Asymptotic Bayesian Generalization Error in Topic Model and Stochastic Matrix Factorization

In this paper, we derive the asymptotic behavior of the Bayesian generalization error in the topic model. By theoretical analysis of the maximum pole of the zeta function (real log canonical threshold) of the topic model, we obtain an upper bound of the Bayesian generalization error and the free energy in the topic model and the stochastic matrix factorization (SMF; it can be regarded as a restriction of the non-negative matrix factorization). The results show that the generalization error in the topic model and SMF becomes smaller than regular statistical models if Bayesian inference is attained.