Bayesian nonparametric model based clustering with intractable distributions: an ABC approach

TL;DR

This paper introduces an approximate Bayesian computational (ABC) method for clustering with nonparametric mixture models when the kernel's normalizing constant is intractable, using Wasserstein distance and adaptive strategies.

Contribution

It develops an ABC-MCMC algorithm tailored for intractable kernels in Bayesian nonparametric clustering, incorporating Wasserstein distance and adaptive parameter tuning.

Findings

The ABC approach effectively handles intractable kernels in clustering.

The adaptive strategy improves algorithm stability and performance.

Application to real network data demonstrates practical utility.

Abstract

Bayesian nonparametric mixture models offer a rich framework for model based clustering. We consider the situation where the kernel of the mixture is available only up to an intractable normalizing constant. In this case, most of the commonly used Markov chain Monte Carlo (MCMC) methods are not suitable. We propose an approximate Bayesian computational (ABC) strategy, whereby we approximate the posterior to avoid the intractability of the kernel. We derive an ABC-MCMC algorithm which combines (i) the use of the predictive distribution induced by the nonparametric prior as proposal and (ii) the use of the Wasserstein distance and its connection to optimal matching problems. To overcome the sensibility with respect to the parameters of our algorithm, we further propose an adaptive strategy. We illustrate the use of the proposed algorithm with several simulation studies and an application on real data, where we cluster a population of networks, comparing its performance with standard MCMC algorithms and validating the adaptive strategy.