Unsupervised Supervised Learning II: Training Margin Based Classifiers without Labels

Many popular linear classifiers, such as logistic regression, boosting, or SVM, are trained by optimizing a margin-based risk function. Traditionally, these risk functions are computed based on a labeled dataset. We develop a novel technique for estimating such risks using only unlabeled data and the marginal label distribution. We prove that the proposed risk estimator is consistent on high-dimensional datasets and demonstrate it on synthetic and real-world data. In particular, we show how the estimate is used for evaluating classifiers in transfer learning, and for training classifiers with no labeled data whatsoever.


Model Selection with the Loss Rank Principle

A key issue in statistics and machine learning is to automatically select the "right" model complexity, e.g., the number of neighbors to be averaged over in k nearest neighbor (kNN) regression or the polynomial degree in regression with polynomials. We suggest a novel principle - the Loss Rank Principle (LoRP) - for model selection in regression and classification. It is based on the loss rank, which counts how many other (fictitious) data would be fitted better. LoRP selects the model that has minimal loss rank. Unlike most penalized maximum likelihood variants (AIC, BIC, MDL), LoRP depends only on the regression functions and the loss function. It works without a stochastic noise model, and is directly applicable to any non-parametric regressor, like kNN.


A Unified Algorithmic Framework for Multi-Dimensional Scaling

In this paper, we propose a unified algorithmic framework for solving many known variants of \mds. Our algorithm is a simple iterative scheme with guaranteed convergence, and is \emph{modular}; by changing the internals of a single subroutine in the algorithm, we can switch cost functions and target spaces easily. In addition to the formal guarantees of convergence, our algorithms are accurate; in most cases, they converge to better quality solutions than existing methods, in comparable time. We expect that this framework will be useful for a number of \mds variants that have not yet been studied. Our framework extends to embedding high-dimensional points lying on a sphere to points on a lower dimensional sphere, preserving geodesic distances. As a compliment to this result, we also extend the Johnson-Lindenstrauss Lemma to this spherical setting, where projecting to a random $O((1/\eps^2) \log n)$-dimensional sphere causes $\eps$-distortion.


Statistical and Computational Tradeoffs in Stochastic Composite Likelihood

Maximum likelihood estimators are often of limited practical use due to the intensive computation they require. We propose a family of alternative estimators that maximize a stochastic variation of the composite likelihood function. Each of the estimators resolve the computation-accuracy tradeoff differently, and taken together they span a continuous spectrum of computation-accuracy tradeoff resolutions. We prove the consistency of the estimators, provide formulas for their asymptotic variance, statistical robustness, and computational complexity. We discuss experimental results in the context of Boltzmann machines and conditional random fields. The theoretical and experimental studies demonstrate the effectiveness of the estimators when the computational resources are insufficient. They also demonstrate that in some cases reduced computational complexity is associated with robustness thereby increasing statistical accuracy.


Exponential Family Hybrid Semi-Supervised Learning

We present an approach to semi-supervised learning based on an exponential family characterization. Our approach generalizes previous work on coupled priors for hybrid generative/discriminative models. Our model is more flexible and natural than previous approaches. Experimental results on several data sets show that our approach also performs better in practice.


Learning by random walks in the weight space of the Ising perceptron

Several variants of a stochastic local search process for constructing the synaptic weights of an Ising perceptron are studied. In this process, binary patterns are sequentially presented to the Ising perceptron and are then learned as the synaptic weight configuration is modified through a chain of single- or double-weight flips within the compatible weight configuration space of the earlier learned patterns. This process is able to reach a storage capacity of $\alpha \approx 0.63$ for pattern length N = 101 and $\alpha \approx 0.41$ for N = 1001. If in addition a relearning process is exploited, the learning performance is further improved to a storage capacity of $\alpha \approx 0.80$ for N = 101 and $\alpha \approx 0.42$ for N=1001. We found that, for a given learning task, the solutions constructed by the random walk learning process are separated by a typical Hamming distance, which decreases with the constraint density $\alpha$ of the learning task; at a fixed value of $\alpha$, the width of the Hamming distance distributions decreases with $N$.


From Frequency to Meaning: Vector Space Models of Semantics

Computers understand very little of the meaning of human language. This profoundly limits our ability to give instructions to computers, the ability of computers to explain their actions to us, and the ability of computers to analyse and process text. Vector space models (VSMs) of semantics are beginning to address these limits. This paper surveys the use of VSMs for semantic processing of text. We organize the literature on VSMs according to the structure of the matrix in a VSM. There are currently three broad classes of VSMs, based on term-document, word-context, and pair-pattern matrices, yielding three classes of applications. We survey a broad range of applications in these three categories and we take a detailed look at a specific open source project in each category. Our goal in this survey is to show the breadth of applications of VSMs for semantics, to provide a new perspective on VSMs for those who are already familiar with the area, and to provide pointers into the literature for those who are less familiar with the field.


Hitting and commute times in large graphs are often misleading

Next to the shortest path distance, the second most popular distance function between vertices in a graph is the commute distance (resistance distance). For two vertices u and v, the hitting time H_{uv} is the expected time it takes a random walk to travel from u to v. The commute time is its symmetrized version C_{uv} = H_{uv} + H_{vu}. In our paper we study the behavior of hitting times and commute distances when the number n of vertices in the graph is very large. We prove that as n converges to infinty, hitting times and commute distances converge to expressions that do not take into account the global structure of the graph at all. Namely, the hitting time H_{uv} converges to 1/d_v and the commute time to 1/d_u + 1/d_v where d_u and d_v denote the degrees of vertices u and v. In these cases, the hitting and commute times are misleading in the sense that they do not provide information about the structure of the graph. We focus on two major classes of random graphs: random geometric graphs (k-nearest neighbor graphs, epsilon-graphs, Gaussian similarity graphs) and random graphs with given expected degrees (in particular, Erdos-Renyi graphs with and without planted partitions)


Faster Rates for training Max-Margin Markov Networks

Structured output prediction is an important machine learning problem both in theory and practice, and the max-margin Markov network (\mcn) is an effective approach. All state-of-the-art algorithms for optimizing \mcn\ objectives take at least $O(1/\epsilon)$ number of iterations to find an $\epsilon$ accurate solution. Recent results in structured optimization suggest that faster rates are possible by exploiting the structure of the objective function. Towards this end \citet{Nesterov05} proposed an excessive gap reduction technique based on Euclidean projections which converges in $O(1/\sqrt{\epsilon})$ iterations on strongly convex functions. Unfortunately when applied to \mcn s, this approach does not admit graphical model factorization which, as in many existing algorithms, is crucial for keeping the cost per iteration tractable. In this paper, we present a new excessive gap reduction technique based on Bregman projections which admits graphical model factorization naturally, and converges in $O(1/\sqrt{\epsilon})$ iterations. Compared with existing algorithms, the convergence rate of our method has better dependence on $\epsilon$ and other parameters of the problem, and can be easily kernelized.


Local Space-Time Smoothing for Version Controlled Documents

Unlike static documents, version controlled documents are continuously edited by one or more authors. Such collaborative revision process makes traditional modeling and visualization techniques inappropriate. In this paper we propose a new representation based on local space-time smoothing that captures important revision patterns. We demonstrate the applicability of our framework using experiments on synthetic and real-world data.


A New Clustering Approach based on Page's Path Similarity for Navigation Patterns Mining

In recent years, predicting the user's next request in web navigation has received much attention. An information source to be used for dealing with such problem is the left information by the previous web users stored at the web access log on the web servers. Purposed systems for this problem work based on this idea that if a large number of web users request specific pages of a website on a given session, it can be concluded that these pages are satisfying similar information needs, and therefore they are conceptually related. In this study, a new clustering approach is introduced that employs logical path storing of a website pages as another parameter which is regarded as a similarity parameter and conceptual relation between web pages. The results of simulation have shown that the proposed approach is more than others precise in determining the clusters.


Evaluation of E-Learners Behaviour using Different Fuzzy Clustering Models: A Comparative Study

This paper introduces an evaluation methodologies for the e-learners' behaviour that will be a feedback to the decision makers in e-learning system. Learner's profile plays a crucial role in the evaluation process to improve the e-learning process performance. The work focuses on the clustering of the e-learners based on their behaviour into specific categories that represent the learner's profiles. The learners' classes named as regular, workers, casual, bad, and absent. The work may answer the question of how to return bad students to be regular ones. The work presented the use of different fuzzy clustering techniques as fuzzy c-means and kernelized fuzzy c-means to find the learners' categories and predict their profiles. The paper presents the main phases as data description, preparation, features selection, and the experiments design using different fuzzy clustering models. Analysis of the obtained results and comparison with the real world behavior of those learners proved that there is a match with percentage of 78%. Fuzzy clustering reflects the learners' behavior more than crisp clustering. Comparison between FCM and KFCM proved that the KFCM is much better than FCM in predicting the learners' behaviour.


Hierarchical Web Page Classification Based on a Topic Model and Neighboring Pages Integration

Most Web page classification models typically apply the bag of words (BOW) model to represent the feature space. The original BOW representation, however, is unable to recognize semantic relationships between terms. One possible solution is to apply the topic model approach based on the Latent Dirichlet Allocation algorithm to cluster the term features into a set of latent topics. Terms assigned into the same topic are semantically related. In this paper, we propose a novel hierarchical classification method based on a topic model and by integrating additional term features from neighboring pages. Our hierarchical classification method consists of two phases: (1) feature representation by using a topic model and integrating neighboring pages, and (2) hierarchical Support Vector Machines (SVM) classification model constructed from a confusion matrix. From the experimental results, the approach of using the proposed hierarchical SVM model by integrating current page with neighboring pages via the topic model yielded the best performance with the accuracy equal to 90.33% and the F1 measure of 90.14%; an improvement of 5.12% and 5.13% over the original SVM model, respectively.


A Survey of Na\"ive Bayes Machine Learning approach in Text Document Classification

Text Document classification aims in associating one or more predefined categories based on the likelihood suggested by the training set of labeled documents. Many machine learning algorithms play a vital role in training the system with predefined categories among which Na\"ive Bayes has some intriguing facts that it is simple, easy to implement and draws better accuracy in large datasets in spite of the na\"ive dependence. The importance of Na\"ive Bayes Machine learning approach has felt hence the study has been taken up for text document classification and the statistical event models available. This survey the various feature selection methods has been discussed and compared along with the metrics related to text document classification.


Supermartingales in Prediction with Expert Advice

We apply the method of defensive forecasting, based on the use of game-theoretic supermartingales, to prediction with expert advice. In the traditional setting of a countable number of experts and a finite number of outcomes, the Defensive Forecasting Algorithm is very close to the well-known Aggregating Algorithm. Not only the performance guarantees but also the predictions are the same for these two methods of fundamentally different nature. We discuss also a new setting where the experts can give advice conditional on the learner's future decision. Both the algorithms can be adapted to the new setting and give the same performance guarantees as in the traditional setting. Finally, we outline an application of defensive forecasting to a setting with several loss functions.


Structure-Aware Stochastic Control for Transmission Scheduling

In this paper, we consider the problem of real-time transmission scheduling over time-varying channels. We first formulate the transmission scheduling problem as a Markov decision process (MDP) and systematically unravel the structural properties (e.g. concavity in the state-value function and monotonicity in the optimal scheduling policy) exhibited by the optimal solutions. We then propose an online learning algorithm which preserves these structural properties and achieves -optimal solutions for an arbitrarily small . The advantages of the proposed online method are that: (i) it does not require a priori knowledge of the traffic arrival and channel statistics and (ii) it adaptively approximates the state-value functions using piece-wise linear functions and has low storage and computation complexity. We also extend the proposed low-complexity online learning solution to the prioritized data transmission. The simulation results demonstrate that the proposed method achieves significantly better utility (or delay)-energy trade-offs when comparing to existing state-of-art online optimization methods.


Inductive Logic Programming in Databases: from Datalog to DL+log

In this paper we address an issue that has been brought to the attention of the database community with the advent of the Semantic Web, i.e. the issue of how ontologies (and semantics conveyed by them) can help solving typical database problems, through a better understanding of KR aspects related to databases. In particular, we investigate this issue from the ILP perspective by considering two database problems, (i) the definition of views and (ii) the definition of constraints, for a database whose schema is represented also by means of an ontology. Both can be reformulated as ILP problems and can benefit from the expressive and deductive power of the KR framework DL+log. We illustrate the application scenarios by means of examples. Keywords: Inductive Logic Programming, Relational Databases, Ontologies, Description Logics, Hybrid Knowledge Representation and Reasoning Systems. Note: To appear in Theory and Practice of Logic Programming (TPLP).


Near-Optimal Evasion of Convex-Inducing Classifiers

Classifiers are often used to detect miscreant activities. We study how an adversary can efficiently query a classifier to elicit information that allows the adversary to evade detection at near-minimal cost. We generalize results of Lowd and Meek (2005) to convex-inducing classifiers. We present algorithms that construct undetected instances of near-minimal cost using only polynomially many queries in the dimension of the space and without reverse engineering the decision boundary.


A New Heuristic for Feature Selection by Consistent Biclustering

Given a set of data, biclustering aims at finding simultaneous partitions in biclusters of its samples and of the features which are used for representing the samples. Consistent biclusterings allow to obtain correct classifications of the samples from the known classification of the features, and vice versa, and they are very useful for performing supervised classifications. The problem of finding consistent biclusterings can be seen as a feature selection problem, where the features that are not relevant for classification purposes are removed from the set of data, while the total number of features is maximized in order to preserve information. This feature selection problem can be formulated as a linear fractional 0-1 optimization problem. We propose a reformulation of this problem as a bilevel optimization problem, and we present a heuristic algorithm for an efficient solution of the reformulated problem. Computational experiments show that the presented algorithm is able to find better solutions with respect to the ones obtained by employing previously presented heuristic algorithms.


A Formal Approach to Modeling the Memory of a Living Organism

We consider a living organism as an observer of the evolution of its environment recording sensory information about the state space X of the environment in real time. Sensory information is sampled and then processed on two levels. On the biological level, the organism serves as an evaluation mechanism of the subjective relevance of the incoming data to the observer: the observer assigns excitation values to events in X it could recognize using its sensory equipment. On the algorithmic level, sensory input is used for updating a database, the memory of the observer whose purpose is to serve as a geometric/combinatorial model of X, whose nodes are weighted by the excitation values produced by the evaluation mechanism. These values serve as a guidance system for deciding how the database should transform as observation data mounts. We define a searching problem for the proposed model and discuss the model's flexibility and its computational efficiency, as well as the possibility of implementing it as a dynamic network of neuron-like units. We show how various easily observable properties of the human memory and thought process can be explained within the framework of this model. These include: reasoning (with efficiency bounds), errors, temporary and permanent loss of information. We are also able to define general learning problems in terms of the new model, such as the language acquisition problem.


Adaptive Submodularity: Theory and Applications in Active Learning and Stochastic Optimization

Solving stochastic optimization problems under partial observability, where one needs to adaptively make decisions with uncertain outcomes, is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive submodularity, generalizing submodular set functions to adaptive policies. We prove that if a problem satisfies this property, a simple adaptive greedy algorithm is guaranteed to be competitive with the optimal policy. In addition to providing performance guarantees for both stochastic maximization and coverage, adaptive submodularity can be exploited to drastically speed up the greedy algorithm by using lazy evaluations. We illustrate the usefulness of the concept by giving several examples of adaptive submodular objectives arising in diverse applications including sensor placement, viral marketing and active learning. Proving adaptive submodularity for these problems allows us to recover existing results in these applications as special cases, improve approximation guarantees and handle natural generalizations.


Gene Expression Data Knowledge Discovery using Global and Local Clustering

To understand complex biological systems, the research community has produced huge corpus of gene expression data. A large number of clustering approaches have been proposed for the analysis of gene expression data. However, extracting important biological knowledge is still harder. To address this task, clustering techniques are used. In this paper, hybrid Hierarchical k-Means algorithm is used for clustering and biclustering gene expression data is used. To discover both local and global clustering structure biclustering and clustering algorithms are utilized. A validation technique, Figure of Merit is used to determine the quality of clustering results. Appropriate knowledge is mined from the clusters by embedding a BLAST similarity search program into the clustering and biclustering process. To discover both local and global clustering structure biclustering and clustering algorithms are utilized. To determine the quality of clustering results, a validation technique, Figure of Merit is used. Appropriate knowledge is mined from the clusters by embedding a BLAST similarity search program into the clustering and biclustering process.


Unbeatable Imitation

We show that for many classes of symmetric two-player games, the simple decision rule "imitate-the-best" can hardly be beaten by any other decision rule. We provide necessary and sufficient conditions for imitation to be unbeatable and show that it can only be beaten by much in games that are of the rock-scissors-paper variety. Thus, in many interesting examples, like 2x2 games, Cournot duopoly, price competition, rent seeking, public goods games, common pool resource games, minimum effort coordination games, arms race, search, bargaining, etc., imitation cannot be beaten by much even by a very clever opponent.


Large Margin Boltzmann Machines and Large Margin Sigmoid Belief Networks

Current statistical models for structured prediction make simplifying assumptions about the underlying output graph structure, such as assuming a low-order Markov chain, because exact inference becomes intractable as the tree-width of the underlying graph increases. Approximate inference algorithms, on the other hand, force one to trade off representational power with computational efficiency. In this paper, we propose two new types of probabilistic graphical models, large margin Boltzmann machines (LMBMs) and large margin sigmoid belief networks (LMSBNs), for structured prediction. LMSBNs in particular allow a very fast inference algorithm for arbitrary graph structures that runs in polynomial time with a high probability. This probability is data-distribution dependent and is maximized in learning. The new approach overcomes the representation-efficiency trade-off in previous models and allows fast structured prediction with complicated graph structures. We present results from applying a fully connected model to multi-label scene classification and demonstrate that the proposed approach can yield significant performance gains over current state-of-the-art methods.


Incorporating Side Information in Probabilistic Matrix Factorization with Gaussian Processes

Probabilistic matrix factorization (PMF) is a powerful method for modeling data associated with pairwise relationships, finding use in collaborative filtering, computational biology, and document analysis, among other areas. In many domains, there is additional information that can assist in prediction. For example, when modeling movie ratings, we might know when the rating occurred, where the user lives, or what actors appear in the movie. It is difficult, however, to incorporate this side information into the PMF model. We propose a framework for incorporating side information by coupling together multiple PMF problems via Gaussian process priors. We replace scalar latent features with functions that vary over the space of side information. The GP priors on these functions require them to vary smoothly and share information. We successfully use this new method to predict the scores of professional basketball games, where side information about the venue and date of the game are relevant for the outcome.


Spoken Language Identification Using Hybrid Feature Extraction Methods

This paper introduces and motivates the use of hybrid robust feature extraction technique for spoken language identification (LID) system. The speech recognizers use a parametric form of a signal to get the most important distinguishable features of speech signal for recognition task. In this paper Mel-frequency cepstral coefficients (MFCC), Perceptual linear prediction coefficients (PLP) along with two hybrid features are used for language Identification. Two hybrid features, Bark Frequency Cepstral Coefficients (BFCC) and Revised Perceptual Linear Prediction Coefficients (RPLP) were obtained from combination of MFCC and PLP. Two different classifiers, Vector Quantization (VQ) with Dynamic Time Warping (DTW) and Gaussian Mixture Model (GMM) were used for classification. The experiment shows better identification rate using hybrid feature extraction techniques compared to conventional feature extraction methods.BFCC has shown better performance than MFCC with both classifiers. RPLP along with GMM has shown best identification performance among all feature extraction techniques.


Wavelet-Based Mel-Frequency Cepstral Coefficients for Speaker Identification using Hidden Markov Models

To improve the performance of speaker identification systems, an effective and robust method is proposed to extract speech features, capable of operating in noisy environment. Based on the time-frequency multi-resolution property of wavelet transform, the input speech signal is decomposed into various frequency channels. For capturing the characteristic of the signal, the Mel-Frequency Cepstral Coefficients (MFCCs) of the wavelet channels are calculated. Hidden Markov Models (HMMs) were used for the recognition stage as they give better recognition for the speaker's features than Dynamic Time Warping (DTW). Comparison of the proposed approach with the MFCCs conventional feature extraction method shows that the proposed method not only effectively reduces the influence of noise, but also improves recognition. A recognition rate of 99.3% was obtained using the proposed feature extraction technique compared to 98.7% using the MFCCs. When the test patterns were corrupted by additive white Gaussian noise with 20 dB S/N ratio, the recognition rate was 97.3% using the proposed method compared to 93.3% using the MFCCs.


Etiqueter un corpus oral par apprentissage automatique \`a l'aide de connaissances linguistiques

Thanks to the Eslo1 ("Enqu\^ete sociolinguistique d'Orl\'eans", i.e. "Sociolinguistic Inquiery of Orl\'eans") campain, a large oral corpus has been gathered and transcribed in a textual format. The purpose of the work presented here is to associate a morpho-syntactic label to each unit of this corpus. To this aim, we have first studied the specificities of the necessary labels, and their various possible levels of description. This study has led to a new original hierarchical structuration of labels. Then, considering that our new set of labels was different from the one used in every available software, and that these softwares usually do not fit for oral data, we have built a new labeling tool by a Machine Learning approach, from data labeled by Cordial and corrected by hand. We have applied linear CRF (Conditional Random Fields) trying to take the best possible advantage of the linguistic knowledge that was used to define the set of labels. We obtain an accuracy between 85 and 90%, depending of the parameters used.


Offline Signature Identification by Fusion of Multiple Classifiers using Statistical Learning Theory

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


Unbiased Offline Evaluation of Contextual-bandit-based News Article Recommendation Algorithms

Contextual bandit algorithms have become popular for online recommendation systems such as Digg, Yahoo! Buzz, and news recommendation in general. \emph{Offline} evaluation of the effectiveness of new algorithms in these applications is critical for protecting online user experiences but very challenging due to their "partial-label" nature. Common practice is to create a simulator which simulates the online environment for the problem at hand and then run an algorithm against this simulator. However, creating simulator itself is often difficult and modeling bias is usually unavoidably introduced. In this paper, we introduce a \emph{replay} methodology for contextual bandit algorithm evaluation. Different from simulator-based approaches, our method is completely data-driven and very easy to adapt to different applications. More importantly, our method can provide provably unbiased evaluations. Our empirical results on a large-scale news article recommendation dataset collected from Yahoo! Front Page conform well with our theoretical results. Furthermore, comparisons between our offline replay and online bucket evaluation of several contextual bandit algorithms show accuracy and effectiveness of our offline evaluation method.


Facial Expression Representation and Recognition Using 2DHLDA, Gabor Wavelets, and Ensemble Learning

In this paper, a novel method for representation and recognition of the facial expressions in two-dimensional image sequences is presented. We apply a variation of two-dimensional heteroscedastic linear discriminant analysis (2DHLDA) algorithm, as an efficient dimensionality reduction technique, to Gabor representation of the input sequence. 2DHLDA is an extension of the two-dimensional linear discriminant analysis (2DLDA) approach and it removes the equal within-class covariance. By applying 2DHLDA in two directions, we eliminate the correlations between both image columns and image rows. Then, we perform a one-dimensional LDA on the new features. This combined method can alleviate the small sample size problem and instability encountered by HLDA. Also, employing both geometric and appearance features and using an ensemble learning scheme based on data fusion, we create a classifier which can efficiently classify the facial expressions. The proposed method is robust to illumination changes and it can properly represent temporal information as well as subtle changes in facial muscles. We provide experiments on Cohn-Kanade database that show the superiority of the proposed method. KEYWORDS: two-dimensional heteroscedastic linear discriminant analysis (2DHLDA), subspace learning, facial expression analysis, Gabor wavelets, ensemble learning.


Exploratory Analysis of Functional Data via Clustering and Optimal Segmentation

We propose in this paper an exploratory analysis algorithm for functional data. The method partitions a set of functions into $K$ clusters and represents each cluster by a simple prototype (e.g., piecewise constant). The total number of segments in the prototypes, $P$, is chosen by the user and optimally distributed among the clusters via two dynamic programming algorithms. The practical relevance of the method is shown on two real world datasets.


Recognizing Combinations of Facial Action Units with Different Intensity Using a Mixture of Hidden Markov Models and Neural Network

Facial Action Coding System consists of 44 action units (AUs) and more than 7000 combinations. Hidden Markov models (HMMs) classifier has been used successfully to recognize facial action units (AUs) and expressions due to its ability to deal with AU dynamics. However, a separate HMM is necessary for each single AU and each AU combination. Since combinations of AU numbering in thousands, a more efficient method will be needed. In this paper an accurate real-time sequence-based system for representation and recognition of facial AUs is presented. Our system has the following characteristics: 1) employing a mixture of HMMs and neural network, we develop a novel accurate classifier, which can deal with AU dynamics, recognize subtle changes, and it is also robust to intensity variations, 2) although we use an HMM for each single AU only, by employing a neural network we can recognize each single and combination AU, and 3) using both geometric and appearance-based features, and applying efficient dimension reduction techniques, our system is robust to illumination changes and it can represent the temporal information involved in formation of the facial expressions. Extensive experiments on Cohn-Kanade database show the superiority of the proposed method, in comparison with other classifiers. Keywords: classifier design and evaluation, data fusion, facial action units (AUs), hidden Markov models (HMMs), neural network (NN).


Multilinear Biased Discriminant Analysis: A Novel Method for Facial Action Unit Representation

In this paper a novel efficient method for representation of facial action units by encoding an image sequence as a fourth-order tensor is presented. The multilinear tensor-based extension of the biased discriminant analysis (BDA) algorithm, called multilinear biased discriminant analysis (MBDA), is first proposed. Then, we apply the MBDA and two-dimensional BDA (2DBDA) algorithms, as the dimensionality reduction techniques, to Gabor representations and the geometric features of the input image sequence respectively. The proposed scheme can deal with the asymmetry between positive and negative samples as well as curse of dimensionality dilemma. Extensive experiments on Cohn-Kanade database show the superiority of the proposed method for representation of the subtle changes and the temporal information involved in formation of the facial expressions. As an accurate tool, this representation can be applied to many areas such as recognition of spontaneous and deliberate facial expressions, multi modal/media human computer interaction and lie detection efforts.


Using Rough Set and Support Vector Machine for Network Intrusion Detection

The main function of IDS (Intrusion Detection System) is to protect the system, analyze and predict the behaviors of users. Then these behaviors will be considered an attack or a normal behavior. Though IDS has been developed for many years, the large number of return alert messages makes managers maintain system inefficiently. In this paper, we use RST (Rough Set Theory) and SVM (Support Vector Machine) to detect intrusions. First, RST is used to preprocess the data and reduce the dimensions. Next, the features were selected by RST will be sent to SVM model to learn and test respectively. The method is effective to decrease the space density of data. The experiments will compare the results with different methods and show RST and SVM schema could improve the false positive rate and accuracy.


Extended Two-Dimensional PCA for Efficient Face Representation and Recognition

In this paper a novel method called Extended Two-Dimensional PCA (E2DPCA) is proposed which is an extension to the original 2DPCA. We state that the covariance matrix of 2DPCA is equivalent to the average of the main diagonal of the covariance matrix of PCA. This implies that 2DPCA eliminates some covariance information that can be useful for recognition. E2DPCA instead of just using the main diagonal considers a radius of r diagonals around it and expands the averaging so as to include the covariance information within those diagonals. The parameter r unifies PCA and 2DPCA. r = 1 produces the covariance of 2DPCA, r = n that of PCA. Hence, by controlling r it is possible to control the trade-offs between recognition accuracy and energy compression (fewer coefficients), and between training and recognition complexity. Experiments on ORL face database show improvement in both recognition accuracy and recognition time over the original 2DPCA.


Message-Passing Inference on a Factor Graph for Collaborative Filtering

This paper introduces a novel message-passing (MP) framework for the collaborative filtering (CF) problem associated with recommender systems. We model the movie-rating prediction problem popularized by the Netflix Prize, using a probabilistic factor graph model and study the model by deriving generalization error bounds in terms of the training error. Based on the model, we develop a new MP algorithm, termed IMP, for learning the model. To show superiority of the IMP algorithm, we compare it with the closely related expectation-maximization (EM) based algorithm and a number of other matrix completion algorithms. Our simulation results on Netflix data show that, while the methods perform similarly with large amounts of data, the IMP algorithm is superior for small amounts of data. This improves the cold-start problem of the CF systems in practice. Another advantage of the IMP algorithm is that it can be analyzed using the technique of density evolution (DE) that was originally developed for MP decoding of error-correcting codes.


On Tsallis Entropy Bias and Generalized Maximum Entropy Models

In density estimation task, maximum entropy model (Maxent) can effectively use reliable prior information via certain constraints, i.e., linear constraints without empirical parameters. However, reliable prior information is often insufficient, and the selection of uncertain constraints becomes necessary but poses considerable implementation complexity. Improper setting of uncertain constraints can result in overfitting or underfitting. To solve this problem, a generalization of Maxent, under Tsallis entropy framework, is proposed. The proposed method introduces a convex quadratic constraint for the correction of (expected) Tsallis entropy bias (TEB). Specifically, we demonstrate that the expected Tsallis entropy of sampling distributions is smaller than the Tsallis entropy of the underlying real distribution. This expected entropy reduction is exactly the (expected) TEB, which can be expressed by a closed-form formula and act as a consistent and unbiased correction. TEB indicates that the entropy of a specific sampling distribution should be increased accordingly. This entails a quantitative re-interpretation of the Maxent principle. By compensating TEB and meanwhile forcing the resulting distribution to be close to the sampling distribution, our generalized TEBC Maxent can be expected to alleviate the overfitting and underfitting. We also present a connection between TEB and Lidstone estimator. As a result, TEB-Lidstone estimator is developed by analytically identifying the rate of probability correction in Lidstone. Extensive empirical evaluation shows promising performance of both TEBC Maxent and TEB-Lidstone in comparison with various state-of-the-art density estimation methods.


Ontology-supported processing of clinical text using medical knowledge integration for multi-label classification of diagnosis coding

This paper discusses the knowledge integration of clinical information extracted from distributed medical ontology in order to ameliorate a machine learning-based multi-label coding assignment system. The proposed approach is implemented using a decision tree based cascade hierarchical technique on the university hospital data for patients with Coronary Heart Disease (CHD). The preliminary results obtained show a satisfactory finding.


An Analytical Study on Behavior of Clusters Using K Means, EM and K* Means Algorithm

Clustering is an unsupervised learning method that constitutes a cornerstone of an intelligent data analysis process. It is used for the exploration of inter-relationships among a collection of patterns, by organizing them into homogeneous clusters. Clustering has been dynamically applied to a variety of tasks in the field of Information Retrieval (IR). Clustering has become one of the most active area of research and the development. Clustering attempts to discover the set of consequential groups where those within each group are more closely related to one another than the others assigned to different groups. The resultant clusters can provide a structure for organizing large bodies of text for efficient browsing and searching. There exists a wide variety of clustering algorithms that has been intensively studied in the clustering problem. Among the algorithms that remain the most common and effectual, the iterative optimization clustering algorithms have been demonstrated reasonable performance for clustering, e.g. the Expectation Maximization (EM) algorithm and its variants, and the well known k-means algorithm. This paper presents an analysis on how partition method clustering techniques - EM, K -means and K* Means algorithm work on heartspect dataset with below mentioned features - Purity, Entropy, CPU time, Cluster wise analysis, Mean value analysis and inter cluster distance. Thus the paper finally provides the experimental results of datasets for five clusters to strengthen the results that the quality of the behavior in clusters in EM algorithm is far better than k-means algorithm and k*means algorithm.


State-Space Dynamics Distance for Clustering Sequential Data

This paper proposes a novel similarity measure for clustering sequential data. We first construct a common state-space by training a single probabilistic model with all the sequences in order to get a unified representation for the dataset. Then, distances are obtained attending to the transition matrices induced by each sequence in that state-space. This approach solves some of the usual overfitting and scalability issues of the existing semi-parametric techniques, that rely on training a model for each sequence. Empirical studies on both synthetic and real-world datasets illustrate the advantages of the proposed similarity measure for clustering sequences.


An optimized recursive learning algorithm for three-layer feedforward neural networks for mimo nonlinear system identifications

Back-propagation with gradient method is the most popular learning algorithm for feed-forward neural networks. However, it is critical to determine a proper fixed learning rate for the algorithm. In this paper, an optimized recursive algorithm is presented for online learning based on matrix operation and optimization methods analytically, which can avoid the trouble to select a proper learning rate for the gradient method. The proof of weak convergence of the proposed algorithm also is given. Although this approach is proposed for three-layer, feed-forward neural networks, it could be extended to multiple layer feed-forward neural networks. The effectiveness of the proposed algorithms applied to the identification of behavior of a two-input and two-output non-linear dynamic system is demonstrated by simulation experiments.


Dynamic Policy Programming

In this paper, we propose a novel policy iteration method, called dynamic policy programming (DPP), to estimate the optimal policy in the infinite-horizon Markov decision processes. We prove the finite-iteration and asymptotic l\infty-norm performance-loss bounds for DPP in the presence of approximation/estimation error. The bounds are expressed in terms of the l\infty-norm of the average accumulated error as opposed to the l\infty-norm of the error in the case of the standard approximate value iteration (AVI) and the approximate policy iteration (API). This suggests that DPP can achieve a better performance than AVI and API since it averages out the simulation noise caused by Monte-Carlo sampling throughout the learning process. We examine this theoretical results numerically by com- paring the performance of the approximate variants of DPP with existing reinforcement learning (RL) methods on different problem domains. Our results show that, in all cases, DPP-based algorithms outperform other RL methods by a wide margin.


Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory

In regular statistical models, the leave-one-out cross-validation is asymptotically equivalent to the Akaike information criterion. However, since many learning machines are singular statistical models, the asymptotic behavior of the cross-validation remains unknown. In previous studies, we established the singular learning theory and proposed a widely applicable information criterion, the expectation value of which is asymptotically equal to the average Bayes generalization loss. In the present paper, we theoretically compare the Bayes cross-validation loss and the widely applicable information criterion and prove two theorems. First, the Bayes cross-validation loss is asymptotically equivalent to the widely applicable information criterion as a random variable. Therefore, model selection and hyperparameter optimization using these two values are asymptotically equivalent. Second, the sum of the Bayes generalization error and the Bayes cross-validation error is asymptotically equal to $2\lambda/n$, where $\lambda$ is the real log canonical threshold and $n$ is the number of training samples. Therefore the relation between the cross-validation error and the generalization error is determined by the algebraic geometrical structure of a learning machine. We also clarify that the deviance information criteria are different from the Bayes cross-validation and the widely applicable information criterion.


Generation and Interpretation of Temporal Decision Rules

We present a solution to the problem of understanding a system that produces a sequence of temporally ordered observations. Our solution is based on generating and interpreting a set of temporal decision rules. A temporal decision rule is a decision rule that can be used to predict or retrodict the value of a decision attribute, using condition attributes that are observed at times other than the decision attribute's time of observation. A rule set, consisting of a set of temporal decision rules with the same decision attribute, can be interpreted by our Temporal Investigation Method for Enregistered Record Sequences (TIMERS) to signify an instantaneous, an acausal or a possibly causal relationship between the condition attributes and the decision attribute. We show the effectiveness of our method, by describing a number of experiments with both synthetic and real temporal data.


From open quantum systems to open quantum maps

For a class of quantized open chaotic systems satisfying a natural dynamical assumption, we show that the study of the resolvent, and hence of scattering and resonances, can be reduced to the study of a family of open quantum maps, that is of finite dimensional operators obtained by quantizing the Poincar\'e map associated with the flow near the set of trapped trajectories.


Bregman Distance to L1 Regularized Logistic Regression

In this work we investigate the relationship between Bregman distances and regularized Logistic Regression model. We present a detailed study of Bregman Distance minimization, a family of generalized entropy measures associated with convex functions. We convert the L1-regularized logistic regression into this more general framework and propose a primal-dual method based algorithm for learning the parameters. We pose L1-regularized logistic regression into Bregman distance minimization and then apply non-linear constrained optimization techniques to estimate the parameters of the logistic model.


Settling the Polynomial Learnability of Mixtures of Gaussians

Given data drawn from a mixture of multivariate Gaussians, a basic problem is to accurately estimate the mixture parameters. We give an algorithm for this problem that has a running time, and data requirement polynomial in the dimension and the inverse of the desired accuracy, with provably minimal assumptions on the Gaussians. As simple consequences of our learning algorithm, we can perform near-optimal clustering of the sample points and density estimation for mixtures of k Gaussians, efficiently. The building blocks of our algorithm are based on the work Kalai et al. [STOC 2010] that gives an efficient algorithm for learning mixtures of two Gaussians by considering a series of projections down to one dimension, and applying the method of moments to each univariate projection. A major technical hurdle in Kalai et al. is showing that one can efficiently learn univariate mixtures of two Gaussians. In contrast, because pathological scenarios can arise when considering univariate projections of mixtures of more than two Gaussians, the bulk of the work in this paper concerns how to leverage an algorithm for learning univariate mixtures (of many Gaussians) to yield an efficient algorithm for learning in high dimensions. Our algorithm employs hierarchical clustering and rescaling, together with delicate methods for backtracking and recovering from failures that can occur in our univariate algorithm. Finally, while the running time and data requirements of our algorithm depend exponentially on the number of Gaussians in the mixture, we prove that such a dependence is necessary.


Efficient Learning with Partially Observed Attributes

We describe and analyze efficient algorithms for learning a linear predictor from examples when the learner can only view a few attributes of each training example. This is the case, for instance, in medical research, where each patient participating in the experiment is only willing to go through a small number of tests. Our analysis bounds the number of additional examples sufficient to compensate for the lack of full information on each training example. We demonstrate the efficiency of our algorithms by showing that when running on digit recognition data, they obtain a high prediction accuracy even when the learner gets to see only four pixels of each image.


Evolutionary Inference for Function-valued Traits: Gaussian Process Regression on Phylogenies

Biological data objects often have both of the following features: (i) they are functions rather than single numbers or vectors, and (ii) they are correlated due to phylogenetic relationships. In this paper we give a flexible statistical model for such data, by combining assumptions from phylogenetics with Gaussian processes. We describe its use as a nonparametric Bayesian prior distribution, both for prediction (placing posterior distributions on ancestral functions) and model selection (comparing rates of evolution across a phylogeny, or identifying the most likely phylogenies consistent with the observed data). Our work is integrative, extending the popular phylogenetic Brownian Motion and Ornstein-Uhlenbeck models to functional data and Bayesian inference, and extending Gaussian Process regression to phylogenies. We provide a brief illustration of the application of our method.


Polynomial Learning of Distribution Families

The question of polynomial learnability of probability distributions, particularly Gaussian mixture distributions, has recently received significant attention in theoretical computer science and machine learning. However, despite major progress, the general question of polynomial learnability of Gaussian mixture distributions still remained open. The current work resolves the question of polynomial learnability for Gaussian mixtures in high dimension with an arbitrary fixed number of components. The result on learning Gaussian mixtures relies on an analysis of distributions belonging to what we call "polynomial families" in low dimension. These families are characterized by their moments being polynomial in parameters and include almost all common probability distributions as well as their mixtures and products. Using tools from real algebraic geometry, we show that parameters of any distribution belonging to such a family can be learned in polynomial time and using a polynomial number of sample points. The result on learning polynomial families is quite general and is of independent interest. To estimate parameters of a Gaussian mixture distribution in high dimensions, we provide a deterministic algorithm for dimensionality reduction. This allows us to reduce learning a high-dimensional mixture to a polynomial number of parameter estimations in low dimension. Combining this reduction with the results on polynomial families yields our result on learning arbitrary Gaussian mixtures in high dimensions.


Clustering processes

The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist, under most general non-parametric assumptions. The notion of consistency is as follows: two samples should be put into the same cluster if and only if they were generated by the same distribution. With this notion of consistency, clustering generalizes such classical statistical problems as homogeneity testing and process classification. We show that, for the case of a known number of clusters, consistency can be achieved under the only assumption that the joint distribution of the data is stationary ergodic (no parametric or Markovian assumptions, no assumptions of independence, neither between nor within the samples). If the number of clusters is unknown, consistency can be achieved under appropriate assumptions on the mixing rates of the processes. (again, no parametric or independence assumptions). In both cases we give examples of simple (at most quadratic in each argument) algorithms which are consistent.


Optimism in Reinforcement Learning and Kullback-Leibler Divergence

We consider model-based reinforcement learning in finite Markov De- cision Processes (MDPs), focussing on so-called optimistic strategies. In MDPs, optimism can be implemented by carrying out extended value it- erations under a constraint of consistency with the estimated model tran- sition probabilities. The UCRL2 algorithm by Auer, Jaksch and Ortner (2009), which follows this strategy, has recently been shown to guarantee near-optimal regret bounds. In this paper, we strongly argue in favor of using the Kullback-Leibler (KL) divergence for this purpose. By studying the linear maximization problem under KL constraints, we provide an ef- ficient algorithm, termed KL-UCRL, for solving KL-optimistic extended value iteration. Using recent deviation bounds on the KL divergence, we prove that KL-UCRL provides the same guarantees as UCRL2 in terms of regret. However, numerical experiments on classical benchmarks show a significantly improved behavior, particularly when the MDP has reduced connectivity. To support this observation, we provide elements of com- parison between the two algorithms based on geometric considerations.


Designing neural networks that process mean values of random variables

We introduce a class of neural networks derived from probabilistic models in the form of Bayesian networks. By imposing additional assumptions about the nature of the probabilistic models represented in the networks, we derive neural networks with standard dynamics that require no training to determine the synaptic weights, that perform accurate calculation of the mean values of the random variables, that can pool multiple sources of evidence, and that deal cleanly and consistently with inconsistent or contradictory evidence. The presented neural networks capture many properties of Bayesian networks, providing distributed versions of probabilistic models.


Learning from Multiple Outlooks

We propose a novel problem formulation of learning a single task when the data are provided in different feature spaces. Each such space is called an outlook, and is assumed to contain both labeled and unlabeled data. The objective is to take advantage of the data from all the outlooks to better classify each of the outlooks. We devise an algorithm that computes optimal affine mappings from different outlooks to a target outlook by matching moments of the empirical distributions. We further derive a probabilistic interpretation of the resulting algorithm and a sample complexity bound indicating how many samples are needed to adequately find the mapping. We report the results of extensive experiments on activity recognition tasks that show the value of the proposed approach in boosting performance.


A Geometric View of Conjugate Priors

In Bayesian machine learning, conjugate priors are popular, mostly due to mathematical convenience. In this paper, we show that there are deeper reasons for choosing a conjugate prior. Specifically, we formulate the conjugate prior in the form of Bregman divergence and show that it is the inherent geometry of conjugate priors that makes them appropriate and intuitive. This geometric interpretation allows one to view the hyperparameters of conjugate priors as the {\it effective} sample points, thus providing additional intuition. We use this geometric understanding of conjugate priors to derive the hyperparameters and expression of the prior used to couple the generative and discriminative components of a hybrid model for semi-supervised learning.


Large Margin Multiclass Gaussian Classification with Differential Privacy

As increasing amounts of sensitive personal information is aggregated into data repositories, it has become important to develop mechanisms for processing the data without revealing information about individual data instances. The differential privacy model provides a framework for the development and theoretical analysis of such mechanisms. In this paper, we propose an algorithm for learning a discriminatively trained multi-class Gaussian classifier that satisfies differential privacy using a large margin loss function with a perturbed regularization term. We present a theoretical upper bound on the excess risk of the classifier introduced by the perturbation.


Distributive Stochastic Learning for Delay-Optimal OFDMA Power and Subband Allocation

In this paper, we consider the distributive queue-aware power and subband allocation design for a delay-optimal OFDMA uplink system with one base station, $K$ users and $N_F$ independent subbands. Each mobile has an uplink queue with heterogeneous packet arrivals and delay requirements. We model the problem as an infinite horizon average reward Markov Decision Problem (MDP) where the control actions are functions of the instantaneous Channel State Information (CSI) as well as the joint Queue State Information (QSI). To address the distributive requirement and the issue of exponential memory requirement and computational complexity, we approximate the subband allocation Q-factor by the sum of the per-user subband allocation Q-factor and derive a distributive online stochastic learning algorithm to estimate the per-user Q-factor and the Lagrange multipliers (LM) simultaneously and determine the control actions using an auction mechanism. We show that under the proposed auction mechanism, the distributive online learning converges almost surely (with probability 1). For illustration, we apply the proposed distributive stochastic learning framework to an application example with exponential packet size distribution. We show that the delay-optimal power control has the {\em multi-level water-filling} structure where the CSI determines the instantaneous power allocation and the QSI determines the water-level. The proposed algorithm has linear signaling overhead and computational complexity $\mathcal O(KN)$, which is desirable from an implementation perspective.


Adaptive Bases for Reinforcement Learning

We consider the problem of reinforcement learning using function approximation, where the approximating basis can change dynamically while interacting with the environment. A motivation for such an approach is maximizing the value function fitness to the problem faced. Three errors are considered: approximation square error, Bellman residual, and projected Bellman residual. Algorithms under the actor-critic framework are presented, and shown to converge. The advantage of such an adaptive basis is demonstrated in simulations.


Generative and Latent Mean Map Kernels

We introduce two kernels that extend the mean map, which embeds probability measures in Hilbert spaces. The generative mean map kernel (GMMK) is a smooth similarity measure between probabilistic models. The latent mean map kernel (LMMK) generalizes the non-iid formulation of Hilbert space embeddings of empirical distributions in order to incorporate latent variable models. When comparing certain classes of distributions, the GMMK exhibits beneficial regularization and generalization properties not shown for previous generative kernels. We present experiments comparing support vector machine performance using the GMMK and LMMK between hidden Markov models to the performance of other methods on discrete and continuous observation sequence data. The results suggest that, in many cases, the GMMK has generalization error competitive with or better than other methods.


Statistical Learning in Automated Troubleshooting: Application to LTE Interference Mitigation

This paper presents a method for automated healing as part of off-line automated troubleshooting. The method combines statistical learning with constraint optimization. The automated healing aims at locally optimizing radio resource management (RRM) or system parameters of cells with poor performance in an iterative manner. The statistical learning processes the data using Logistic Regression (LR) to extract closed form (functional) relations between Key Performance Indicators (KPIs) and Radio Resource Management (RRM) parameters. These functional relations are then processed by an optimization engine which proposes new parameter values. The advantage of the proposed formulation is the small number of iterations required by the automated healing method to converge, making it suitable for off-line implementation. The proposed method is applied to heal an Inter-Cell Interference Coordination (ICIC) process in a 3G Long Term Evolution (LTE) network which is based on soft-frequency reuse scheme. Numerical simulations illustrate the benefits of the proposed approach.


Machine Learning for Galaxy Morphology Classification

In this work, decision tree learning algorithms and fuzzy inferencing systems are applied for galaxy morphology classification. In particular, the CART, the C4.5, the Random Forest and fuzzy logic algorithms are studied and reliable classifiers are developed to distinguish between spiral galaxies, elliptical galaxies or star/unknown galactic objects. Morphology information for the training and testing datasets is obtained from the Galaxy Zoo project while the corresponding photometric and spectra parameters are downloaded from the SDSS DR7 catalogue.


A Unifying View of Multiple Kernel Learning

Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization strategies. In this paper we present a unifying general optimization criterion for multiple kernel learning and show how existing formulations are subsumed as special cases. We also derive the criterion's dual representation, which is suitable for general smooth optimization algorithms. Finally, we evaluate multiple kernel learning in this framework analytically using a Rademacher complexity bound on the generalization error and empirically in a set of experiments.


Feature Selection with Conjunctions of Decision Stumps and Learning from Microarray Data

One of the objectives of designing feature selection learning algorithms is to obtain classifiers that depend on a small number of attributes and have verifiable future performance guarantees. There are few, if any, approaches that successfully address the two goals simultaneously. Performance guarantees become crucial for tasks such as microarray data analysis due to very small sample sizes resulting in limited empirical evaluation. To the best of our knowledge, such algorithms that give theoretical bounds on the future performance have not been proposed so far in the context of the classification of gene expression data. In this work, we investigate the premise of learning a conjunction (or disjunction) of decision stumps in Occam's Razor, Sample Compression, and PAC-Bayes learning settings for identifying a small subset of attributes that can be used to perform reliable classification tasks. We apply the proposed approaches for gene identification from DNA microarray data and compare our results to those of well known successful approaches proposed for the task. We show that our algorithm not only finds hypotheses with much smaller number of genes while giving competitive classification accuracy but also have tight risk guarantees on future performance unlike other approaches. The proposed approaches are general and extensible in terms of both designing novel algorithms and application to other domains.


Active Learning for Hidden Attributes in Networks

In many networks, vertices have hidden attributes, or types, that are correlated with the networks topology. If the topology is known but these attributes are not, and if learning the attributes is costly, we need a method for choosing which vertex to query in order to learn as much as possible about the attributes of the other vertices. We assume the network is generated by a stochastic block model, but we make no assumptions about its assortativity or disassortativity. We choose which vertex to query using two methods: 1) maximizing the mutual information between its attributes and those of the others (a well-known approach in active learning) and 2) maximizing the average agreement between two independent samples of the conditional Gibbs distribution. Experimental results show that both these methods do much better than simple heuristics. They also consistently identify certain vertices as important by querying them early on.


The Complex Gaussian Kernel LMS algorithm

Although the real reproducing kernels are used in an increasing number of machine learning problems, complex kernels have not, yet, been used, in spite of their potential interest in applications such as communications. In this work, we focus our attention on the complex gaussian kernel and its possible application in the complex Kernel LMS algorithm. In order to derive the gradients needed to develop the complex kernel LMS (CKLMS), we employ the powerful tool of Wirtinger's Calculus, which has recently attracted much attention in the signal processing community. Writinger's calculus simplifies computations and offers an elegant tool for treating complex signals. To this end, the notion of Writinger's calculus is extended to include complex RKHSs. Experiments verify that the CKLMS offers significant performance improvements over the traditional complex LMS or Widely Linear complex LMS (WL-LMS) algorithms, when dealing with nonlinearities.


Extension of Wirtinger Calculus in RKH Spaces and the Complex Kernel LMS

Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. However, so far, the emphasis has been on batch techniques. It is only recently, that online adaptive techniques have been considered in the context of signal processing tasks. To the best of our knowledge, no kernel-based strategy has been developed, so far, that is able to deal with complex valued signals. In this paper, we take advantage of a technique called complexification of real RKHSs to attack this problem. In order to derive gradients and subgradients of operators that need to be defined on the associated complex RKHSs, we employ the powerful tool ofWirtinger's Calculus, which has recently attracted much attention in the signal processing community. Writinger's calculus simplifies computations and offers an elegant tool for treating complex signals. To this end, in this paper, the notion of Writinger's calculus is extended, for the first time, to include complex RKHSs and use it to derive the Complex Kernel Least-Mean-Square (CKLMS) algorithm. Experiments verify that the CKLMS can be used to derive nonlinear stable algorithms, which offer significant performance improvements over the traditional complex LMS orWidely Linear complex LMS (WL-LMS) algorithms, when dealing with nonlinearities.


Estimating small moments of data stream in nearly optimal space-time

For each $p \in (0,2]$, we present a randomized algorithm that returns an $\epsilon$-approximation of the $p$th frequency moment of a data stream $F_p = \sum_{i = 1}^n \abs{f_i}^p$. The algorithm requires space $O(\epsilon^{-2} \log (mM)(\log n))$ and processes each stream update using time $O((\log n) (\log \epsilon^{-1}))$. It is nearly optimal in terms of space (lower bound $O(\epsilon^{-2} \log (mM))$ as well as time and is the first algorithm with these properties. The technique separates heavy hitters from the remaining items in the stream using an appropriate threshold and estimates the contribution of the heavy hitters and the light elements to $F_p$ separately. A key component is the design of an unbiased estimator for $\abs{f_i}^p$ whose data structure has low update time and low variance.


Improving Semi-Supervised Support Vector Machines Through Unlabeled Instances Selection

Semi-supervised support vector machines (S3VMs) are a kind of popular approaches which try to improve learning performance by exploiting unlabeled data. Though S3VMs have been found helpful in many situations, they may degenerate performance and the resultant generalization ability may be even worse than using the labeled data only. In this paper, we try to reduce the chance of performance degeneration of S3VMs. Our basic idea is that, rather than exploiting all unlabeled data, the unlabeled instances should be selected such that only the ones which are very likely to be helpful are exploited, while some highly risky unlabeled instances are avoided. We propose the S3VM-\emph{us} method by using hierarchical clustering to select the unlabeled instances. Experiments on a broad range of data sets over eighty-eight different settings show that the chance of performance degeneration of S3VM-\emph{us} is much smaller than that of existing S3VMs.


Prediction with Expert Advice under Discounted Loss

We study prediction with expert advice in the setting where the losses are accumulated with some discounting---the impact of old losses may gradually vanish. We generalize the Aggregating Algorithm and the Aggregating Algorithm for Regression to this case, propose a suitable new variant of exponential weights algorithm, and prove respective loss bounds.


On the Finite Time Convergence of Cyclic Coordinate Descent Methods

Cyclic coordinate descent is a classic optimization method that has witnessed a resurgence of interest in machine learning. Reasons for this include its simplicity, speed and stability, as well as its competitive performance on $\ell_1$ regularized smooth optimization problems. Surprisingly, very little is known about its finite time convergence behavior on these problems. Most existing results either just prove convergence or provide asymptotic rates. We fill this gap in the literature by proving $O(1/k)$ convergence rates (where $k$ is the iteration counter) for two variants of cyclic coordinate descent under an isotonicity assumption. Our analysis proceeds by comparing the objective values attained by the two variants with each other, as well as with the gradient descent algorithm. We show that the iterates generated by the cyclic coordinate descent methods remain better than those of gradient descent uniformly over time.


Detecting Blackholes and Volcanoes in Directed Networks

In this paper, we formulate a novel problem for finding blackhole and volcano patterns in a large directed graph. Specifically, a blackhole pattern is a group which is made of a set of nodes in a way such that there are only inlinks to this group from the rest nodes in the graph. In contrast, a volcano pattern is a group which only has outlinks to the rest nodes in the graph. Both patterns can be observed in real world. For instance, in a trading network, a blackhole pattern may represent a group of traders who are manipulating the market. In the paper, we first prove that the blackhole mining problem is a dual problem of finding volcanoes. Therefore, we focus on finding the blackhole patterns. Along this line, we design two pruning schemes to guide the blackhole finding process. In the first pruning scheme, we strategically prune the search space based on a set of pattern-size-independent pruning rules and develop an iBlackhole algorithm. The second pruning scheme follows a divide-and-conquer strategy to further exploit the pruning results from the first pruning scheme. Indeed, a target directed graphs can be divided into several disconnected subgraphs by the first pruning scheme, and thus the blackhole finding can be conducted in each disconnected subgraph rather than in a large graph. Based on these two pruning schemes, we also develop an iBlackhole-DC algorithm. Finally, experimental results on real-world data show that the iBlackhole-DC algorithm can be several orders of magnitude faster than the iBlackhole algorithm, which has a huge computational advantage over a brute-force method.


Robustness and Generalization

We derive generalization bounds for learning algorithms based on their robustness: the property that if a testing sample is "similar" to a training sample, then the testing error is close to the training error. This provides a novel approach, different from the complexity or stability arguments, to study generalization of learning algorithms. We further show that a weak notion of robustness is both sufficient and necessary for generalizability, which implies that robustness is a fundamental property for learning algorithms to work.


Context models on sequences of covers

We present a class of models that, via a simple construction, enables exact, incremental, non-parametric, polynomial-time, Bayesian inference of conditional measures. The approach relies upon creating a sequence of covers on the conditioning variable and maintaining a different model for each set within a cover. Inference remains tractable by specifying the probabilistic model in terms of a random walk within the sequence of covers. We demonstrate the approach on problems of conditional density estimation, which, to our knowledge is the first closed-form, non-parametric Bayesian approach to this problem.


Online Learning of Noisy Data with Kernels

We study online learning when individual instances are corrupted by adversarially chosen random noise. We assume the noise distribution is unknown, and may change over time with no restriction other than having zero mean and bounded variance. Our technique relies on a family of unbiased estimators for non-linear functions, which may be of independent interest. We show that a variant of online gradient descent can learn functions in any dot-product (e.g., polynomial) or Gaussian kernel space with any analytic convex loss function. Our variant uses randomized estimates that need to query a random number of noisy copies of each instance, where with high probability this number is upper bounded by a constant. Allowing such multiple queries cannot be avoided: Indeed, we show that online learning is in general impossible when only one noisy copy of each instance can be accessed.


A Short Introduction to Model Selection, Kolmogorov Complexity and Minimum Description Length (MDL)

The concept of overfitting in model selection is explained and demonstrated with an example. After providing some background information on information theory and Kolmogorov complexity, we provide a short explanation of Minimum Description Length and error minimization. We conclude with a discussion of the typical features of overfitting in model selection.


Eigenvectors for clustering: Unipartite, bipartite, and directed graph cases

This paper presents a concise tutorial on spectral clustering for broad spectrum graphs which include unipartite (undirected) graph, bipartite graph, and directed graph. We show how to transform bipartite graph and directed graph into corresponding unipartite graph, therefore allowing a unified treatment to all cases. In bipartite graph, we show that the relaxed solution to the $K$-way co-clustering can be found by computing the left and right eigenvectors of the data matrix. This gives a theoretical basis for $K$-way spectral co-clustering algorithms proposed in the literatures. We also show that solving row and column co-clustering is equivalent to solving row and column clustering separately, thus giving a theoretical support for the claim: ``column clustering implies row clustering and vice versa''. And in the last part, we generalize the Ky Fan theorem---which is the central theorem for explaining spectral clustering---to rectangular complex matrix motivated by the results from bipartite graph analysis.


Hierarchical Clustering for Finding Symmetries and Other Patterns in Massive, High Dimensional Datasets

Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. "Structure" can be understood as symmetry and a range of symmetries are expressed by hierarchy. Such symmetries directly point to invariants, that pinpoint intrinsic properties of the data and of the background empirical domain of interest. We review many aspects of hierarchy here, including ultrametric topology, generalized ultrametric, linkages with lattices and other discrete algebraic structures and with p-adic number representations. By focusing on symmetries in data we have a powerful means of structuring and analyzing massive, high dimensional data stores. We illustrate the powerfulness of hierarchical clustering in case studies in chemistry and finance, and we provide pointers to other published case studies.


Structural Drift: The Population Dynamics of Sequential Learning

We introduce a theory of sequential causal inference in which learners in a chain estimate a structural model from their upstream teacher and then pass samples from the model to their downstream student. It extends the population dynamics of genetic drift, recasting Kimura's selectively neutral theory as a special case of a generalized drift process using structured populations with memory. We examine the diffusion and fixation properties of several drift processes and propose applications to learning, inference, and evolution. We also demonstrate how the organization of drift process space controls fidelity, facilitates innovations, and leads to information loss in sequential learning with and without memory.


Evolution with Drifting Targets

We consider the question of the stability of evolutionary algorithms to gradual changes, or drift, in the target concept. We define an algorithm to be resistant to drift if, for some inverse polynomial drift rate in the target function, it converges to accuracy 1 -- \epsilon , with polynomial resources, and then stays within that accuracy indefinitely, except with probability \epsilon , at any one time. We show that every evolution algorithm, in the sense of Valiant (2007; 2009), can be converted using the Correlational Query technique of Feldman (2008), into such a drift resistant algorithm. For certain evolutionary algorithms, such as for Boolean conjunctions, we give bounds on the rates of drift that they can resist. We develop some new evolution algorithms that are resistant to significant drift. In particular, we give an algorithm for evolving linear separators over the spherically symmetric distribution that is resistant to a drift rate of O(\epsilon /n), and another algorithm over the more general product normal distributions that resists a smaller drift rate. The above translation result can be also interpreted as one on the robustness of the notion of evolvability itself under changes of definition. As a second result in that direction we show that every evolution algorithm can be converted to a quasi-monotonic one that can evolve from any starting point without the performance ever dipping significantly below that of the starting point. This permits the somewhat unnatural feature of arbitrary performance degradations to be removed from several known robustness translations.


Graph-Structured Multi-task Regression and an Efficient Optimization Method for General Fused Lasso

We consider the problem of learning a structured multi-task regression, where the output consists of multiple responses that are related by a graph and the correlated response variables are dependent on the common inputs in a sparse but synergistic manner. Previous methods such as l1/l2-regularized multi-task regression assume that all of the output variables are equally related to the inputs, although in many real-world problems, outputs are related in a complex manner. In this paper, we propose graph-guided fused lasso (GFlasso) for structured multi-task regression that exploits the graph structure over the output variables. We introduce a novel penalty function based on fusion penalty to encourage highly correlated outputs to share a common set of relevant inputs. In addition, we propose a simple yet efficient proximal-gradient method for optimizing GFlasso that can also be applied to any optimization problems with a convex smooth loss and the general class of fusion penalty defined on arbitrary graph structures. By exploiting the structure of the non-smooth ''fusion penalty'', our method achieves a faster convergence rate than the standard first-order method, sub-gradient method, and is significantly more scalable than the widely adopted second-order cone-programming and quadratic-programming formulations. In addition, we provide an analysis of the consistency property of the GFlasso model. Experimental results not only demonstrate the superiority of GFlasso over the standard lasso but also show the efficiency and scalability of our proximal-gradient method.


Learning Kernel-Based Halfspaces with the Zero-One Loss

We describe and analyze a new algorithm for agnostically learning kernel-based halfspaces with respect to the \emph{zero-one} loss function. Unlike most previous formulations which rely on surrogate convex loss functions (e.g. hinge-loss in SVM and log-loss in logistic regression), we provide finite time/sample guarantees with respect to the more natural zero-one loss function. The proposed algorithm can learn kernel-based halfspaces in worst-case time $\poly(\exp(L\log(L/\epsilon)))$, for $\emph{any}$ distribution, where $L$ is a Lipschitz constant (which can be thought of as the reciprocal of the margin), and the learned classifier is worse than the optimal halfspace by at most $\epsilon$. We also prove a hardness result, showing that under a certain cryptographic assumption, no algorithm can learn kernel-based halfspaces in time polynomial in $L$.


Distantly Labeling Data for Large Scale Cross-Document Coreference

Cross-document coreference, the problem of resolving entity mentions across multi-document collections, is crucial to automated knowledge base construction and data mining tasks. However, the scarcity of large labeled data sets has hindered supervised machine learning research for this task. In this paper we develop and demonstrate an approach based on ``distantly-labeling'' a data set from which we can train a discriminative cross-document coreference model. In particular we build a dataset of more than a million people mentions extracted from 3.5 years of New York Times articles, leverage Wikipedia for distant labeling with a generative model (and measure the reliability of such labeling); then we train and evaluate a conditional random field coreference model that has factors on cross-document entities as well as mention-pairs. This coreference model obtains high accuracy in resolving mentions and entities that are not present in the training data, indicating applicability to non-Wikipedia data. Given the large amount of data, our work is also an exercise demonstrating the scalability of our approach.


Smoothing proximal gradient method for general structured sparse regression

We study the problem of estimating high-dimensional regression models regularized by a structured sparsity-inducing penalty that encodes prior structural information on either the input or output variables. We consider two widely adopted types of penalties of this kind as motivating examples: (1) the general overlapping-group-lasso penalty, generalized from the group-lasso penalty; and (2) the graph-guided-fused-lasso penalty, generalized from the fused-lasso penalty. For both types of penalties, due to their nonseparability and nonsmoothness, developing an efficient optimization method remains a challenging problem. In this paper we propose a general optimization approach, the smoothing proximal gradient (SPG) method, which can solve structured sparse regression problems with any smooth convex loss under a wide spectrum of structured sparsity-inducing penalties. Our approach combines a smoothing technique with an effective proximal gradient method. It achieves a convergence rate significantly faster than the standard first-order methods, subgradient methods, and is much more scalable than the most widely used interior-point methods. The efficiency and scalability of our method are demonstrated on both simulation experiments and real genetic data sets.


On Recursive Edit Distance Kernels with Application to Time Series Classification

This paper proposes some extensions to the work on kernels dedicated to string or time series global alignment based on the aggregation of scores obtained by local alignments. The extensions we propose allow to construct, from classical recursive definition of elastic distances, recursive edit distance (or time-warp) kernels that are positive definite if some sufficient conditions are satisfied. The sufficient conditions we end-up with are original and weaker than those proposed in earlier works, although a recursive regularizing term is required to get the proof of the positive definiteness as a direct consequence of the Haussler's convolution theorem. The classification experiment we conducted on three classical time warp distances (two of which being metrics), using Support Vector Machine classifier, leads to conclude that, when the pairwise distance matrix obtained from the training data is \textit{far} from definiteness, the positive definite recursive elastic kernels outperform in general the distance substituting kernels for the classical elastic distances we have tested.


Wirtinger's Calculus in general Hilbert Spaces

The present report, has been inspired by the need of the author and its colleagues to understand the underlying theory of Wirtinger's Calculus and to further extend it to include the kernel case. The aim of the present manuscript is twofold: a) it endeavors to provide a more rigorous presentation of the related material, focusing on aspects that the author finds more insightful and b) it extends the notions of Wirtinger's calculus on general Hilbert spaces (such as Reproducing Hilbert Kernel Spaces).


Ranked bandits in metric spaces: learning optimally diverse rankings over large document collections

Most learning to rank research has assumed that the utility of different documents is independent, which results in learned ranking functions that return redundant results. The few approaches that avoid this have rather unsatisfyingly lacked theoretical foundations, or do not scale. We present a learning-to-rank formulation that optimizes the fraction of satisfied users, with several scalable algorithms that explicitly takes document similarity and ranking context into account. Our formulation is a non-trivial common generalization of two multi-armed bandit models from the literature: "ranked bandits" (Radlinski et al., ICML 2008) and "Lipschitz bandits" (Kleinberg et al., STOC 2008). We present theoretical justifications for this approach, as well as a near-optimal algorithm. Our evaluation adds optimizations that improve empirical performance, and shows that our algorithms learn orders of magnitude more quickly than previous approaches.


Using Soft Constraints To Learn Semantic Models Of Descriptions Of Shapes

The contribution of this paper is to provide a semantic model (using soft constraints) of the words used by web-users to describe objects in a language game; a game in which one user describes a selected object of those composing the scene, and another user has to guess which object has been described. The given description needs to be non ambiguous and accurate enough to allow other users to guess the described shape correctly. To build these semantic models the descriptions need to be analyzed to extract the syntax and words' classes used. We have modeled the meaning of these descriptions using soft constraints as a way for grounding the meaning. The descriptions generated by the system took into account the context of the object to avoid ambiguous descriptions, and allowed users to guess the described object correctly 72% of the times.


Using a Kernel Adatron for Object Classification with RCS Data

Rapid identification of object from radar cross section (RCS) signals is important for many space and military applications. This identification is a problem in pattern recognition which either neural networks or support vector machines should prove to be high-speed. Bayesian networks would also provide value but require significant preprocessing of the signals. In this paper, we describe the use of a support vector machine for object identification from synthesized RCS data. Our best results are from data fusion of X-band and S-band signals, where we obtained 99.4%, 95.3%, 100% and 95.6% correct identification for cylinders, frusta, spheres, and polygons, respectively. We also compare our results with a Bayesian approach and show that the SVM is three orders of magnitude faster, as measured by the number of floating point operations.


On the clustering aspect of nonnegative matrix factorization

This paper provides a theoretical explanation on the clustering aspect of nonnegative matrix factorization (NMF). We prove that even without imposing orthogonality nor sparsity constraint on the basis and/or coefficient matrix, NMF still can give clustering results, thus providing a theoretical support for many works, e.g., Xu et al. [1] and Kim et al. [2], that show the superiority of the standard NMF as a clustering method.


Empirical learning aided by weak domain knowledge in the form of feature importance

Standard hybrid learners that use domain knowledge require stronger knowledge that is hard and expensive to acquire. However, weaker domain knowledge can benefit from prior knowledge while being cost effective. Weak knowledge in the form of feature relative importance (FRI) is presented and explained. Feature relative importance is a real valued approximation of a feature's importance provided by experts. Advantage of using this knowledge is demonstrated by IANN, a modified multilayer neural network algorithm. IANN is a very simple modification of standard neural network algorithm but attains significant performance gains. Experimental results in the field of molecular biology show higher performance over other empirical learning algorithms including standard backpropagation and support vector machines. IANN performance is even comparable to a theory refinement system KBANN that uses stronger domain knowledge. This shows Feature relative importance can improve performance of existing empirical learning algorithms significantly with minimal effort.


Multi-View Active Learning in the Non-Realizable Case

The sample complexity of active learning under the realizability assumption has been well-studied. The realizability assumption, however, rarely holds in practice. In this paper, we theoretically characterize the sample complexity of active learning in the non-realizable case under multi-view setting. We prove that, with unbounded Tsybakov noise, the sample complexity of multi-view active learning can be $\widetilde{O}(\log\frac{1}{\epsilon})$, contrasting to single-view setting where the polynomial improvement is the best possible achievement. We also prove that in general multi-view setting the sample complexity of active learning with unbounded Tsybakov noise is $\widetilde{O}(\frac{1}{\epsilon})$, where the order of $1/\epsilon$ is independent of the parameter in Tsybakov noise, contrasting to previous polynomial bounds where the order of $1/\epsilon$ is related to the parameter in Tsybakov noise.


On the Relation between Realizable and Nonrealizable Cases of the Sequence Prediction Problem

A sequence $x_1,\dots,x_n,\dots$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, one is required to give conditional probabilities of the next observation. The realizable case is when the measure $\mu$ belongs to an arbitrary but known class $\mathcal C$ of process measures. The non-realizable case is when $\mu$ is completely arbitrary, but the prediction performance is measured with respect to a given set $\mathcal C$ of process measures. We are interested in the relations between these problems and between their solutions, as well as in characterizing the cases when a solution exists and finding these solutions. We show that if the quality of prediction is measured using the total variation distance, then these problems coincide, while if it is measured using the expected average KL divergence, then they are different. For some of the formalizations we also show that when a solution exists, it can be obtained as a Bayes mixture over a countable subset of $\mathcal C$. We also obtain several characterization of those sets $\mathcal C$ for which solutions to the considered problems exist. As an illustration to the general results obtained, we show that a solution to the non-realizable case of the sequence prediction problem exists for the set of all finite-memory processes, but does not exist for the set of all stationary processes. It should be emphasized that the framework is completely general: the processes measures considered are not required to be i.i.d., mixing, stationary, or to belong to any parametric family.


Information theoretic model validation for clustering

Model selection in clustering requires (i) to specify a suitable clustering principle and (ii) to control the model order complexity by choosing an appropriate number of clusters depending on the noise level in the data. We advocate an information theoretic perspective where the uncertainty in the measurements quantizes the set of data partitionings and, thereby, induces uncertainty in the solution space of clusterings. A clustering model, which can tolerate a higher level of fluctuations in the measurements than alternative models, is considered to be superior provided that the clustering solution is equally informative. This tradeoff between \emph{informativeness} and \emph{robustness} is used as a model selection criterion. The requirement that data partitionings should generalize from one data set to an equally probable second data set gives rise to a new notion of structure induced information.


Prediction with Advice of Unknown Number of Experts

In the framework of prediction with expert advice, we consider a recently introduced kind of regret bounds: the bounds that depend on the effective instead of nominal number of experts. In contrast to the NormalHedge bound, which mainly depends on the effective number of experts and also weakly depends on the nominal one, we obtain a bound that does not contain the nominal number of experts at all. We use the defensive forecasting method and introduce an application of defensive forecasting to multivalued supermartingales.


Predictive PAC learnability: a paradigm for learning from exchangeable input data

Exchangeable random variables form an important and well-studied generalization of i.i.d. variables, however simple examples show that no nontrivial concept or function classes are PAC learnable under general exchangeable data inputs $X_1,X_2,\ldots$. Inspired by the work of Berti and Rigo on a Glivenko--Cantelli theorem for exchangeable inputs, we propose a new paradigm, adequate for learning from exchangeable data: predictive PAC learnability. A learning rule $\mathcal L$ for a function class $\mathscr F$ is predictive PAC if for every $\e,\delta>0$ and each function $f\in {\mathscr F}$, whenever $\abs{\sigma}\geq s(\delta,\e)$, we have with confidence $1-\delta$ that the expected difference between $f(X_{n+1})$ and the image of $f\vert\sigma$ under $\mathcal L$ does not exceed $\e$ conditionally on $X_1,X_2,\ldots,X_n$. Thus, instead of learning the function $f$ as such, we are learning to a given accuracy $\e$ the predictive behaviour of $f$ at the future points $X_i(\omega)$, $i>n$ of the sample path. Using de Finetti's theorem, we show that if a universally separable function class $\mathscr F$ is distribution-free PAC learnable under i.i.d. inputs, then it is distribution-free predictive PAC learnable under exchangeable inputs, with a slightly worse sample complexity.