is essential to select the important features to increase the detection rate. This paper focuses on implementing two feature selection methods namely, markov blanket discovery and genetic algorithm. In genetic algorithm, bayesian network is constructed over the collected features and fitness function is calculated. Based on the fitness value the features are selected. Markov blanket discovery also uses bayesian network and the features are selected depending on the minimum description length. During the evaluation phase, the performances of both approaches are compared based on detection rate and false alarm rate.

cs.LG

0912.3983

http://arxiv.org/pdf/0912.3983v1

2009-12-20T05:21:45Z

2009-12-20T05:21:45Z

Performance Analysis of AIM-K-means & K-means in Quality Cluster Generation

Among all the partition based clustering algorithms K-means is the most popular and well known method. It generally shows impressive results even in considerably large data sets. The computational complexity of K-means does not suffer from the size of the data set. The main disadvantage faced in performing this clustering is that the selection of initial means. If the user does not have adequate knowledge about the data set, it may lead to erroneous results. The algorithm Automatic Initialization of Means (AIM), which is an extension to K-means, has been proposed to overcome the problem of initial mean generation. In this paper an attempt has been made to compare the performance of the algorithms through implementation

cs.LG

10.1109/TIT.2011.2182033

0912.3995

http://arxiv.org/abs/0912.3995v4

2010-06-09T23:24:13Z

2009-12-21T00:08:19Z

Gaussian Process Optimization in the Bandit Setting: No Regret and Experimental Design

Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multi-armed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low RKHS norm. We resolve the important open problem of deriving regret bounds for this setting, which imply novel convergence rates for GP optimization. We analyze GP-UCB, an intuitive upper-confidence based algorithm, and bound its cumulative regret in terms of maximal information gain, establishing a novel connection between GP optimization and experimental design. Moreover, by bounding the latter in terms of operator spectra, we obtain explicit sublinear regret bounds for many commonly used covariance functions. In some important cases, our bounds have surprisingly weak dependence on the dimensionality. In our experiments on real sensor data, GP-UCB compares favorably with other heuristical GP optimization approaches.

cs.LG cs.AI

0912.4473

http://arxiv.org/pdf/0912.4473v2

2010-06-26T22:47:44Z

2009-12-22T18:03:55Z

Learning to Predict Combinatorial Structures

The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions to ensure efficient, polynomial time estimation of model parameters. For several combinatorial structures, including cycles, partially ordered sets, permutations and other graph classes, these assumptions do not hold. In this thesis, we address the problem of designing learning algorithms for predicting combinatorial structures by introducing two new assumptions: (i) The first assumption is that a particular counting problem can be solved efficiently. The consequence is a generalisation of the classical ridge regression for structured prediction. (ii) The second assumption is that a particular sampling problem can be solved efficiently. The consequence is a new technique for designing and analysing probabilistic structured prediction models. These results can be applied to solve several complex learning problems including but not limited to multi-label classification, multi-category hierarchical classification, and label ranking.

cs.LG cs.AI cs.IT math.IT math.ST stat.TH

0912.4883

http://arxiv.org/pdf/0912.4883v1

2009-12-24T15:29:32Z

2009-12-24T15:29:32Z

On Finding Predictors for Arbitrary Families of Processes

The problem is sequence prediction in the following setting. A sequence $x_1,...,x_n,...$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, it is required to give the conditional probabilities of the next observation. The measure $\mu$ belongs to an arbitrary but known class $C$ of stochastic process measures. We are interested in predictors $\rho$ whose conditional probabilities converge (in some sense) to the "true" $\mu$-conditional probabilities if any $\mu\in C$ is chosen to generate the sequence. The contribution of this work is in characterizing the families $C$ for which such predictors exist, and in providing a specific and simple form in which to look for a solution. We show that if any predictor works, then there exists a Bayesian predictor, whose prior is discrete, and which works too. We also find several sufficient and necessary conditions for the existence of a predictor, in terms of topological characterizations of the family $C$, as well as in terms of local behaviour of the measures in $C$, which in some cases lead to procedures for constructing such predictors. It should be emphasized that the framework is completely general: the stochastic processes considered are not required to be i.i.d., stationary, or to belong to any parametric or countable family.

cs.CC cs.CG cs.DM cs.LG math.PR

10.1145/2395116.2395118

0912.4884

http://arxiv.org/abs/0912.4884v2

2012-09-12T23:33:10Z

2009-12-24T15:35:56Z

An Invariance Principle for Polytopes

Let X be randomly chosen from {-1,1}^n, and let Y be randomly chosen from the standard spherical Gaussian on R^n. For any (possibly unbounded) polytope P formed by the intersection of k halfspaces, we prove that |Pr [X belongs to P] - Pr [Y belongs to P]| < log^{8/5}k * Delta, where Delta is a parameter that is small for polytopes formed by the intersection of "regular" halfspaces (i.e., halfspaces with low influence). The novelty of our invariance principle is the polylogarithmic dependence on k. Previously, only bounds that were at least linear in k were known. We give two important applications of our main result: (1) A polylogarithmic in k bound on the Boolean noise sensitivity of intersections of k "regular" halfspaces (previous work gave bounds linear in k). (2) A pseudorandom generator (PRG) with seed length O((log n)*poly(log k,1/delta)) that delta-fools all polytopes with k faces with respect to the Gaussian distribution. We also obtain PRGs with similar parameters that fool polytopes formed by intersection of regular halfspaces over the hypercube. Using our PRG constructions, we obtain the first deterministic quasi-polynomial time algorithms for approximately counting the number of solutions to a broad class of integer programs, including dense covering problems and contingency tables.

cs.LG cs.AI

0912.5029

http://arxiv.org/pdf/0912.5029v1

2009-12-26T16:32:46Z

2009-12-26T16:32:46Z

Complexity of stochastic branch and bound methods for belief tree search in Bayesian reinforcement learning

There has been a lot of recent work on Bayesian methods for reinforcement learning exhibiting near-optimal online performance. The main obstacle facing such methods is that in most problems of interest, the optimal solution involves planning in an infinitely large tree. However, it is possible to obtain stochastic lower and upper bounds on the value of each tree node. This enables us to use stochastic branch and bound algorithms to search the tree efficiently. This paper proposes two such algorithms and examines their complexity in this setting.

stat.ME cs.LG physics.soc-ph q-bio.QM stat.AP

10.1214/09-AOAS321

0912.5193

http://arxiv.org/abs/0912.5193v3

2013-08-29T06:50:07Z

2009-12-28T17:56:50Z

Ranking relations using analogies in biological and information networks

Analogical reasoning depends fundamentally on the ability to learn and generalize about relations between objects. We develop an approach to relational learning which, given a set of pairs of objects $\mathbf{S}=\{A^{(1)}:B^{(1)},A^{(2)}:B^{(2)},\ldots,A^{(N)}:B ^{(N)}\}$, measures how well other pairs A:B fit in with the set $\mathbf{S}$. Our work addresses the following question: is the relation between objects A and B analogous to those relations found in $\mathbf{S}$? Such questions are particularly relevant in information retrieval, where an investigator might want to search for analogous pairs of objects that match the query set of interest. There are many ways in which objects can be related, making the task of measuring analogies very challenging. Our approach combines a similarity measure on function spaces with Bayesian analysis to produce a ranking. It requires data containing features of the objects of interest and a link matrix specifying which relationships exist; no further attributes of such relationships are necessary. We illustrate the potential of our method on text analysis and information networks. An application on discovering functional interactions between pairs of proteins is discussed in detail, where we show that our approach can work in practice even if a small set of protein pairs is provided.

stat.ME cs.LG physics.soc-ph q-bio.MN stat.ML

0912.5410

http://arxiv.org/pdf/0912.5410v1

2009-12-29T17:53:13Z

2009-12-29T17:53:13Z

A survey of statistical network models

Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.

cs.LG

1001.0405

http://arxiv.org/pdf/1001.0405v1

2010-01-03T19:54:40Z

2010-01-03T19:54:40Z

Optimal Query Complexity for Reconstructing Hypergraphs

In this paper we consider the problem of reconstructing a hidden weighted hypergraph of constant rank using additive queries. We prove the following: Let $G$ be a weighted hidden hypergraph of constant rank with n vertices and $m$ hyperedges. For any $m$ there exists a non-adaptive algorithm that finds the edges of the graph and their weights using $$ O(\frac{m\log n}{\log m}) $$ additive queries. This solves the open problem in [S. Choi, J. H. Kim. Optimal Query Complexity Bounds for Finding Graphs. {\em STOC}, 749--758,~2008]. When the weights of the hypergraph are integers that are less than $O(poly(n^d/m))$ where $d$ is the rank of the hypergraph (and therefore for unweighted hypergraphs) there exists a non-adaptive algorithm that finds the edges of the graph and their weights using $$ O(\frac{m\log \frac{n^d}{m}}{\log m}). $$ additive queries. Using the information theoretic bound the above query complexities are tight.

cs.CG cs.CV cs.LG

1001.0591

http://arxiv.org/pdf/1001.0591v2

2011-03-13T22:40:00Z

2010-01-04T22:21:08Z

Comparing Distributions and Shapes using the Kernel Distance

Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis, measure theory and geometric measure theory, and have a rich structure that includes an isometric embedding into a (possibly infinite dimensional) Hilbert space. They have recently been applied to numerous problems in machine learning and shape analysis. In this paper, we provide the first algorithmic analysis of these distance metrics. Our main contributions are as follows: (i) We present fast approximation algorithms for computing the kernel distance between two point sets P and Q that runs in near-linear time in the size of (P cup Q) (note that an explicit calculation would take quadratic time). (ii) We present polynomial-time algorithms for approximately minimizing the kernel distance under rigid transformation; they run in time O(n + poly(1/epsilon, log n)). (iii) We provide several general techniques for reducing complex objects to convenient sparse representations (specifically to point sets or sets of points sets) which approximately preserve the kernel distance. In particular, this allows us to reduce problems of computing the kernel distance between various types of objects such as curves, surfaces, and distributions to computing the kernel distance between point sets. These take advantage of the reproducing kernel Hilbert space and a new relation linking binary range spaces to continuous range spaces with bounded fat-shattering dimension.

stat.ME cs.LG stat.ML

1001.0597

http://arxiv.org/pdf/1001.0597v2

2011-01-21T15:42:15Z

2010-01-04T22:47:31Z

Inference of global clusters from locally distributed data

We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over the covariate domain. We propose a novel Bayesian nonparametric method reposing on the formalism of spatial modeling and a nested hierarchy of Dirichlet processes. We provide an analysis of the model properties, relating and contrasting the notions of local and global clusters. We also provide an efficient inference algorithm, and demonstrate the utility of our method in several data examples, including the problem of object tracking and a global clustering analysis of functional data where the functional identity information is not available.

cs.LG cs.CY cs.IR

1001.0700

http://arxiv.org/pdf/1001.0700v1

2010-01-05T13:06:21Z

2010-01-05T13:06:21Z

Vandalism Detection in Wikipedia: a Bag-of-Words Classifier Approach

A bag-of-words based probabilistic classifier is trained using regularized logistic regression to detect vandalism in the English Wikipedia. Isotonic regression is used to calibrate the class membership probabilities. Learning curve, reliability, ROC, and cost analysis are performed.

cs.LG

1001.0879

http://arxiv.org/pdf/1001.0879v1

2010-01-06T12:40:13Z

2010-01-06T12:40:13Z

Linear Probability Forecasting

Multi-class classification is one of the most important tasks in machine learning. In this paper we consider two online multi-class classification problems: classification by a linear model and by a kernelized model. The quality of predictions is measured by the Brier loss function. We suggest two computationally efficient algorithms to work with these problems and prove theoretical guarantees on their losses. We kernelize one of the algorithms and prove theoretical guarantees on its loss. We perform experiments and compare our algorithms with logistic regression.

cs.NI cs.LG

1001.1009

http://arxiv.org/pdf/1001.1009v1

2010-01-06T23:33:49Z

2010-01-06T23:33:49Z

Multi-path Probabilistic Available Bandwidth Estimation through Bayesian Active Learning

Knowing the largest rate at which data can be sent on an end-to-end path such that the egress rate is equal to the ingress rate with high probability can be very practical when choosing transmission rates in video streaming or selecting peers in peer-to-peer applications. We introduce probabilistic available bandwidth, which is defined in terms of ingress rates and egress rates of traffic on a path, rather than in terms of capacity and utilization of the constituent links of the path like the standard available bandwidth metric. In this paper, we describe a distributed algorithm, based on a probabilistic graphical model and Bayesian active learning, for simultaneously estimating the probabilistic available bandwidth of multiple paths through a network. Our procedure exploits the fact that each packet train provides information not only about the path it traverses, but also about any path that shares a link with the monitored path. Simulations and PlanetLab experiments indicate that this process can dramatically reduce the number of probes required to generate accurate estimates.

cs.LG cs.AI cs.CV

1001.1020

http://arxiv.org/pdf/1001.1020v1

2010-01-07T06:34:21Z

2010-01-07T06:34:21Z

An Empirical Evaluation of Four Algorithms for Multi-Class Classification: Mart, ABC-Mart, Robust LogitBoost, and ABC-LogitBoost

This empirical study is mainly devoted to comparing four tree-based boosting algorithms: mart, abc-mart, robust logitboost, and abc-logitboost, for multi-class classification on a variety of publicly available datasets. Some of those datasets have been thoroughly tested in prior studies using a broad range of classification algorithms including SVM, neural nets, and deep learning. In terms of the empirical classification errors, our experiment results demonstrate: 1. Abc-mart considerably improves mart. 2. Abc-logitboost considerably improves (robust) logitboost. 3. Robust) logitboost} considerably improves mart on most datasets. 4. Abc-logitboost considerably improves abc-mart on most datasets. 5. These four boosting algorithms (especially abc-logitboost) outperform SVM on many datasets. 6. Compared to the best deep learning methods, these four boosting algorithms (especially abc-logitboost) are competitive.

cs.CV cs.LG

1001.1027

http://arxiv.org/pdf/1001.1027v5

2017-06-07T17:05:16Z

2010-01-07T06:22:56Z

An Unsupervised Algorithm For Learning Lie Group Transformations

We present several theoretical contributions which allow Lie groups to be fit to high dimensional datasets. Transformation operators are represented in their eigen-basis, reducing the computational complexity of parameter estimation to that of training a linear transformation model. A transformation specific "blurring" operator is introduced that allows inference to escape local minima via a smoothing of the transformation space. A penalty on traversed manifold distance is added which encourages the discovery of sparse, minimal distance, transformations between states. Both learning and inference are demonstrated using these methods for the full set of affine transformations on natural image patches. Transformation operators are then trained on natural video sequences. It is shown that the learned video transformations provide a better description of inter-frame differences than the standard motion model based on rigid translation.

cs.LG

1001.1079

http://arxiv.org/pdf/1001.1079v1

2010-01-07T14:41:21Z

2010-01-07T14:41:21Z

Measuring Latent Causal Structure

Discovering latent representations of the observed world has become increasingly more relevant in data analysis. Much of the effort concentrates on building latent variables which can be used in prediction problems, such as classification and regression. A related goal of learning latent structure from data is that of identifying which hidden common causes generate the observations, such as in applications that require predicting the effect of policies. This will be the main problem tackled in our contribution: given a dataset of indicators assumed to be generated by unknown and unmeasured common causes, we wish to discover which hidden common causes are those, and how they generate our data. This is possible under the assumption that observed variables are linear functions of the latent causes with additive noise. Previous results in the literature present solutions for the case where each observed variable is a noisy function of a single latent variable. We show how to extend the existing results for some cases where observed variables measure more than one latent variable.

cs.CV cs.LG

1001.2605

http://arxiv.org/pdf/1001.2605v1

2010-01-15T03:03:24Z

2010-01-15T03:03:24Z

An Explicit Nonlinear Mapping for Manifold Learning

Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data manifold to the output embedding. This prohibits the application of manifold learning methods in many practical problems such as classification and target detection. Previously, in order to provide explicit mappings for manifold learning methods, many methods have been proposed to get an approximate explicit representation mapping with the assumption that there exists a linear projection between the high-dimensional data samples and their low-dimensional embedding. However, this linearity assumption may be too restrictive. In this paper, an explicit nonlinear mapping is proposed for manifold learning, based on the assumption that there exists a polynomial mapping between the high-dimensional data samples and their low-dimensional representations. As far as we know, this is the first time that an explicit nonlinear mapping for manifold learning is given. In particular, we apply this to the method of Locally Linear Embedding (LLE) and derive an explicit nonlinear manifold learning algorithm, named Neighborhood Preserving Polynomial Embedding (NPPE). Experimental results on both synthetic and real-world data show that the proposed mapping is much more effective in preserving the local neighborhood information and the nonlinear geometry of the high-dimensional data samples than previous work.

cs.LG cs.AI

1001.2709

http://arxiv.org/pdf/1001.2709v1

2010-01-15T15:10:39Z

2010-01-15T15:10:39Z

Kernel machines with two layers and multiple kernel learning

In this paper, the framework of kernel machines with two layers is introduced, generalizing classical kernel methods. The new learning methodology provide a formal connection between computational architectures with multiple layers and the theme of kernel learning in standard regularization methods. First, a representer theorem for two-layer networks is presented, showing that finite linear combinations of kernels on each layer are optimal architectures whenever the corresponding functions solve suitable variational problems in reproducing kernel Hilbert spaces (RKHS). The input-output map expressed by these architectures turns out to be equivalent to a suitable single-layer kernel machines in which the kernel function is also learned from the data. Recently, the so-called multiple kernel learning methods have attracted considerable attention in the machine learning literature. In this paper, multiple kernel learning methods are shown to be specific cases of kernel machines with two layers in which the second layer is linear. Finally, a simple and effective multiple kernel learning method called RLS2 (regularized least squares with two layers) is introduced, and his performances on several learning problems are extensively analyzed. An open source MATLAB toolbox to train and validate RLS2 models with a Graphic User Interface is available.

nlin.AO cond-mat.dis-nn cs.AI cs.LG stat.ML

1001.2813

http://arxiv.org/pdf/1001.2813v1

2010-01-18T01:10:17Z

2010-01-18T01:10:17Z

A Monte Carlo Algorithm for Universally Optimal Bayesian Sequence Prediction and Planning

The aim of this work is to address the question of whether we can in principle design rational decision-making agents or artificial intelligences embedded in computable physics such that their decisions are optimal in reasonable mathematical senses. Recent developments in rare event probability estimation, recursive bayesian inference, neural networks, and probabilistic planning are sufficient to explicitly approximate reinforcement learners of the AIXI style with non-trivial model classes (here, the class of resource-bounded Turing machines). Consideration of the effects of resource limitations in a concrete implementation leads to insights about possible architectures for learning systems using optimal decision makers as components.

cs.LG

10.1088/1742-6596/233/1/012014

1001.2957

http://arxiv.org/abs/1001.2957v2

2010-03-16T04:47:17Z

2010-01-18T05:34:09Z

Asymptotic Learning Curve and Renormalizable Condition in Statistical Learning Theory

Bayes statistics and statistical physics have the common mathematical structure, where the log likelihood function corresponds to the random Hamiltonian. Recently, it was discovered that the asymptotic learning curves in Bayes estimation are subject to a universal law, even if the log likelihood function can not be approximated by any quadratic form. However, it is left unknown what mathematical property ensures such a universal law. In this paper, we define a renormalizable condition of the statistical estimation problem, and show that, under such a condition, the asymptotic learning curves are ensured to be subject to the universal law, even if the true distribution is unrealizable and singular for a statistical model. Also we study a nonrenormalizable case, in which the learning curves have the different asymptotic behaviors from the universal law.

cs.IT cs.LG math.IT math.ST stat.TH

10.1109/ISIT.2010.5513384

1001.3090

http://arxiv.org/abs/1001.3090v2

2010-06-13T19:18:47Z

2010-01-18T17:07:03Z

Feature Extraction for Universal Hypothesis Testing via Rank-constrained Optimization

This paper concerns the construction of tests for universal hypothesis testing problems, in which the alternate hypothesis is poorly modeled and the observation space is large. The mismatched universal test is a feature-based technique for this purpose. In prior work it is shown that its finite-observation performance can be much better than the (optimal) Hoeffding test, and good performance depends crucially on the choice of features. The contributions of this paper include: 1) We obtain bounds on the number of \epsilon distinguishable distributions in an exponential family. 2) This motivates a new framework for feature extraction, cast as a rank-constrained optimization problem. 3) We obtain a gradient-based algorithm to solve the rank-constrained optimization problem and prove its local convergence.

cs.IT cs.LG math.IT math.ST stat.TH

10.1109/TIT.2010.2094817

1001.3448

http://arxiv.org/abs/1001.3448v4

2011-01-27T18:55:05Z

2010-01-20T02:57:15Z

The dynamics of message passing on dense graphs, with applications to compressed sensing

Approximate message passing algorithms proved to be extremely effective in reconstructing sparse signals from a small number of incoherent linear measurements. Extensive numerical experiments further showed that their dynamics is accurately tracked by a simple one-dimensional iteration termed state evolution. In this paper we provide the first rigorous foundation to state evolution. We prove that indeed it holds asymptotically in the large system limit for sensing matrices with independent and identically distributed gaussian entries. While our focus is on message passing algorithms for compressed sensing, the analysis extends beyond this setting, to a general class of algorithms on dense graphs. In this context, state evolution plays the role that density evolution has for sparse graphs. The proof technique is fundamentally different from the standard approach to density evolution, in that it copes with large number of short loops in the underlying factor graph. It relies instead on a conditioning technique recently developed by Erwin Bolthausen in the context of spin glass theory.

cs.LG

1001.3478

http://arxiv.org/pdf/1001.3478v1

2010-01-20T07:30:02Z

2010-01-20T07:30:02Z

Role of Interestingness Measures in CAR Rule Ordering for Associative Classifier: An Empirical Approach

Associative Classifier is a novel technique which is the integration of Association Rule Mining and Classification. The difficult task in building Associative Classifier model is the selection of relevant rules from a large number of class association rules (CARs). A very popular method of ordering rules for selection is based on confidence, support and antecedent size (CSA). Other methods are based on hybrid orderings in which CSA method is combined with other measures. In the present work, we study the effect of using different interestingness measures of Association rules in CAR rule ordering and selection for associative classifier.

cs.CV cs.LG

1001.4140

http://arxiv.org/pdf/1001.4140v1

2010-01-23T08:53:49Z

2010-01-23T08:53:49Z

SVM-based Multiview Face Recognition by Generalization of Discriminant Analysis

Identity verification of authentic persons by their multiview faces is a real valued problem in machine vision. Multiview faces are having difficulties due to non-linear representation in the feature space. This paper illustrates the usability of the generalization of LDA in the form of canonical covariate for face recognition to multiview faces. In the proposed work, the Gabor filter bank is used to extract facial features that characterized by spatial frequency, spatial locality and orientation. Gabor face representation captures substantial amount of variations of the face instances that often occurs due to illumination, pose and facial expression changes. Convolution of Gabor filter bank to face images of rotated profile views produce Gabor faces with high dimensional features vectors. Canonical covariate is then used to Gabor faces to reduce the high dimensional feature spaces into low dimensional subspaces. Finally, support vector machines are trained with canonical sub-spaces that contain reduced set of features and perform recognition task. The proposed system is evaluated with UMIST face database. The experiment results demonstrate the efficiency and robustness of the proposed system with high recognition rates.

cs.NE cs.LG

1001.4301

http://arxiv.org/pdf/1001.4301v1

2010-01-25T02:09:42Z

2010-01-25T02:09:42Z

Probabilistic Approach to Neural Networks Computation Based on Quantum Probability Model Probabilistic Principal Subspace Analysis Example

In this paper, we introduce elements of probabilistic model that is suitable for modeling of learning algorithms in biologically plausible artificial neural networks framework. Model is based on two of the main concepts in quantum physics - a density matrix and the Born rule. As an example, we will show that proposed probabilistic interpretation is suitable for modeling of on-line learning algorithms for PSA, which are preferably realized by a parallel hardware based on very simple computational units. Proposed concept (model) can be used in the context of improving algorithm convergence speed, learning factor choice, or input signal scale robustness. We are going to see how the Born rule and the Hebbian learning rule are connected

cs.LG cs.SY math.OC math.ST stat.TH

1001.4475

http://arxiv.org/pdf/1001.4475v2

2011-04-13T07:03:48Z

2010-01-25T16:30:15Z

X-Armed Bandits

We consider a generalization of stochastic bandits where the set of arms, $\cX$, is allowed to be a generic measurable space and the mean-payoff function is "locally Lipschitz" with respect to a dissimilarity function that is known to the decision maker. Under this condition we construct an arm selection policy, called HOO (hierarchical optimistic optimization), with improved regret bounds compared to previous results for a large class of problems. In particular, our results imply that if $\cX$ is the unit hypercube in a Euclidean space and the mean-payoff function has a finite number of global maxima around which the behavior of the function is locally continuous with a known smoothness degree, then the expected regret of HOO is bounded up to a logarithmic factor by $\sqrt{n}$, i.e., the rate of growth of the regret is independent of the dimension of the space. We also prove the minimax optimality of our algorithm when the dissimilarity is a metric. Our basic strategy has quadratic computational complexity as a function of the number of time steps and does not rely on the doubling trick. We also introduce a modified strategy, which relies on the doubling trick but runs in linearithmic time. Both results are improvements with respect to previous approaches.

cs.LG

10.1016/j.eij.2011.02.007

1001.5007

http://arxiv.org/abs/1001.5007v2

2010-01-27T21:23:03Z

2010-01-27T19:24:33Z

Trajectory Clustering and an Application to Airspace Monitoring

This paper presents a framework aimed at monitoring the behavior of aircraft in a given airspace. Nominal trajectories are determined and learned using data driven methods. Standard procedures are used by air traffic controllers (ATC) to guide aircraft, ensure the safety of the airspace, and to maximize the runway occupancy. Even though standard procedures are used by ATC, the control of the aircraft remains with the pilots, leading to a large variability in the flight patterns observed. Two methods to identify typical operations and their variability from recorded radar tracks are presented. This knowledge base is then used to monitor the conformance of current operations against operations previously identified as standard. A tool called AirTrajectoryMiner is presented, aiming at monitoring the instantaneous health of the airspace, in real time. The airspace is "healthy" when all aircraft are flying according to the nominal procedures. A measure of complexity is introduced, measuring the conformance of current flight to nominal flight patterns. When an aircraft does not conform, the complexity increases as more attention from ATC is required to ensure a safe separation between aircraft.

cs.NE cs.LG

1001.5348

http://arxiv.org/pdf/1001.5348v1

2010-01-29T08:10:26Z

2010-01-29T08:10:26Z

Performance Comparisons of PSO based Clustering

In this paper we have investigated the performance of PSO Particle Swarm Optimization based clustering on few real world data sets and one artificial data set. The performances are measured by two metric namely quantization error and inter-cluster distance. The K means clustering algorithm is first implemented for all data sets, the results of which form the basis of comparison of PSO based approaches. We have explored different variants of PSO such as gbest, lbest ring, lbest vonneumann and Hybrid PSO for comparison purposes. The results reveal that PSO based clustering algorithms perform better compared to K means in all data sets.

cs.CV cs.DB cs.LG

1002.0383

http://arxiv.org/pdf/1002.0383v1

2010-02-02T02:30:22Z

2010-02-02T02:30:22Z

Feature Level Clustering of Large Biometric Database

This paper proposes an efficient technique for partitioning large biometric database during identification. In this technique feature vector which comprises of global and local descriptors extracted from offline signature are used by fuzzy clustering technique to partition the database. As biometric features posses no natural order of sorting, thus it is difficult to index them alphabetically or numerically. Hence, some supervised criteria is required to partition the search space. At the time of identification the fuzziness criterion is introduced to find the nearest clusters for declaring the identity of query sample. The system is tested using bin-miss rate and performs better in comparison to traditional k-means approach.

cs.CV cs.LG

1002.0416

http://arxiv.org/pdf/1002.0416v1

2010-02-02T08:15:20Z

2010-02-02T08:15:20Z

Fusion of Multiple Matchers using SVM for Offline Signature Identification

This paper uses Support Vector Machines (SVM) to fuse multiple classifiers for an offline signature system. From the signature images, global and local features are extracted and the signatures are verified with the help of Gaussian empirical rule, Euclidean and Mahalanobis distance based classifiers. SVM is used to fuse matching scores of these matchers. Finally, recognition of query signatures is done by comparing it with all signatures of the database. The proposed system is tested on a signature database contains 5400 offline signatures of 600 individuals and the results are found to be promising.

cs.LG

1002.0709

http://arxiv.org/pdf/1002.0709v1

2010-02-03T11:31:24Z

2010-02-03T11:31:24Z

Aggregating Algorithm competing with Banach lattices

The paper deals with on-line regression settings with signals belonging to a Banach lattice. Our algorithms work in a semi-online setting where all the inputs are known in advance and outcomes are unknown and given step by step. We apply the Aggregating Algorithm to construct a prediction method whose cumulative loss over all the input vectors is comparable with the cumulative loss of any linear functional on the Banach lattice. As a by-product we get an algorithm that takes signals from an arbitrary domain. Its cumulative loss is comparable with the cumulative loss of any predictor function from Besov and Triebel-Lizorkin spaces. We describe several applications of our setting.

stat.AP cs.LG stat.ML

10.1109/ALLERTON.2016.7852262

1002.0747

http://arxiv.org/abs/1002.0747v3

2016-06-26T01:23:28Z

2010-02-03T14:11:06Z

Efficient Bayesian Learning in Social Networks with Gaussian Estimators

We consider a group of Bayesian agents who try to estimate a state of the world $\theta$ through interaction on a social network. Each agent $v$ initially receives a private measurement of $\theta$: a number $S_v$ picked from a Gaussian distribution with mean $\theta$ and standard deviation one. Then, in each discrete time iteration, each reveals its estimate of $\theta$ to its neighbors, and, observing its neighbors' actions, updates its belief using Bayes' Law. This process aggregates information efficiently, in the sense that all the agents converge to the belief that they would have, had they access to all the private measurements. We show that this process is computationally efficient, so that each agent's calculation can be easily carried out. We also show that on any graph the process converges after at most $2N \cdot D$ steps, where $N$ is the number of agents and $D$ is the diameter of the network. Finally, we show that on trees and on distance transitive-graphs the process converges after $D$ steps, and that it preserves privacy, so that agents learn very little about the private signal of most other agents, despite the efficient aggregation of information. Our results extend those in an unpublished manuscript of the first and last authors.

cs.IT cs.LG math.IT math.ST stat.TH

1002.0757

http://arxiv.org/pdf/1002.0757v1

2010-02-03T15:11:21Z

2010-02-03T15:11:21Z

Prequential Plug-In Codes that Achieve Optimal Redundancy Rates even if the Model is Wrong

We analyse the prequential plug-in codes relative to one-parameter exponential families M. We show that if data are sampled i.i.d. from some distribution outside M, then the redundancy of any plug-in prequential code grows at rate larger than 1/2 ln(n) in the worst case. This means that plug-in codes, such as the Rissanen-Dawid ML code, may behave inferior to other important universal codes such as the 2-part MDL, Shtarkov and Bayes codes, for which the redundancy is always 1/2 ln(n) + O(1). However, we also show that a slight modification of the ML plug-in code, "almost" in the model, does achieve the optimal redundancy even if the the true distribution is outside M.

cs.LG

1002.1144

http://arxiv.org/pdf/1002.1144v1

2010-02-05T08:27:17Z

2010-02-05T08:27:17Z

A CHAID Based Performance Prediction Model in Educational Data Mining

The performance in higher secondary school education in India is a turning point in the academic lives of all students. As this academic performance is influenced by many factors, it is essential to develop predictive data mining model for students' performance so as to identify the slow learners and study the influence of the dominant factors on their academic performance. In the present investigation, a survey cum experimental methodology was adopted to generate a database and it was constructed from a primary and a secondary source. While the primary data was collected from the regular students, the secondary data was gathered from the school and office of the Chief Educational Officer (CEO). A total of 1000 datasets of the year 2006 from five different schools in three different districts of Tamilnadu were collected. The raw data was preprocessed in terms of filling up missing values, transforming values in one form into another and relevant attribute/ variable selection. As a result, we had 772 student records, which were used for CHAID prediction model construction. A set of prediction rules were extracted from CHIAD prediction model and the efficiency of the generated CHIAD prediction model was found. The accuracy of the present model was compared with other model and it has been found to be satisfactory.

cs.LG

1002.1156

http://arxiv.org/pdf/1002.1156v1

2010-02-05T08:59:05Z

2010-02-05T08:59:05Z

Dimensionality Reduction: An Empirical Study on the Usability of IFE-CF (Independent Feature Elimination- by C-Correlation and F-Correlation) Measures

The recent increase in dimensionality of data has thrown a great challenge to the existing dimensionality reduction methods in terms of their effectiveness. Dimensionality reduction has emerged as one of the significant preprocessing steps in machine learning applications and has been effective in removing inappropriate data, increasing learning accuracy, and improving comprehensibility. Feature redundancy exercises great influence on the performance of classification process. Towards the better classification performance, this paper addresses the usefulness of truncating the highly correlated and redundant attributes. Here, an effort has been made to verify the utility of dimensionality reduction by applying LVQ (Learning Vector Quantization) method on two Benchmark datasets of 'Pima Indian Diabetic patients' and 'Lung cancer patients'.

cs.AI cs.LG cs.RO

1002.1480

http://arxiv.org/pdf/1002.1480v1

2010-02-07T19:58:46Z

2010-02-07T19:58:46Z

A Minimum Relative Entropy Controller for Undiscounted Markov Decision Processes

Adaptive control problems are notoriously difficult to solve even in the presence of plant-specific controllers. One way to by-pass the intractable computation of the optimal policy is to restate the adaptive control as the minimization of the relative entropy of a controller that ignores the true plant dynamics from an informed controller. The solution is given by the Bayesian control rule-a set of equations characterizing a stochastic adaptive controller for the class of possible plant dynamics. Here, the Bayesian control rule is applied to derive BCR-MDP, a controller to solve undiscounted Markov decision processes with finite state and action spaces and unknown dynamics. In particular, we derive a non-parametric conjugate prior distribution over the policy space that encapsulates the agent's whole relevant history and we present a Gibbs sampler to draw random policies from this distribution. Preliminary results show that BCR-MDP successfully avoids sub-optimal limit cycles due to its built-in mechanism to balance exploration versus exploitation.

cs.LG

1002.1782

http://arxiv.org/pdf/1002.1782v3

2010-05-13T03:32:05Z

2010-02-09T07:32:59Z

Online Distributed Sensor Selection

A key problem in sensor networks is to decide which sensors to query when, in order to obtain the most useful information (e.g., for performing accurate prediction), subject to constraints (e.g., on power and bandwidth). In many applications the utility function is not known a priori, must be learned from data, and can even change over time. Furthermore for large sensor networks solving a centralized optimization problem to select sensors is not feasible, and thus we seek a fully distributed solution. In this paper, we present Distributed Online Greedy (DOG), an efficient, distributed algorithm for repeatedly selecting sensors online, only receiving feedback about the utility of the selected sensors. We prove very strong theoretical no-regret guarantees that apply whenever the (unknown) utility function satisfies a natural diminishing returns property called submodularity. Our algorithm has extremely low communication requirements, and scales well to large sensor deployments. We extend DOG to allow observation-dependent sensor selection. We empirically demonstrate the effectiveness of our algorithm on several real-world sensing tasks.

cs.LG

1002.2044

http://arxiv.org/pdf/1002.2044v1

2010-02-10T09:08:56Z

2010-02-10T09:08:56Z

On the Stability of Empirical Risk Minimization in the Presence of Multiple Risk Minimizers

Recently Kutin and Niyogi investigated several notions of algorithmic stability--a property of a learning map conceptually similar to continuity--showing that training-stability is sufficient for consistency of Empirical Risk Minimization while distribution-free CV-stability is necessary and sufficient for having finite VC-dimension. This paper concerns a phase transition in the training stability of ERM, conjectured by the same authors. Kutin and Niyogi proved that ERM on finite hypothesis spaces containing a unique risk minimizer has training stability that scales exponentially with sample size, and conjectured that the existence of multiple risk minimizers prevents even super-quadratic convergence. We prove this result for the strictly weaker notion of CV-stability, positively resolving the conjecture.

cs.CV cs.LG

1002.2050

http://arxiv.org/pdf/1002.2050v1

2010-02-10T10:16:57Z

2010-02-10T10:16:57Z

Intrinsic dimension estimation of data by principal component analysis

Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however, becomes ineffective when data have a nonlinear structure. In this paper, we propose a new PCA-based method to estimate intrinsic dimension of data with nonlinear structures. Our method works by first finding a minimal cover of the data set, then performing PCA locally on each subset in the cover and finally giving the estimation result by checking up the data variance on all small neighborhood regions. The proposed method utilizes the whole data set to estimate its intrinsic dimension and is convenient for incremental learning. In addition, our new PCA procedure can filter out noise in data and converge to a stable estimation with the neighborhood region size increasing. Experiments on synthetic and real world data sets show effectiveness of the proposed method.

q-fin.TR cs.LG cs.MA

1002.2171

http://arxiv.org/pdf/1002.2171v1

2010-02-10T18:48:43Z

2010-02-10T18:48:43Z

Reverse Engineering Financial Markets with Majority and Minority Games using Genetic Algorithms

Using virtual stock markets with artificial interacting software investors, aka agent-based models (ABMs), we present a method to reverse engineer real-world financial time series. We model financial markets as made of a large number of interacting boundedly rational agents. By optimizing the similarity between the actual data and that generated by the reconstructed virtual stock market, we obtain parameters and strategies, which reveal some of the inner workings of the target stock market. We validate our approach by out-of-sample predictions of directional moves of the Nasdaq Composite Index.

cs.IT cs.AI cs.LG math.IT

1002.2240

http://arxiv.org/pdf/1002.2240v1

2010-02-10T23:19:56Z

2010-02-10T23:19:56Z

A Generalization of the Chow-Liu Algorithm and its Application to Statistical Learning

We extend the Chow-Liu algorithm for general random variables while the previous versions only considered finite cases. In particular, this paper applies the generalization to Suzuki's learning algorithm that generates from data forests rather than trees based on the minimum description length by balancing the fitness of the data to the forest and the simplicity of the forest. As a result, we successfully obtain an algorithm when both of the Gaussian and finite random variables are present.

cs.LG cs.CY

1002.2425

http://arxiv.org/pdf/1002.2425v1

2010-02-11T20:41:28Z

2010-02-11T20:41:28Z

Application of k Means Clustering algorithm for prediction of Students Academic Performance

The ability to monitor the progress of students academic performance is a critical issue to the academic community of higher learning. A system for analyzing students results based on cluster analysis and uses standard statistical algorithms to arrange their scores data according to the level of their performance is described. In this paper, we also implemented k mean clustering algorithm for analyzing students result data. The model was combined with the deterministic model to analyze the students results of a private Institution in Nigeria which is a good benchmark to monitor the progression of academic performance of students in higher Institution for the purpose of making an effective decision by the academic planners.

cs.LG

1002.2780

http://arxiv.org/pdf/1002.2780v1

2010-02-14T16:37:04Z

2010-02-14T16:37:04Z

Collaborative Filtering in a Non-Uniform World: Learning with the Weighted Trace Norm

We show that matrix completion with trace-norm regularization can be significantly hurt when entries of the matrix are sampled non-uniformly. We introduce a weighted version of the trace-norm regularizer that works well also with non-uniform sampling. Our experimental results demonstrate that the weighted trace-norm regularization indeed yields significant gains on the (highly non-uniformly sampled) Netflix dataset.

cs.AI cs.LG

1002.3086

http://arxiv.org/pdf/1002.3086v1

2010-02-16T14:14:59Z

2010-02-16T14:14:59Z

Convergence of Bayesian Control Rule

Recently, new approaches to adaptive control have sought to reformulate the problem as a minimization of a relative entropy criterion to obtain tractable solutions. In particular, it has been shown that minimizing the expected deviation from the causal input-output dependencies of the true plant leads to a new promising stochastic control rule called the Bayesian control rule. This work proves the convergence of the Bayesian control rule under two sufficient assumptions: boundedness, which is an ergodicity condition; and consistency, which is an instantiation of the sure-thing principle.

cs.LG cs.AI

10.1109/ISCC.2008.4625611

1002.3174

http://arxiv.org/abs/1002.3174v3

2012-03-16T21:31:17Z

2010-02-17T10:18:07Z

A new approach to content-based file type detection

File type identification and file type clustering may be difficult tasks that have an increasingly importance in the field of computer and network security. Classical methods of file type detection including considering file extensions and magic bytes can be easily spoofed. Content-based file type detection is a newer way that is taken into account recently. In this paper, a new content-based method for the purpose of file type detection and file type clustering is proposed that is based on the PCA and neural networks. The proposed method has a good accuracy and is fast enough.