Statistical learning with indirect observations

Sébastien Loustau (1)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

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 $X$.

Mots clés: Statistical learning; Inverse problem; Pattern recognition; Empirical processes

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Machine Learning [stat.ML]

Sébastien Loustau. Statistical learning with indirect observations. 2012. ⟨hal-00664125v1⟩