Observed associations in a database may be due in whole or part to variations in unrecorded (latent) variables. Identifying such variables and their causal relationships with one another is a principal goal in many scientific and practical domains. Previous work shows that, given a partition of observed variables such that members of a class share only a single latent common cause, standard search algorithms for causal Bayes nets can infer structural relations between latent variables. We introduce an algorithm for discovering such partitions when they exist. Uniquely among available procedures, the algorithm is (asymptotically) correct under standard assumptions in causal Bayes net search algorithms, requires no prior knowledge of the number of latent variables, and does not depend on the mathematical form of the relationships among the latent variables. We evaluate the algorithm on a variety of simulated data sets.

Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood estimation in the case of continuous variables with a Gaussian joint distribution, sometimes termed a covariance graph model. We present a new fitting algorithm which exploits standard regression techniques and establish its convergence properties. Moreover, we contrast our procedure to existing estimation methods.

There is no known efficient method for selecting k Gaussian features from n which achieve the lowest Bayesian classification error. We show an example of how greedy algorithms faced with this task are led to give results that are not optimal. This motivates us to propose a more robust approach. We present a Branch and Bound algorithm for finding a subset of k independent Gaussian features which minimizes the naive Bayesian classification error. Our algorithm uses additive monotonic distance measures to produce bounds for the Bayesian classification error in order to exclude many feature subsets from evaluation, while still returning an optimal solution. We test our method on synthetic data as well as data obtained from gene expression profiling.

Despite its simplicity, the naive Bayes classifier has surprised machine learning researchers by exhibiting good performance on a variety of learning problems. Encouraged by these results, researchers have looked to overcome naive Bayes primary weakness - attribute independence - and improve the performance of the algorithm. This paper presents a locally weighted version of naive Bayes that relaxes the independence assumption by learning local models at prediction time. Experimental results show that locally weighted naive Bayes rarely degrades accuracy compared to standard naive Bayes and, in many cases, improves accuracy dramatically. The main advantage of this method compared to other techniques for enhancing naive Bayes is its conceptual and computational simplicity.

Learning with hidden variables is a central challenge in probabilistic graphical models that has important implications for many real-life problems. The classical approach is using the Expectation Maximization (EM) algorithm. This algorithm, however, can get trapped in local maxima. In this paper we explore a new approach that is based on the Information Bottleneck principle. In this approach, we view the learning problem as a tradeoff between two information theoretic objectives. The first is to make the hidden variables uninformative about the identity of specific instances. The second is to make the hidden variables informative about the observed attributes. By exploring different tradeoffs between these two objectives, we can gradually converge on a high-scoring solution. As we show, the resulting, Information Bottleneck Expectation Maximization (IB-EM) algorithm, manages to find solutions that are superior to standard EM methods.

Methods for learning Bayesian network structure can discover dependency structure between observed variables, and have been shown to be useful in many applications. However, in domains that involve a large number of variables, the space of possible network structures is enormous, making it difficult, for both computational and statistical reasons, to identify a good model. In this paper, we consider a solution to this problem, suitable for domains where many variables have similar behavior. Our method is based on a new class of models, which we call module networks. A module network explicitly represents the notion of a module - a set of variables that have the same parents in the network and share the same conditional probability distribution. We define the semantics of module networks, and describe an algorithm that learns a module network from data. The algorithm learns both the partitioning of the variables into modules and the dependency structure between the variables. We evaluate our algorithm on synthetic data, and on real data in the domains of gene expression and the stock market. Our results show that module networks generalize better than Bayesian networks, and that the learned module network structure reveals regularities that are obscured in learned Bayesian networks.

The Hierarchical Mixture of Experts (HME) is a well-known tree-based model for regression and classification, based on soft probabilistic splits. In its original formulation it was trained by maximum likelihood, and is therefore prone to over-fitting. Furthermore the maximum likelihood framework offers no natural metric for optimizing the complexity and structure of the tree. Previous attempts to provide a Bayesian treatment of the HME model have relied either on ad-hoc local Gaussian approximations or have dealt with related models representing the joint distribution of both input and output variables. In this paper we describe a fully Bayesian treatment of the HME model based on variational inference. By combining local and global variational methods we obtain a rigourous lower bound on the marginal probability of the data under the model. This bound is optimized during the training phase, and its resulting value can be used for model order selection. We present results using this approach for a data set describing robot arm kinematics.

Collaborative filtering (CF) allows the preferences of multiple users to be pooled to make recommendations regarding unseen products. We consider in this paper the problem of online and interactive CF: given the current ratings associated with a user, what queries (new ratings) would most improve the quality of the recommendations made? We cast this terms of expected value of information (EVOI); but the online computational cost of computing optimal queries is prohibitive. We show how offline prototyping and computation of bounds on EVOI can be used to dramatically reduce the required online computation. The framework we develop is general, but we focus on derivations and empirical study in the specific case of the multiple-cause vector quantization model.

We present and implement two algorithms for analytic asymptotic evaluation of the marginal likelihood of data given a Bayesian network with hidden nodes. As shown by previous work, this evaluation is particularly hard for latent Bayesian network models, namely networks that include hidden variables, where asymptotic approximation deviates from the standard BIC score. Our algorithms solve two central difficulties in asymptotic evaluation of marginal likelihood integrals, namely, evaluation of regular dimensionality drop for latent Bayesian network models and computation of non-standard approximation formulas for singular statistics for these models. The presented algorithms are implemented in Matlab and Maple and their usage is demonstrated for marginal likelihood approximations for Bayesian networks with hidden variables.

Continuous time Bayesian networks (CTBNs) describe structured stochastic processes with finitely many states that evolve over continuous time. A CTBN is a directed (possibly cyclic) dependency graph over a set of variables, each of which represents a finite state continuous time Markov process whose transition model is a function of its parents. We address the problem of learning parameters and structure of a CTBN from fully observed data. We define a conjugate prior for CTBNs, and show how it can be used both for Bayesian parameter estimation and as the basis of a Bayesian score for structure learning. Because acyclicity is not a constraint in CTBNs, we can show that the structure learning problem is significantly easier, both in theory and in practice, than structure learning for dynamic Bayesian networks (DBNs). Furthermore, as CTBNs can tailor the parameters and dependency structure to the different time granularities of the evolution of different variables, they can provide a better fit to continuous-time processes than DBNs with a fixed time granularity.