Poster

Sparse Bayesian Learning via Stepwise Regression

Sebastian Ament · Carla Gomes

Keywords: [ Sparsity and Compressed Sensing ] [ Algorithms ]

[ Abstract ]
[ Paper ] [ Visit Poster at Spot B3 in Virtual World ]
Thu 22 Jul 9 a.m. PDT — 11 a.m. PDT
 
Spotlight presentation: Bayesian Methods
Thu 22 Jul 7 a.m. PDT — 8 a.m. PDT

Abstract:

Sparse Bayesian Learning (SBL) is a powerful framework for attaining sparsity in probabilistic models. Herein, we propose a coordinate ascent algorithm for SBL termed Relevance Matching Pursuit (RMP) and show that, as its noise variance parameter goes to zero, RMP exhibits a surprising connection to Stepwise Regression. Further, we derive novel guarantees for Stepwise Regression algorithms, which also shed light on RMP. Our guarantees for Forward Regression improve on deterministic and probabilistic results for Orthogonal Matching Pursuit with noise. Our analysis of Backward Regression culminates in a bound on the residual of the optimal solution to the subset selection problem that, if satisfied, guarantees the optimality of the result. To our knowledge, this bound is the first that can be computed in polynomial time and depends chiefly on the smallest singular value of the matrix. We report numerical experiments using a variety of feature selection algorithms. Notably, RMP and its limiting variant are both efficient and maintain strong performance with correlated features.

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