Risk estimation for matrix recovery with spectral regularization

@article{Deledalle2012RiskEF,
title={Risk estimation for matrix recovery with spectral regularization},
author={Charles-Alban Deledalle and Samuel Vaiter and Gabriel Peyr{\'e} and Mohamed-Jalal Fadili and Charles Dossal},
journal={CoRR},
year={2012},
volume={abs/1205.1482}
}

In this paper, we develop an approach to recursively estimate the quadratic risk for matrix recovery problems regularized with spectral functions. Toward this end, in the spirit of the SURE theory, a key step is to compute the (weak) derivative and divergence of a solution with respect to the observations. As such a solution is not available in closed form, but rather through a proximal splitting algorithm, we propose to recursively compute the divergence from the sequence of iterates. A second… CONTINUE READING