Dirichlet Process Mixture Models with Shrinkage Prior

TL;DR

This paper introduces Dirichlet Process Mixture models with shrinkage priors, specifically Horseshoe and Normal-Gamma, improving prediction and variable selection in high-dimensional clustering tasks.

Contribution

It develops novel DPM models with shrinkage priors for better prediction and variable selection, especially in high-dimensional settings.

Findings

Horseshoe DPM outperforms standard DPM in simulations.

Shrinkage priors improve clustering accuracy.

Models show better predictive performance on real data.

Abstract

We propose Dirichlet Process Mixture (DPM) models for prediction and cluster-wise variable selection, based on two choices of shrinkage baseline prior distributions for the linear regression coefficients, namely the Horseshoe prior and Normal-Gamma prior. We show in a simulation study that each of the two proposed DPM models tend to outperform the standard DPM model based on the non-shrinkage normal prior, in terms of predictive, variable selection, and clustering accuracy. This is especially true for the Horseshoe model, and when the number of covariates exceeds the within-cluster sample size. A real data set is analyzed to illustrate the proposed modeling methodology, where both proposed DPM models again attained better predictive accuracy.