Constructing Computationally Eecient Bayesian Models via Unsupervised Clustering

Given a set of samples of an unknown probability distribution, we study the problem of constructing a good approximative Bayesian network model of the probability distribution in question. This task can be viewed as a search problem, where the goal is to nd a maximal probability network model, given the data. In this work, we do not make an attempt to learn arbitrarily complex multi-connected Bayesian network structures, since such resulting models can be unsuitable for practical purposes due to the exponential amount of time required for the reasoning task. Instead, we restrict ourselves to a special class of simple tree-structured Bayesian networks called Bayesian prototype trees, for which a polynomial time algorithm for Bayesian reasoning exists. We show how the probability of a given Bayesian prototype tree model can be evaluated, given the data, and how this evaluation criterion can be used in a stochastic simulated annealing algorithm for searching the model space. The simulated annealing algorithm provably nds the maximal probability model, provided that a suucient amount of time is used.