A Bayesian Learning Coefficient of Generalization Error and Vandermonde Matrix-Type Singularities |
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Authors: | Miki Aoyagi |
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Affiliation: | 1. Advanced Research Institute for the Sciences and Humanities , Nihon University , Tokyo, Japan aoyagi.miki@nihon-u.ac.jp |
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Abstract: | The coefficient of the main term of the generalization error in Bayesian estimation is called a Bayesian learning coefficient. In this article, we first introduce Vandermonde matrix type singularities and show certain orthogonality conditions of them. Recently, it has been recognized that Vandermonde matrix type singularities are related to Bayesian learning coefficients for several hierarchical learning models. By applying the orthogonality conditions of them, we show that their log canonical threshold also corresponds to the Bayesian learning coefficient for normal mixture models, and we obtain the explicit computational results in dimension one. |
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Keywords: | Generalization error Hierarchical learning models Normal mixture models Resolution of singularities Zeta function |
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