Automated Analytic Asymptotic Evaluation of the Marginal Likelihood for Latent Models

TL;DR

This paper introduces two algorithms for analytically approximating the marginal likelihood in Bayesian networks with hidden variables, addressing challenges posed by latent models and singularities.

Contribution

The paper presents novel algorithms that accurately evaluate the marginal likelihood for latent Bayesian networks, overcoming issues with regularity and singularities.

Findings

Algorithms successfully approximate marginal likelihood in complex models

Implementation in Matlab and Maple demonstrates practical applicability

Improved accuracy over standard BIC approximation for latent models

Abstract

We present and implement 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 for latent Bayesian network models, namely networks that include hidden variables, where asymptotic approximation deviates from the standard BIC score. Our algorithms solve two central difficulties in asymptotic evaluation of marginal likelihood integrals, namely, evaluation of regular dimensionality drop for latent Bayesian network models and computation of non-standard approximation formulas for singular statistics for these models. The presented algorithms are implemented in Matlab and Maple and their usage is demonstrated for marginal likelihood approximations for Bayesian networks with hidden variables.