Modelling and computation using NCoRM mixtures for density regression

TL;DR

This paper introduces a new nonparametric regression modeling approach using normalized compound random measure mixtures, along with a novel inference algorithm based on pseudo-marginal Metropolis-Hastings, demonstrated on density regression tasks.

Contribution

It develops a new inference method for normalized compound random measure mixtures and applies it to density regression, expanding the toolkit for nonparametric Bayesian modeling.

Findings

Effective density regression demonstrated

Novel unbiased Laplace functional estimation method

Successful application of the inference algorithm

Abstract

Normalized compound random measures are flexible nonparametric priors for related distributions. We consider building general nonparametric regression models using normalized compound random measure mixture models. Posterior inference is made using a novel pseudo-marginal Metropolis-Hastings sampler for normalized compound random measure mixture models. The algorithm makes use of a new general approach to the unbiased estimation of Laplace functionals of compound random measures (which includes completely random measures as a special case). The approach is illustrated on problems of density regression.