Massively-parallel best subset selection for ordinary least-squares regression

Abstract

Selecting an optimal subset of k out of d features for linear regression models given n training instances is often considered intractable for feature spaces with hundreds or thousands of dimensions. We propose an efficient massively-parallel implementation for selecting such optimal feature subsets in a brute-force fashion for small k. By exploiting the enormous compute power provided by modern parallel devices such as graphics processing units, it can deal with thousands of input dimensions even using standard commodity hardware only. We evaluate the practical runtime using artificial datasets and sketch the applicability of our framework in the context of astronomy