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Bayesian Generalization Error of Poisson Mixture and Simplex Vandermonde Matrix Type Singularity
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.Comment: 33 page