{"paper":{"title":"2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization","license":"","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Vladimir Koltchinskii","submitted_at":"2007-08-01T12:31:18Z","abstract_excerpt":"Let $\\mathcal{F}$ be a class of measurable functions $f:S\\mapsto [0,1]$ defined on a probability space $(S,\\mathcal{A},P)$. Given a sample (X_1,...,X_n) of i.i.d. random variables taking values in S with common distribution P, let P_n denote the empirical measure based on (X_1,...,X_n). We study an empirical risk minimization problem $P_nf\\to \\min$, $f\\in \\mathcal{F}$. Given a solution $\\hat{f}_n$ of this problem, the goal is to obtain very general upper bounds on its excess risk \\[\\mathcal{E}_P(\\hat{f}_n):=P\\hat{f}_n-\\inf_{f\\in \\mathcal{F}}Pf,\\] expressed in terms of relevant geometric parame"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.0083","kind":"arxiv","version":1},"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"}