A Class of Dependent Random Distributions Based on Atom Skipping

TL;DR

The paper introduces the Plaid Atoms Model (PAM), a Bayesian nonparametric approach that uses atom skipping to generate dependent clustering patterns across multiple groups, enabling interpretable posterior inference.

Contribution

It presents a novel atom skipping mechanism within a Bayesian nonparametric framework to model dependent distributions and clusters across groups, with theoretical analysis and practical extensions.

Findings

PAM effectively captures overlapping and non-overlapping clusters across groups.

The model provides interpretable posterior probabilities for cluster exclusivity.

Simulation and real data demonstrate superior performance over existing models.

Abstract

We propose the Plaid Atoms Model (PAM), a novel Bayesian nonparametric model for grouped data. Founded on an idea of `atom skipping', PAM is part of a well-established category of models that generate dependent random distributions and clusters across multiple groups. Atom skipping referrs to stochastically assigning 0 weights to atoms in an infinite mixture. Deploying atom skipping across groups, PAM produces a dependent clustering pattern with overlapping and non-overlapping clusters across groups. As a result, interpretable posterior inference is possible such as reporting the posterior probability of a cluster being exclusive to a single group or shared among a subset of groups. We discuss the theoretical properties of the proposed and related models. Minor extensions of the proposed model for multivariate or count data are presented. Simulation studies and applications using real-world datasets illustrate the performance of the new models with comparison to existing models.