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

0810.5636

http://arxiv.org/pdf/0810.5636v1

2008-10-31T07:58:31Z

2008-10-31T07:58:31Z

On the Possibility of Learning in Reactive Environments with Arbitrary Dependence

We address the problem of reinforcement learning in which observations may exhibit an arbitrary form of stochastic dependence on past observations and actions, i.e. environments more general than (PO)MDPs. The task for an agent is to attain the best possible asymptotic reward where the true generating environment is unknown but belongs to a known countable family of environments. We find some sufficient conditions on the class of environments under which an agent exists which attains the best asymptotic reward for any environment in the class. We analyze how tight these conditions are and how they relate to different probabilistic assumptions known in reinforcement learning and related fields, such as Markov Decision Processes and mixing conditions.

cs.LG

0811.0139

http://arxiv.org/pdf/0811.0139v1

2008-11-02T08:02:43Z

2008-11-02T08:02:43Z

Entropy, Perception, and Relativity

In this paper, I expand Shannon's definition of entropy into a new form of entropy that allows integration of information from different random events. Shannon's notion of entropy is a special case of my more general definition of entropy. I define probability using a so-called performance function, which is de facto an exponential distribution. Assuming that my general notion of entropy reflects the true uncertainty about a probabilistic event, I understand that our perceived uncertainty differs. I claim that our perception is the result of two opposing forces similar to the two famous antagonists in Chinese philosophy: Yin and Yang. Based on this idea, I show that our perceived uncertainty matches the true uncertainty in points determined by the golden ratio. I demonstrate that the well-known sigmoid function, which we typically employ in artificial neural networks as a non-linear threshold function, describes the actual performance. Furthermore, I provide a motivation for the time dilation in Einstein's Special Relativity, basically claiming that although time dilation conforms with our perception, it does not correspond to reality. At the end of the paper, I show how to apply this theoretical framework to practical applications. I present recognition rates for a pattern recognition problem, and also propose a network architecture that can take advantage of general entropy to solve complex decision problems.

cs.LG cs.AI stat.ML

10.3758/BRM.41.4.1201

0811.0146

http://arxiv.org/abs/0811.0146v3

2009-05-14T12:51:44Z

2008-11-02T09:21:40Z

Effect of Tuned Parameters on a LSA MCQ Answering Model

This paper presents the current state of a work in progress, whose objective is to better understand the effects of factors that significantly influence the performance of Latent Semantic Analysis (LSA). A difficult task, which consists in answering (French) biology Multiple Choice Questions, is used to test the semantic properties of the truncated singular space and to study the relative influence of main parameters. A dedicated software has been designed to fine tune the LSA semantic space for the Multiple Choice Questions task. With optimal parameters, the performances of our simple model are quite surprisingly equal or superior to those of 7th and 8th grades students. This indicates that semantic spaces were quite good despite their low dimensions and the small sizes of training data sets. Besides, we present an original entropy global weighting of answers' terms of each question of the Multiple Choice Questions which was necessary to achieve the model's success.

cs.LG cs.IR

0811.1250

http://arxiv.org/pdf/0811.1250v1

2008-11-08T23:23:08Z

2008-11-08T23:23:08Z

Adaptive Base Class Boost for Multi-class Classification

We develop the concept of ABC-Boost (Adaptive Base Class Boost) for multi-class classification and present ABC-MART, a concrete implementation of ABC-Boost. The original MART (Multiple Additive Regression Trees) algorithm has been very successful in large-scale applications. For binary classification, ABC-MART recovers MART. For multi-class classification, ABC-MART considerably improves MART, as evaluated on several public data sets.

cs.LG

0811.1629

http://arxiv.org/pdf/0811.1629v1

2008-11-11T05:09:08Z

2008-11-11T05:09:08Z

Stability Bound for Stationary Phi-mixing and Beta-mixing Processes

Most generalization bounds in learning theory are based on some measure of the complexity of the hypothesis class used, independently of any algorithm. In contrast, the notion of algorithmic stability can be used to derive tight generalization bounds that are tailored to specific learning algorithms by exploiting their particular properties. However, as in much of learning theory, existing stability analyses and bounds apply only in the scenario where the samples are independently and identically distributed. In many machine learning applications, however, this assumption does not hold. The observations received by the learning algorithm often have some inherent temporal dependence. This paper studies the scenario where the observations are drawn from a stationary phi-mixing or beta-mixing sequence, a widely adopted assumption in the study of non-i.i.d. processes that implies a dependence between observations weakening over time. We prove novel and distinct stability-based generalization bounds for stationary phi-mixing and beta-mixing sequences. These bounds strictly generalize the bounds given in the i.i.d. case and apply to all stable learning algorithms, thereby extending the use of stability-bounds to non-i.i.d. scenarios. We also illustrate the application of our phi-mixing generalization bounds to general classes of learning algorithms, including Support Vector Regression, Kernel Ridge Regression, and Support Vector Machines, and many other kernel regularization-based and relative entropy-based regularization algorithms. These novel bounds can thus be viewed as the first theoretical basis for the use of these algorithms in non-i.i.d. scenarios.

cs.IT cs.LG math.IT

0811.1790

http://arxiv.org/pdf/0811.1790v1

2008-11-11T22:46:10Z

2008-11-11T22:46:10Z

Robust Regression and Lasso

Lasso, or $\ell^1$ regularized least squares, has been explored extensively for its remarkable sparsity properties. It is shown in this paper that the solution to Lasso, in addition to its sparsity, has robustness properties: it is the solution to a robust optimization problem. This has two important consequences. First, robustness provides a connection of the regularizer to a physical property, namely, protection from noise. This allows a principled selection of the regularizer, and in particular, generalizations of Lasso that also yield convex optimization problems are obtained by considering different uncertainty sets. Secondly, robustness can itself be used as an avenue to exploring different properties of the solution. In particular, it is shown that robustness of the solution explains why the solution is sparse. The analysis as well as the specific results obtained differ from standard sparsity results, providing different geometric intuition. Furthermore, it is shown that the robust optimization formulation is related to kernel density estimation, and based on this approach, a proof that Lasso is consistent is given using robustness directly. Finally, a theorem saying that sparsity and algorithmic stability contradict each other, and hence Lasso is not stable, is presented.

cs.LG

0811.2016

http://arxiv.org/pdf/0811.2016v1

2008-11-13T01:23:47Z

2008-11-13T01:23:47Z

Land Cover Mapping Using Ensemble Feature Selection Methods

Ensemble classification is an emerging approach to land cover mapping whereby the final classification output is a result of a consensus of classifiers. Intuitively, an ensemble system should consist of base classifiers which are diverse i.e. classifiers whose decision boundaries err differently. In this paper ensemble feature selection is used to impose diversity in ensembles. The features of the constituent base classifiers for each ensemble were created through an exhaustive search algorithm using different separability indices. For each ensemble, the classification accuracy was derived as well as a diversity measure purported to give a measure of the inensemble diversity. The correlation between ensemble classification accuracy and diversity measure was determined to establish the interplay between the two variables. From the findings of this paper, diversity measures as currently formulated do not provide an adequate means upon which to constitute ensembles for land cover mapping.

cs.LG cs.AI

0811.4413

http://arxiv.org/pdf/0811.4413v6

2012-07-06T23:29:02Z

2008-11-26T20:22:51Z

A Spectral Algorithm for Learning Hidden Markov Models

Hidden Markov Models (HMMs) are one of the most fundamental and widely used statistical tools for modeling discrete time series. In general, learning HMMs from data is computationally hard (under cryptographic assumptions), and practitioners typically resort to search heuristics which suffer from the usual local optima issues. We prove that under a natural separation condition (bounds on the smallest singular value of the HMM parameters), there is an efficient and provably correct algorithm for learning HMMs. The sample complexity of the algorithm does not explicitly depend on the number of distinct (discrete) observations---it implicitly depends on this quantity through spectral properties of the underlying HMM. This makes the algorithm particularly applicable to settings with a large number of observations, such as those in natural language processing where the space of observation is sometimes the words in a language. The algorithm is also simple, employing only a singular value decomposition and matrix multiplications.

cs.LG cs.AI

0811.4458

http://arxiv.org/pdf/0811.4458v2

2009-10-20T18:58:20Z

2008-11-27T01:02:33Z

Learning Class-Level Bayes Nets for Relational Data

Many databases store data in relational format, with different types of entities and information about links between the entities. The field of statistical-relational learning (SRL) has developed a number of new statistical models for such data. In this paper we focus on learning class-level or first-order dependencies, which model the general database statistics over attributes of linked objects and links (e.g., the percentage of A grades given in computer science classes). Class-level statistical relationships are important in themselves, and they support applications like policy making, strategic planning, and query optimization. Most current SRL methods find class-level dependencies, but their main task is to support instance-level predictions about the attributes or links of specific entities. We focus only on class-level prediction, and describe algorithms for learning class-level models that are orders of magnitude faster for this task. Our algorithms learn Bayes nets with relational structure, leveraging the efficiency of single-table nonrelational Bayes net learners. An evaluation of our methods on three data sets shows that they are computationally feasible for realistic table sizes, and that the learned structures represent the statistical information in the databases well. After learning compiles the database statistics into a Bayes net, querying these statistics via Bayes net inference is faster than with SQL queries, and does not depend on the size of the database.

cs.CG cs.DS cs.LG

0812.0382

http://arxiv.org/pdf/0812.0382v1

2008-12-01T22:55:39Z

2008-12-01T22:55:39Z

k-means requires exponentially many iterations even in the plane

The k-means algorithm is a well-known method for partitioning n points that lie in the d-dimensional space into k clusters. Its main features are simplicity and speed in practice. Theoretically, however, the best known upper bound on its running time (i.e. O(n^{kd})) can be exponential in the number of points. Recently, Arthur and Vassilvitskii [3] showed a super-polynomial worst-case analysis, improving the best known lower bound from \Omega(n) to 2^{\Omega(\sqrt{n})} with a construction in d=\Omega(\sqrt{n}) dimensions. In [3] they also conjectured the existence of superpolynomial lower bounds for any d >= 2. Our contribution is twofold: we prove this conjecture and we improve the lower bound, by presenting a simple construction in the plane that leads to the exponential lower bound 2^{\Omega(n)}.

cs.DS cs.LG

0812.0389

http://arxiv.org/pdf/0812.0389v4

2009-11-09T15:50:32Z

2008-12-01T23:17:35Z

Approximation Algorithms for Bregman Co-clustering and Tensor Clustering

In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor clustering [8,34]. Like k-means, these more general problems also suffer from the NP-hardness of the associated optimization. Researchers have developed approximation algorithms of varying degrees of sophistication for k-means, k-medians, and more recently also for Bregman clustering [2]. However, there seem to be no approximation algorithms for Bregman co- and tensor clustering. In this paper we derive the first (to our knowledge) guaranteed methods for these increasingly important clustering settings. Going beyond Bregman divergences, we also prove an approximation factor for tensor clustering with arbitrary separable metrics. Through extensive experiments we evaluate the characteristics of our method, and show that it also has practical impact.

cs.LG cs.AI cs.CV cs.GT cs.MA cs.NE quant-ph

10.1088/1751-8113/42/44/445303

0812.0743

http://arxiv.org/abs/0812.0743v2

2009-10-10T09:10:36Z

2008-12-03T15:46:03Z

A Novel Clustering Algorithm Based on Quantum Games

Enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum game with the problem of data clustering, and then develop a quantum-game-based clustering algorithm, in which data points in a dataset are considered as players who can make decisions and implement quantum strategies in quantum games. After each round of a quantum game, each player's expected payoff is calculated. Later, he uses a link-removing-and-rewiring (LRR) function to change his neighbors and adjust the strength of links connecting to them in order to maximize his payoff. Further, algorithms are discussed and analyzed in two cases of strategies, two payoff matrixes and two LRR functions. Consequently, the simulation results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the clustering algorithms have fast rates of convergence. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.

cs.LG cs.CC

0812.0933

http://arxiv.org/pdf/0812.0933v1

2008-12-04T13:34:26Z

2008-12-04T13:34:26Z

Decision trees are PAC-learnable from most product distributions: a smoothed analysis

We consider the problem of PAC-learning decision trees, i.e., learning a decision tree over the n-dimensional hypercube from independent random labeled examples. Despite significant effort, no polynomial-time algorithm is known for learning polynomial-sized decision trees (even trees of any super-constant size), even when examples are assumed to be drawn from the uniform distribution on {0,1}^n. We give an algorithm that learns arbitrary polynomial-sized decision trees for {\em most product distributions}. In particular, consider a random product distribution where the bias of each bit is chosen independently and uniformly from, say, [.49,.51]. Then with high probability over the parameters of the product distribution and the random examples drawn from it, the algorithm will learn any tree. More generally, in the spirit of smoothed analysis, we consider an arbitrary product distribution whose parameters are specified only up to a [-c,c] accuracy (perturbation), for an arbitrarily small positive constant c.

cs.IR cs.LG

10.1186/gb-2008-9-s2-s11

0812.1029

http://arxiv.org/abs/0812.1029v1

2008-12-04T21:37:35Z

2008-12-04T21:37:35Z

Uncovering protein interaction in abstracts and text using a novel linear model and word proximity networks

We participated in three of the protein-protein interaction subtasks of the Second BioCreative Challenge: classification of abstracts relevant for protein-protein interaction (IAS), discovery of protein pairs (IPS) and text passages characterizing protein interaction (ISS) in full text documents. We approached the abstract classification task with a novel, lightweight linear model inspired by spam-detection techniques, as well as an uncertainty-based integration scheme. We also used a Support Vector Machine and the Singular Value Decomposition on the same features for comparison purposes. Our approach to the full text subtasks (protein pair and passage identification) includes a feature expansion method based on word-proximity networks. Our approach to the abstract classification task (IAS) was among the top submissions for this task in terms of the measures of performance used in the challenge evaluation (accuracy, F-score and AUC). We also report on a web-tool we produced using our approach: the Protein Interaction Abstract Relevance Evaluator (PIARE). Our approach to the full text tasks resulted in one of the highest recall rates as well as mean reciprocal rank of correct passages. Our approach to abstract classification shows that a simple linear model, using relatively few features, is capable of generalizing and uncovering the conceptual nature of protein-protein interaction from the bibliome. Since the novel approach is based on a very lightweight linear model, it can be easily ported and applied to similar problems. In full text problems, the expansion of word features with word-proximity networks is shown to be useful, though the need for some improvements is discussed.

cs.MM cs.LG

0812.1244

http://arxiv.org/pdf/0812.1244v1

2008-12-05T23:14:41Z

2008-12-05T23:14:41Z

Decomposition Principles and Online Learning in Cross-Layer Optimization for Delay-Sensitive Applications

In this paper, we propose a general cross-layer optimization framework in which we explicitly consider both the heterogeneous and dynamically changing characteristics of delay-sensitive applications and the underlying time-varying network conditions. We consider both the independently decodable data units (DUs, e.g. packets) and the interdependent DUs whose dependencies are captured by a directed acyclic graph (DAG). We first formulate the cross-layer design as a non-linear constrained optimization problem by assuming complete knowledge of the application characteristics and the underlying network conditions. The constrained cross-layer optimization is decomposed into several cross-layer optimization subproblems for each DU and two master problems. The proposed decomposition method determines the necessary message exchanges between layers for achieving the optimal cross-layer solution. However, the attributes (e.g. distortion impact, delay deadline etc) of future DUs as well as the network conditions are often unknown in the considered real-time applications. The impact of current cross-layer actions on the future DUs can be characterized by a state-value function in the Markov decision process (MDP) framework. Based on the dynamic programming solution to the MDP, we develop a low-complexity cross-layer optimization algorithm using online learning for each DU transmission. This online algorithm can be implemented in real-time in order to cope with unknown source characteristics, network dynamics and resource constraints. Our numerical results demonstrate the efficiency of the proposed online algorithm.

cs.LG

0812.1357

http://arxiv.org/pdf/0812.1357v1

2008-12-07T15:22:27Z

2008-12-07T15:22:27Z

A Novel Clustering Algorithm Based on Quantum Random Walk

The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum random walk (QRW) with the problem of data clustering, and develop two clustering algorithms based on the one dimensional QRW. Then, the probability distributions on the positions induced by QRW in these algorithms are investigated, which also indicates the possibility of obtaining better results. Consequently, the experimental results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the clustering algorithms are of fast rates of convergence. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.

cs.LG

0812.1869

http://arxiv.org/pdf/0812.1869v1

2008-12-10T09:00:40Z

2008-12-10T09:00:40Z

Convex Sparse Matrix Factorizations

We present a convex formulation of dictionary learning for sparse signal decomposition. Convexity is obtained by replacing the usual explicit upper bound on the dictionary size by a convex rank-reducing term similar to the trace norm. In particular, our formulation introduces an explicit trade-off between size and sparsity of the decomposition of rectangular matrices. Using a large set of synthetic examples, we compare the estimation abilities of the convex and non-convex approaches, showing that while the convex formulation has a single local minimum, this may lead in some cases to performance which is inferior to the local minima of the non-convex formulation.

cs.DS cs.GT cs.LG

0812.2291

http://arxiv.org/pdf/0812.2291v7

2013-06-03T21:03:36Z

2008-12-12T04:13:01Z

Characterizing Truthful Multi-Armed Bandit Mechanisms

We consider a multi-round auction setting motivated by pay-per-click auctions for Internet advertising. In each round the auctioneer selects an advertiser and shows her ad, which is then either clicked or not. An advertiser derives value from clicks; the value of a click is her private information. Initially, neither the auctioneer nor the advertisers have any information about the likelihood of clicks on the advertisements. The auctioneer's goal is to design a (dominant strategies) truthful mechanism that (approximately) maximizes the social welfare. If the advertisers bid their true private values, our problem is equivalent to the "multi-armed bandit problem", and thus can be viewed as a strategic version of the latter. In particular, for both problems the quality of an algorithm can be characterized by "regret", the difference in social welfare between the algorithm and the benchmark which always selects the same "best" advertisement. We investigate how the design of multi-armed bandit algorithms is affected by the restriction that the resulting mechanism must be truthful. We find that truthful mechanisms have certain strong structural properties -- essentially, they must separate exploration from exploitation -- and they incur much higher regret than the optimal multi-armed bandit algorithms. Moreover, we provide a truthful mechanism which (essentially) matches our lower bound on regret.

cs.CV cs.LG

0812.2574

http://arxiv.org/pdf/0812.2574v1

2008-12-13T19:09:03Z

2008-12-13T19:09:03Z

Feature Selection By KDDA For SVM-Based MultiView Face Recognition

Applications such as face recognition that deal with high-dimensional data need a mapping technique that introduces representation of low-dimensional features with enhanced discriminatory power and a proper classifier, able to classify those complex features. Most of traditional Linear Discriminant Analysis suffer from the disadvantage that their optimality criteria are not directly related to the classification ability of the obtained feature representation. Moreover, their classification accuracy is affected by the "small sample size" problem which is often encountered in FR tasks. In this short paper, we combine nonlinear kernel based mapping of data called KDDA with Support Vector machine classifier to deal with both of the shortcomings in an efficient and cost effective manner. The proposed here method is compared, in terms of classification accuracy, to other commonly used FR methods on UMIST face database. Results indicate that the performance of the proposed method is overall superior to those of traditional FR approaches, such as the Eigenfaces, Fisherfaces, and D-LDA methods and traditional linear classifiers.

cs.CV cs.LG

0812.2575

http://arxiv.org/pdf/0812.2575v1

2008-12-13T19:14:53Z

2008-12-13T19:14:53Z

Face Detection Using Adaboosted SVM-Based Component Classifier

Recently, Adaboost has been widely used to improve the accuracy of any given learning algorithm. In this paper we focus on designing an algorithm to employ combination of Adaboost with Support Vector Machine as weak component classifiers to be used in Face Detection Task. To obtain a set of effective SVM-weaklearner Classifier, this algorithm adaptively adjusts the kernel parameter in SVM instead of using a fixed one. Proposed combination outperforms in generalization in comparison with SVM on imbalanced classification problem. The proposed here method is compared, in terms of classification accuracy, to other commonly used Adaboost methods, such as Decision Trees and Neural Networks, on CMU+MIT face database. Results indicate that the performance of the proposed method is overall superior to previous Adaboost approaches.

cs.LG

0812.3145

http://arxiv.org/pdf/0812.3145v2

2008-12-16T21:05:28Z

2008-12-16T20:41:06Z

Binary Classification Based on Potentials

We introduce a simple and computationally trivial method for binary classification based on the evaluation of potential functions. We demonstrate that despite the conceptual and computational simplicity of the method its performance can match or exceed that of standard Support Vector Machine methods.

cs.LG cs.CG

0812.3147

http://arxiv.org/pdf/0812.3147v1

2008-12-16T20:58:24Z

2008-12-16T20:58:24Z

Comparison of Binary Classification Based on Signed Distance Functions with Support Vector Machines

We investigate the performance of a simple signed distance function (SDF) based method by direct comparison with standard SVM packages, as well as K-nearest neighbor and RBFN methods. We present experimental results comparing the SDF approach with other classifiers on both synthetic geometric problems and five benchmark clinical microarray data sets. On both geometric problems and microarray data sets, the non-optimized SDF based classifiers perform just as well or slightly better than well-developed, standard SVM methods. These results demonstrate the potential accuracy of SDF-based methods on some types of problems.

quant-ph cs.LG

0812.3429

http://arxiv.org/pdf/0812.3429v3

2012-03-15T03:31:18Z

2008-12-17T22:46:18Z

Quantum Predictive Learning and Communication Complexity with Single Input

We define a new model of quantum learning that we call Predictive Quantum (PQ). This is a quantum analogue of PAC, where during the testing phase the student is only required to answer a polynomial number of testing queries. We demonstrate a relational concept class that is efficiently learnable in PQ, while in any "reasonable" classical model exponential amount of training data would be required. This is the first unconditional separation between quantum and classical learning. We show that our separation is the best possible in several ways; in particular, there is no analogous result for a functional class, as well as for several weaker versions of quantum learning. In order to demonstrate tightness of our separation we consider a special case of one-way communication that we call single-input mode, where Bob receives no input. Somewhat surprisingly, this setting becomes nontrivial when relational communication tasks are considered. In particular, any problem with two-sided input can be transformed into a single-input relational problem of equal classical one-way cost. We show that the situation is different in the quantum case, where the same transformation can make the communication complexity exponentially larger. This happens if and only if the original problem has exponential gap between quantum and classical one-way communication costs. We believe that these auxiliary results might be of independent interest.

cs.LG

0812.3465

http://arxiv.org/pdf/0812.3465v2

2010-02-24T15:54:49Z

2008-12-18T07:59:33Z

Linearly Parameterized Bandits

We consider bandit problems involving a large (possibly infinite) collection of arms, in which the expected reward of each arm is a linear function of an $r$-dimensional random vector $\mathbf{Z} \in \mathbb{R}^r$, where $r \geq 2$. The objective is to minimize the cumulative regret and Bayes risk. When the set of arms corresponds to the unit sphere, we prove that the regret and Bayes risk is of order $\Theta(r \sqrt{T})$, by establishing a lower bound for an arbitrary policy, and showing that a matching upper bound is obtained through a policy that alternates between exploration and exploitation phases. The phase-based policy is also shown to be effective if the set of arms satisfies a strong convexity condition. For the case of a general set of arms, we describe a near-optimal policy whose regret and Bayes risk admit upper bounds of the form $O(r \sqrt{T} \log^{3/2} T)$.

cs.LG cs.AI

0812.4044

http://arxiv.org/pdf/0812.4044v3

2016-04-03T21:41:38Z

2008-12-21T17:45:27Z

The Offset Tree for Learning with Partial Labels

We present an algorithm, called the Offset Tree, for learning to make decisions in situations where the payoff of only one choice is observed, rather than all choices. The algorithm reduces this setting to binary classification, allowing one to reuse of any existing, fully supervised binary classification algorithm in this partial information setting. We show that the Offset Tree is an optimal reduction to binary classification. In particular, it has regret at most $(k-1)$ times the regret of the binary classifier it uses (where $k$ is the number of choices), and no reduction to binary classification can do better. This reduction is also computationally optimal, both at training and test time, requiring just $O(\log_2 k)$ work to train on an example or make a prediction. Experiments with the Offset Tree show that it generally performs better than several alternative approaches.

cs.LG cs.AI

10.1109/TNN.2010.2095882

0812.4235

http://arxiv.org/abs/0812.4235v2

2010-01-11T15:37:43Z

2008-12-22T16:34:39Z

Client-server multi-task learning from distributed datasets

A client-server architecture to simultaneously solve multiple learning tasks from distributed datasets is described. In such architecture, each client is associated with an individual learning task and the associated dataset of examples. The goal of the architecture is to perform information fusion from multiple datasets while preserving privacy of individual data. The role of the server is to collect data in real-time from the clients and codify the information in a common database. The information coded in this database can be used by all the clients to solve their individual learning task, so that each client can exploit the informative content of all the datasets without actually having access to private data of others. The proposed algorithmic framework, based on regularization theory and kernel methods, uses a suitable class of mixed effect kernels. The new method is illustrated through a simulated music recommendation system.

cs.CL cs.AI cs.LG

10.1613/jair.2693

0812.4446

http://arxiv.org/abs/0812.4446v1

2008-12-23T20:08:53Z

2008-12-23T20:08:53Z

The Latent Relation Mapping Engine: Algorithm and Experiments

Many AI researchers and cognitive scientists have argued that analogy is the core of cognition. The most influential work on computational modeling of analogy-making is Structure Mapping Theory (SMT) and its implementation in the Structure Mapping Engine (SME). A limitation of SME is the requirement for complex hand-coded representations. We introduce the Latent Relation Mapping Engine (LRME), which combines ideas from SME and Latent Relational Analysis (LRA) in order to remove the requirement for hand-coded representations. LRME builds analogical mappings between lists of words, using a large corpus of raw text to automatically discover the semantic relations among the words. We evaluate LRME on a set of twenty analogical mapping problems, ten based on scientific analogies and ten based on common metaphors. LRME achieves human-level performance on the twenty problems. We compare LRME with a variety of alternative approaches and find that they are not able to reach the same level of performance.

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

0812.4580

http://arxiv.org/pdf/0812.4580v1

2008-12-25T00:27:22Z

2008-12-25T00:27:22Z

Feature Markov Decision Processes

General purpose intelligent learning agents cycle through (complex,non-MDP) sequences of observations, actions, and rewards. On the other hand, reinforcement learning is well-developed for small finite state Markov Decision Processes (MDPs). So far it is an art performed by human designers to extract the right state representation out of the bare observations, i.e. to reduce the agent setup to the MDP framework. Before we can think of mechanizing this search for suitable MDPs, we need a formal objective criterion. The main contribution of this article is to develop such a criterion. I also integrate the various parts into one learning algorithm. Extensions to more realistic dynamic Bayesian networks are developed in a companion article.

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

0812.4581

http://arxiv.org/pdf/0812.4581v1

2008-12-25T00:32:45Z

2008-12-25T00:32:45Z

Feature Dynamic Bayesian Networks

Feature Markov Decision Processes (PhiMDPs) are well-suited for learning agents in general environments. Nevertheless, unstructured (Phi)MDPs are limited to relatively simple environments. Structured MDPs like Dynamic Bayesian Networks (DBNs) are used for large-scale real-world problems. In this article I extend PhiMDP to PhiDBN. The primary contribution is to derive a cost criterion that allows to automatically extract the most relevant features from the environment, leading to the "best" DBN representation. I discuss all building blocks required for a complete general learning algorithm.

cs.LG

0812.4952

http://arxiv.org/pdf/0812.4952v4

2009-05-20T17:40:23Z

2008-12-29T18:29:08Z

Importance Weighted Active Learning

We present a practical and statistically consistent scheme for actively learning binary classifiers under general loss functions. Our algorithm uses importance weighting to correct sampling bias, and by controlling the variance, we are able to give rigorous label complexity bounds for the learning process. Experiments on passively labeled data show that this approach reduces the label complexity required to achieve good predictive performance on many learning problems.

cs.LG cs.AI cs.CV physics.soc-ph

0812.5032

http://arxiv.org/pdf/0812.5032v1

2008-12-30T08:30:27Z

2008-12-30T08:30:27Z

A New Clustering Algorithm Based Upon Flocking On Complex Network

We have proposed a model based upon flocking on a complex network, and then developed two clustering algorithms on the basis of it. In the algorithms, firstly a \textit{k}-nearest neighbor (knn) graph as a weighted and directed graph is produced among all data points in a dataset each of which is regarded as an agent who can move in space, and then a time-varying complex network is created by adding long-range links for each data point. Furthermore, each data point is not only acted by its \textit{k} nearest neighbors but also \textit{r} long-range neighbors through fields established in space by them together, so it will take a step along the direction of the vector sum of all fields. It is more important that these long-range links provides some hidden information for each data point when it moves and at the same time accelerate its speed converging to a center. As they move in space according to the proposed model, data points that belong to the same class are located at a same position gradually, whereas those that belong to different classes are away from one another. Consequently, the experimental results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the rates of convergence of clustering algorithms are fast enough. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.

cs.LG cs.CV cs.GT nlin.AO

10.1016/j.eswa.2010.02.050

0812.5064

http://arxiv.org/abs/0812.5064v2

2010-03-19T13:30:08Z

2008-12-30T13:22:31Z

A Novel Clustering Algorithm Based Upon Games on Evolving Network

This paper introduces a model based upon games on an evolving network, and develops three clustering algorithms according to it. In the clustering algorithms, data points for clustering are regarded as players who can make decisions in games. On the network describing relationships among data points, an edge-removing-and-rewiring (ERR) function is employed to explore in a neighborhood of a data point, which removes edges connecting to neighbors with small payoffs, and creates new edges to neighbors with larger payoffs. As such, the connections among data points vary over time. During the evolution of network, some strategies are spread in the network. As a consequence, clusters are formed automatically, in which data points with the same evolutionarily stable strategy are collected as a cluster, so the number of evolutionarily stable strategies indicates the number of clusters. Moreover, the experimental results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the comparison with other algorithms also provides an indication of the effectiveness of the proposed algorithms.

cs.IT cs.LG math.IT

0901.0252

http://arxiv.org/pdf/0901.0252v1

2009-01-02T16:46:05Z

2009-01-02T16:46:05Z

MIMO decoding based on stochastic reconstruction from multiple projections

Least squares (LS) fitting is one of the most fundamental techniques in science and engineering. It is used to estimate parameters from multiple noisy observations. In many problems the parameters are known a-priori to be bounded integer valued, or they come from a finite set of values on an arbitrary finite lattice. In this case finding the closest vector becomes NP-Hard problem. In this paper we propose a novel algorithm, the Tomographic Least Squares Decoder (TLSD), that not only solves the ILS problem, better than other sub-optimal techniques, but also is capable of providing the a-posteriori probability distribution for each element in the solution vector. The algorithm is based on reconstruction of the vector from multiple two-dimensional projections. The projections are carefully chosen to provide low computational complexity. Unlike other iterative techniques, such as the belief propagation, the proposed algorithm has ensured convergence. We also provide simulated experiments comparing the algorithm to other sub-optimal algorithms.

cs.LG

0901.0753

http://arxiv.org/pdf/0901.0753v1

2009-01-07T04:36:58Z

2009-01-07T04:36:58Z

Distributed Preemption Decisions: Probabilistic Graphical Model, Algorithm and Near-Optimality

Cooperative decision making is a vision of future network management and control. Distributed connection preemption is an important example where nodes can make intelligent decisions on allocating resources and controlling traffic flows for multi-class service networks. A challenge is that nodal decisions are spatially dependent as traffic flows trespass multiple nodes in a network. Hence the performance-complexity trade-off becomes important, i.e., how accurate decisions are versus how much information is exchanged among nodes. Connection preemption is known to be NP-complete. Centralized preemption is optimal but computationally intractable. Decentralized preemption is computationally efficient but may result in a poor performance. This work investigates distributed preemption where nodes decide whether and which flows to preempt using only local information exchange with neighbors. We develop, based on the probabilistic graphical models, a near-optimal distributed algorithm. The algorithm is used by each node to make collectively near-optimal preemption decisions. We study trade-offs between near-optimal performance and complexity that corresponds to the amount of information-exchange of the distributed algorithm. The algorithm is validated by both analysis and simulation.

cs.LG cs.CV

0901.0760

http://arxiv.org/pdf/0901.0760v2

2009-12-09T07:18:30Z

2009-01-07T06:47:47Z

A Theoretical Analysis of Joint Manifolds

The emergence of low-cost sensor architectures for diverse modalities has made it possible to deploy sensor arrays that capture a single event from a large number of vantage points and using multiple modalities. In many scenarios, these sensors acquire very high-dimensional data such as audio signals, images, and video. To cope with such high-dimensional data, we typically rely on low-dimensional models. Manifold models provide a particularly powerful model that captures the structure of high-dimensional data when it is governed by a low-dimensional set of parameters. However, these models do not typically take into account dependencies among multiple sensors. We thus propose a new joint manifold framework for data ensembles that exploits such dependencies. We show that simple algorithms can exploit the joint manifold structure to improve their performance on standard signal processing applications. Additionally, recent results concerning dimensionality reduction for manifolds enable us to formulate a network-scalable data compression scheme that uses random projections of the sensed data. This scheme efficiently fuses the data from all sensors through the addition of such projections, regardless of the data modalities and dimensions.

cs.IT cs.LG math.IT

10.1109/TIT.2009.2015987

0901.1904

http://arxiv.org/abs/0901.1904v1

2009-01-13T22:55:52Z

2009-01-13T22:55:52Z

Joint universal lossy coding and identification of stationary mixing sources with general alphabets

We consider the problem of joint universal variable-rate lossy coding and identification for parametric classes of stationary $\beta$-mixing sources with general (Polish) alphabets. Compression performance is measured in terms of Lagrangians, while identification performance is measured by the variational distance between the true source and the estimated source. Provided that the sources are mixing at a sufficiently fast rate and satisfy certain smoothness and Vapnik-Chervonenkis learnability conditions, it is shown that, for bounded metric distortions, there exist universal schemes for joint lossy compression and identification whose Lagrangian redundancies converge to zero as $\sqrt{V_n \log n /n}$ as the block length $n$ tends to infinity, where $V_n$ is the Vapnik-Chervonenkis dimension of a certain class of decision regions defined by the $n$-dimensional marginal distributions of the sources; furthermore, for each $n$, the decoder can identify $n$-dimensional marginal of the active source up to a ball of radius $O(\sqrt{V_n\log n/n})$ in variational distance, eventually with probability one. The results are supplemented by several examples of parametric sources satisfying the regularity conditions.

cs.IT cs.LG math.IT

0901.1905

http://arxiv.org/pdf/0901.1905v2

2009-04-30T15:31:14Z

2009-01-13T23:03:26Z

Achievability results for statistical learning under communication constraints

The problem of statistical learning is to construct an accurate predictor of a random variable as a function of a correlated random variable on the basis of an i.i.d. training sample from their joint distribution. Allowable predictors are constrained to lie in some specified class, and the goal is to approach asymptotically the performance of the best predictor in the class. We consider two settings in which the learning agent only has access to rate-limited descriptions of the training data, and present information-theoretic bounds on the predictor performance achievable in the presence of these communication constraints. Our proofs do not assume any separation structure between compression and learning and rely on a new class of operational criteria specifically tailored to joint design of encoders and learning algorithms in rate-constrained settings.

cs.LG

0901.2376

http://arxiv.org/pdf/0901.2376v1

2009-01-16T01:00:39Z

2009-01-16T01:00:39Z

A Limit Theorem in Singular Regression Problem

In statistical problems, a set of parameterized probability distributions is used to estimate the true probability distribution. If Fisher information matrix at the true distribution is singular, then it has been left unknown what we can estimate about the true distribution from random samples. In this paper, we study a singular regression problem and prove a limit theorem which shows the relation between the singular regression problem and two birational invariants, a real log canonical threshold and a singular fluctuation. The obtained theorem has an important application to statistics, because it enables us to estimate the generalization error from the training error without any knowledge of the true probability distribution.

cs.LG stat.ML

0901.3150

http://arxiv.org/pdf/0901.3150v4

2009-09-17T09:26:46Z

2009-01-20T21:32:57Z

Matrix Completion from a Few Entries

Let M be a random (alpha n) x n matrix of rank r<<n, and assume that a uniformly random subset E of its entries is observed. We describe an efficient algorithm that reconstructs M from |E| = O(rn) observed entries with relative root mean square error RMSE <= C(rn/|E|)^0.5 . Further, if r=O(1), M can be reconstructed exactly from |E| = O(n log(n)) entries. These results apply beyond random matrices to general low-rank incoherent matrices. This settles (in the case of bounded rank) a question left open by Candes and Recht and improves over the guarantees for their reconstruction algorithm. The complexity of our algorithm is O(|E|r log(n)), which opens the way to its use for massive data sets. In the process of proving these statements, we obtain a generalization of a celebrated result by Friedman-Kahn-Szemeredi and Feige-Ofek on the spectrum of sparse random matrices.

cs.LG stat.ML

0901.3202

http://arxiv.org/pdf/0901.3202v1

2009-01-21T08:05:19Z

2009-01-21T08:05:19Z

Model-Consistent Sparse Estimation through the Bootstrap

We consider the least-square linear regression problem with regularization by the $\ell^1$-norm, a problem usually referred to as the Lasso. In this paper, we first present a detailed asymptotic analysis of model consistency of the Lasso in low-dimensional settings. For various decays of the regularization parameter, we compute asymptotic equivalents of the probability of correct model selection. For a specific rate decay, we show that the Lasso selects all the variables that should enter the model with probability tending to one exponentially fast, while it selects all other variables with strictly positive probability. We show that this property implies that if we run the Lasso for several bootstrapped replications of a given sample, then intersecting the supports of the Lasso bootstrap estimates leads to consistent model selection. This novel variable selection procedure, referred to as the Bolasso, is extended to high-dimensional settings by a provably consistent two-step procedure.

cs.LG cs.CV

10.1109/TPAMI.2010.47

0901.3590

On the Dual Formulation of Boosting Algorithms

We study boosting algorithms from a new perspective. We show that the Lagrange dual problems of AdaBoost, LogitBoost and soft-margin LPBoost with generalized hinge loss are all entropy maximization problems. By looking at the dual problems of these boosting algorithms, we show that the success of boosting algorithms can be understood in terms of maintaining a better margin distribution by maximizing margins and at the same time controlling the margin variance.We also theoretically prove that, approximately, AdaBoost maximizes the average margin, instead of the minimum margin. The duality formulation also enables us to develop column generation based optimization algorithms, which are totally corrective. We show that they exhibit almost identical classification results to that of standard stage-wise additive boosting algorithms but with much faster convergence rates. Therefore fewer weak classifiers are needed to build the ensemble using our proposed optimization technique.

cs.LG

10.1075/is.12.1.05fon

0901.4012

http://arxiv.org/abs/0901.4012v3

2009-11-28T20:11:11Z

2009-01-26T15:12:13Z

Cross-situational and supervised learning in the emergence of communication

Scenarios for the emergence or bootstrap of a lexicon involve the repeated interaction between at least two agents who must reach a consensus on how to name N objects using H words. Here we consider minimal models of two types of learning algorithms: cross-situational learning, in which the individuals determine the meaning of a word by looking for something in common across all observed uses of that word, and supervised operant conditioning learning, in which there is strong feedback between individuals about the intended meaning of the words. Despite the stark differences between these learning schemes, we show that they yield the same communication accuracy in the realistic limits of large N and H, which coincides with the result of the classical occupancy problem of randomly assigning N objects to H words.

math.ST cs.LG stat.ML stat.TH

0901.4137

http://arxiv.org/pdf/0901.4137v1

2009-01-26T23:05:06Z

2009-01-26T23:05:06Z

Practical Robust Estimators for the Imprecise Dirichlet Model

Walley's Imprecise Dirichlet Model (IDM) for categorical i.i.d. data extends the classical Dirichlet model to a set of priors. It overcomes several fundamental problems which other approaches to uncertainty suffer from. Yet, to be useful in practice, one needs efficient ways for computing the imprecise=robust sets or intervals. The main objective of this work is to derive exact, conservative, and approximate, robust and credible interval estimates under the IDM for a large class of statistical estimators, including the entropy and mutual information.

cs.IT cs.LG math.IT stat.CO

10.1109/ISIT.2009.5205777

0901.4192

http://arxiv.org/abs/0901.4192v3

2009-07-04T03:25:13Z

2009-01-27T08:24:57Z

Fixing Convergence of Gaussian Belief Propagation

Gaussian belief propagation (GaBP) is an iterative message-passing algorithm for inference in Gaussian graphical models. It is known that when GaBP converges it converges to the correct MAP estimate of the Gaussian random vector and simple sufficient conditions for its convergence have been established. In this paper we develop a double-loop algorithm for forcing convergence of GaBP. Our method computes the correct MAP estimate even in cases where standard GaBP would not have converged. We further extend this construction to compute least-squares solutions of over-constrained linear systems. We believe that our construction has numerous applications, since the GaBP algorithm is linked to solution of linear systems of equations, which is a fundamental problem in computer science and engineering. As a case study, we discuss the linear detection problem. We show that using our new construction, we are able to force convergence of Montanari's linear detection algorithm, in cases where it would originally fail. As a consequence, we are able to increase significantly the number of users that can transmit concurrently.

cs.LG cs.DM

0901.4876

http://arxiv.org/pdf/0901.4876v1

2009-01-30T12:44:29Z

2009-01-30T12:44:29Z

Non-Confluent NLC Graph Grammar Inference by Compressing Disjoint Subgraphs

Grammar inference deals with determining (preferable simple) models/grammars consistent with a set of observations. There is a large body of research on grammar inference within the theory of formal languages. However, there is surprisingly little known on grammar inference for graph grammars. In this paper we take a further step in this direction and work within the framework of node label controlled (NLC) graph grammars. Specifically, we characterize, given a set of disjoint and isomorphic subgraphs of a graph $G$, whether or not there is a NLC graph grammar rule which can generate these subgraphs to obtain $G$. This generalizes previous results by assuming that the set of isomorphic subgraphs is disjoint instead of non-touching. This leads naturally to consider the more involved ``non-confluent'' graph grammar rules.

stat.ML cs.LG

0902.0392

http://arxiv.org/pdf/0902.0392v2

2011-09-21T08:13:36Z

2009-02-02T22:37:23Z

Tree Exploration for Bayesian RL Exploration

Research in reinforcement learning has produced algorithms for optimal decision making under uncertainty that fall within two main types. The first employs a Bayesian framework, where optimality improves with increased computational time. This is because the resulting planning task takes the form of a dynamic programming problem on a belief tree with an infinite number of states. The second type employs relatively simple algorithm which are shown to suffer small regret within a distribution-free framework. This paper presents a lower bound and a high probability upper bound on the optimal value function for the nodes in the Bayesian belief tree, which are analogous to similar bounds in POMDPs. The bounds are then used to create more efficient strategies for exploring the tree. The resulting algorithms are compared with the distribution-free algorithm UCB1, as well as a simpler baseline algorithm on multi-armed bandit problems.

cs.AI cs.LG

0902.1227

http://arxiv.org/pdf/0902.1227v2

2009-12-11T06:18:30Z

2009-02-07T07:50:02Z

Discovering general partial orders in event streams

Frequent episode discovery is a popular framework for pattern discovery in event streams. An episode is a partially ordered set of nodes with each node associated with an event type. Efficient (and separate) algorithms exist for episode discovery when the associated partial order is total (serial episode) and trivial (parallel episode). In this paper, we propose efficient algorithms for discovering frequent episodes with general partial orders. These algorithms can be easily specialized to discover serial or parallel episodes. Also, the algorithms are flexible enough to be specialized for mining in the space of certain interesting subclasses of partial orders. We point out that there is an inherent combinatorial explosion in frequent partial order mining and most importantly, frequency alone is not a sufficient measure of interestingness. We propose a new interestingness measure for general partial order episodes and a discovery method based on this measure, for filtering out uninteresting partial orders. Simulations demonstrate the effectiveness of our algorithms.

cs.LG

0902.1258

http://arxiv.org/pdf/0902.1258v1

2009-02-07T18:01:09Z

2009-02-07T18:01:09Z

Extraction de concepts sous contraintes dans des donn\'ees d'expression de g\`enes

In this paper, we propose a technique to extract constrained formal concepts.

cs.LG

0902.1259

http://arxiv.org/pdf/0902.1259v1

2009-02-07T18:01:56Z

2009-02-07T18:01:56Z

Database Transposition for Constrained (Closed) Pattern Mining

Recently, different works proposed a new way to mine patterns in databases with pathological size. For example, experiments in genome biology usually provide databases with thousands of attributes (genes) but only tens of objects (experiments). In this case, mining the "transposed" database runs through a smaller search space, and the Galois connection allows to infer the closed patterns of the original database. We focus here on constrained pattern mining for those unusual databases and give a theoretical framework for database and constraint transposition. We discuss the properties of constraint transposition and look into classical constraints. We then address the problem of generating the closed patterns of the original database satisfying the constraint, starting from those mined in the "transposed" database. Finally, we show how to generate all the patterns satisfying the constraint from the closed ones.

cs.LG

0902.1284

http://arxiv.org/pdf/0902.1284v2

2009-06-02T16:23:28Z

2009-02-08T02:30:06Z

Multi-Label Prediction via Compressed Sensing

We consider multi-label prediction problems with large output spaces under the assumption of output sparsity -- that the target (label) vectors have small support. We develop a general theory for a variant of the popular error correcting output code scheme, using ideas from compressed sensing for exploiting this sparsity. The method can be regarded as a simple reduction from multi-label regression problems to binary regression problems. We show that the number of subproblems need only be logarithmic in the total number of possible labels, making this approach radically more efficient than others. We also state and prove robustness guarantees for this method in the form of regret transform bounds (in general), and also provide a more detailed analysis for the linear prediction setting.

cs.MA cs.LG

0902.2751

http://arxiv.org/pdf/0902.2751v4

2009-03-01T10:35:34Z

2009-02-16T18:39:53Z

Object Classification by means of Multi-Feature Concept Learning in a Multi Expert-Agent System

Classification of some objects in classes of concepts is an essential and even breathtaking task in many applications. A solution is discussed here based on Multi-Agent systems. A kernel of some expert agents in several classes is to consult a central agent decide among the classification problem of a certain object. This kernel is moderated with the center agent, trying to manage the querying agents for any decision problem by means of a data-header like feature set. Agents have cooperation among concepts related to the classes of this classification decision-making; and may affect on each others' results on a certain query object in a multi-agent learning approach. This leads to an online feature learning via the consulting trend. The performance is discussed to be much better in comparison to some other prior trends while system's message passing overload is decreased to less agents and the expertism helps the performance and operability of system win the comparison.

cs.AI cs.LG

0902.3176

http://arxiv.org/pdf/0902.3176v4

2010-02-03T15:03:58Z

2009-02-18T16:01:24Z

Error-Correcting Tournaments

We present a family of pairwise tournaments reducing $k$-class classification to binary classification. These reductions are provably robust against a constant fraction of binary errors. The results improve on the PECOC construction \cite{SECOC} with an exponential improvement in computation, from $O(k)$ to $O(\log_2 k)$, and the removal of a square root in the regret dependence, matching the best possible computation and regret up to a constant.

cs.LG cs.DM cs.DS

0902.3223

http://arxiv.org/pdf/0902.3223v1

2009-02-18T19:12:59Z

2009-02-18T19:12:59Z

An Exact Algorithm for the Stratification Problem with Proportional Allocation

We report a new optimal resolution for the statistical stratification problem under proportional sampling allocation among strata. Consider a finite population of N units, a random sample of n units selected from this population and a number L of strata. Thus, we have to define which units belong to each stratum so as to minimize the variance of a total estimator for one desired variable of interest in each stratum,and consequently reduce the overall variance for such quantity. In order to solve this problem, an exact algorithm based on the concept of minimal path in a graph is proposed and assessed. Computational results using real data from IBGE (Brazilian Central Statistical Office) are provided.

cs.LG

0902.3373

http://arxiv.org/pdf/0902.3373v1

2009-02-19T13:47:53Z

2009-02-19T13:47:53Z

Learning rules from multisource data for cardiac monitoring

This paper formalises the concept of learning symbolic rules from multisource data in a cardiac monitoring context. Our sources, electrocardiograms and arterial blood pressure measures, describe cardiac behaviours from different viewpoints. To learn interpretable rules, we use an Inductive Logic Programming (ILP) method. We develop an original strategy to cope with the dimensionality issues caused by using this ILP technique on a rich multisource language. The results show that our method greatly improves the feasibility and the efficiency of the process while staying accurate. They also confirm the benefits of using multiple sources to improve the diagnosis of cardiac arrhythmias.

cs.LG cs.AI

0902.3430

http://arxiv.org/pdf/0902.3430v3

2023-11-30T22:47:15Z

2009-02-19T18:42:16Z

Domain Adaptation: Learning Bounds and Algorithms

This paper addresses the general problem of domain adaptation which arises in a variety of applications where the distribution of the labeled sample available somewhat differs from that of the test data. Building on previous work by Ben-David et al. (2007), we introduce a novel distance between distributions, discrepancy distance, that is tailored to adaptation problems with arbitrary loss functions. We give Rademacher complexity bounds for estimating the discrepancy distance from finite samples for different loss functions. Using this distance, we derive novel generalization bounds for domain adaptation for a wide family of loss functions. We also present a series of novel adaptation bounds for large classes of regularization-based algorithms, including support vector machines and kernel ridge regression based on the empirical discrepancy. This motivates our analysis of the problem of minimizing the empirical discrepancy for various loss functions for which we also give novel algorithms. We report the results of preliminary experiments that demonstrate the benefits of our discrepancy minimization algorithms for domain adaptation.

stat.ML cs.LG math.ST stat.TH

0902.3526

http://arxiv.org/pdf/0902.3526v2

2009-03-27T14:50:53Z

2009-02-20T07:39:13Z

Online Multi-task Learning with Hard Constraints

We discuss multi-task online learning when a decision maker has to deal simultaneously with M tasks. The tasks are related, which is modeled by imposing that the M-tuple of actions taken by the decision maker needs to satisfy certain constraints. We give natural examples of such restrictions and then discuss a general class of tractable constraints, for which we introduce computationally efficient ways of selecting actions, essentially by reducing to an on-line shortest path problem. We briefly discuss "tracking" and "bandit" versions of the problem and extend the model in various ways, including non-additive global losses and uncountably infinite sets of tasks.

cs.LG

0902.3846

http://arxiv.org/pdf/0902.3846v1

2009-02-23T04:05:48Z

2009-02-23T04:05:48Z

Uniqueness of Low-Rank Matrix Completion by Rigidity Theory

The problem of completing a low-rank matrix from a subset of its entries is often encountered in the analysis of incomplete data sets exhibiting an underlying factor model with applications in collaborative filtering, computer vision and control. Most recent work had been focused on constructing efficient algorithms for exact or approximate recovery of the missing matrix entries and proving lower bounds for the number of known entries that guarantee a successful recovery with high probability. A related problem from both the mathematical and algorithmic point of view is the distance geometry problem of realizing points in a Euclidean space from a given subset of their pairwise distances. Rigidity theory answers basic questions regarding the uniqueness of the realization satisfying a given partial set of distances. We observe that basic ideas and tools of rigidity theory can be adapted to determine uniqueness of low-rank matrix completion, where inner products play the role that distances play in rigidity theory. This observation leads to an efficient randomized algorithm for testing both local and global unique completion. Crucial to our analysis is a new matrix, which we call the completion matrix, that serves as the analogue of the rigidity matrix.

cs.LG

0902.4127

http://arxiv.org/pdf/0902.4127v2

2009-03-23T16:28:41Z

2009-02-24T11:47:03Z

Prediction with expert evaluators' advice

We introduce a new protocol for prediction with expert advice in which each expert evaluates the learner's and his own performance using a loss function that may change over time and may be different from the loss functions used by the other experts. The learner's goal is to perform better or not much worse than each expert, as evaluated by that expert, for all experts simultaneously. If the loss functions used by the experts are all proper scoring rules and all mixable, we show that the defensive forecasting algorithm enjoys the same performance guarantee as that attainable by the Aggregating Algorithm in the standard setting and known to be optimal. This result is also applied to the case of "specialist" (or "sleeping") experts. In this case, the defensive forecasting algorithm reduces to a simple modification of the Aggregating Algorithm.

cs.LG

0902.4228

http://arxiv.org/pdf/0902.4228v1

2009-02-24T20:38:32Z

2009-02-24T20:38:32Z

Multiplicative updates For Non-Negative Kernel SVM

We present multiplicative updates for solving hard and soft margin support vector machines (SVM) with non-negative kernels. They follow as a natural extension of the updates for non-negative matrix factorization. No additional param- eter setting, such as choosing learning, rate is required. Ex- periments demonstrate rapid convergence to good classifiers. We analyze the rates of asymptotic convergence of the up- dates and establish tight bounds. We test the performance on several datasets using various non-negative kernels and report equivalent generalization errors to that of a standard SVM.

cs.LG cs.IT math.IT

0903.0064

http://arxiv.org/pdf/0903.0064v2

2009-04-19T04:18:30Z

2009-02-28T11:17:12Z

Manipulation Robustness of Collaborative Filtering Systems

A collaborative filtering system recommends to users products that similar users like. Collaborative filtering systems influence purchase decisions, and hence have become targets of manipulation by unscrupulous vendors. We provide theoretical and empirical results demonstrating that while common nearest neighbor algorithms, which are widely used in commercial systems, can be highly susceptible to manipulation, two classes of collaborative filtering algorithms which we refer to as linear and asymptotically linear are relatively robust. These results provide guidance for the design of future collaborative filtering systems.

cs.LG

0903.1125

http://arxiv.org/pdf/0903.1125v1

2009-03-05T22:39:46Z

2009-03-05T22:39:46Z

Efficient Human Computation

Collecting large labeled data sets is a laborious and expensive task, whose scaling up requires division of the labeling workload between many teachers. When the number of classes is large, miscorrespondences between the labels given by the different teachers are likely to occur, which, in the extreme case, may reach total inconsistency. In this paper we describe how globally consistent labels can be obtained, despite the absence of teacher coordination, and discuss the possible efficiency of this process in terms of human labor. We define a notion of label efficiency, measuring the ratio between the number of globally consistent labels obtained and the number of labels provided by distributed teachers. We show that the efficiency depends critically on the ratio alpha between the number of data instances seen by a single teacher, and the number of classes. We suggest several algorithms for the distributed labeling problem, and analyze their efficiency as a function of alpha. In addition, we provide an upper bound on label efficiency for the case of completely uncoordinated teachers, and show that efficiency approaches 0 as the ratio between the number of labels each teacher provides and the number of classes drops (i.e. alpha goes to 0).

cs.MA cs.GT cs.LG

0903.2282

http://arxiv.org/pdf/0903.2282v1

2009-03-12T21:49:36Z

2009-03-12T21:49:36Z

Multiagent Learning in Large Anonymous Games

In large systems, it is important for agents to learn to act effectively, but sophisticated multi-agent learning algorithms generally do not scale. An alternative approach is to find restricted classes of games where simple, efficient algorithms converge. It is shown that stage learning efficiently converges to Nash equilibria in large anonymous games if best-reply dynamics converge. Two features are identified that improve convergence. First, rather than making learning more difficult, more agents are actually beneficial in many settings. Second, providing agents with statistical information about the behavior of others can significantly reduce the number of observations needed.

0903.2299

http://arxiv.org/pdf/0903.2299v3

2013-07-08T15:17:20Z

2009-03-13T13:47:03Z

Differential Contrastive Divergence

This paper has been retracted.

cs.LG cs.AI

0903.2851

http://arxiv.org/pdf/0903.2851v2

2010-01-18T23:58:51Z

2009-03-16T20:48:33Z

A parameter-free hedging algorithm

We study the problem of decision-theoretic online learning (DTOL). Motivated by practical applications, we focus on DTOL when the number of actions is very large. Previous algorithms for learning in this framework have a tunable learning rate parameter, and a barrier to using online-learning in practical applications is that it is not understood how to set this parameter optimally, particularly when the number of actions is large. In this paper, we offer a clean solution by proposing a novel and completely parameter-free algorithm for DTOL. We introduce a new notion of regret, which is more natural for applications with a large number of actions. We show that our algorithm achieves good performance with respect to this new notion of regret; in addition, it also achieves performance close to that of the best bounds achieved by previous algorithms with optimally-tuned parameters, according to previous notions of regret.

cs.LG cs.AI cs.CV

0903.2862

http://arxiv.org/pdf/0903.2862v2

2010-01-19T00:15:59Z

2009-03-16T21:26:55Z

Tracking using explanation-based modeling

We study the tracking problem, namely, estimating the hidden state of an object over time, from unreliable and noisy measurements. The standard framework for the tracking problem is the generative framework, which is the basis of solutions such as the Bayesian algorithm and its approximation, the particle filters. However, the problem with these solutions is that they are very sensitive to model mismatches. In this paper, motivated by online learning, we introduce a new framework -- an {\em explanatory} framework -- for tracking. We provide an efficient tracking algorithm for this framework. We provide experimental results comparing our algorithm to the Bayesian algorithm on simulated data. Our experiments show that when there are slight model mismatches, our algorithm vastly outperforms the Bayesian algorithm.

cs.LG

10.1134/S2070046609040013

0903.2870

http://arxiv.org/abs/0903.2870v2

2009-06-24T14:10:45Z

2009-03-16T22:52:06Z

On $p$-adic Classification

A $p$-adic modification of the split-LBG classification method is presented in which first clusterings and then cluster centers are computed which locally minimise an energy function. The outcome for a fixed dataset is independent of the prime number $p$ with finitely many exceptions. The methods are applied to the construction of $p$-adic classifiers in the context of learning.

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

0903.2890

http://arxiv.org/pdf/0903.2890v2

2010-05-28T08:33:21Z

2009-03-17T01:39:01Z

Kalman Filtering with Intermittent Observations: Weak Convergence to a Stationary Distribution

The paper studies the asymptotic behavior of Random Algebraic Riccati Equations (RARE) arising in Kalman filtering when the arrival of the observations is described by a Bernoulli i.i.d. process. We model the RARE as an order-preserving, strongly sublinear random dynamical system (RDS). Under a sufficient condition, stochastic boundedness, and using a limit-set dichotomy result for order-preserving, strongly sublinear RDS, we establish the asymptotic properties of the RARE: the sequence of random prediction error covariance matrices converges weakly to a unique invariant distribution, whose support exhibits fractal behavior. In particular, this weak convergence holds under broad conditions and even when the observations arrival rate is below the critical probability for mean stability. We apply the weak-Feller property of the Markov process governing the RARE to characterize the support of the limiting invariant distribution as the topological closure of a countable set of points, which, in general, is not dense in the set of positive semi-definite matrices. We use the explicit characterization of the support of the invariant distribution and the almost sure ergodicity of the sample paths to easily compute the moments of the invariant distribution. A one dimensional example illustrates that the support is a fractured subset of the non-negative reals with self-similarity properties.

cs.LG cs.AI

0903.2972

http://arxiv.org/pdf/0903.2972v3

2009-05-20T18:44:07Z

2009-03-17T14:24:13Z

Optimistic Simulated Exploration as an Incentive for Real Exploration

Many reinforcement learning exploration techniques are overly optimistic and try to explore every state. Such exploration is impossible in environments with the unlimited number of states. I propose to use simulated exploration with an optimistic model to discover promising paths for real exploration. This reduces the needs for the real exploration.

cs.MM cs.AI cs.LG

0903.3103

http://arxiv.org/pdf/0903.3103v1

2009-03-18T08:17:05Z

2009-03-18T08:17:05Z

Efficiently Learning a Detection Cascade with Sparse Eigenvectors

In this work, we first show that feature selection methods other than boosting can also be used for training an efficient object detector. In particular, we introduce Greedy Sparse Linear Discriminant Analysis (GSLDA) \cite{Moghaddam2007Fast} for its conceptual simplicity and computational efficiency; and slightly better detection performance is achieved compared with \cite{Viola2004Robust}. Moreover, we propose a new technique, termed Boosted Greedy Sparse Linear Discriminant Analysis (BGSLDA), to efficiently train a detection cascade. BGSLDA exploits the sample re-weighting property of boosting and the class-separability criterion of GSLDA.

cs.LG cs.IR

0903.3257

http://arxiv.org/pdf/0903.3257v1

2009-03-18T23:50:29Z

2009-03-18T23:50:29Z

A New Local Distance-Based Outlier Detection Approach for Scattered Real-World Data

Detecting outliers which are grossly different from or inconsistent with the remaining dataset is a major challenge in real-world KDD applications. Existing outlier detection methods are ineffective on scattered real-world datasets due to implicit data patterns and parameter setting issues. We define a novel "Local Distance-based Outlier Factor" (LDOF) to measure the {outlier-ness} of objects in scattered datasets which addresses these issues. LDOF uses the relative location of an object to its neighbours to determine the degree to which the object deviates from its neighbourhood. Properties of LDOF are theoretically analysed including LDOF's lower bound and its false-detection probability, as well as parameter settings. In order to facilitate parameter settings in real-world applications, we employ a top-n technique in our outlier detection approach, where only the objects with the highest LDOF values are regarded as outliers. Compared to conventional approaches (such as top-n KNN and top-n LOF), our method top-n LDOF is more effective at detecting outliers in scattered data. It is also easier to set parameters, since its performance is relatively stable over a large range of parameter values, as illustrated by experimental results on both real-world and synthetic datasets.

cs.LG stat.AP

0903.3329

http://arxiv.org/pdf/0903.3329v1

2009-03-19T13:44:35Z

2009-03-19T13:44:35Z

Optimal Policies Search for Sensor Management

This paper introduces a new approach to solve sensor management problems. Classically sensor management problems can be well formalized as Partially-Observed Markov Decision Processes (POMPD). The original approach developped here consists in deriving the optimal parameterized policy based on a stochastic gradient estimation. We assume in this work that it is possible to learn the optimal policy off-line (in simulation) using models of the environement and of the sensor(s). The learned policy can then be used to manage the sensor(s). In order to approximate the gradient in a stochastic context, we introduce a new method to approximate the gradient, based on Infinitesimal Perturbation Approximation (IPA). The effectiveness of this general framework is illustrated by the managing of an Electronically Scanned Array Radar. First simulations results are finally proposed.

cs.LG cs.IT math.IT math.PR

0903.3667

http://arxiv.org/pdf/0903.3667v5

2011-01-02T08:43:03Z

2009-03-21T14:16:05Z

How random are a learner's mistakes?

Given a random binary sequence $X^{(n)}$ of random variables, $X_{t},$ $t=1,2,...,n$, for instance, one that is generated by a Markov source (teacher) of order $k^{*}$ (each state represented by $k^{*}$ bits). Assume that the probability of the event $X_{t}=1$ is constant and denote it by $\beta$. Consider a learner which is based on a parametric model, for instance a Markov model of order $k$, who trains on a sequence $x^{(m)}$ which is randomly drawn by the teacher. Test the learner's performance by giving it a sequence $x^{(n)}$ (generated by the teacher) and check its predictions on every bit of $x^{(n)}.$ An error occurs at time $t$ if the learner's prediction $Y_{t}$ differs from the true bit value $X_{t}$. Denote by $\xi^{(n)}$ the sequence of errors where the error bit $\xi_{t}$ at time $t$ equals 1 or 0 according to whether the event of an error occurs or not, respectively. Consider the subsequence $\xi^{(\nu)}$ of $\xi^{(n)}$ which corresponds to the errors of predicting a 0, i.e., $\xi^{(\nu)}$ consists of the bits of $\xi^{(n)}$ only at times $t$ such that $Y_{t}=0.$ In this paper we compute an estimate on the deviation of the frequency of 1s of $\xi^{(\nu)}$ from $\beta$. The result shows that the level of randomness of $\xi^{(\nu)}$ decreases relative to an increase in the complexity of the learner.

cs.LG cs.AI

0903.4217

http://arxiv.org/pdf/0903.4217v2

2009-06-03T21:19:34Z

2009-03-25T00:28:44Z

Conditional Probability Tree Estimation Analysis and Algorithms

We consider the problem of estimating the conditional probability of a label in time $O(\log n)$, where $n$ is the number of possible labels. We analyze a natural reduction of this problem to a set of binary regression problems organized in a tree structure, proving a regret bound that scales with the depth of the tree. Motivated by this analysis, we propose the first online algorithm which provably constructs a logarithmic depth tree on the set of labels to solve this problem. We test the algorithm empirically, showing that it works succesfully on a dataset with roughly $10^6$ labels.

cs.DM cs.LG

0903.4527

http://arxiv.org/pdf/0903.4527v2

2009-11-14T05:41:45Z

2009-03-26T08:32:33Z

Graph polynomials and approximation of partition functions with Loopy Belief Propagation

The Bethe approximation, or loopy belief propagation algorithm is a successful method for approximating partition functions of probabilistic models associated with a graph. Chertkov and Chernyak derived an interesting formula called Loop Series Expansion, which is an expansion of the partition function. The main term of the series is the Bethe approximation while other terms are labeled by subgraphs called generalized loops. In our recent paper, we derive the loop series expansion in form of a polynomial with coefficients positive integers, and extend the result to the expansion of marginals. In this paper, we give more clear derivation for the results and discuss the properties of the polynomial which is introduced in the paper.

cs.LG cs.CG cs.CV math.OC stat.ML

0903.4817

http://arxiv.org/pdf/0903.4817v3

2012-10-25T23:47:12Z

2009-03-27T17:23:31Z

An Exponential Lower Bound on the Complexity of Regularization Paths

For a variety of regularized optimization problems in machine learning, algorithms computing the entire solution path have been developed recently. Most of these methods are quadratic programs that are parameterized by a single parameter, as for example the Support Vector Machine (SVM). Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but the entire path of solutions, making the selection of an optimal parameter much easier. It has been assumed that these piecewise linear solution paths have only linear complexity, i.e. linearly many bends. We prove that for the support vector machine this complexity can be exponential in the number of training points in the worst case. More strongly, we construct a single instance of n input points in d dimensions for an SVM such that at least \Theta(2^{n/2}) = \Theta(2^d) many distinct subsets of support vectors occur as the regularization parameter changes.

cs.LG cs.AI cs.CV

0903.4856

http://arxiv.org/pdf/0903.4856v1

2009-03-27T18:16:04Z

2009-03-27T18:16:04Z

A Combinatorial Algorithm to Compute Regularization Paths

For a wide variety of regularization methods, algorithms computing the entire solution path have been developed recently. Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but the entire path of solutions, making the selection of an optimal parameter much easier. Most of the currently used algorithms are not robust in the sense that they cannot deal with general or degenerate input. Here we present a new robust, generic method for parametric quadratic programming. Our algorithm directly applies to nearly all machine learning applications, where so far every application required its own different algorithm. We illustrate the usefulness of our method by applying it to a very low rank problem which could not be solved by existing path tracking methods, namely to compute part-worth values in choice based conjoint analysis, a popular technique from market research to estimate consumers preferences on a class of parameterized options.

cs.LG cond-mat.dis-nn physics.data-an

10.1016/j.physa.2009.08.030

0903.4860

http://arxiv.org/abs/0903.4860v1

2009-03-27T17:29:16Z

2009-03-27T17:29:16Z

Learning Multiple Belief Propagation Fixed Points for Real Time Inference

In the context of inference with expectation constraints, we propose an approach based on the "loopy belief propagation" algorithm LBP, as a surrogate to an exact Markov Random Field MRF modelling. A prior information composed of correlations among a large set of N variables, is encoded into a graphical model; this encoding is optimized with respect to an approximate decoding procedure LBP, which is used to infer hidden variables from an observed subset. We focus on the situation where the underlying data have many different statistical components, representing a variety of independent patterns. Considering a single parameter family of models we show how LBP may be used to encode and decode efficiently such information, without solving the NP hard inverse problem yielding the optimal MRF. Contrary to usual practice, we work in the non-convex Bethe free energy minimization framework, and manage to associate a belief propagation fixed point to each component of the underlying probabilistic mixture. The mean field limit is considered and yields an exact connection with the Hopfield model at finite temperature and steady state, when the number of mixture components is proportional to the number of variables. In addition, we provide an enhanced learning procedure, based on a straightforward multi-parameter extension of the model in conjunction with an effective continuous optimization procedure. This is performed using the stochastic search heuristic CMAES and yields a significant improvement with respect to the single parameter basic model.

cs.AI cs.LG cs.RO

0903.4930

http://arxiv.org/pdf/0903.4930v1

2009-03-28T01:09:00Z

2009-03-28T01:09:00Z

Time manipulation technique for speeding up reinforcement learning in simulations

A technique for speeding up reinforcement learning algorithms by using time manipulation is proposed. It is applicable to failure-avoidance control problems running in a computer simulation. Turning the time of the simulation backwards on failure events is shown to speed up the learning by 260% and improve the state space exploration by 12% on the cart-pole balancing task, compared to the conventional Q-learning and Actor-Critic algorithms.

cs.LG stat.ML

0903.5328

http://arxiv.org/pdf/0903.5328v1

2009-03-30T22:08:02Z

2009-03-30T22:08:02Z

A Stochastic View of Optimal Regret through Minimax Duality

We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal to the maximum, over joint distributions of the adversary's action sequence, of the difference between a sum of minimal expected losses and the minimal empirical loss. We show that the optimal regret has a natural geometric interpretation, since it can be viewed as the gap in Jensen's inequality for a concave functional--the minimizer over the player's actions of expected loss--defined on a set of probability distributions. We use this expression to obtain upper and lower bounds on the regret of an optimal strategy for a variety of online learning problems. Our method provides upper bounds without the need to construct a learning algorithm; the lower bounds provide explicit optimal strategies for the adversary.

math.PR cs.LG math.ST stat.TH

0903.5342

http://arxiv.org/pdf/0903.5342v1

2009-03-30T23:24:08Z

2009-03-30T23:24:08Z

Exact Non-Parametric Bayesian Inference on Infinite Trees

Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A Bayesian would assign a data-independent prior probability to "subdivide", which leads to a prior over infinite(ly many) trees. We derive an exact, fast, and simple inference algorithm for such a prior, for the data evidence, the predictive distribution, the effective model dimension, moments, and other quantities. We prove asymptotic convergence and consistency results, and illustrate the behavior of our model on some prototypical functions.

0904.0545

http://arxiv.org/pdf/0904.0545v2

2011-09-06T15:24:24Z

2009-04-03T10:38:06Z

Time Hopping technique for faster reinforcement learning in simulations

This preprint has been withdrawn by the author for revision

cs.AI cs.LG cs.RO

0904.0546

http://arxiv.org/pdf/0904.0546v1

2009-04-03T10:42:28Z

2009-04-03T10:42:28Z

Eligibility Propagation to Speed up Time Hopping for Reinforcement Learning

A mechanism called Eligibility Propagation is proposed to speed up the Time Hopping technique used for faster Reinforcement Learning in simulations. Eligibility Propagation provides for Time Hopping similar abilities to what eligibility traces provide for conventional Reinforcement Learning. It propagates values from one state to all of its temporal predecessors using a state transitions graph. Experiments on a simulated biped crawling robot confirm that Eligibility Propagation accelerates the learning process more than 3 times.

cs.AI cs.LG

10.1109/TSP.2009.2034916

0904.0643

http://arxiv.org/abs/0904.0643v1

2009-04-03T19:29:47Z

2009-04-03T19:29:47Z

Performing Nonlinear Blind Source Separation with Signal Invariants

Given a time series of multicomponent measurements x(t), the usual objective of nonlinear blind source separation (BSS) is to find a "source" time series s(t), comprised of statistically independent combinations of the measured components. In this paper, the source time series is required to have a density function in (s,ds/dt)-space that is equal to the product of density functions of individual components. This formulation of the BSS problem has a solution that is unique, up to permutations and component-wise transformations. Separability is shown to impose constraints on certain locally invariant (scalar) functions of x, which are derived from local higher-order correlations of the data's velocity dx/dt. The data are separable if and only if they satisfy these constraints, and, if the constraints are satisfied, the sources can be explicitly constructed from the data. The method is illustrated by using it to separate two speech-like sounds recorded with a single microphone.

cs.LG cs.CC

0904.0648

http://arxiv.org/pdf/0904.0648v1

2009-04-03T20:30:24Z

2009-04-03T20:30:24Z

Evolvability need not imply learnability

We show that Boolean functions expressible as monotone disjunctive normal forms are PAC-evolvable under a uniform distribution on the Boolean cube if the hypothesis size is allowed to remain fixed. We further show that this result is insufficient to prove the PAC-learnability of monotone Boolean functions, thereby demonstrating a counter-example to a recent claim to the contrary. We further discuss scenarios wherein evolvability and learnability will coincide as well as scenarios under which they differ. The implications of the latter case on the prospects of learning in complex hypothesis spaces is briefly examined.

stat.ML cs.LG

0904.0776

http://arxiv.org/pdf/0904.0776v1

2009-04-05T14:21:49Z

2009-04-05T14:21:49Z

Induction of High-level Behaviors from Problem-solving Traces using Machine Learning Tools

This paper applies machine learning techniques to student modeling. It presents a method for discovering high-level student behaviors from a very large set of low-level traces corresponding to problem-solving actions in a learning environment. Basic actions are encoded into sets of domain-dependent attribute-value patterns called cases. Then a domain-independent hierarchical clustering identifies what we call general attitudes, yielding automatic diagnosis expressed in natural language, addressed in principle to teachers. The method can be applied to individual students or to entire groups, like a class. We exhibit examples of this system applied to thousands of students' actions in the domain of algebraic transformations.

cs.LG

0904.0814

http://arxiv.org/pdf/0904.0814v1

2009-04-05T20:08:44Z

2009-04-05T20:08:44Z

Stability Analysis and Learning Bounds for Transductive Regression Algorithms

This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the stability of these algorithms. It also shows that a number of widely used transductive regression algorithms are in fact unstable. Finally, it reports the results of experiments with local transductive regression demonstrating the benefit of our stability bounds for model selection, for one of the algorithms, in particular for determining the radius of the local neighborhood used by the algorithm.

cs.LG cs.CG

0904.1227

http://arxiv.org/pdf/0904.1227v1

2009-04-07T21:15:42Z

2009-04-07T21:15:42Z

Learning convex bodies is hard

We show that learning a convex body in $\RR^d$, given random samples from the body, requires $2^{\Omega(\sqrt{d/\eps})}$ samples. By learning a convex body we mean finding a set having at most $\eps$ relative symmetric difference with the input body. To prove the lower bound we construct a hard to learn family of convex bodies. Our construction of this family is very simple and based on error correcting codes.

cs.AI cs.LG

0904.1579

http://arxiv.org/pdf/0904.1579v1

2009-04-09T18:26:36Z

2009-04-09T18:26:36Z

Online prediction of ovarian cancer

In this paper we apply computer learning methods to diagnosing ovarian cancer using the level of the standard biomarker CA125 in conjunction with information provided by mass-spectrometry. We are working with a new data set collected over a period of 7 years. Using the level of CA125 and mass-spectrometry peaks, our algorithm gives probability predictions for the disease. To estimate classification accuracy we convert probability predictions into strict predictions. Our algorithm makes fewer errors than almost any linear combination of the CA125 level and one peak's intensity (taken on the log scale). To check the power of our algorithm we use it to test the hypothesis that CA125 and the peaks do not contain useful information for the prediction of the disease at a particular time before the diagnosis. Our algorithm produces $p$-values that are better than those produced by the algorithm that has been previously applied to this data set. Our conclusion is that the proposed algorithm is more reliable for prediction on new data.

cond-mat.dis-nn cond-mat.stat-mech cs.LG

10.1088/1742-5468/2009/07/P07026

0904.1700

http://arxiv.org/abs/0904.1700v2

2009-06-09T13:08:39Z

2009-04-10T15:19:14Z

Recovering the state sequence of hidden Markov models using mean-field approximations

Inferring the sequence of states from observations is one of the most fundamental problems in Hidden Markov Models. In statistical physics language, this problem is equivalent to computing the marginals of a one-dimensional model with a random external field. While this task can be accomplished through transfer matrix methods, it becomes quickly intractable when the underlying state space is large. This paper develops several low-complexity approximate algorithms to address this inference problem when the state space becomes large. The new algorithms are based on various mean-field approximations of the transfer matrix. Their performances are studied in detail on a simple realistic model for DNA pyrosequencing.

cs.NE cs.LG

0904.1888

http://arxiv.org/pdf/0904.1888v1

2009-04-13T00:59:10Z

2009-04-13T00:59:10Z

On Fodor on Darwin on Evolution

Jerry Fodor argues that Darwin was wrong about "natural selection" because (1) it is only a tautology rather than a scientific law that can support counterfactuals ("If X had happened, Y would have happened") and because (2) only minds can select. Hence Darwin's analogy with "artificial selection" by animal breeders was misleading and evolutionary explanation is nothing but post-hoc historical narrative. I argue that Darwin was right on all counts.

cs.LG cs.CV

0904.2037

http://arxiv.org/pdf/0904.2037v3

2010-01-06T09:00:26Z

2009-04-14T01:57:12Z

Boosting through Optimization of Margin Distributions

Boosting has attracted much research attention in the past decade. The success of boosting algorithms may be interpreted in terms of the margin theory. Recently it has been shown that generalization error of classifiers can be obtained by explicitly taking the margin distribution of the training data into account. Most of the current boosting algorithms in practice usually optimizes a convex loss function and do not make use of the margin distribution. In this work we design a new boosting algorithm, termed margin-distribution boosting (MDBoost), which directly maximizes the average margin and minimizes the margin variance simultaneously. This way the margin distribution is optimized. A totally-corrective optimization algorithm based on column generation is proposed to implement MDBoost. Experiments on UCI datasets show that MDBoost outperforms AdaBoost and LPBoost in most cases.

cs.LG

0904.2160

http://arxiv.org/pdf/0904.2160v1

2009-04-14T17:32:00Z

2009-04-14T17:32:00Z

Inferring Dynamic Bayesian Networks using Frequent Episode Mining

Motivation: Several different threads of research have been proposed for modeling and mining temporal data. On the one hand, approaches such as dynamic Bayesian networks (DBNs) provide a formal probabilistic basis to model relationships between time-indexed random variables but these models are intractable to learn in the general case. On the other, algorithms such as frequent episode mining are scalable to large datasets but do not exhibit the rigorous probabilistic interpretations that are the mainstay of the graphical models literature. Results: We present a unification of these two seemingly diverse threads of research, by demonstrating how dynamic (discrete) Bayesian networks can be inferred from the results of frequent episode mining. This helps bridge the modeling emphasis of the former with the counting emphasis of the latter. First, we show how, under reasonable assumptions on data characteristics and on influences of random variables, the optimal DBN structure can be computed using a greedy, local, algorithm. Next, we connect the optimality of the DBN structure with the notion of fixed-delay episodes and their counts of distinct occurrences. Finally, to demonstrate the practical feasibility of our approach, we focus on a specific (but broadly applicable) class of networks, called excitatory networks, and show how the search for the optimal DBN structure can be conducted using just information from frequent episodes. Application on datasets gathered from mathematical models of spiking neurons as well as real neuroscience datasets are presented. Availability: Algorithmic implementations, simulator codebases, and datasets are available from our website at http://neural-code.cs.vt.edu/dbn

cs.MA cs.LG

0904.2320

http://arxiv.org/pdf/0904.2320v1

2009-04-15T13:49:42Z

2009-04-15T13:49:42Z

Why Global Performance is a Poor Metric for Verifying Convergence of Multi-agent Learning

Experimental verification has been the method of choice for verifying the stability of a multi-agent reinforcement learning (MARL) algorithm as the number of agents grows and theoretical analysis becomes prohibitively complex. For cooperative agents, where the ultimate goal is to optimize some global metric, the stability is usually verified by observing the evolution of the global performance metric over time. If the global metric improves and eventually stabilizes, it is considered a reasonable verification of the system's stability. The main contribution of this note is establishing the need for better experimental frameworks and measures to assess the stability of large-scale adaptive cooperative systems. We show an experimental case study where the stability of the global performance metric can be rather deceiving, hiding an underlying instability in the system that later leads to a significant drop in performance. We then propose an alternative metric that relies on agents' local policies and show, experimentally, that our proposed metric is more effective (than the traditional global performance metric) in exposing the instability of MARL algorithms.

cs.AI cs.LG

0904.2595

http://arxiv.org/pdf/0904.2595v1

2009-04-16T21:30:30Z

2009-04-16T21:30:30Z

A Methodology for Learning Players' Styles from Game Records

We describe a preliminary investigation into learning a Chess player's style from game records. The method is based on attempting to learn features of a player's individual evaluation function using the method of temporal differences, with the aid of a conventional Chess engine architecture. Some encouraging results were obtained in learning the styles of two recent Chess world champions, and we report on our attempt to use the learnt styles to discriminate between the players from game records by trying to detect who was playing white and who was playing black. We also discuss some limitations of our approach and propose possible directions for future research. The method we have presented may also be applicable to other strategic games, and may even be generalisable to other domains where sequences of agents' actions are recorded.

cs.LG cs.AI

0904.2623

http://arxiv.org/pdf/0904.2623v2

2009-06-05T03:54:58Z

2009-04-17T03:48:02Z

Exponential Family Graph Matching and Ranking

We present a method for learning max-weight matching predictors in bipartite graphs. The method consists of performing maximum a posteriori estimation in exponential families with sufficient statistics that encode permutations and data features. Although inference is in general hard, we show that for one very relevant application - web page ranking - exact inference is efficient. For general model instances, an appropriate sampler is readily available. Contrary to existing max-margin matching models, our approach is statistically consistent and, in addition, experiments with increasing sample sizes indicate superior improvement over such models. We apply the method to graph matching in computer vision as well as to a standard benchmark dataset for learning web page ranking, in which we obtain state-of-the-art results, in particular improving on max-margin variants. The drawback of this method with respect to max-margin alternatives is its runtime for large graphs, which is comparatively high.

cs.DS cs.LG

0904.3151

http://arxiv.org/pdf/0904.3151v1

2009-04-21T01:03:06Z

2009-04-21T01:03:06Z

Efficient Construction of Neighborhood Graphs by the Multiple Sorting Method

Neighborhood graphs are gaining popularity as a concise data representation in machine learning. However, naive graph construction by pairwise distance calculation takes $O(n^2)$ runtime for $n$ data points and this is prohibitively slow for millions of data points. For strings of equal length, the multiple sorting method (Uno, 2008) can construct an $\epsilon$-neighbor graph in $O(n+m)$ time, where $m$ is the number of $\epsilon$-neighbor pairs in the data. To introduce this remarkably efficient algorithm to continuous domains such as images, signals and texts, we employ a random projection method to convert vectors to strings. Theoretical results are presented to elucidate the trade-off between approximation quality and computation time. Empirical results show the efficiency of our method in comparison to fast nearest neighbor alternatives.

cs.AI cs.LG

0904.3352

http://arxiv.org/pdf/0904.3352v1

2009-04-21T22:07:24Z

2009-04-21T22:07:24Z

Optimistic Initialization and Greediness Lead to Polynomial Time Learning in Factored MDPs - Extended Version

In this paper we propose an algorithm for polynomial-time reinforcement learning in factored Markov decision processes (FMDPs). The factored optimistic initial model (FOIM) algorithm, maintains an empirical model of the FMDP in a conventional way, and always follows a greedy policy with respect to its model. The only trick of the algorithm is that the model is initialized optimistically. We prove that with suitable initialization (i) FOIM converges to the fixed point of approximate value iteration (AVI); (ii) the number of steps when the agent makes non-near-optimal decisions (with respect to the solution of AVI) is polynomial in all relevant quantities; (iii) the per-step costs of the algorithm are also polynomial. To our best knowledge, FOIM is the first algorithm with these properties. This extended version contains the rigorous proofs of the main theorem. A version of this paper appeared in ICML'09.

cs.LG

0904.3664

http://arxiv.org/pdf/0904.3664v1

2009-04-23T11:40:57Z

2009-04-23T11:40:57Z

Introduction to Machine Learning: Class Notes 67577

Introduction to Machine learning covering Statistical Inference (Bayes, EM, ML/MaxEnt duality), algebraic and spectral methods (PCA, LDA, CCA, Clustering), and PAC learning (the Formal model, VC dimension, Double Sampling theorem).

cs.LG cs.AI

0904.3667

http://arxiv.org/pdf/0904.3667v1

2009-04-23T11:48:38Z

2009-04-23T11:48:38Z

Considerations upon the Machine Learning Technologies

Artificial intelligence offers superior techniques and methods by which problems from diverse domains may find an optimal solution. The Machine Learning technologies refer to the domain of artificial intelligence aiming to develop the techniques allowing the computers to "learn". Some systems based on Machine Learning technologies tend to eliminate the necessity of the human intelligence while the others adopt a man-machine collaborative approach.

cs.LG

0904.4527

http://arxiv.org/pdf/0904.4527v1

2009-04-29T03:16:20Z

2009-04-29T03:16:20Z

Limits of Learning about a Categorical Latent Variable under Prior Near-Ignorance

In this paper, we consider the coherent theory of (epistemic) uncertainty of Walley, in which beliefs are represented through sets of probability distributions, and we focus on the problem of modeling prior ignorance about a categorical random variable. In this setting, it is a known result that a state of prior ignorance is not compatible with learning. To overcome this problem, another state of beliefs, called \emph{near-ignorance}, has been proposed. Near-ignorance resembles ignorance very closely, by satisfying some principles that can arguably be regarded as necessary in a state of ignorance, and allows learning to take place. What this paper does, is to provide new and substantial evidence that also near-ignorance cannot be really regarded as a way out of the problem of starting statistical inference in conditions of very weak beliefs. The key to this result is focusing on a setting characterized by a variable of interest that is \emph{latent}. We argue that such a setting is by far the most common case in practice, and we provide, for the case of categorical latent variables (and general \emph{manifest} variables) a condition that, if satisfied, prevents learning to take place under prior near-ignorance. This condition is shown to be easily satisfied even in the most common statistical problems. We regard these results as a strong form of evidence against the possibility to adopt a condition of prior near-ignorance in real statistical problems.