Posterior Consistency for Bayesian Relevance Vector Machines

TL;DR

This paper establishes theoretical guarantees for Bayesian relevance vector machines in high-dimensional settings, demonstrating posterior consistency and contraction rates for a new class of priors.

Contribution

It introduces a novel class of global-local priors for relevance vector machines and proves their posterior consistency and contraction rates.

Findings

Proves posterior consistency for the proposed Bayesian model.

Derives posterior contraction rates under the new priors.

Extends theoretical understanding of Bayesian relevance vector machines.

Abstract

Statistical modeling and inference problems with sample sizes substantially smaller than the number of available covariates are challenging. Chakraborty et al. (2012) did a full hierarchical Bayesian analysis of nonlinear regression in such situations using relevance vector machines based on reproducing kernel Hilbert space (RKHS). But they did not provide any theoretical properties associated with their procedure. The present paper revisits their problem, introduces a new class of global-local priors different from theirs, and provides results on posterior consistency as well as posterior contraction rates