Group SLOPE Penalized Low-Rank Tensor Regression

This article aims to seek a selection and estimation procedure for a class of tensor regression problems with multivariate covariates and matrix responses, which can provide theoretical guarantees for model selection in finite samples. Considering the frontal slice sparsity and low-rankness inherited in the coefficient tensor, we formulate the regression procedure as a group SLOPE penalized low-rank tensor optimization problem based on an orthogonal decomposition, namely TgSLOPE. This procedure provably controls the newly introduced tensor group false discovery rate (TgFDR), …

article low matrix model selection multivariate regression responses sparsity tensor