Risk estimation for matrix recovery with spectral regularization

Abstract : 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. To show the potential applicability of our approach, we exemplify it on a matrix completion problem to objectively and automatically select the regularization parameter.
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https://hal.archives-ouvertes.fr/hal-00695326
Contributor : Charles-Alban Deledalle <>
Submitted on : Wednesday, October 31, 2012 - 5:20:44 PM
Last modification on : Thursday, February 7, 2019 - 5:47:11 PM
Document(s) archivé(s) le : Friday, February 1, 2013 - 3:40:13 AM

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  • HAL Id : hal-00695326, version 3
  • ARXIV : 1205.1482

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Charles-Alban Deledalle, Samuel Vaiter, Gabriel Peyré, Jalal M. Fadili, Charles Dossal. Risk estimation for matrix recovery with spectral regularization. ICML'2012 workshop on Sparsity, Dictionaries and Projections in Machine Learning and Signal Processing, Jun 2012, Edinburgh, United Kingdom. ⟨hal-00695326v3⟩

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