Sparse methods for automatic relevance determination

This work considers methods for imposing sparsity in Bayesian regression with applications in non linear system identification. We first review automatic relevance determination (ARD) and analytically demonstrate the need to additional regularization or thresholding to achieve sparse models. We then discuss two classes of methods, regularization based and thresholding based, which build on ARD to learn parsimonious solutions to linear problems. In the case of orthogonal features, we analytically demonstrate favorable performance with regard to learning a small set of active terms in a linear system with a sparse solution. Several example problems are presented to compare the set of proposed methods in terms of advantages and limitations to ARD in bases with hundreds of elements. The aim of this paper is to analyze and understand the assumptions that lead to several algorithms and to provide theoretical and empirical results so that the reader may gain insight and make more informed choices regarding sparse Bayesian regression. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper considers methods for imposing sparsity in Bayesian regression and discusses the need for additional regularization or thresholding on top of automatic relevance determination (ARD). Two classes of methods, regularization-based and thresholding-based, are proposed to learn parsimonious solutions to linear problems. Analytical demonstrations show favorable performance in learning a small set of active terms in a linear system with a sparse solution.