Rate Optimal Denoising of Simultaneously Sparse and Low Rank Matrices

Dan Yang, Zongming Ma, Andreas Buja.

Year: 2016, Volume: 17, Issue: 92, Pages: 1−27


We study minimax rates for denoising simultaneously sparse and low rank matrices in high dimensions. We show that an iterative thresholding algorithm achieves (near) optimal rates adaptively under mild conditions for a large class of loss functions. Numerical experiments on synthetic datasets also demonstrate the competitive performance of the proposed method.