2016/12/02 by Antik Chakraborty, Anirban Bhattacharya, Chakraborty, Antik +3 · 2 citations
Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Sparse and Compressive Sensing Techniques #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1612.00877
openalex publication_date 2016/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a Bayesian methodology aimed at simultaneously estimating low-rank\nand row-sparse matrices in a high-dimensional multiple-response linear\nregression model. We consider a carefully devised shrinkage prior on the matrix\nof regression coefficients which obviates the need to specify a prior on the\nrank, and shrinks the regression matrix towards low-rank and row-sparse\nstructures. We provide theoretical support to the proposed methodology by\nproving minimax optimality of the posterior mean under the prediction risk in\nultra-high dimensional settings where the number of predictors can grow\nsub-exponentially relative to the sample size. A one-step post-processing\nscheme induced by group lasso penalties on the rows of the estimated\ncoefficient matrix is proposed for variable selection, with default choices of\ntuning parameters. We additionally provide an estimate of the rank using a\nnovel optimization function achieving dimension reduction in the covariate\nspace. We exhibit the performance of the proposed methodology in an extensive\nsimulation study and a real data example.\n