On Model Selection, Bayesian Networks, and the Fisher Information Integral

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http://hdl.handle.net/10138/175523

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Zou , Y & Roos , T 2017 , ' On Model Selection, Bayesian Networks, and the Fisher Information Integral ' , New Generation Computing , vol. 35 , no. 1 , pp. 5-27 . https://doi.org/10.1007/s00354-016-0002-y

Title: On Model Selection, Bayesian Networks, and the Fisher Information Integral
Author: Zou, Yuan; Roos, Teemu
Contributor: University of Helsinki, Department of Computer Science
University of Helsinki, Department of Computer Science
Date: 2017-01
Language: eng
Number of pages: 23
Belongs to series: New Generation Computing
ISSN: 0288-3635
URI: http://hdl.handle.net/10138/175523
Abstract: We study BIC-like model selection criteria and in particular, their refinements that include a constant term involving the Fisher information matrix. We perform numerical simulations that enable increasingly accurate approximation of this constant in the case of Bayesian networks. We observe that for complex Bayesian network models, the constant term is a negative number with a very large absolute value that dominates the other terms for small and moderate sample sizes. For networks with a fixed number of parameters, d, the leading term in the complexity penalty, which is proportional to d, is the same. However, as we show, the constant term can vary significantly depending on the network structure even if the number of parameters is fixed. Based on our experiments, we conjecture that the distribution of the nodes’ outdegree is a key factor. Furthermore, we demonstrate that the constant term can have a dramatic effect on model selection performance for small sample sizes.
Subject: 112 Statistics and probability
Fisher information integral
Bayesian networks
normalized maximum likelihood
Model selection
BIC
113 Computer and information sciences
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