Reviews: Low-rank Interaction with Sparse Additive Effects Model for Large Data Frames

Summary ------- This paper introduces a new statistical model for matrices of heterogeneous data (data frames) based on the exponential family. The features of this model are: i) modeling additive effects in a sparse way, ii) modeling low-rank interactions. The parameters of this model are then estimated by maximizing the likelihood with sparse and low-rank regularizations. In addition, this work comes with statistical guarantees and optimization convergence guarantees of the proposed algorithm. Numerical experiments concludes the manuscript. Quality ------- This paper is mathematically rigorous and technically sound.