Locally Minimax Optimal Predictive Modeling with Bayesian Networks

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Tomi Silander, Teemu Roos, Petri Myllymaki ;
Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics, PMLR 5:504-511, 2009.

Abstract

We propose an information-theoretic approach for predictive modeling with Bayesian networks. Our approach is based on the minimax optimal Normalized Maximum Likelihood (NML) distribution, motivated by the MDL principle. In particular, we present a parameter learning method which, together with a previously introduced NML-based model selection criterion, provides a way to construct highly predictive Bayesian network models from data. The method is parameter-free and robust, unlike the currently popular Bayesian marginal likelihood approach which has been shown to be sensitive to the choice of prior hyperparameters. Empirical tests show that the proposed method compares favorably with the Bayesian approach in predictive tasks.

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