Group SLOPE Penalized CP Low-Rank Tensor Regression
share
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 CANDECOMP/PARAFAC (CP) decomposition, namely TgSLOPE. This procedure provably controls the newly introduced tensor group false discovery rate (TgFDR), provided that the predictor matrix is column-orthogonal. Moreover, we establish the asymptotically minimax convergence with respect to the ℓ_2-loss of TgSLOPE estimator at the frontal slice level. For efficient problem resolution, we equivalently transform the TgSLOPE problem into a difference-of-convex (DC) program with the level-coercive objective function. This allows us to solve the reformulation problem of TgSLOPE by an efficient proximal DC algorithm (DCA) with global convergence. Numerical studies conducted on synthetic data and a real human brain connection data illustrate the efficacy of the proposed TgSLOPE estimation procedure.
READ FULL TEXT