SPARSE LINEAR REGRESSIONWITH BETA PROCESS PRIORS

A Bayesian approximation to finding the minimum `0 norm solution for an underdetermined linear system is proposed that is based on the beta process prior. The beta process lin-ear 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 demon-strate 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. Index Terms — Bayesian nonparametrics, beta process, sparse linear regression, compressive sensin