Automated Analytic Asymptotic Evaluation of the Marginal

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