Reviews: Boosted Sparse and Low-Rank Tensor Regression

This paper examines the problem of tensor regression and proposes a boosted sparse low-rank model that produces interpretable results. In their low-rank tensor regression model, unit-rank tensors from the CP decomposition of the coefficient tensor is assumed to be sparse. This assumption allows for an interpretable model where the outcome is related to only a subset of features. For model estimation, the authors use a divide-and-conquer strategy to learn the sparse CP decomposition, based on an existing sequential extraction method, where sparse unit-rank problems are sequentially solved. Instead of using an alternating convex search (ACS) approach, the authors use a stage-wise unit-rank tensor factorization algorithm to learn the model.