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Technical Report NC-TR-95-033
Constructing Computationally
Efficient Bayesian Models via Unsupervised Clustering
Petri
Myllymäki and Henry Tirri
University of Helsinki
Finland
Abstract
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 find 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 finds the maximal probability model,
provided that a sufficient amount of time is used.
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