L2RM: Low-rank Linear Regression Models for High-dimensional Matrix Responses.

ABSTRACT: The aim of this paper is to develop a low-rank linear regression model (L2RM) to correlate a high-dimensional response matrix with a high dimensional vector of covariates when coefficient matrices have low-rank structures. We propose a fast and efficient screening procedure based on the spectral norm of each coefficient matrix in order to deal with the case when the number of covariates is extremely large. We develop an efficient estimation procedure based on the trace norm regularization, which explicitly imposes the low rank structure of coefficient matrices. When both the dimension of response matrix and that of covariate vector diverge at the exponential order of the sample size, we investigate the sure independence screening property under some mild conditions. We also systematically

SUBMITTER: Kong D 

PROVIDER: S-EPMC7781207 | biostudies-literature | 2020 Apr

REPOSITORIES: biostudies-literature