Generalized SURE for optimal shrinkage of singular values in low-rank matrix denoising

Abstract : We consider the problem of estimating a low-rank signal matrix from noisy measurements under the assumption that the distribution of the data matrix belongs to an exponential family. In this setting, we derive generalized Stein's unbiased risk estimation (SURE) formulas that hold for any spectral estimators which shrink or threshold the singular values of the data matrix. This leads to new data-driven shrinkage rules, whose optimality is discussed using tools from random matrix theory and through numerical experiments. Our approach is compared to recent results on asymptotically optimal shrinking rules for Gaussian noise. It also leads to new procedures for singular values shrinkage in matrix denoising for Poisson-distributed or Gamma-distributed measurements.
Type de document :
Pré-publication, Document de travail
2016
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https://hal.archives-ouvertes.fr/hal-01323285
Contributeur : Jérémie Bigot <>
Soumis le : lundi 30 mai 2016 - 12:49:49
Dernière modification le : mercredi 27 juillet 2016 - 14:48:48

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  • HAL Id : hal-01323285, version 1
  • ARXIV : 1605.07412

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Jérémie Bigot, Charles-Alban Deledalle, Delphine Féral. Generalized SURE for optimal shrinkage of singular values in low-rank matrix denoising. 2016. <hal-01323285>

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