Dependent Modeling of Temporal Sequences of Random Partitions

TL;DR

This paper introduces a new class of models for directly capturing dependence in sequences of random partitions, addressing limitations of existing Bayesian nonparametric approaches, and demonstrates their effectiveness through simulations and real data applications.

Contribution

The paper proposes a novel approach to model dependent sequences of partitions directly, avoiding issues with dependent random measures in Bayesian nonparametrics.

Findings

Models produce partitions that evolve smoothly over time

Method effectively captures spatio-temporal dependence in environmental data

Simulation results show natural and gradual partition evolution

Abstract

We consider the task of modeling a dependent sequence of random partitions. It is well-known that a random measure in Bayesian nonparametrics induces a distribution over random partitions. The community has therefore assumed that the best approach to obtain a dependent sequence of random partitions is through modeling dependent random measures. We argue that this approach is problematic and show that the random partition model induced by dependent Bayesian nonparametric priors exhibit counter-intuitive dependence among partitions even though the dependence for the sequence of random probability measures is intuitive. Because of this, we advocate instead to model the sequence of random partitions directly when clustering is of principal interest. To this end, we develop a class of dependent random partition models that explicitly models dependence in a sequence of partitions. We derive conditional and marginal properties of the joint partition model and devise computational strategies when employing the method in Bayesian modeling. In the case of temporal dependence, we demonstrate through simulation how the methodology produces partitions that evolve gently and naturally over time. We further illustrate the utility of the method by applying it to an environmental data set that exhibits spatio-temporal dependence.