Matrix denoising for weighted loss functions and heterogeneous signals

Understand

We consider the problem of estimating a low-rank matrix from a noisy observed matrix.

• Previous work has shown that the optimal method depends crucially on the choice of loss function.
• In this paper, we use a family of weighted loss functions, which arise naturally for problems such as submatrix denoising, denoising with heteroscedastic noise, and denoising with missing data.
• However, weighted loss functions are challenging to analyze because they are not orthogonally-invariant.