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.
翻译:在本文中,我们得出了主题模型中贝叶斯普遍化错误的无症状行为。通过对主题模型中zeta函数(正对正对金库阈值)的最大极进行理论分析,我们获得了贝叶斯普遍化错误和主题模型中自由能量和随机矩阵因子化的上限(SMF;它可以被视为对非负矩阵因子化的限制 ) 。 结果表明,如果实现贝叶斯推论,主题模型和SMF的概括性错误比常规统计模型要小。