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Risk estimation for matrix recovery with spectral regularization
- Publication Year :
- 2012
-
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.<br />Comment: This version is an update of our original paper presented at ICML'2012 workshop on Sparsity, Dictionaries and Projections in Machine Learning and Signal Processing
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1205.1482
- Document Type :
- Working Paper