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...

This literature review discusses different methods under the general rubric of learning Bayesian networks from data, and includes some overlapping work on more general probabilistic networks. Connections are drawn between the statistical, neural network, and uncertainty communities, and between the different methodological communities, such as Bayesian, description length, and classical statistics. Basic concepts for learning and Bayesian networks are introduced and methods are then reviewed. Methods are discussed for learning parameters of a probabilistic network, for learning the structure, and for learning hidden variables. The presentation avoids formal definitions and theorems, as these are plentiful in the literature, and instead illustrates key concepts with simplified examples. Keywords--- Bayesian networks, graphical models, hidden variables, learning, learning structure, probabilistic networks, knowledge discovery. I. Introduction Probabilistic networks or probabilistic gra...

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Clustering is often used for discovering structure in data. Clustering systems differ in the objective function used to evaluate clustering quality and the control strategy used to search the space of clusterings. Ideally, the search strategy should consistently construct clusterings of high quality, but be computationally inexpensive as well. In general, we cannot have it both ways, but we can partition the search so that a system inexpensively constructs a `tentative' clustering for initial examination, followed by iterative optimization, which continues to search in background for improved clusterings. Given this motivation, we evaluate an inexpensive strategy for creating initial clusterings, coupled with several control strategies for iterative optimization, each of which repeatedly modifies an initial clustering in search of a better one. One of these methods appears novel as an iterative optimization strategy in clustering contexts. Once a clustering has been construct...

Latent class models are used for cluster analysis of categorical data. Underlying such a model is the assumption that the observed variables are mutually independent given the class variable. A serious problem with the use of latent class models, known as local dependence, is that this assumption is often untrue. In this paper we propose hierarchical latent class models as a framework where the local dependence problem can be addressed in a principled manner. We develop a search-based algorithm for learning hierarchical latent class models from data. The algorithm is evaluated using both synthetic and real-world data.

Statistical methods for automatically extracting information about associations between words or documents from large collections of text have the potential to have considerable impact in a number of areas, such as information retrieval and natural-language-based user interfaces. However, even huge bodies of text yield highly unreliable estimates of the probability of relatively common events, and, in fact, perfectly reasonable events may not occur in the training data at all. This is known as the sparse data problem. Traditional approaches to the sparse data problem use crude approximations. We propose a different solution: if we are able to organize the data into classes of similar events, then, if information about an event is lacking, we can estimate its behavior from information about similar events. This thesis presents two such similarity-based approaches, where, in general, we measure similarity by the Kullback-Leibler divergence, an information-theoretic quantity. Our first approach is to build soft, hierarchical clusters: soft, because each event belongs to each cluster with some probability; hierarchical, because cluster centroids are iteratively split to model finer distinctions. Our clustering method, which uses the technique of deterministic annealing,

There are many different ways of representing knowledge, and for each of these ways there are many different discovery algorithms. How can we compare different representations? How can we mix, match and merge representations and algorithms on new problems with their own unique requirements? This chapter introduces probabilistic modeling as a philosophy for addressing these questions and presents graphical models for representing probabilistic models. Probabilistic graphical models are a unified qualitative and quantitative framework for representing and reasoning with probabilities and independencies. 4.1 Introduction Perhaps one common element of the discovery systems described in this and previous books on knowledge discovery is that they are all different. Since the class of discovery problems is a challenging one, we cannot write a single program to address all of knowledge discovery. The KEFIR discovery system applied to health care by Matheus, Piatetsky-Shapiro, and McNeill (199...

. It is shown that Bayesian inference from data modeled by a mixture distribution can feasibly be performed via Monte Carlo simulation. This method exhibits the true Bayesian predictive distribution, implicitly integrating over the entire underlying parameter space. An infinite number of mixture components can be accommodated without difficulty, using a prior distribution for mixing proportions that selects a reasonable subset of components to explain any finite training set. The need to decide on a "correct" number of components is thereby avoided. The feasibility of the method is shown empirically for a simple classification task. Introduction Mixture distributions [8, 20] are an appropriate tool for modeling processes whose output is thought to be generated by several different underlying mechanisms, or to come from several different populations. One aim of a mixture model analysis may be to identify and characterize these underlying "latent classes" [2, 7], either for some scient...

We present an approach to model-based hierarchical clustering by formulating an objective function based on a Bayesian analysis. This model organizes the data into a cluster hierarchy while specifying a complex feature-set partitioning that is a key component of our model. Features can have either a unique distribution in every cluster or a common distribution over some (or even all) of the clusters. The cluster subsets over which these features have such a common distribution correspond to the nodes (clusters) of the tree representing the hierarchy. We apply this general model to the problem of document clustering for which we use a multinomial likelihood function and Dirichlet priors. Our algorithm consists of a two-stage process wherein we first perform a flat clustering followed by a modified hierarchical agglomerative merging process that includes determining the features that will have common distributions over the merged clusters. The regularization induced...

this document. Before these are discussed however, perhaps we should have a tutorial on Bayesian probability theory and its application to model comparison problems. 2 Probability theory and Occam's razor