DeepAI

# Automated Analytic Asymptotic Evaluation of the Marginal Likelihood for Latent Models

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.

• 2 publications
• 25 publications
02/13/2013

### Asymptotic Model Selection for Directed Networks with Hidden Variables

We extend the Bayesian Information Criterion (BIC), an asymptotic approx...
12/12/2012

### Asymptotic Model Selection for Naive Bayesian Networks

We develop a closed form asymptotic formula to compute the marginal like...
02/13/2013

### Efficient Approximations for the Marginal Likelihood of Incomplete Data Given a Bayesian Network

We discuss Bayesian methods for learning Bayesian networks when data set...
03/15/2012

### Learning networks determined by the ratio of prior and data

Recent reports have described that the equivalent sample size (ESS) in a...
01/10/2013

### Classifier Learning with Supervised Marginal Likelihood

It has been argued that in supervised classification tasks, in practice ...
08/11/2020

### Evidence bounds in singular models: probabilistic and variational perspectives

The marginal likelihood or evidence in Bayesian statistics contains an i...
01/17/2016

### On-line Bayesian System Identification

We consider an on-line system identification setting, in which new data ...