🤖 AI Summary
This work addresses the computational inefficiency often encountered in enriched Dirichlet process mixture models within Bayesian nonparametric inference, particularly when employing complex MCMC algorithms or handling large-scale data. The authors propose an improved truncation approximation strategy integrated with variational Bayes, which substantially simplifies model implementation and accelerates inference. The resulting variational solution serves as a high-quality initialization for Gibbs sampling and is further enhanced by combining blocked Gibbs updates with Pólya urn sampling schemes, enabling efficient implementation within the Nimble platform. Experimental results demonstrate that the proposed approach achieves substantial gains in computational efficiency and practical usability while preserving inferential accuracy.
📝 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.