Automated analytic asymptotic evaluation of the marginal likelihood for latent models
Dmitry Rusakov, Dan Geiger · 2002
We present two algorithms for analytic asymptotic evaluation of the marginal likelihood of data given a Bayesian network with hidden nodes. As shown by previous work, this evaluation is particularly hard because for these models asymptotic approximation of the marginal likelihood deviates from the standard BIC score. Our algorithms compute regular dimensionality drop for latent models and compute the non-standard approximation formulas for singular statistics for these models. The presented algorithms are implemented in Matlab and Maple and their usage is demonstrated on several examples. In this paper we address the problem of computing anaiytic asymptotic approximations of marginai ii~eiihoods and present two computer programs that compute such approximations. Our algorithms are developed in the context of Bayesian networks with hidden variables, where the evaluation of marginal likelihood was shown to be particularly hard (Rusakov & Geiger, 2002). Consider the evaluation of the marginal likelihood given a Bayesian network model. Under some regularity conditions, the asymptotic form of the log marginal likelihood for Bayesian network models without hidden variables is specified by the standard BIC fornula: 1