Common Failure Modes of Subcluster-based Sampling in Dirichlet Process Gaussian Mixture Models -- and a Deep-learning Solution

TL;DR

This paper analyzes failure modes of a subcluster-based sampling method in Dirichlet Process Gaussian Mixture Models and introduces deep learning-based solutions to improve clustering performance and convergence.

Contribution

It identifies limitations of random subcluster initialization and proposes deep learning-based methods as effective replacements to enhance sampler efficiency.

Findings

Deep learning-based initialization improves split proposals.

Enhanced sampler stability and faster convergence.

Significant performance gains over traditional methods.

Abstract

The Dirichlet Process Gaussian Mixture Model (DPGMM) is often used to cluster data when the number of clusters is unknown. One main DPGMM inference paradigm relies on sampling. Here we consider a known state-of-art sampler (proposed by Chang and Fisher III (2013) and improved by Dinari et al. (2019)), analyze its failure modes, and show how to improve it, often drastically. Concretely, in that sampler, whenever a new cluster is formed it is augmented with two subclusters whose labels are initialized at random. Upon their evolution, the subclusters serve to propose a split of the parent cluster. We show that the random initialization is often problematic and hurts the otherwise-effective sampler. Specifically, we demonstrate that this initialization tends to lead to poor split proposals and/or too many iterations before a desired split is accepted. This slows convergence and can damage the clustering. As a remedy, we propose two drop-in-replacement options for the subcluster-initialization subroutine. The first is an intuitive heuristic while the second is based on deep learning. We show that the proposed approach yields better splits, which in turn translate to substantial improvements in performance, results, and stability.