DeepAI

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

We discuss Bayesian methods for learning Bayesian networks when data sets are incomplete. In particular, we examine asymptotic approximations for the marginal likelihood of incomplete data given a Bayesian network. We consider the Laplace approximation and the less accurate but more efficient BIC/MDL approximation. We also consider approximations proposed by Draper (1993) and Cheeseman and Stutz (1995). These approximations are as efficient as BIC/MDL, but their accuracy has not been studied in any depth. We compare the accuracy of these approximations under the assumption that the Laplace approximation is the most accurate. In experiments using synthetic data generated from discrete naive-Bayes models having a hidden root node, we find that the CS measure is the most accurate.

• 14 publications
• 53 publications
02/13/2013

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

We extend the Bayesian Information Criterion (BIC), an asymptotic approx...
10/19/2012

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

We present and implement two algorithms for analytic asymptotic evaluati...
07/22/2021

### Laplace and Saddlepoint Approximations in High Dimensions

We examine the behaviour of the Laplace and saddlepoint approximations i...
12/12/2012

### Asymptotic Model Selection for Naive Bayesian Networks

We develop a closed form asymptotic formula to compute the marginal like...
01/14/2021

### Bayesian inference with tmbstan for a state-space model with VAR(1) state equation

When using R package tmbstan for Bayesian inference, the built-in featur...
04/24/2022

### A recursive algorithm for an efficient and accurate computation of incomplete Bessel functions

In a previous work, we developed an algorithm for the computation of inc...
04/29/2020

### Identifiability and Consistency of Bayesian Network Structure Learning from Incomplete Data

Bayesian network (BN) structure learning from complete data has been ext...