{"paper":{"title":"Statistical learning with indirect observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"S\\'ebastien Loustau (LAREMA)","submitted_at":"2012-01-30T06:57:56Z","abstract_excerpt":"Let $(X,Y)\\in\\mathcal{X}\\times \\mathcal{Y}$ be a random couple with unknown distribution $P$. Let $\\GG$ be a class of measurable functions and $\\ell$ a loss function. The problem of statistical learning deals with the estimation of the Bayes: $$g^*=\\arg\\min_{g\\in\\GG}\\E_P \\ell(g(X),Y). $$ In this paper, we study this problem when we deal with a contaminated sample $(Z_1,Y_1),..., (Z_n,Y_n)$ of i.i.d. indirect observations. Each input $Z_i$, $i=1,...,n$ is distributed from a density $Af$, where $A$ is a known compact linear operator and $f$ is the density of the direct input $X$.\nWe derive fast "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6115","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}