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Stein COnsistent Risk Estimator (SCORE) for hard thresholding

Abstract : In this work, we construct a risk estimator for hard thresholding which can be used as a basis to solve the difficult task of automatically selecting the threshold. As hard thresholding is not even continuous, Stein's lemma cannot be used to get an unbiased estimator of degrees of freedom, hence of the risk. We prove that under a mild condition, our estimator of the degrees of freedom, although biased, is consistent. Numerical evidence shows that our estimator outperforms another biased risk estimator.
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https://hal.archives-ouvertes.fr/hal-00776303
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Submitted on : Tuesday, April 28, 2015 - 9:05:17 AM
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  • HAL Id : hal-00776303, version 2
  • ARXIV : 1301.5874

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Charles-Alban Deledalle, Gabriel Peyré, Jalal M. Fadili. Stein COnsistent Risk Estimator (SCORE) for hard thresholding. Signal Processing with Adaptive Sparse Structured Representations., Jul 2013, Lausanne, Switzerland. ⟨hal-00776303v2⟩

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