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Bayesian Generalization Error of Poisson Mixture and Simplex Vandermonde Matrix Type Singularity

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arxiv 1912.13289 v1 pith:KQ4AVDVX submitted 2019-12-31 math.ST stat.TH

Kenichiro Sato , Sumio Watanabe This is my paper · ORCID
classification math.STstat.TH
keywords mixturepoissonbayesiandistributionequalerrorgeneralizationmatrix
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A Poisson mixture is one of the practically important models in computer science, biology, and sociology. However, the theoretical property has not been studied because the posterior distribution can not be approximated by any normal distribution. Such a model is called singular and it is known that Real Log Canonical Threshold (RLCT) is equal to the coefficient of the asymptotically main term of the Bayesian generalization error. In this paper, we derive RLCT of a simplex Vandermonde matrix type singularity which is equal to that of a Poisson mixture in general cases.

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  1. Upper Bounds for Local Learning Coefficients of Three-Layer Neural Networks

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    An upper-bound formula for local learning coefficients at singular points of three-layer networks is derived via blow-ups and matches known exact coefficients when the input dimension is one.

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