Generalized Polya Urn for Time-varying Dirichlet Process Mixtures

TL;DR

This paper introduces a time-varying Dirichlet Process Mixture model using a generalized Polya urn scheme, enabling density estimation and clustering on evolving data distributions with inference via MCMC and SMC methods.

Contribution

It proposes a novel class of dynamic DPM models that adapt over time, addressing limitations of static models for evolving data.

Findings

Effective modeling of evolving data distributions.

Successful application to various real-world datasets.

Demonstrated advantages over traditional static DPMs.

Abstract

Dirichlet Process Mixtures (DPMs) are a popular class of statistical models to perform density estimation and clustering. However, when the data available have a distribution evolving over time, such models are inadequate. We introduce here a class of time-varying DPMs which ensures that at each time step the random distribution follows a DPM model. Our model relies on an intuitive and simple generalized Polya urn scheme. Inference is performed using Markov chain Monte Carlo and Sequential Monte Carlo. We demonstrate our model on various applications.