Estimation of Kullback-Leibler losses for noisy recovery problems within the exponential family

Abstract : We address the question of estimating Kullback-Leibler losses rather than squared losses in recovery problems where the noise is distributed within the exponential family. Inspired by Stein unbiased risk estimator (SURE), we exhibit conditions under which these losses can be unbiasedly estimated or estimated with a controlled bias. Simulations on parameter selection problems in applications to image denoising and variable selection with Gamma and Poisson noises illustrate the interest of Kullback-Leibler losses and the proposed estimators.
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Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2017, 11 (2), pp.3141-3164. <https://projecteuclid.org/euclid.ejs/1503972028>
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https://hal.archives-ouvertes.fr/hal-01248431
Contributeur : Charles-Alban Deledalle <>
Soumis le : samedi 19 août 2017 - 01:40:17
Dernière modification le : mardi 29 août 2017 - 18:15:16

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  • HAL Id : hal-01248431, version 3
  • ARXIV : 1512.08191

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Charles-Alban Deledalle. Estimation of Kullback-Leibler losses for noisy recovery problems within the exponential family. Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2017, 11 (2), pp.3141-3164. <https://projecteuclid.org/euclid.ejs/1503972028>. <hal-01248431v3>

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