Bayesian sparse multiple regression for simultaneous rank reduction and variable selection.

ABSTRACT: We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of regression coefficients which obviates the need to specify a prior on the rank, and shrinks the regression matrix towards low-rank and row-sparse structures. We provide theoretical support to the proposed methodology by proving minimax optimality of the posterior mean under the prediction risk in ultra-high dimensional settings where the number of predictors can grow sub-exponentially relative to the sample size. A one-step post-processing scheme induced by group lasso penalties on the rows of the estimated coefficient matrix is proposed for variable selection,

SUBMITTER: Chakraborty A 

PROVIDER: S-EPMC7584295 | biostudies-literature | 2020 Mar

REPOSITORIES: biostudies-literature