hal-00664125, version 2
Statistical learning with indirect observations
(29/01/2012)
Résumé : Given a random couple $(X,Y)$ with unknown distribution $P$, the problem of statistical learning consists in the estimation of the Bayes $g^*=\arg\min_{\GG}\E_P l(g(X),Y),$ where $\GG$ is a class of candidate functions and $l$ is a loss function. In this paper we adress this problem when we have at our disposal a corrupted sample $\mathcal{D}_n=\{(Z_1,Y_1),\ldots , (Z_n,Y_n)\}$ of i.i.d. indirect observations. It means that the inputs $Z_i$, $i=1,\ldots n$ are distributed from the density $Af$, where $A$ is a known compact linear operator and $f$ is the density of the direct input $X$.
- 1 :
- CNRS : UMR6093 – Université d'Angers
- Domaine : Mathématiques/Statistiques
Statistiques/ThéorieStatistiques/Machine Learning - Mots-clés : Statistical learning – Inverse problem – Pattern recognition – Empirical processes – Fast rates
- Versions disponibles : v1 (30-01-2012) v2 (15-02-2012) v3 (10-07-2012)
- hal-00664125, version 2
- http://hal.archives-ouvertes.fr/hal-00664125
- oai:hal.archives-ouvertes.fr:hal-00664125
- Contributeur :
- Soumis le : Mercredi 15 Février 2012, 13:53:44
- Dernière modification le : Mercredi 15 Février 2012, 14:05:57
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