A discomfort-informed adaptive Gibbs sampler for finite mixture models

TL;DR

This paper presents an adaptive Gibbs sampler for finite mixture models that enhances convergence efficiency by focusing updates on potentially misclassified observations, demonstrated through simulations and real data.

Contribution

The paper introduces a novel discomfort-informed adaptive Gibbs sampler that improves convergence efficiency in Bayesian finite mixture model inference.

Findings

Faster convergence compared to existing methods

More efficient use of computational resources

Effective in real data applications

Abstract

Finite mixture models are frequently used to uncover latent structures in high-dimensional datasets (e.g.\ identifying clusters of patients in electronic health records). The inference of such structures can be performed in a Bayesian framework, and involves the use of sampling algorithms such as Gibbs samplers aimed at deriving posterior distribution of the probabilities of observations to belong to specific clusters. Unfortunately, traditional implementations of Gibbs samplers in this context often face critical challenges, such as inefficient use of computational resources and unnecessary updates for observations that are highly likely to remain in their current cluster. This paper introduces a new adaptive Gibbs sampler that improves the convergence efficiency over existing methods. In particular, our sampler is guided by a function that, at each iteration, uses the past of the chain to focus the updating on observations potentially misclassified in the current clustering, i.e.\ those with a low probability of belonging to their current component. Through simulation studies and two real data analyses, we empirically demonstrate that, in terms of convergence time, our method tends to perform more efficiently compared to state-of-the-art approaches.