Sparse Methods for Automatic Relevance Determination
This work addresses the need for more interpretable and efficient models in system identification, but it is incremental as it builds on existing ARD techniques.
The paper tackles the problem of achieving sparsity in Bayesian regression for nonlinear system identification by analyzing and extending automatic relevance determination (ARD) with regularization and thresholding methods. It provides theoretical and empirical results, demonstrating favorable performance in learning sparse solutions for linear systems with orthogonal covariates.
This work considers methods for imposing sparsity in Bayesian regression with applications in nonlinear 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 covariates, we analytically demonstrate favorable performance with regards 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.