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

Understand

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.