Sparse linear regression with beta process priors

Bo Chen, John Paisley, Lawrence Carin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Scopus citations

Abstract

A Bayesian approximation to finding the minimum ℓ0 norm solution for an underdetermined linear system is proposed that is based on the beta process prior. The beta process linear regression (BP-LR) model finds sparse solutions to the underdetermined model y = Φx + ∈, by modeling the vector x as an element-wise product of a non-sparse weight vector, w, and a sparse binary vector, z, that is drawn from the beta process prior. The hierarchical model is fully conjugate and therefore is amenable to fast inference methods. We demonstrate the model on a compressive sensing problem and on a correlated-feature problem, where we show the ability of the BP-LR to selectively remove the irrelevant features, while preserving the relevant groups of correlated features. ©2010 IEEE.
Original languageEnglish (US)
Title of host publicationICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Pages1234-1237
Number of pages4
DOIs
StatePublished - Nov 8 2010
Externally publishedYes

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