Sparse-posterior Gaussian Processes for general likelihoods

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate GP methods have been proposed that essentially map the large dataset into a small set of basis points. Among them, two state-of-the-art methods are sparse pseudo-input Gaussian process (SPGP) (Snelson and Ghahramani, 2006) and variablesigma GP (VSGP) Walder et al. (2008), which generalizes SPGP and allows each basis point to have its own length scale. However, VSGP was only derived for regression. In this paper, we propose a new sparse GP framework that uses expectation propagation to directly approximate general GP likelihoods using a sparse and smooth basis. It includes both SPGP and VSGP for regression as special cases. Plus as an EP algorithm, it inherits the ability to process data online. As a particular choice of approximating family, we blur each basis point with a Gaussian distribution that has a full covariance matrix representing the data distribution around that basis point; as a result, we can summarize local data manifold information with a small set of basis points. Our experiments demonstrate that this framework outperforms previous GP classification methods on benchmark datasets in terms of minimizing divergence to the non-sparse GP solution as well as lower misclassification rate.


Irregular-Time Bayesian Networks

In many fields observations are performed irregularly along time, due to either measurement limitations or lack of a constant immanent rate. While discrete-time Markov models (as Dynamic Bayesian Networks) introduce either inefficient computation or an information loss to reasoning about such processes, continuous-time Markov models assume either a discrete state space (as Continuous-Time Bayesian Networks), or a flat continuous state space (as stochastic differential equations). To address these problems, we present a new modeling class called Irregular-Time Bayesian Networks (ITBNs), generalizing Dynamic Bayesian Networks, allowing substantially more compact representations, and increasing the expressivity of the temporal dynamics. In addition, a globally optimal solution is guaranteed when learning temporal systems, provided that they are fully observed at the same irregularly spaced time-points, and a semiparametric subclass of ITBNs is introduced to allow further adaptation to the irregular nature of the available data.


Inference by Minimizing Size, Divergence, or their Sum

We speed up marginal inference by ignoring factors that do not significantly contribute to overall accuracy. In order to pick a suitable subset of factors to ignore, we propose three schemes: minimizing the number of model factors under a bound on the KL divergence between pruned and full models; minimizing the KL divergence under a bound on factor count; and minimizing the weighted sum of KL divergence and factor count. All three problems are solved using an approximation of the KL divergence than can be calculated in terms of marginals computed on a simple seed graph. Applied to synthetic image denoising and to three different types of NLP parsing models, this technique performs marginal inference up to 11 times faster than loopy BP, with graph sizes reduced up to 98%-at comparable error in marginals and parsing accuracy. We also show that minimizing the weighted sum of divergence and size is substantially faster than minimizing either of the other objectives based on the approximation to divergence presented here.


Modeling Events with Cascades of Poisson Processes

We present a probabilistic model of events in continuous time in which each event triggers a Poisson process of successor events. The ensemble of observed events is thereby modeled as a superposition of Poisson processes. Efficient inference is feasible under this model with an EM algorithm. Moreover, the EM algorithm can be implemented as a distributed algorithm, permitting the model to be applied to very large datasets. We apply these techniques to the modeling of Twitter messages and the revision history of Wikipedia.


A Bayesian Matrix Factorization Model for Relational Data

Relational learning can be used to augment one data source with other correlated sources of information, to improve predictive accuracy. We frame a large class of relational learning problems as matrix factorization problems, and propose a hierarchical Bayesian model. Training our Bayesian model using random-walk Metropolis-Hastings is impractically slow, and so we develop a block Metropolis-Hastings sampler which uses the gradient and Hessian of the likelihood to dynamically tune the proposal. We demonstrate that a predictive model of brain response to stimuli can be improved by augmenting it with side information about the stimuli.


Variance-Based Rewards for Approximate Bayesian Reinforcement Learning

The explore{exploit dilemma is one of the central challenges in Reinforcement Learning (RL). Bayesian RL solves the dilemma by providing the agent with information in the form of a prior distribution over environments; however, full Bayesian planning is intractable. Planning with the mean MDP is a common myopic approximation of Bayesian planning. We derive a novel reward bonus that is a function of the posterior distribution over environments, which, when added to the reward in planning with the mean MDP, results in an agent which explores efficiently and effectively. Although our method is similar to existing methods when given an uninformative or unstructured prior, unlike existing methods, our method can exploit structured priors. We prove that our method results in a polynomial sample complexity and empirically demonstrate its advantages in a structured exploration task.


Bayesian Inference in Monte-Carlo Tree Search

Monte-Carlo Tree Search (MCTS) methods are drawing great interest after yielding breakthrough results in computer Go. This paper proposes a Bayesian approach to MCTS that is inspired by distributionfree approaches such as UCT [13], yet significantly differs in important respects. The Bayesian framework allows potentially much more accurate (Bayes-optimal) estimation of node values and node uncertainties from a limited number of simulation trials. We further propose propagating inference in the tree via fast analytic Gaussian approximation methods: this can make the overhead of Bayesian inference manageable in domains such as Go, while preserving high accuracy of expected-value estimates. We find substantial empirical outperformance of UCT in an idealized bandit-tree test environment, where we can obtain valuable insights by comparing with known ground truth. Additionally we rigorously prove on-policy and off-policy convergence of the proposed methods.


Bayesian Model Averaging Using the k-best Bayesian Network Structures

We study the problem of learning Bayesian network structures from data. We develop an algorithm for finding the k-best Bayesian network structures. We propose to compute the posterior probabilities of hypotheses of interest by Bayesian model averaging over the k-best Bayesian networks. We present empirical results on structural discovery over several real and synthetic data sets and show that the method outperforms the model selection method and the state of-the-art MCMC methods.


Learning networks determined by the ratio of prior and data

Recent reports have described that the equivalent sample size (ESS) in a Dirichlet prior plays an important role in learning Bayesian networks. This paper provides an asymptotic analysis of the marginal likelihood score for a Bayesian network. Results show that the ratio of the ESS and sample size determine the penalty of adding arcs in learning Bayesian networks. The number of arcs increases monotonically as the ESS increases; the number of arcs monotonically decreases as the ESS decreases. Furthermore, the marginal likelihood score provides a unified expression of various score metrics by changing prior knowledge.


Online Semi-Supervised Learning on Quantized Graphs

In this paper, we tackle the problem of online semi-supervised learning (SSL). When data arrive in a stream, the dual problems of computation and data storage arise for any SSL method. We propose a fast approximate online SSL algorithm that solves for the harmonic solution on an approximate graph. We show, both empirically and theoretically, that good behavior can be achieved by collapsing nearby points into a set of local "representative points" that minimize distortion. Moreover, we regularize the harmonic solution to achieve better stability properties. We apply our algorithm to face recognition and optical character recognition applications to show that we can take advantage of the manifold structure to outperform the previous methods. Unlike previous heuristic approaches, we show that our method yields provable performance bounds.


Speeding up the binary Gaussian process classification

Gaussian processes (GP) are attractive building blocks for many probabilistic models. Their drawbacks, however, are the rapidly increasing inference time and memory requirement alongside increasing data. The problem can be alleviated with compactly supported (CS) covariance functions, which produce sparse covariance matrices that are fast in computations and cheap to store. CS functions have previously been used in GP regression but here the focus is in a classification problem. This brings new challenges since the posterior inference has to be done approximately. We utilize the expectation propagation algorithm and show how its standard implementation has to be modified to obtain computational benefits from the sparse covariance matrices. We study four CS covariance functions and show that they may lead to substantial speed up in the inference time compared to globally supported functions.


Primal View on Belief Propagation

It is known that fixed points of loopy belief propagation (BP) correspond to stationary points of the Bethe variational problem, where we minimize the Bethe free energy subject to normalization and marginalization constraints. Unfortunately, this does not entirely explain BP because BP is a dual rather than primal algorithm to solve the Bethe variational problem -- beliefs are infeasible before convergence. Thus, we have no better understanding of BP than as an algorithm to seek for a common zero of a system of non-linear functions, not explicitly related to each other. In this theoretical paper, we show that these functions are in fact explicitly related -- they are the partial derivatives of a single function of reparameterizations. That means, BP seeks for a stationary point of a single function, without any constraints. This function has a very natural form: it is a linear combination of local log-partition functions, exactly as the Bethe entropy is the same linear combination of local entropies.


Modeling Multiple Annotator Expertise in the Semi-Supervised Learning Scenario

Learning algorithms normally assume that there is at most one annotation or label per data point. However, in some scenarios, such as medical diagnosis and on-line collaboration,multiple annotations may be available. In either case, obtaining labels for data points can be expensive and time-consuming (in some circumstances ground-truth may not exist). Semi-supervised learning approaches have shown that utilizing the unlabeled data is often beneficial in these cases. This paper presents a probabilistic semi-supervised model and algorithm that allows for learning from both unlabeled and labeled data in the presence of multiple annotators. We assume that it is known what annotator labeled which data points. The proposed approach produces annotator models that allow us to provide (1) estimates of the true label and (2) annotator variable expertise for both labeled and unlabeled data. We provide numerical comparisons under various scenarios and with respect to standard semi-supervised learning. Experiments showed that the presented approach provides clear advantages over multi-annotator methods that do not use the unlabeled data and over methods that do not use multi-labeler information.


Hybrid Generative/Discriminative Learning for Automatic Image Annotation

Automatic image annotation (AIA) raises tremendous challenges to machine learning as it requires modeling of data that are both ambiguous in input and output, e.g., images containing multiple objects and labeled with multiple semantic tags. Even more challenging is that the number of candidate tags is usually huge (as large as the vocabulary size) yet each image is only related to a few of them. This paper presents a hybrid generative-discriminative classifier to simultaneously address the extreme data-ambiguity and overfitting-vulnerability issues in tasks such as AIA. Particularly: (1) an Exponential-Multinomial Mixture (EMM) model is established to capture both the input and output ambiguity and in the meanwhile to encourage prediction sparsity; and (2) the prediction ability of the EMM model is explicitly maximized through discriminative learning that integrates variational inference of graphical models and the pairwise formulation of ordinal regression. Experiments show that our approach achieves both superior annotation performance and better tag scalability.


Learning Structural Changes of Gaussian Graphical Models in Controlled Experiments

Graphical models are widely used in scienti fic and engineering research to represent conditional independence structures between random variables. In many controlled experiments, environmental changes or external stimuli can often alter the conditional dependence between the random variables, and potentially produce significant structural changes in the corresponding graphical models. Therefore, it is of great importance to be able to detect such structural changes from data, so as to gain novel insights into where and how the structural changes take place and help the system adapt to the new environment. Here we report an effective learning strategy to extract structural changes in Gaussian graphical model using l1-regularization based convex optimization. We discuss the properties of the problem formulation and introduce an efficient implementation by the block coordinate descent algorithm. We demonstrate the principle of the approach on a numerical simulation experiment, and we then apply the algorithm to the modeling of gene regulatory networks under different conditions and obtain promising yet biologically plausible results.


Source Separation and Higher-Order Causal Analysis of MEG and EEG

Separation of the sources and analysis of their connectivity have been an important topic in EEG/MEG analysis. To solve this problem in an automatic manner, we propose a two-layer model, in which the sources are conditionally uncorrelated from each other, but not independent; the dependence is caused by the causality in their time-varying variances (envelopes). The model is identified in two steps. We first propose a new source separation technique which takes into account the autocorrelations (which may be time-varying) and time-varying variances of the sources. The causality in the envelopes is then discovered by exploiting a special kind of multivariate GARCH (generalized autoregressive conditional heteroscedasticity) model. The resulting causal diagram gives the effective connectivity between the separated sources; in our experimental results on MEG data, sources with similar functions are grouped together, with negative influences between groups, and the groups are connected via some interesting sources.


Invariant Gaussian Process Latent Variable Models and Application in Causal Discovery

In nonlinear latent variable models or dynamic models, if we consider the latent variables as confounders (common causes), the noise dependencies imply further relations between the observed variables. Such models are then closely related to causal discovery in the presence of nonlinear confounders, which is a challenging problem. However, generally in such models the observation noise is assumed to be independent across data dimensions, and consequently the noise dependencies are ignored. In this paper we focus on the Gaussian process latent variable model (GPLVM), from which we develop an extended model called invariant GPLVM (IGPLVM), which can adapt to arbitrary noise covariances. With the Gaussian process prior put on a particular transformation of the latent nonlinear functions, instead of the original ones, the algorithm for IGPLVM involves almost the same computational loads as that for the original GPLVM. Besides its potential application in causal discovery, IGPLVM has the advantage that its estimated latent nonlinear manifold is invariant to any nonsingular linear transformation of the data. Experimental results on both synthetic and realworld data show its encouraging performance in nonlinear manifold learning and causal discovery.


A Convex Formulation for Learning Task Relationships in Multi-Task Learning

Multi-task learning is a learning paradigm which seeks to improve the generalization performance of a learning task with the help of some other related tasks. In this paper, we propose a regularization formulation for learning the relationships between tasks in multi-task learning. This formulation can be viewed as a novel generalization of the regularization framework for single-task learning. Besides modeling positive task correlation, our method, called multi-task relationship learning (MTRL), can also describe negative task correlation and identify outlier tasks based on the same underlying principle. Under this regularization framework, the objective function of MTRL is convex. For efficiency, we use an alternating method to learn the optimal model parameters for each task as well as the relationships between tasks. We study MTRL in the symmetric multi-task learning setting and then generalize it to the asymmetric setting as well. We also study the relationships between MTRL and some existing multi-task learning methods. Experiments conducted on a toy problem as well as several benchmark data sets demonstrate the effectiveness of MTRL.


Automatic Tuning of Interactive Perception Applications

Interactive applications incorporating high-data rate sensing and computer vision are becoming possible due to novel runtime systems and the use of parallel computation resources. To allow interactive use, such applications require careful tuning of multiple application parameters to meet required fidelity and latency bounds. This is a nontrivial task, often requiring expert knowledge, which becomes intractable as resources and application load characteristics change. This paper describes a method for automatic performance tuning that learns application characteristics and effects of tunable parameters online, and constructs models that are used to maximize fidelity for a given latency constraint. The paper shows that accurate latency models can be learned online, knowledge of application structure can be used to reduce the complexity of the learning task, and operating points can be found that achieve 90% of the optimal fidelity by exploring the parameter space only 3% of the time.


Learning Feature Hierarchies with Centered Deep Boltzmann Machines

Deep Boltzmann machines are in principle powerful models for extracting the hierarchical structure of data. Unfortunately, attempts to train layers jointly (without greedy layer-wise pretraining) have been largely unsuccessful. We propose a modification of the learning algorithm that initially recenters the output of the activation functions to zero. This modification leads to a better conditioned Hessian and thus makes learning easier. We test the algorithm on real data and demonstrate that our suggestion, the centered deep Boltzmann machine, learns a hierarchy of increasingly abstract representations and a better generative model of data.


Data Mining: A Prediction for Performance Improvement of Engineering Students using Classification

Now-a-days the amount of data stored in educational database increasing rapidly. These databases contain hidden information for improvement of students' performance. Educational data mining is used to study the data available in the educational field and bring out the hidden knowledge from it. Classification methods like decision trees, Bayesian network etc can be applied on the educational data for predicting the student's performance in examination. This prediction will help to identify the weak students and help them to score better marks. The C4.5, ID3 and CART decision tree algorithms are applied on engineering student's data to predict their performance in the final exam. The outcome of the decision tree predicted the number of students who are likely to pass, fail or promoted to next year. The results provide steps to improve the performance of the students who were predicted to fail or promoted. After the declaration of the results in the final examination the marks obtained by the students are fed into the system and the results were analyzed for the next session. The comparative analysis of the results states that the prediction has helped the weaker students to improve and brought out betterment in the result.


Learning loopy graphical models with latent variables: Efficient methods and guarantees

The problem of structure estimation in graphical models with latent variables is considered. We characterize conditions for tractable graph estimation and develop efficient methods with provable guarantees. We consider models where the underlying Markov graph is locally tree-like, and the model is in the regime of correlation decay. For the special case of the Ising model, the number of samples $n$ required for structural consistency of our method scales as $n=\Omega(\theta_{\min}^{-\delta\eta(\eta+1)-2}\log p)$, where p is the number of variables, $\theta_{\min}$ is the minimum edge potential, $\delta$ is the depth (i.e., distance from a hidden node to the nearest observed nodes), and $\eta$ is a parameter which depends on the bounds on node and edge potentials in the Ising model. Necessary conditions for structural consistency under any algorithm are derived and our method nearly matches the lower bound on sample requirements. Further, the proposed method is practical to implement and provides flexibility to control the number of latent variables and the cycle lengths in the output graph.


Distributed Cooperative Q-learning for Power Allocation in Cognitive Femtocell Networks

In this paper, we propose a distributed reinforcement learning (RL) technique called distributed power control using Q-learning (DPC-Q) to manage the interference caused by the femtocells on macro-users in the downlink. The DPC-Q leverages Q-Learning to identify the sub-optimal pattern of power allocation, which strives to maximize femtocell capacity, while guaranteeing macrocell capacity level in an underlay cognitive setting. We propose two different approaches for the DPC-Q algorithm: namely, independent, and cooperative. In the former, femtocells learn independently from each other while in the latter, femtocells share some information during learning in order to enhance their performance. Simulation results show that the independent approach is capable of mitigating the interference generated by the femtocells on macro-users. Moreover, the results show that cooperation enhances the performance of the femtocells in terms of speed of convergence, fairness and aggregate femtocell capacity.


On Training Deep Boltzmann Machines

The deep Boltzmann machine (DBM) has been an important development in the quest for powerful "deep" probabilistic models. To date, simultaneous or joint training of all layers of the DBM has been largely unsuccessful with existing training methods. We introduce a simple regularization scheme that encourages the weight vectors associated with each hidden unit to have similar norms. We demonstrate that this regularization can be easily combined with standard stochastic maximum likelihood to yield an effective training strategy for the simultaneous training of all layers of the deep Boltzmann machine.


Semi-Supervised Single- and Multi-Domain Regression with Multi-Domain Training

We address the problems of multi-domain and single-domain regression based on distinct and unpaired labeled training sets for each of the domains and a large unlabeled training set from all domains. We formulate these problems as a Bayesian estimation with partial knowledge of statistical relations. We propose a worst-case design strategy and study the resulting estimators. Our analysis explicitly accounts for the cardinality of the labeled sets and includes the special cases in which one of the labeled sets is very large or, in the other extreme, completely missing. We demonstrate our estimators in the context of removing expressions from facial images and in the context of audio-visual word recognition, and provide comparisons to several recently proposed multi-modal learning algorithms.


On the Equivalence between Herding and Conditional Gradient Algorithms

We show that the herding procedure of Welling (2009) takes exactly the form of a standard convex optimization algorithm--namely a conditional gradient algorithm minimizing a quadratic moment discrepancy. This link enables us to invoke convergence results from convex optimization and to consider faster alternatives for the task of approximating integrals in a reproducing kernel Hilbert space. We study the behavior of the different variants through numerical simulations. The experiments indicate that while we can improve over herding on the task of approximating integrals, the original herding algorithm tends to approach more often the maximum entropy distribution, shedding more light on the learning bias behind herding.


A Novel Training Algorithm for HMMs with Partial and Noisy Access to the States

This paper proposes a new estimation algorithm for the parameters of an HMM as to best account for the observed data. In this model, in addition to the observation sequence, we have \emph{partial} and \emph{noisy} access to the hidden state sequence as side information. This access can be seen as "partial labeling" of the hidden states. Furthermore, we model possible mislabeling in the side information in a joint framework and derive the corresponding EM updates accordingly. In our simulations, we observe that using this side information, we considerably improve the state recognition performance, up to 70%, with respect to the "achievable margin" defined by the baseline algorithms. Moreover, our algorithm is shown to be robust to the training conditions.


Adaptive Mixture Methods Based on Bregman Divergences

We investigate adaptive mixture methods that linearly combine outputs of $m$ constituent filters running in parallel to model a desired signal. We use "Bregman divergences" and obtain certain multiplicative updates to train the linear combination weights under an affine constraint or without any constraints. We use unnormalized relative entropy and relative entropy to define two different Bregman divergences that produce an unnormalized exponentiated gradient update and a normalized exponentiated gradient update on the mixture weights, respectively. We then carry out the mean and the mean-square transient analysis of these adaptive algorithms when they are used to combine outputs of $m$ constituent filters. We illustrate the accuracy of our results and demonstrate the effectiveness of these updates for sparse mixture systems.


Very Short Literature Survey From Supervised Learning To Surrogate Modeling

The past century was era of linear systems. Either systems (especially industrial ones) were simple (quasi)linear or linear approximations were accurate enough. In addition, just at the ending decades of the century profusion of computing devices were available, before then due to lack of computational resources it was not easy to evaluate available nonlinear system studies. At the moment both these two conditions changed, systems are highly complex and also pervasive amount of computation strength is cheap and easy to achieve. For recent era, a new branch of supervised learning well known as surrogate modeling (meta-modeling, surface modeling) has been devised which aimed at answering new needs of modeling realm. This short literature survey is on to introduce surrogate modeling to whom is familiar with the concepts of supervised learning. Necessity, challenges and visions of the topic are considered.


Parallel Matrix Factorization for Binary Response

Predicting user affinity to items is an important problem in applications like content optimization, computational advertising, and many more. While bilinear random effect models (matrix factorization) provide state-of-the-art performance when minimizing RMSE through a Gaussian response model on explicit ratings data, applying it to imbalanced binary response data presents additional challenges that we carefully study in this paper. Data in many applications usually consist of users' implicit response that are often binary -- clicking an item or not; the goal is to predict click rates, which is often combined with other measures to calculate utilities to rank items at runtime of the recommender systems. Because of the implicit nature, such data are usually much larger than explicit rating data and often have an imbalanced distribution with a small fraction of click events, making accurate click rate prediction difficult. In this paper, we address two problems. First, we show previous techniques to estimate bilinear random effect models with binary data are less accurate compared to our new approach based on adaptive rejection sampling, especially for imbalanced response. Second, we develop a parallel bilinear random effect model fitting framework using Map-Reduce paradigm that scales to massive datasets. Our parallel algorithm is based on a "divide and conquer" strategy coupled with an ensemble approach. Through experiments on the benchmark MovieLens data, a small Yahoo! Front Page data set, and a large Yahoo! Front Page data set that contains 8M users and 1B binary observations, we show that careful handling of binary response as well as identifiability issues are needed to achieve good performance for click rate prediction, and that the proposed adaptive rejection sampler and the partitioning as well as ensemble techniques significantly improve model performance.


$k$-MLE: A fast algorithm for learning statistical mixture models

We describe $k$-MLE, a fast and efficient local search algorithm for learning finite statistical mixtures of exponential families such as Gaussian mixture models. Mixture models are traditionally learned using the expectation-maximization (EM) soft clustering technique that monotonically increases the incomplete (expected complete) likelihood. Given prescribed mixture weights, the hard clustering $k$-MLE algorithm iteratively assigns data to the most likely weighted component and update the component models using Maximum Likelihood Estimators (MLEs). Using the duality between exponential families and Bregman divergences, we prove that the local convergence of the complete likelihood of $k$-MLE follows directly from the convergence of a dual additively weighted Bregman hard clustering. The inner loop of $k$-MLE can be implemented using any $k$-means heuristic like the celebrated Lloyd's batched or Hartigan's greedy swap updates. We then show how to update the mixture weights by minimizing a cross-entropy criterion that implies to update weights by taking the relative proportion of cluster points, and reiterate the mixture parameter update and mixture weight update processes until convergence. Hard EM is interpreted as a special case of $k$-MLE when both the component update and the weight update are performed successively in the inner loop. To initialize $k$-MLE, we propose $k$-MLE++, a careful initialization of $k$-MLE guaranteeing probabilistically a global bound on the best possible complete likelihood.


Distribution Free Prediction Bands

We study distribution free, nonparametric prediction bands with a special focus on their finite sample behavior. First we investigate and develop different notions of finite sample coverage guarantees. Then we give a new prediction band estimator by combining the idea of "conformal prediction" (Vovk et al. 2009) with nonparametric conditional density estimation. The proposed estimator, called COPS (Conformal Optimized Prediction Set), always has finite sample guarantee in a stronger sense than the original conformal prediction estimator. Under regularity conditions the estimator converges to an oracle band at a minimax optimal rate. A fast approximation algorithm and a data driven method for selecting the bandwidth are developed. The method is illustrated first in simulated data. Then, an application shows that the proposed method gives desirable prediction intervals in an automatic way, as compared to the classical linear regression modeling.


A Regularization Approach for Prediction of Edges and Node Features in Dynamic Graphs

We consider the two problems of predicting links in a dynamic graph sequence and predicting functions defined at each node of the graph. In many applications, the solution of one problem is useful for solving the other. Indeed, if these functions reflect node features, then they are related through the graph structure. In this paper, we formulate a hybrid approach that simultaneously learns the structure of the graph and predicts the values of the node-related functions. Our approach is based on the optimization of a joint regularization objective. We empirically test the benefits of the proposed method with both synthetic and real data. The results indicate that joint regularization improves prediction performance over the graph evolution and the node features.


Transfer Learning, Soft Distance-Based Bias, and the Hierarchical BOA

An automated technique has recently been proposed to transfer learning in the hierarchical Bayesian optimization algorithm (hBOA) based on distance-based statistics. The technique enables practitioners to improve hBOA efficiency by collecting statistics from probabilistic models obtained in previous hBOA runs and using the obtained statistics to bias future hBOA runs on similar problems. The purpose of this paper is threefold: (1) test the technique on several classes of NP-complete problems, including MAXSAT, spin glasses and minimum vertex cover; (2) demonstrate that the technique is effective even when previous runs were done on problems of different size; (3) provide empirical evidence that combining transfer learning with other efficiency enhancement techniques can often yield nearly multiplicative speedups.


A Bayesian Model Committee Approach to Forecasting Global Solar Radiation

This paper proposes to use a rather new modelling approach in the realm of solar radiation forecasting. In this work, two forecasting models: Autoregressive Moving Average (ARMA) and Neural Network (NN) models are combined to form a model committee. The Bayesian inference is used to affect a probability to each model in the committee. Hence, each model's predictions are weighted by their respective probability. The models are fitted to one year of hourly Global Horizontal Irradiance (GHI) measurements. Another year (the test set) is used for making genuine one hour ahead (h+1) out-of-sample forecast comparisons. The proposed approach is benchmarked against the persistence model. The very first results show an improvement brought by this approach.


Credal Classification based on AODE and compression coefficients

Bayesian model averaging (BMA) is an approach to average over alternative models; yet, it usually gets excessively concentrated around the single most probable model, therefore achieving only sub-optimal classification performance. The compression-based approach (Boulle, 2007) overcomes this problem, averaging over the different models by applying a logarithmic smoothing over the models' posterior probabilities. This approach has shown excellent performances when applied to ensembles of naive Bayes classifiers. AODE is another ensemble of models with high performance (Webb, 2005), based on a collection of non-naive classifiers (called SPODE) whose probabilistic predictions are aggregated by simple arithmetic mean. Aggregating the SPODEs via BMA rather than by arithmetic mean deteriorates the performance; instead, we aggregate the SPODEs via the compression coefficients and we show that the resulting classifier obtains a slight but consistent improvement over AODE. However, an important issue in any Bayesian ensemble of models is the arbitrariness in the choice of the prior over the models. We address this problem by the paradigm of credal classification, namely by substituting the unique prior with a set of priors. Credal classifier automatically recognize the prior-dependent instances, namely the instances whose most probable class varies, when different priors are considered; in these cases, credal classifiers remain reliable by returning a set of classes rather than a single class. We thus develop the credal version of both the BMA-based and the compression-based ensemble of SPODEs, substituting the single prior over the models by a set of priors. Experiments show that both credal classifiers provide higher classification reliability than their determinate counterparts; moreover the compression-based credal classifier compares favorably to previous credal classifiers.


Spectral dimensionality reduction for HMMs

Hidden Markov Models (HMMs) can be accurately approximated using co-occurrence frequencies of pairs and triples of observations by using a fast spectral method in contrast to the usual slow methods like EM or Gibbs sampling. We provide a new spectral method which significantly reduces the number of model parameters that need to be estimated, and generates a sample complexity that does not depend on the size of the observation vocabulary. We present an elementary proof giving bounds on the relative accuracy of probability estimates from our model. (Correlaries show our bounds can be weakened to provide either L1 bounds or KL bounds which provide easier direct comparisons to previous work.) Our theorem uses conditions that are checkable from the data, instead of putting conditions on the unobservable Markov transition matrix.


Statistical Mechanics of Dictionary Learning

Finding a basis matrix (dictionary) by which objective signals are represented sparsely is of major relevance in various scientific and technological fields. We consider a problem to learn a dictionary from a set of training signals. We employ techniques of statistical mechanics of disordered systems to evaluate the size of the training set necessary to typically succeed in the dictionary learning. The results indicate that the necessary size is much smaller than previously estimated, which theoretically supports and/or encourages the use of dictionary learning in practical situations.


Transforming Graph Representations for Statistical Relational Learning

Relational data representations have become an increasingly important topic due to the recent proliferation of network datasets (e.g., social, biological, information networks) and a corresponding increase in the application of statistical relational learning (SRL) algorithms to these domains. In this article, we examine a range of representation issues for graph-based relational data. Since the choice of relational data representation for the nodes, links, and features can dramatically affect the capabilities of SRL algorithms, we survey approaches and opportunities for relational representation transformation designed to improve the performance of these algorithms. This leads us to introduce an intuitive taxonomy for data representation transformations in relational domains that incorporates link transformation and node transformation as symmetric representation tasks. In particular, the transformation tasks for both nodes and links include (i) predicting their existence, (ii) predicting their label or type, (iii) estimating their weight or importance, and (iv) systematically constructing their relevant features. We motivate our taxonomy through detailed examples and use it to survey and compare competing approaches for each of these tasks. We also discuss general conditions for transforming links, nodes, and features. Finally, we highlight challenges that remain to be addressed.


A Lipschitz Exploration-Exploitation Scheme for Bayesian Optimization

The problem of optimizing unknown costly-to-evaluate functions has been studied for a long time in the context of Bayesian Optimization. Algorithms in this field aim to find the optimizer of the function by asking only a few function evaluations at locations carefully selected based on a posterior model. In this paper, we assume the unknown function is Lipschitz continuous. Leveraging the Lipschitz property, we propose an algorithm with a distinct exploration phase followed by an exploitation phase. The exploration phase aims to select samples that shrink the search space as much as possible. The exploitation phase then focuses on the reduced search space and selects samples closest to the optimizer. Considering the Expected Improvement (EI) as a baseline, we empirically show that the proposed algorithm significantly outperforms EI.


Near-Optimal Algorithms for Online Matrix Prediction

In several online prediction problems of recent interest the comparison class is composed of matrices with bounded entries. For example, in the online max-cut problem, the comparison class is matrices which represent cuts of a given graph and in online gambling the comparison class is matrices which represent permutations over n teams. Another important example is online collaborative filtering in which a widely used comparison class is the set of matrices with a small trace norm. In this paper we isolate a property of matrices, which we call (beta,tau)-decomposability, and derive an efficient online learning algorithm, that enjoys a regret bound of O*(sqrt(beta tau T)) for all problems in which the comparison class is composed of (beta,tau)-decomposable matrices. By analyzing the decomposability of cut matrices, triangular matrices, and low trace-norm matrices, we derive near optimal regret bounds for online max-cut, online gambling, and online collaborative filtering. In particular, this resolves (in the affirmative) an open problem posed by Abernethy (2010); Kleinberg et al (2010). Finally, we derive lower bounds for the three problems and show that our upper bounds are optimal up to logarithmic factors. In particular, our lower bound for the online collaborative filtering problem resolves another open problem posed by Shamir and Srebro (2011).


A New Approach to Speeding Up Topic Modeling

Latent Dirichlet allocation (LDA) is a widely-used probabilistic topic modeling paradigm, and recently finds many applications in computer vision and computational biology. In this paper, we propose a fast and accurate batch algorithm, active belief propagation (ABP), for training LDA. Usually batch LDA algorithms require repeated scanning of the entire corpus and searching the complete topic space. To process massive corpora having a large number of topics, the training iteration of batch LDA algorithms is often inefficient and time-consuming. To accelerate the training speed, ABP actively scans the subset of corpus and searches the subset of topic space for topic modeling, therefore saves enormous training time in each iteration. To ensure accuracy, ABP selects only those documents and topics that contribute to the largest residuals within the residual belief propagation (RBP) framework. On four real-world corpora, ABP performs around $10$ to $100$ times faster than state-of-the-art batch LDA algorithms with a comparable topic modeling accuracy.


A New Fuzzy Stacked Generalization Technique and Analysis of its Performance

In this study, a new Stacked Generalization technique called Fuzzy Stacked Generalization (FSG) is proposed to minimize the difference between N -sample and large-sample classification error of the Nearest Neighbor classifier. The proposed FSG employs a new hierarchical distance learning strategy to minimize the error difference. For this purpose, we first construct an ensemble of base-layer fuzzy k- Nearest Neighbor (k-NN) classifiers, each of which receives a different feature set extracted from the same sample set. The fuzzy membership values computed at the decision space of each fuzzy k-NN classifier are concatenated to form the feature vectors of a fusion space. Finally, the feature vectors are fed to a meta-layer classifier to learn the degree of accuracy of the decisions of the base-layer classifiers for meta-layer classification. Rather than the power of the individual base layer-classifiers, diversity and cooperation of the classifiers become an important issue to improve the overall performance of the proposed FSG. A weak base-layer classifier may boost the overall performance more than a strong classifier, if it is capable of recognizing the samples, which are not recognized by the rest of the classifiers, in its own feature space. The experiments explore the type of the collaboration among the individual classifiers required for an improved performance of the suggested architecture. Experiments on multiple feature real-world datasets show that the proposed FSG performs better than the state of the art ensemble learning algorithms such as Adaboost, Random Subspace and Rotation Forest. On the other hand, compatible performances are observed in the experiments on single feature multi-attribute datasets.


The Kernelized Stochastic Batch Perceptron

We present a novel approach for training kernel Support Vector Machines, establish learning runtime guarantees for our method that are better then those of any other known kernelized SVM optimization approach, and show that our method works well in practice compared to existing alternatives.


Validation of nonlinear PCA

Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for model selection, including cross-validation and more generally the use of an independent test set, fail when applied to nonlinear PCA because of its inherent unsupervised characteristics. This paper presents a new approach for validating the complexity of nonlinear PCA models by using the error in missing data estimation as a criterion for model selection. It is motivated by the idea that only the model of optimal complexity is able to predict missing values with the highest accuracy. While standard test set validation usually favours over-fitted nonlinear PCA models, the proposed model validation approach correctly selects the optimal model complexity.


Relax and Localize: From Value to Algorithms

We show a principled way of deriving online learning algorithms from a minimax analysis. Various upper bounds on the minimax value, previously thought to be non-constructive, are shown to yield algorithms. This allows us to seamlessly recover known methods and to derive new ones. Our framework also captures such "unorthodox" methods as Follow the Perturbed Leader and the R^2 forecaster. We emphasize that understanding the inherent complexity of the learning problem leads to the development of algorithms. We define local sequential Rademacher complexities and associated algorithms that allow us to obtain faster rates in online learning, similarly to statistical learning theory. Based on these localized complexities we build a general adaptive method that can take advantage of the suboptimality of the observed sequence. We present a number of new algorithms, including a family of randomized methods that use the idea of a "random playout". Several new versions of the Follow-the-Perturbed-Leader algorithms are presented, as well as methods based on the Littlestone's dimension, efficient methods for matrix completion with trace norm, and algorithms for the problems of transductive learning and prediction with static experts.


PID Parameters Optimization by Using Genetic Algorithm

Time delays are components that make time-lag in systems response. They arise in physical, chemical, biological and economic systems, as well as in the process of measurement and computation. In this work, we implement Genetic Algorithm (GA) in determining PID controller parameters to compensate the delay in First Order Lag plus Time Delay (FOLPD) and compare the results with Iterative Method and Ziegler-Nichols rule results.


Fast ALS-based tensor factorization for context-aware recommendation from implicit feedback

Albeit, the implicit feedback based recommendation problem - when only the user history is available but there are no ratings - is the most typical setting in real-world applications, it is much less researched than the explicit feedback case. State-of-the-art algorithms that are efficient on the explicit case cannot be straightforwardly transformed to the implicit case if scalability should be maintained. There are few if any implicit feedback benchmark datasets, therefore new ideas are usually experimented on explicit benchmarks. In this paper, we propose a generic context-aware implicit feedback recommender algorithm, coined iTALS. iTALS apply a fast, ALS-based tensor factorization learning method that scales linearly with the number of non-zero elements in the tensor. The method also allows us to incorporate diverse context information into the model while maintaining its computational efficiency. In particular, we present two such context-aware implementation variants of iTALS. The first incorporates seasonality and enables to distinguish user behavior in different time intervals. The other views the user history as sequential information and has the ability to recognize usage pattern typical to certain group of items, e.g. to automatically tell apart product types or categories that are typically purchased repetitively (collectibles, grocery goods) or once (household appliances). Experiments performed on three implicit datasets (two proprietary ones and an implicit variant of the Netflix dataset) show that by integrating context-aware information with our factorization framework into the state-of-the-art implicit recommender algorithm the recommendation quality improves significantly.


Distribution-Dependent Sample Complexity of Large Margin Learning

We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of the data distribution, and show distribution-specific upper and lower bounds on the sample complexity, both governed by the margin-adapted dimension of the data distribution. The upper bounds are universal, and the lower bounds hold for the rich family of sub-Gaussian distributions with independent features. We conclude that this new quantity tightly characterizes the true sample complexity of large-margin classification. To prove the lower bound, we develop several new tools of independent interest. These include new connections between shattering and hardness of learning, new properties of shattering with linear classifiers, and a new lower bound on the smallest eigenvalue of a random Gram matrix generated by sub-Gaussian variables. Our results can be used to quantitatively compare large margin learning to other learning rules, and to improve the effectiveness of methods that use sample complexity bounds, such as active learning.


Fast projections onto mixed-norm balls with applications

Joint sparsity offers powerful structural cues for feature selection, especially for variables that are expected to demonstrate a "grouped" behavior. Such behavior is commonly modeled via group-lasso, multitask lasso, and related methods where feature selection is effected via mixed-norms. Several mixed-norm based sparse models have received substantial attention, and for some cases efficient algorithms are also available. Surprisingly, several constrained sparse models seem to be lacking scalable algorithms. We address this deficiency by presenting batch and online (stochastic-gradient) optimization methods, both of which rely on efficient projections onto mixed-norm balls. We illustrate our methods by applying them to the multitask lasso. We conclude by mentioning some open problems.


Learning Fuzzy {\beta}-Certain and {\beta}-Possible rules from incomplete quantitative data by rough sets

The rough-set theory proposed by Pawlak, has been widely used in dealing with data classification problems. The original rough-set model is, however, quite sensitive to noisy data. Tzung thus proposed deals with the problem of producing a set of fuzzy certain and fuzzy possible rules from quantitative data with a predefined tolerance degree of uncertainty and misclassification. This model allowed, which combines the variable precision rough-set model and the fuzzy set theory, is thus proposed to solve this problem. This paper thus deals with the problem of producing a set of fuzzy certain and fuzzy possible rules from incomplete quantitative data with a predefined tolerance degree of uncertainty and misclassification. A new method, incomplete quantitative data for rough-set model and the fuzzy set theory, is thus proposed to solve this problem. It first transforms each quantitative value into a fuzzy set of linguistic terms using membership functions and then finding incomplete quantitative data with lower and the fuzzy upper approximations. It second calculates the fuzzy {\beta}-lower and the fuzzy {\beta}-upper approximations. The certain and possible rules are then generated based on these fuzzy approximations. These rules can then be used to classify unknown objects.


Minimal model of associative learning for cross-situational lexicon acquisition

An explanation for the acquisition of word-object mappings is the associative learning in a cross-situational scenario. Here we present analytical results of the performance of a simple associative learning algorithm for acquiring a one-to-one mapping between $N$ objects and $N$ words based solely on the co-occurrence between objects and words. In particular, a learning trial in our learning scenario consists of the presentation of $C + 1 < N$ objects together with a target word, which refers to one of the objects in the context. We find that the learning times are distributed exponentially and the learning rates are given by $\ln{[\frac{N(N-1)}{C + (N-1)^{2}}]}$ in the case the $N$ target words are sampled randomly and by $\frac{1}{N} \ln [\frac{N-1}{C}] $ in the case they follow a deterministic presentation sequence. This learning performance is much superior to those exhibited by humans and more realistic learning algorithms in cross-situational experiments. We show that introduction of discrimination limitations using Weber's law and forgetting reduce the performance of the associative algorithm to the human level.


UCB Algorithm for Exponential Distributions

We introduce in this paper a new algorithm for Multi-Armed Bandit (MAB) problems. A machine learning paradigm popular within Cognitive Network related topics (e.g., Spectrum Sensing and Allocation). We focus on the case where the rewards are exponentially distributed, which is common when dealing with Rayleigh fading channels. This strategy, named Multiplicative Upper Confidence Bound (MUCB), associates a utility index to every available arm, and then selects the arm with the highest index. For every arm, the associated index is equal to the product of a multiplicative factor by the sample mean of the rewards collected by this arm. We show that the MUCB policy has a low complexity and is order optimal.


The threshold EM algorithm for parameter learning in bayesian network with incomplete data

Bayesian networks (BN) are used in a big range of applications but they have one issue concerning parameter learning. In real application, training data are always incomplete or some nodes are hidden. To deal with this problem many learning parameter algorithms are suggested foreground EM, Gibbs sampling and RBE algorithms. In order to limit the search space and escape from local maxima produced by executing EM algorithm, this paper presents a learning parameter algorithm that is a fusion of EM and RBE algorithms. This algorithm incorporates the range of a parameter into the EM algorithm. This range is calculated by the first step of RBE algorithm allowing a regularization of each parameter in bayesian network after the maximization step of the EM algorithm. The threshold EM algorithm is applied in brain tumor diagnosis and show some advantages and disadvantages over the EM algorithm.


Density-sensitive semisupervised inference

Semisupervised methods are techniques for using labeled data $(X_1,Y_1),\ldots,(X_n,Y_n)$ together with unlabeled data $X_{n+1},\ldots,X_N$ to make predictions. These methods invoke some assumptions that link the marginal distribution $P_X$ of X to the regression function f(x). For example, it is common to assume that f is very smooth over high density regions of $P_X$. Many of the methods are ad-hoc and have been shown to work in specific examples but are lacking a theoretical foundation. We provide a minimax framework for analyzing semisupervised methods. In particular, we study methods based on metrics that are sensitive to the distribution $P_X$. Our model includes a parameter $\alpha$ that controls the strength of the semisupervised assumption. We then use the data to adapt to $\alpha$.


The asymptotics of ranking algorithms

We consider the predictive problem of supervised ranking, where the task is to rank sets of candidate items returned in response to queries. Although there exist statistical procedures that come with guarantees of consistency in this setting, these procedures require that individuals provide a complete ranking of all items, which is rarely feasible in practice. Instead, individuals routinely provide partial preference information, such as pairwise comparisons of items, and more practical approaches to ranking have aimed at modeling this partial preference data directly. As we show, however, such an approach raises serious theoretical challenges. Indeed, we demonstrate that many commonly used surrogate losses for pairwise comparison data do not yield consistency; surprisingly, we show inconsistency even in low-noise settings. With these negative results as motivation, we present a new approach to supervised ranking based on aggregation of partial preferences, and we develop $U$-statistic-based empirical risk minimization procedures. We present an asymptotic analysis of these new procedures, showing that they yield consistency results that parallel those available for classification. We complement our theoretical results with an experiment studying the new procedures in a large-scale web-ranking task.


On Power-law Kernels, corresponding Reproducing Kernel Hilbert Space and Applications

The role of kernels is central to machine learning. Motivated by the importance of power-law distributions in statistical modeling, in this paper, we propose the notion of power-law kernels to investigate power-laws in learning problem. We propose two power-law kernels by generalizing Gaussian and Laplacian kernels. This generalization is based on distributions, arising out of maximization of a generalized information measure known as nonextensive entropy that is very well studied in statistical mechanics. We prove that the proposed kernels are positive definite, and provide some insights regarding the corresponding Reproducing Kernel Hilbert Space (RKHS). We also study practical significance of both kernels in classification and regression, and present some simulation results.


Knapsack based Optimal Policies for Budget-Limited Multi-Armed Bandits

In budget-limited multi-armed bandit (MAB) problems, the learner's actions are costly and constrained by a fixed budget. Consequently, an optimal exploitation policy may not be to pull the optimal arm repeatedly, as is the case in other variants of MAB, but rather to pull the sequence of different arms that maximises the agent's total reward within the budget. This difference from existing MABs means that new approaches to maximising the total reward are required. Given this, we develop two pulling policies, namely: (i) KUBE; and (ii) fractional KUBE. Whereas the former provides better performance up to 40% in our experimental settings, the latter is computationally less expensive. We also prove logarithmic upper bounds for the regret of both policies, and show that these bounds are asymptotically optimal (i.e. they only differ from the best possible regret by a constant factor).


Learning Topic Models - Going beyond SVD

Topic Modeling is an approach used for automatic comprehension and classification of data in a variety of settings, and perhaps the canonical application is in uncovering thematic structure in a corpus of documents. A number of foundational works both in machine learning and in theory have suggested a probabilistic model for documents, whereby documents arise as a convex combination of (i.e. distribution on) a small number of topic vectors, each topic vector being a distribution on words (i.e. a vector of word-frequencies). Similar models have since been used in a variety of application areas; the Latent Dirichlet Allocation or LDA model of Blei et al. is especially popular. Theoretical studies of topic modeling focus on learning the model's parameters assuming the data is actually generated from it. Existing approaches for the most part rely on Singular Value Decomposition(SVD), and consequently have one of two limitations: these works need to either assume that each document contains only one topic, or else can only recover the span of the topic vectors instead of the topic vectors themselves. This paper formally justifies Nonnegative Matrix Factorization(NMF) as a main tool in this context, which is an analog of SVD where all vectors are nonnegative. Using this tool we give the first polynomial-time algorithm for learning topic models without the above two limitations. The algorithm uses a fairly mild assumption about the underlying topic matrix called separability, which is usually found to hold in real-life data. A compelling feature of our algorithm is that it generalizes to models that incorporate topic-topic correlations, such as the Correlated Topic Model and the Pachinko Allocation Model. We hope that this paper will motivate further theoretical results that use NMF as a replacement for SVD - just as NMF has come to replace SVD in many applications.


A technical study and analysis on fuzzy similarity based models for text classification

In this new and current era of technology, advancements and techniques, efficient and effective text document classification is becoming a challenging and highly required area to capably categorize text documents into mutually exclusive categories. Fuzzy similarity provides a way to find the similarity of features among various documents. In this paper, a technical review on various fuzzy similarity based models is given. These models are discussed and compared to frame out their use and necessity. A tour of different methodologies is provided which is based upon fuzzy similarity related concerns. It shows that how text and web documents are categorized efficiently into different categories. Various experimental results of these models are also discussed. The technical comparisons among each model's parameters are shown in the form of a 3-D chart. Such study and technical review provide a strong base of research work done on fuzzy similarity based text document categorization.


A Fuzzy Similarity Based Concept Mining Model for Text Classification

Text Classification is a challenging and a red hot field in the current scenario and has great importance in text categorization applications. A lot of research work has been done in this field but there is a need to categorize a collection of text documents into mutually exclusive categories by extracting the concepts or features using supervised learning paradigm and different classification algorithms. In this paper, a new Fuzzy Similarity Based Concept Mining Model (FSCMM) is proposed to classify a set of text documents into pre - defined Category Groups (CG) by providing them training and preparing on the sentence, document and integrated corpora levels along with feature reduction, ambiguity removal on each level to achieve high system performance. Fuzzy Feature Category Similarity Analyzer (FFCSA) is used to analyze each extracted feature of Integrated Corpora Feature Vector (ICFV) with the corresponding categories or classes. This model uses Support Vector Machine Classifier (SVMC) to classify correctly the training data patterns into two groups; i. e., + 1 and - 1, thereby producing accurate and correct results. The proposed model works efficiently and effectively with great performance and high - accuracy results.


Asymptotic Accuracy of Distribution-Based Estimation for Latent Variables

Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable labels. An asymptotic analysis of the models plays an important role in evaluating the learning process; the result of the analysis is applied not only to theoretical but also to practical situations, such as optimal model selection and active learning. There are many studies of generalization errors, which measure the prediction accuracy of the observable variables. However, the accuracy of estimating the latent variables has not yet been elucidated. For a quantitative evaluation of this, the present paper formulates distribution-based functions for the errors in the estimation of the latent variables. The asymptotic behavior is analyzed for both the maximum likelihood and the Bayes methods.


Robust Nonnegative Matrix Factorization via $L_1$ Norm Regularization

Nonnegative Matrix Factorization (NMF) is a widely used technique in many applications such as face recognition, motion segmentation, etc. It approximates the nonnegative data in an original high dimensional space with a linear representation in a low dimensional space by using the product of two nonnegative matrices. In many applications data are often partially corrupted with large additive noise. When the positions of noise are known, some existing variants of NMF can be applied by treating these corrupted entries as missing values. However, the positions are often unknown in many real world applications, which prevents the usage of traditional NMF or other existing variants of NMF. This paper proposes a Robust Nonnegative Matrix Factorization (RobustNMF) algorithm that explicitly models the partial corruption as large additive noise without requiring the information of positions of noise. In practice, large additive noise can be used to model outliers. In particular, the proposed method jointly approximates the clean data matrix with the product of two nonnegative matrices and estimates the positions and values of outliers/noise. An efficient iterative optimization algorithm with a solid theoretical justification has been proposed to learn the desired matrix factorization. Experimental results demonstrate the advantages of the proposed algorithm.


A Simple Explanation of A Spectral Algorithm for Learning Hidden Markov Models

A simple linear algebraic explanation of the algorithm in "A Spectral Algorithm for Learning Hidden Markov Models" (COLT 2009). Most of the content is in Figure 2; the text just makes everything precise in four nearly-trivial claims.


Concept Modeling with Superwords

In information retrieval, a fundamental goal is to transform a document into concepts that are representative of its content. The term "representative" is in itself challenging to define, and various tasks require different granularities of concepts. In this paper, we aim to model concepts that are sparse over the vocabulary, and that flexibly adapt their content based on other relevant semantic information such as textual structure or associated image features. We explore a Bayesian nonparametric model based on nested beta processes that allows for inferring an unknown number of strictly sparse concepts. The resulting model provides an inherently different representation of concepts than a standard LDA (or HDP) based topic model, and allows for direct incorporation of semantic features. We demonstrate the utility of this representation on multilingual blog data and the Congressional Record.


Modeling Relational Data via Latent Factor Blockmodel

In this paper we address the problem of modeling relational data, which appear in many applications such as social network analysis, recommender systems and bioinformatics. Previous studies either consider latent feature based models but disregarding local structure in the network, or focus exclusively on capturing local structure of objects based on latent blockmodels without coupling with latent characteristics of objects. To combine the benefits of the previous work, we propose a novel model that can simultaneously incorporate the effect of latent features and covariates if any, as well as the effect of latent structure that may exist in the data. To achieve this, we model the relation graph as a function of both latent feature factors and latent cluster memberships of objects to collectively discover globally predictive intrinsic properties of objects and capture latent block structure in the network to improve prediction performance. We also develop an optimization transfer algorithm based on the generalized EM-style strategy to learn the latent factors. We prove the efficacy of our proposed model through the link prediction task and cluster analysis task, and extensive experiments on the synthetic data and several real world datasets suggest that our proposed LFBM model outperforms the other state of the art approaches in the evaluated tasks.


Probabilistic Latent Tensor Factorization Model for Link Pattern Prediction in Multi-relational Networks

This paper aims at the problem of link pattern prediction in collections of objects connected by multiple relation types, where each type may play a distinct role. While common link analysis models are limited to single-type link prediction, we attempt here to capture the correlations among different relation types and reveal the impact of various relation types on performance quality. For that, we define the overall relations between object pairs as a \textit{link pattern} which consists in interaction pattern and connection structure in the network, and then use tensor formalization to jointly model and predict the link patterns, which we refer to as \textit{Link Pattern Prediction} (LPP) problem. To address the issue, we propose a Probabilistic Latent Tensor Factorization (PLTF) model by introducing another latent factor for multiple relation types and furnish the Hierarchical Bayesian treatment of the proposed probabilistic model to avoid overfitting for solving the LPP problem. To learn the proposed model we develop an efficient Markov Chain Monte Carlo sampling method. Extensive experiments are conducted on several real world datasets and demonstrate significant improvements over several existing state-of-the-art methods.


Stochastic Feature Mapping for PAC-Bayes Classification

Probabilistic generative modeling of data distributions can potentially exploit hidden information which is useful for discriminative classification. This observation has motivated the development of approaches that couple generative and discriminative models for classification. In this paper, we propose a new approach to couple generative and discriminative models in an unified framework based on PAC-Bayes risk theory. We first derive the model-parameter-independent stochastic feature mapping from a practical MAP classifier operating on generative models. Then we construct a linear stochastic classifier equipped with the feature mapping, and derive the explicit PAC-Bayes risk bounds for such classifier for both supervised and semi-supervised learning. Minimizing the risk bound, using an EM-like iterative procedure, results in a new posterior over hidden variables (E-step) and the update rules of model parameters (M-step). The derivation of the posterior is always feasible due to the way of equipping feature mapping and the explicit form of bounding risk. The derived posterior allows the tuning of generative models and subsequently the feature mappings for better classification. The derived update rules of the model parameters are same to those of the uncoupled models as the feature mapping is model-parameter-independent. Our experiments show that the coupling between data modeling generative model and the discriminative classifier via a stochastic feature mapping in this framework leads to a general classification tool with state-of-the-art performance.


Plug-in martingales for testing exchangeability on-line

A standard assumption in machine learning is the exchangeability of data, which is equivalent to assuming that the examples are generated from the same probability distribution independently. This paper is devoted to testing the assumption of exchangeability on-line: the examples arrive one by one, and after receiving each example we would like to have a valid measure of the degree to which the assumption of exchangeability has been falsified. Such measures are provided by exchangeability martingales. We extend known techniques for constructing exchangeability martingales and show that our new method is competitive with the martingales introduced before. Finally we investigate the performance of our testing method on two benchmark datasets, USPS and Statlog Satellite data; for the former, the known techniques give satisfactory results, but for the latter our new more flexible method becomes necessary.


Distributed Learning, Communication Complexity and Privacy

We consider the problem of PAC-learning from distributed data and analyze fundamental communication complexity questions involved. We provide general upper and lower bounds on the amount of communication needed to learn well, showing that in addition to VC-dimension and covering number, quantities such as the teaching-dimension and mistake-bound of a class play an important role. We also present tight results for a number of common concept classes including conjunctions, parity functions, and decision lists. For linear separators, we show that for non-concentrated distributions, we can use a version of the Perceptron algorithm to learn with much less communication than the number of updates given by the usual margin bound. We also show how boosting can be performed in a generic manner in the distributed setting to achieve communication with only logarithmic dependence on 1/epsilon for any concept class, and demonstrate how recent work on agnostic learning from class-conditional queries can be used to achieve low communication in agnostic settings as well. We additionally present an analysis of privacy, considering both differential privacy and a notion of distributional privacy that is especially appealing in this context.


Efficient Protocols for Distributed Classification and Optimization

In distributed learning, the goal is to perform a learning task over data distributed across multiple nodes with minimal (expensive) communication. Prior work (Daume III et al., 2012) proposes a general model that bounds the communication required for learning classifiers while allowing for $\eps$ training error on linearly separable data adversarially distributed across nodes. In this work, we develop key improvements and extensions to this basic model. Our first result is a two-party multiplicative-weight-update based protocol that uses $O(d^2 \log{1/\eps})$ words of communication to classify distributed data in arbitrary dimension $d$, $\eps$-optimally. This readily extends to classification over $k$ nodes with $O(kd^2 \log{1/\eps})$ words of communication. Our proposed protocol is simple to implement and is considerably more efficient than baselines compared, as demonstrated by our empirical results. In addition, we illustrate general algorithm design paradigms for doing efficient learning over distributed data. We show how to solve fixed-dimensional and high dimensional linear programming efficiently in a distributed setting where constraints may be distributed across nodes. Since many learning problems can be viewed as convex optimization problems where constraints are generated by individual points, this models many typical distributed learning scenarios. Our techniques make use of a novel connection from multipass streaming, as well as adapting the multiplicative-weight-update framework more generally to a distributed setting. As a consequence, our methods extend to the wide range of problems solvable using these techniques.


Learning to Predict the Wisdom of Crowds

The problem of "approximating the crowd" is that of estimating the crowd's majority opinion by querying only a subset of it. Algorithms that approximate the crowd can intelligently stretch a limited budget for a crowdsourcing task. We present an algorithm, "CrowdSense," that works in an online fashion to dynamically sample subsets of labelers based on an exploration/exploitation criterion. The algorithm produces a weighted combination of a subset of the labelers' votes that approximates the crowd's opinion.


Convolutional Neural Networks Applied to House Numbers Digit Classification

We classify digits of real-world house numbers using convolutional neural networks (ConvNets). ConvNets are hierarchical feature learning neural networks whose structure is biologically inspired. Unlike many popular vision approaches that are hand-designed, ConvNets can automatically learn a unique set of features optimized for a given task. We augmented the traditional ConvNet architecture by learning multi-stage features and by using Lp pooling and establish a new state-of-the-art of 94.85% accuracy on the SVHN dataset (45.2% error improvement). Furthermore, we analyze the benefits of different pooling methods and multi-stage features in ConvNets. The source code and a tutorial are available at eblearn.sf.net.


EigenGP: Sparse Gaussian process models with data-dependent eigenfunctions

Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost and it is difficult to design nonstationary GP priors in practice. In this paper, we propose a sparse Gaussian process model, EigenGP, based on the Karhunen-Loeve (KL) expansion of a GP prior. We use the Nystrom approximation to obtain data dependent eigenfunctions and select these eigenfunctions by evidence maximization. This selection reduces the number of eigenfunctions in our model and provides a nonstationary covariance function. To handle nonlinear likelihoods, we develop an efficient expectation propagation (EP) inference algorithm, and couple it with expectation maximization for eigenfunction selection. Because the eigenfunctions of a Gaussian kernel are associated with clusters of samples - including both the labeled and unlabeled - selecting relevant eigenfunctions enables EigenGP to conduct semi-supervised learning. Our experimental results demonstrate improved predictive performance of EigenGP over alternative state-of-the-art sparse GP and semisupervised learning methods for regression, classification, and semisupervised classification.


Learning From An Optimization Viewpoint

In this dissertation we study statistical and online learning problems from an optimization viewpoint.The dissertation is divided into two parts : I. We first consider the question of learnability for statistical learning problems in the general learning setting. The question of learnability is well studied and fully characterized for binary classification and for real valued supervised learning problems using the theory of uniform convergence. However we show that for the general learning setting uniform convergence theory fails to characterize learnability. To fill this void we use stability of learning algorithms to fully characterize statistical learnability in the general setting. Next we consider the problem of online learning. Unlike the statistical learning framework there is a dearth of generic tools that can be used to establish learnability and rates for online learning problems in general. We provide online analogs to classical tools from statistical learning theory like Rademacher complexity, covering numbers, etc. We further use these tools to fully characterize learnability for online supervised learning problems. II. In the second part, for general classes of convex learning problems, we provide appropriate mirror descent (MD) updates for online and statistical learning of these problems. Further, we show that the the MD is near optimal for online convex learning and for most cases, is also near optimal for statistical convex learning. We next consider the problem of convex optimization and show that oracle complexity can be lower bounded by the so called fat-shattering dimension of the associated linear class. Thus we establish a strong connection between offline convex optimization problems and statistical learning problems. We also show that for a large class of high dimensional optimization problems, MD is in fact near optimal even for convex optimization.


Message passing with relaxed moment matching

Bayesian learning is often hampered by large computational expense. As a powerful generalization of popular belief propagation, expectation propagation (EP) efficiently approximates the exact Bayesian computation. Nevertheless, EP can be sensitive to outliers and suffer from divergence for difficult cases. To address this issue, we propose a new approximate inference approach, relaxed expectation propagation (REP). It relaxes the moment matching requirement of expectation propagation by adding a relaxation factor into the KL minimization. We penalize this relaxation with a $l_1$ penalty. As a result, when two distributions in the relaxed KL divergence are similar, the relaxation factor will be penalized to zero and, therefore, we obtain the original moment matching; In the presence of outliers, these two distributions are significantly different and the relaxation factor will be used to reduce the contribution of the outlier. Based on this penalized KL minimization, REP is robust to outliers and can greatly improve the posterior approximation quality over EP. To examine the effectiveness of REP, we apply it to Gaussian process classification, a task known to be suitable to EP. Our classification results on synthetic and UCI benchmark datasets demonstrate significant improvement of REP over EP and Power EP--in terms of algorithmic stability, estimation accuracy and predictive performance.


Discrete Dynamical Genetic Programming in XCS

A number of representation schemes have been presented for use within Learning Classifier Systems, ranging from binary encodings to neural networks. This paper presents results from an investigation into using a discrete dynamical system representation within the XCS Learning Classifier System. In particular, asynchronous random Boolean networks are used to represent the traditional condition-action production system rules. It is shown possible to use self-adaptive, open-ended evolution to design an ensemble of such discrete dynamical systems within XCS to solve a number of well-known test problems.


Fuzzy Dynamical Genetic Programming in XCSF

A number of representation schemes have been presented for use within Learning Classifier Systems, ranging from binary encodings to Neural Networks, and more recently Dynamical Genetic Programming (DGP). This paper presents results from an investigation into using a fuzzy DGP representation within the XCSF Learning Classifier System. In particular, asynchronous Fuzzy Logic Networks are used to represent the traditional condition-action production system rules. It is shown possible to use self-adaptive, open-ended evolution to design an ensemble of such fuzzy dynamical systems within XCSF to solve several well-known continuous-valued test problems.


Learning in Riemannian Orbifolds

Learning in Riemannian orbifolds is motivated by existing machine learning algorithms that directly operate on finite combinatorial structures such as point patterns, trees, and graphs. These methods, however, lack statistical justification. This contribution derives consistency results for learning problems in structured domains and thereby generalizes learning in vector spaces and manifolds.


Supervised feature evaluation by consistency analysis: application to measure sets used to characterise geographic objects

Nowadays, supervised learning is commonly used in many domains. Indeed, many works propose to learn new knowledge from examples that translate the expected behaviour of the considered system. A key issue of supervised learning concerns the description language used to represent the examples. In this paper, we propose a method to evaluate the feature set used to describe them. Our method is based on the computation of the consistency of the example base. We carried out a case study in the domain of geomatic in order to evaluate the sets of measures used to characterise geographic objects. The case study shows that our method allows to give relevant evaluations of measure sets.


Designing generalisation evaluation function through human-machine dialogue

Automated generalisation has known important improvements these last few years. However, an issue that still deserves more study concerns the automatic evaluation of generalised data. Indeed, many automated generalisation systems require the utilisation of an evaluation function to automatically assess generalisation outcomes. In this paper, we propose a new approach dedicated to the design of such a function. This approach allows an imperfectly defined evaluation function to be revised through a man-machine dialogue. The user gives its preferences to the system by comparing generalisation outcomes. Machine Learning techniques are then used to improve the evaluation function. An experiment carried out on buildings shows that our approach significantly improves generalisation evaluation functions defined by users.


A Privacy-Aware Bayesian Approach for Combining Classifier and Cluster Ensembles

This paper introduces a privacy-aware Bayesian approach that combines ensembles of classifiers and clusterers to perform semi-supervised and transductive learning. We consider scenarios where instances and their classification/clustering results are distributed across different data sites and have sharing restrictions. As a special case, the privacy aware computation of the model when instances of the target data are distributed across different data sites, is also discussed. Experimental results show that the proposed approach can provide good classification accuracies while adhering to the data/model sharing constraints.


Supervised Feature Selection in Graphs with Path Coding Penalties and Network Flows

We consider supervised learning problems where the features are embedded in a graph, such as gene expressions in a gene network. In this context, it is of much interest to automatically select a subgraph with few connected components; by exploiting prior knowledge, one can indeed improve the prediction performance or obtain results that are easier to interpret. Regularization or penalty functions for selecting features in graphs have recently been proposed, but they raise new algorithmic challenges. For example, they typically require solving a combinatorially hard selection problem among all connected subgraphs. In this paper, we propose computationally feasible strategies to select a sparse and well-connected subset of features sitting on a directed acyclic graph (DAG). We introduce structured sparsity penalties over paths on a DAG called "path coding" penalties. Unlike existing regularization functions that model long-range interactions between features in a graph, path coding penalties are tractable. The penalties and their proximal operators involve path selection problems, which we efficiently solve by leveraging network flow optimization. We experimentally show on synthetic, image, and genomic data that our approach is scalable and leads to more connected subgraphs than other regularization functions for graphs.


Regret in Online Combinatorial Optimization

We address online linear optimization problems when the possible actions of the decision maker are represented by binary vectors. The regret of the decision maker is the difference between her realized loss and the best loss she would have achieved by picking, in hindsight, the best possible action. Our goal is to understand the magnitude of the best possible (minimax) regret. We study the problem under three different assumptions for the feedback the decision maker receives: full information, and the partial information models of the so-called "semi-bandit" and "bandit" problems. Combining the Mirror Descent algorithm and the INF (Implicitely Normalized Forecaster) strategy, we are able to prove optimal bounds for the semi-bandit case. We also recover the optimal bounds for the full information setting. In the bandit case we discuss existing results in light of a new lower bound, and suggest a conjecture on the optimal regret in that case. Finally we also prove that the standard exponentially weighted average forecaster is provably suboptimal in the setting of online combinatorial optimization.


Energy-Efficient Building HVAC Control Using Hybrid System LBMPC

Improving the energy-efficiency of heating, ventilation, and air-conditioning (HVAC) systems has the potential to realize large economic and societal benefits. This paper concerns the system identification of a hybrid system model of a building-wide HVAC system and its subsequent control using a hybrid system formulation of learning-based model predictive control (LBMPC). Here, the learning refers to model updates to the hybrid system model that incorporate the heating effects due to occupancy, solar effects, outside air temperature (OAT), and equipment, in addition to integrator dynamics inherently present in low-level control. Though we make significant modeling simplifications, our corresponding controller that uses this model is able to experimentally achieve a large reduction in energy usage without any degradations in occupant comfort. It is in this way that we justify the modeling simplifications that we have made. We conclude by presenting results from experiments on our building HVAC testbed, which show an average of 1.5MWh of energy savings per day (p = 0.002) with a 95% confidence interval of 1.0MWh to 2.1MWh of energy savings.


Objective Function Designing Led by User Preferences Acquisition

Many real world problems can be defined as optimisation problems in which the aim is to maximise an objective function. The quality of obtained solution is directly linked to the pertinence of the used objective function. However, designing such function, which has to translate the user needs, is usually fastidious. In this paper, a method to help user objective functions designing is proposed. Our approach, which is highly interactive, is based on man machine dialogue and more particularly on the comparison of problem instance solutions by the user. We propose an experiment in the domain of cartographic generalisation that shows promising results.


Knowledge revision in systems based on an informed tree search strategy : application to cartographic generalisation

Many real world problems can be expressed as optimisation problems. Solving this kind of problems means to find, among all possible solutions, the one that maximises an evaluation function. One approach to solve this kind of problem is to use an informed search strategy. The principle of this kind of strategy is to use problem-specific knowledge beyond the definition of the problem itself to find solutions more efficiently than with an uninformed strategy. This kind of strategy demands to define problem-specific knowledge (heuristics). The efficiency and the effectiveness of systems based on it directly depend on the used knowledge quality. Unfortunately, acquiring and maintaining such knowledge can be fastidious. The objective of the work presented in this paper is to propose an automatic knowledge revision approach for systems based on an informed tree search strategy. Our approach consists in analysing the system execution logs and revising knowledge based on these logs by modelling the revision problem as a knowledge space exploration problem. We present an experiment we carried out in an application domain where informed search strategies are often used: cartographic generalisation.


Sparse Prediction with the $k$-Support Norm

We derive a novel norm that corresponds to the tightest convex relaxation of sparsity combined with an $\ell_2$ penalty. We show that this new {\em $k$-support norm} provides a tighter relaxation than the elastic net and is thus a good replacement for the Lasso or the elastic net in sparse prediction problems. Through the study of the $k$-support norm, we also bound the looseness of the elastic net, thus shedding new light on it and providing justification for its use.


Analysis Operator Learning and Its Application to Image Reconstruction

Exploiting a priori known structural information lies at the core of many image reconstruction methods that can be stated as inverse problems. The synthesis model, which assumes that images can be decomposed into a linear combination of very few atoms of some dictionary, is now a well established tool for the design of image reconstruction algorithms. An interesting alternative is the analysis model, where the signal is multiplied by an analysis operator and the outcome is assumed to be the sparse. This approach has only recently gained increasing interest. The quality of reconstruction methods based on an analysis model severely depends on the right choice of the suitable operator. In this work, we present an algorithm for learning an analysis operator from training images. Our method is based on an $\ell_p$-norm minimization on the set of full rank matrices with normalized columns. We carefully introduce the employed conjugate gradient method on manifolds, and explain the underlying geometry of the constraints. Moreover, we compare our approach to state-of-the-art methods for image denoising, inpainting, and single image super-resolution. Our numerical results show competitive performance of our general approach in all presented applications compared to the specialized state-of-the-art techniques.


Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems

Multi-armed bandit problems are the most basic examples of sequential decision problems with an exploration-exploitation trade-off. This is the balance between staying with the option that gave highest payoffs in the past and exploring new options that might give higher payoffs in the future. Although the study of bandit problems dates back to the Thirties, exploration-exploitation trade-offs arise in several modern applications, such as ad placement, website optimization, and packet routing. Mathematically, a multi-armed bandit is defined by the payoff process associated with each option. In this survey, we focus on two extreme cases in which the analysis of regret is particularly simple and elegant: i.i.d. payoffs and adversarial payoffs. Besides the basic setting of finitely many actions, we also analyze some of the most important variants and extensions, such as the contextual bandit model.


Quantitative Concept Analysis

Formal Concept Analysis (FCA) begins from a context, given as a binary relation between some objects and some attributes, and derives a lattice of concepts, where each concept is given as a set of objects and a set of attributes, such that the first set consists of all objects that satisfy all attributes in the second, and vice versa. Many applications, though, provide contexts with quantitative information, telling not just whether an object satisfies an attribute, but also quantifying this satisfaction. Contexts in this form arise as rating matrices in recommender systems, as occurrence matrices in text analysis, as pixel intensity matrices in digital image processing, etc. Such applications have attracted a lot of attention, and several numeric extensions of FCA have been proposed. We propose the framework of proximity sets (proxets), which subsume partially ordered sets (posets) as well as metric spaces. One feature of this approach is that it extracts from quantified contexts quantified concepts, and thus allows full use of the available information. Another feature is that the categorical approach allows analyzing any universal properties that the classical FCA and the new versions may have, and thus provides structural guidance for aligning and combining the approaches.