Abstract. This paper presents a Bayesian method for constructing probabilistic networks from databases. In particular, we focus on constructing Bayesian belief networks. Potential applications include computer-assisted hypothesis testing, automated scientific discovery, and automated construction of probabilistic expert systems. We extend the basic method to handle missing data and hidden (latent) variables. We show how to perform probabilistic inference by averaging over the inferences of multiple belief networks. Results are presented of a preliminary evaluation of an algorithm for constructing a belief network from a database of cases. Finally, we relate the methods in this paper to previous work, and we discuss open problems.

In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null is one-half. Although there has been much discussion of Bayesian hypothesis testing in the context of criticism of P -values, less attention has been given to the Bayes factor as a practical tool of applied statistics. In this paper we review and discuss the uses of Bayes factors in the context of five scientific applications in genetics, sports, ecology, sociology and psychology.

Recent work in supervised learning has shown that a surprisingly simple Bayesian classifier with strong assumptions of independence among features, called naive Bayes, is competitive with state-of-the-art classifiers such as C4.5. This fact raises the question of whether a classifier with less restrictive assumptions can perform even better. In this paper we evaluate approaches for inducing classifiers from data, based on the theory of learning Bayesian networks. These networks are factored representations of probability distributions that generalize the naive Bayesian classifier and explicitly represent statements about independence. Among these approaches we single out a method we call Tree Augmented Naive Bayes (TAN), which outperforms naive Bayes, yet at the same time maintains the computational simplicity (no search involved) and robustness that characterize naive Bayes. We experimentally tested these approaches, using problems from the University of California at Irvine repository, and compared them to C4.5, naive Bayes, and wrapper methods for feature selection.

A large portion of real-world data is stored in commercial relational database systems. In contrast, most statistical learning methods work only with "flat " data representations. Thus, to apply these methods, we are forced to convert our data into a flat form, thereby losing much of the relational structure present in our database. This paper builds on the recent work on probabilistic relational models (PRMs), and describes how to learn them from databases. PRMs allow the properties of an object to depend probabilistically both on other properties of that object and on properties of related objects. Although PRMs are significantly more expressive than standard models, such as Bayesian networks, we show how to extend well-known statistical methods for learning Bayesian networks to learn these models. We describe both parameter estimation and structure learning — the automatic induction of the dependency structure in a model. Moreover, we show how the learning procedure can exploit standard database retrieval techniques for efficient learning from large datasets. We present experimental results on both real and synthetic relational databases. 1

Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and bio-sequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linear-Gaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data. In particular, the main novel technical contributions of this thesis are as follows: a way of representing Hierarchical HMMs as DBNs, which enables inference to be done in O(T) time instead of O(T 3), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T) space instead of O(T); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of applying Rao-Blackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.

In this paper a framework for maximum a posteriori (MAP) estimation of hidden Markov models (HMM) is presented. Three key issues of MAP estimation, namely the choice of prior distribution family, the specification of the parameters of prior densities and the evaluation of the MAP estimates, are addressed. Using HMMs with Gaussian mixture state observation densities as an example, it is assumed that the prior densities for the HMM parameters can be adequately represented as a product of Dirichlet and normal-Wishart densities. The classical maximum likelihood estimation algorithms, namely the forward-backward algorithm and the segmental k-means algorithm, are expanded and MAP estimation formulas are developed. Prior density estimation issues are discussed for two classes of applications: parameter smoothing and model adaptation, and some experimental results are given illustrating the practical interest of this approach. Because of its adaptive nature, Bayesian learning is shown to serve as a unified approach for a wide range of speech recognition applications

We examine a graphical representation of uncertain knowledge called a Bayesian network. The representation is easy to construct and interpret, yet has formal probabilistic semantics making it suitable for statistical manipulation. We show how we can use the representation to learn new knowledge by combining domain knowledge with statistical data. 1 Introduction Many techniques for learning rely heavily on data. In contrast, the knowledge encoded in expert systems usually comes solely from an expert. In this paper, we examine a knowledge representation, called a Bayesian network, that lets us have the best of both worlds. Namely, the representation allows us to learn new knowledge by combining expert domain knowledge and statistical data. A Bayesian network is a graphical representation of uncertain knowledge that most people find easy to construct and interpret. In addition, the representation has formal probabilistic semantics, making it suitable for statistical manipulation (Howard,...

This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, and the manipulation of probability models from the exponential family. Two standard algorithm schemas for learning are reviewed in a graphical framework: Gibbs sampling and the expectation maximization algorithm. Using these operations and schemas, some popular algorithms can be synthesized from their graphical specification. This includes versions of linear regression, techniques for feed-forward networks, and learning Gaussian and discrete Bayesian networks from data. The paper conclu...

Dynamic probabilistic networks are a compact representation of complex stochastic processes. In this paper we examine how to learn the structure of a DPN from data. We extend structure scoring rules for standard probabilistic networks to the dynamic case, and show how to search for structure when some of the variables are hidden. Finally, we examine two applications where such a technology might be useful: predicting and classifying dynamic behaviors, and learning causal orderings in biological processes. We provide empirical results that demonstrate the applicability of our methods in both domains. 1

Graphical techniques for modeling the dependencies of random variables have been explored in a variety of di erent areas including statistics, statistical physics, arti-cial intelligence, speech recognition, image processing, and genetics. Formalisms for manipulating these models have been developed relatively independently in these research communities. In this paper we explore hidden Markov models (HMMs) and related structures within the general framework of probabilistic independence networks (PINs). The paper contains a self-contained review of the basic principles of PINs. It is shown that the well-known forward-backward (F-B) and Viterbi algorithms for HMMs are special cases of more general inference algorithms for arbitrary PINs. Furthermore, the existence of inference and estimation algorithms for more general graphical models provides a set of analysis tools for HMM practitioners who wish to explore a richer class of HMM structures. Examples of relatively complex models to handle sensor fusion and coarticulation in speech recognition are introduced and treated within the graphical model framework to illustrate the advantages of the general approach. 1