Mieczysław Alojzy Kłopotek

A New Bayesian Tree Construction Method with Decreased Time Complexity

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Abstract

Bayesian networks have many practical applications due to their capability to represent joint probability distribution in many variables in a compact way. There exist efficient reasoning methods for Bayesian networks. Many algorithms for learning Bayesian networks from empirical data have been developed.

A well-known problem with Bayesian networks is the practical limitation for the number of variables for which a Bayesian network can be learned in reasonable time. A remarkable exception here is the Chow/Liu algorithm learning tree-like Bayesian networks. However, its quadratic time and space complexity in the number of variables may prove also prohibitive for high dimensional data.

The paper presents a novel algorithm overcoming this limitation for the tree-like class of Bayesian networks. The new algorithm space consumption grows linearly with the number of variables n while the execution time is proportional to n ln(n), hence both are better than those of Chow/Liu algorithm. This opens new perspectives in construction of Bayesian networks from data containing tens of thousands and more variables, e.g. in automatic text categorization.

Keywords : machine learning, Bayesian networks, Chow/Liu algorithm, time and space complexity