{"paper":{"title":"Fast rates for noisy clustering","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":"2012-05-07T14:57:06Z","abstract_excerpt":"The effect of errors in variables in empirical minimization is investigated. Given a loss $l$ and a set of decision rules $\\mathcal{G}$, we prove a general upper bound for an empirical minimization based on a deconvolution kernel and a noisy sample $Z_i=X_i+\\epsilon_i,i=1,...,n$. We apply this general upper bound to give the rate of convergence for the expected excess risk in noisy clustering. A recent bound from \\citet{levrard} proves that this rate is $\\mathcal{O}(1/n)$ in the direct case, under Pollard's regularity assumptions. Here the effect of noisy measurements gives a rate of the form "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1417","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"}