Flexible clustering via hidden hierarchical Dirichlet priors

TL;DR

This paper introduces a flexible Bayesian clustering model using hidden hierarchical Dirichlet priors, improving on existing methods by better handling multiple populations and providing efficient inference algorithms.

Contribution

It develops a novel nonparametric prior for clustering, derives its distribution, and proposes efficient MCMC algorithms, including a new scheme for multiple populations and homogeneity testing.

Findings

The new model offers more flexible clustering across heterogeneous populations.

The derived algorithms outperform traditional nested Dirichlet process methods.

Illustrative examples demonstrate improved clustering and testing capabilities.

Abstract

The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for clustering probability distributions is the nested Dirichlet process, which however has the drawback of grouping distributions in a single cluster when ties are observed across samples. With the goal of achieving a flexible and effective clustering method for both samples and observations, we investigate a nonparametric prior that arises as the composition of two different discrete random structures and derive a closed-form expression for the induced distribution of the random partition, the fundamental tool regulating the clustering behavior of the model. On the one hand, this allows to gain a deeper insight into the theoretical properties of the model and, on the other hand, it yields an MCMC algorithm for evaluating Bayesian inferences of interest. Moreover, we single out limitations of this algorithm when working with more than two populations and, consequently, devise an alternative more efficient sampling scheme, which as a by-product, allows testing homogeneity between different populations. Finally, we perform a comparison with the nested Dirichlet process and provide illustrative examples of both synthetic and real data.