Minimum Free Energy Principle for Constraint-Based Learning Bayesian Networks

Authors:
Takashi Isozaki;Maomi Ueno
Affiliations:
Graduate School of Information Systems, The University of Electro-Communications, Tokyo, Japan 182-8585 and Research and Technology Group, Fuji Xerox Co., Ltd., Tokyo, Japan 106-0032;Graduate School of Information Systems, The University of Electro-Communications, Tokyo, Japan 182-8585
Venue:
ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part I
Year:
2009

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Abstract

Constraint-based search methods, which are a major approach to learning Bayesian networks, are expected to be effective in causal discovery tasks. However, such methods often suffer from impracticality of classical hypothesis testing for conditional independence when the sample size is insufficiently large. We propose a new conditional independence (CI) testing method that is effective for small samples. Our method uses the minimum free energy principle, which originates from thermodynamics, with the "Data Temperature" assumption recently proposed for relating probabilistic fluctuation to virtual thermal fluctuation. We define free energy using Kullback---Leibler divergence in a manner corresponding to an information-geometric perspective. This CI method incorporates the maximum entropy principle and converges to classical hypothesis tests in asymptotic regions. We provide a simulation study, the results of which show that our method improves the learning performance of the well known PC algorithm in some respects.