Inference of global clusters from locally distributed data

TL;DR

This paper introduces a Bayesian nonparametric approach using nested Dirichlet processes to infer global clusters from data distributed across covariates, effectively capturing heterogeneity and enabling analysis of complex, aggregated data.

Contribution

The paper presents a novel hierarchical Bayesian model that combines spatial modeling with nested Dirichlet processes for global clustering from local data distributions.

Findings

Effective in object tracking applications

Successfully infers global clusters without functional identity info

Provides an efficient inference algorithm

Abstract

We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over the covariate domain. We propose a novel Bayesian nonparametric method reposing on the formalism of spatial modeling and a nested hierarchy of Dirichlet processes. We provide an analysis of the model properties, relating and contrasting the notions of local and global clusters. We also provide an efficient inference algorithm, and demonstrate the utility of our method in several data examples, including the problem of object tracking and a global clustering analysis of functional data where the functional identity information is not available.