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Entropy 2019, 21(1), 32; https://doi.org/10.3390/e21010032

Hidden Node Detection between Observable Nodes Based on Bayesian Clustering

AI Research Center, National Institute of Advanced Industrial Science Technology, 2-4-7 Aomi, Koto-ku, Tokyo 135-0064, Japan
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Received: 15 November 2018 / Revised: 14 December 2018 / Accepted: 3 January 2019 / Published: 7 January 2019
(This article belongs to the Special Issue Bayesian Inference and Information Theory)
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Abstract

Structure learning is one of the main concerns in studies of Bayesian networks. In the present paper, we consider networks consisting of both observable and hidden nodes, and propose a method to investigate the existence of a hidden node between observable nodes, where all nodes are discrete. This corresponds to the model selection problem between the networks with and without the middle hidden node. When the network includes a hidden node, it has been known that there are singularities in the parameter space, and the Fisher information matrix is not positive definite. Then, the many conventional criteria for structure learning based on the Laplace approximation do not work. The proposed method is based on Bayesian clustering, and its asymptotic property justifies the result; the redundant labels are eliminated and the simplest structure is detected even if there are singularities. View Full-Text
Keywords: Bayesian clustering; structure learning in singular cases; model selection Bayesian clustering; structure learning in singular cases; model selection
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Yamazaki, K.; Motomura, Y. Hidden Node Detection between Observable Nodes Based on Bayesian Clustering. Entropy 2019, 21, 32.

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