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2012

Risk estimation for matrix recovery with spectral regularization

Deledalle, Charles-Alban, Vaiter, Samuel, Peyré, Gabriel et al.

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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 challenge that we unlocked is the computation of the (weak) derivative of the proximity operator of a spectral function.

Risk estimation for matrix recovery with spectral regularization · Around

Built on

Estimation of the mean of a multivariate normal distribution
Stein, C.M · 1981
Earlier work this paper cites.
The convex analysis of unitarily invariant matrix functions
Lewis, A.S · 1995
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Twice differentiable spectral functions
Lewis, A.S. and Sendov, H.S · 2001
Earlier work this paper cites.
Matrix Rank Minimization with Applications
Fazel, M · 2002
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