Matrix denoising for weighted loss functions and heterogeneous signals

02/25/2019
by   William Leeb, et al.
0

We consider the problem of recovering a low-rank matrix from a noisy observed matrix. Previous work has shown that the optimal method for recovery depends crucially on the choice of loss function. We use a family of weighted loss functions, which arise naturally in many settings such as heteroscedastic noise and missing data. Weighted loss functions are challenging to analyze because they are not orthogonally-invariant. We derive optimal spectral denoisers for these weighted loss functions. By combining different weights, we then use these optimal denoisers to construct a new denoiser that exploits heterogeneity in the signal matrix for more accurate recovery with unweighted loss.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset