Sparse Tensor Additive Regression
This work addresses tensor regression for applications like medical imaging and digital marketing, but it is incremental as it builds on existing nonparametric and sparse methods.
The authors tackled the problem of modeling scalar responses from tensor covariates by proposing Sparse Tensor Additive Regression (STAR), which exploits sparse and low-rank structures and achieves competitive performance in simulations and click-through-rate prediction.
Tensors are becoming prevalent in modern applications such as medical imaging and digital marketing. In this paper, we propose a sparse tensor additive regression (STAR) that models a scalar response as a flexible nonparametric function of tensor covariates. The proposed model effectively exploits the sparse and low-rank structures in the tensor additive regression. We formulate the parameter estimation as a non-convex optimization problem, and propose an efficient penalized alternating minimization algorithm. We establish a non-asymptotic error bound for the estimator obtained from each iteration of the proposed algorithm, which reveals an interplay between the optimization error and the statistical rate of convergence. We demonstrate the efficacy of STAR through extensive comparative simulation studies, and an application to the click-through-rate prediction in online advertising.