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

Charles-Alban Deledalle (1)

1 IMB - Institut de Mathématiques de Bordeaux

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.

Mots clés: Exponential family; Kullback-Leibler divergence; Model selection; Stein unbiased risk estimator

Domaines: Applications [stat.AP]; Méthodologie [stat.ME]; Traitement des images [eess.IV]; Théorie [stat.TH]

Charles-Alban Deledalle. Estimation of Kullback-Leibler losses for noisy recovery problems within the exponential family. Electronic Journal of Statistics , 2017, 11 (2), pp.3141-3164. ⟨hal-01248431v3⟩