Statistical learning with indirect observations

Details Statistical learning with indirect observations Statistical learning with indirect observations

2012-01-30

arxiv.org/abs/1201.6115v2

Mathematics

Statistics Theory

Scientific paper

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 $\mathcal{D}_n=\{(Z_1,Y_1),..., (Z_n,Y_n)\}$ of i.i.d. indirect observations. It means that the inputs $Z_i$, $i=1,... n$ are distributed from the density $Af$, where $A$ is a known compact linear operator and $f$ is the density of the direct input $X$.

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