Variational Bayes and Truncation approximations for Enriched Dirichlet process mixtures

TL;DR

This paper introduces a variational Bayes approach with truncation approximations for Enriched Dirichlet process mixtures, improving computational efficiency and providing practical inference tools for large datasets.

Contribution

It develops a variational Bayes estimator for EDPMs using truncation, enhancing inference efficiency and enabling easier implementation of Gibbs sampling methods.

Findings

The variational Bayes estimator improves computational speed.

The truncation approximation's accuracy is theoretically derived.

Validated through simulations and real data application.

Abstract

A common impediment in conducting inference for Bayesian nonparametric models is either the need for complex MCMC algorithms and/or computational run-time for large datasets. We propose solutions here for Enriched Dirichlet process mixtures (EDPM). We derive a variational Bayes estimator based on a previously developed truncation approximation for EDPMs. The variational Bayes estimator can be used in two ways: 1) to develop a more efficient truncation approximation; 2) as good initial values for a blocked Gibbs sampler based on this more efficient truncation approximation or for a polya urn sampler. We derive the accuracy of this more efficient truncation approximation and demonstrate how this allows for simple implementation of a blocked Gibbs Sampler EDPMs in Nimble. We confirm the validity of the approximations by simulations and illustrate on a real data set.