A Latent-Variable Bayesian Nonparametric Regression Model

TL;DR

This paper presents a Bayesian nonparametric regression model using a latent Gaussian process to create dependent, data-driven partitions, enabling flexible modeling of complex relationships in data.

Contribution

It introduces a novel latent-variable Bayesian nonparametric regression model with dependent partitions based on a Gaussian process prior.

Findings

Successfully applied to real education data.

Performs well on simulated complex data.

Captures dependencies among data clusters.

Abstract

We introduce a random partition model for Bayesian nonparametric regression. The model is based on infinitely-many disjoint regions of the range of a latent covariate-dependent Gaussian process. Given a realization of the process, the cluster of dependent variable responses that share a common region are assumed to arise from the same distribution. Also, the latent Gaussian process prior allows for the random partitions (i.e., clusters of the observations) to exhibit dependencies among one another. The model is illustrated through the analysis of a real data set arising from education, and through the analysis of simulated data that were generated from complex data-generating models.