2013/07/30 by Weiguang Wang, Wang, Weiguang, Yingbin Liang +3
Engineering · Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1307.7993
openalex publication_date 2013/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate a multivariate multi-response (MVMR) linear regression problem, which contains multiple linear regression models with differently distributed design matrices, and different regression and output vectors. The goal is to recover the support union of all regression vectors using l1/l2-regularized Lasso. We characterize sufficient and necessary conditions on sample complexity as a sharp threshold to guarantee successful recovery of the support union. Namely, if the sample size is above the threshold, then l1/l2-regularized Lasso correctly recovers the support union; and if the sample size is below the threshold, l1/l2-regularized Lasso fails to recover the support union. In particular, the threshold precisely captures the impact of the sparsity of regression vectors and the statistical properties of the design matrices on sample complexity. Therefore, the threshold function also captures the advantages of joint support union recovery using multi-task Lasso over individual support recovery using single-task Lasso.