Rate Optimal Denoising of Simultaneously Sparse and Low Rank Matrices

TL;DR

This paper investigates the optimal rates for denoising matrices that are both sparse and low rank, proposing an iterative thresholding method that adapts to various loss functions and performs well in practice.

Contribution

It introduces an adaptive iterative thresholding algorithm that achieves near-optimal minimax rates for denoising simultaneously sparse and low rank matrices.

Findings

The proposed method attains near minimax optimal rates.

Numerical experiments show competitive performance.

The approach is effective under mild conditions.

Abstract

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.