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Information Center for Mathematical Science

PAC

Information Center for Mathematical Science

PAC

Unbiased Risk Estimates for Singular Value Thresholding and Spectral Estimators
Author Emmanuel J. Candes (Stanford University)
Homepage Url http://www-stat.stanford.edu/~candes/publications.html
Coauthors Carlos A. Sing-Long, Joshua D. Trzasko
Abstract In an increasing number of applications, it is of interest to recover an approximately low-rank data matrix from noisy observations. This paper develops an unbiased risk estimate—holding in a Gaussian model—for any spectral estimator obeying some mild regularity assumptions. In particular, we give an unbiased risk estimate formula for singular value thresholding (SVT), a popular estimation strategy which applies a soft-thresholding rule to the singular values of the noisy observations. Among other things, our formulas offer a principled and automated way of selecting regularization parameters in a variety of problems. In particular, we demonstrate the utility of the unbiased risk estimation for SVT-based denoising of real clinical cardiac MRI series data. We also give new results concerning the differentiability of certain matrix-valued functions.
Abstract Url http://www-stat.stanford.edu/~candes/papers/SURE_SVT.pdf