Sparse Methods for Automatic Relevance Determination
- URL: http://arxiv.org/abs/2005.08741v1
- Date: Mon, 18 May 2020 14:08:49 GMT
- Title: Sparse Methods for Automatic Relevance Determination
- Authors: Samuel H. Rudy and Themistoklis P. Sapsis
- Abstract summary: 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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
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