Asymptotic Behavior of Bayesian Generalization Error in Multinomial Mixtures
Machine Learning
2022-03-15 v1 Statistics Theory
Statistics Theory
Abstract
Multinomial mixtures are widely used in the information engineering field, however, their mathematical properties are not yet clarified because they are singular learning models. In fact, the models are non-identifiable and their Fisher information matrices are not positive definite. In recent years, the mathematical foundation of singular statistical models are clarified by using algebraic geometric methods. In this paper, we clarify the real log canonical thresholds and multiplicities of the multinomial mixtures and elucidate their asymptotic behaviors of generalization error and free energy.
Cite
@article{arxiv.2203.06884,
title = {Asymptotic Behavior of Bayesian Generalization Error in Multinomial Mixtures},
author = {Takumi Watanabe and Sumio Watanabe},
journal= {arXiv preprint arXiv:2203.06884},
year = {2022}
}