Variable Selection for Nonparametric Gaussian Process Priors: Models and Computational Strategies

TL;DR

This paper develops a flexible nonparametric Gaussian process modeling framework for various data types, including survival data, and introduces a variable selection method with efficient computational strategies, validated on simulated and benchmark datasets.

Contribution

It presents a unified Gaussian process approach for diverse data types and introduces a novel variable selection framework with efficient MCMC algorithms.

Findings

Flexible Gaussian process models for different data types

Effective variable selection using mixture priors

Computational strategies outperform existing methods

Abstract

This paper presents a unified treatment of Gaussian process models that extends to data from the exponential dispersion family and to survival data. Our specific interest is in the analysis of data sets with predictors that have an a priori unknown form of possibly nonlinear associations to the response. The modeling approach we describe incorporates Gaussian processes in a generalized linear model framework to obtain a class of nonparametric regression models where the covariance matrix depends on the predictors. We consider, in particular, continuous, categorical and count responses. We also look into models that account for survival outcomes. We explore alternative covariance formulations for the Gaussian process prior and demonstrate the flexibility of the construction. Next, we focus on the important problem of selecting variables from the set of possible predictors and describe a general framework that employs mixture priors. We compare alternative MCMC strategies for posterior inference and achieve a computationally efficient and practical approach. We demonstrate performances on simulated and benchmark data sets.