{"paper":{"title":"Robust Nonparametric Regression under Huber's $\\epsilon$-contamination Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.LG","stat.ME","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Aarti Singh, Pradeep Ravikumar, Simon S. Du, Sivaraman Balakrishnan, Yining Wang","submitted_at":"2018-05-26T00:39:12Z","abstract_excerpt":"We consider the non-parametric regression problem under Huber's $\\epsilon$-contamination model, in which an $\\epsilon$ fraction of observations are subject to arbitrary adversarial noise. We first show that a simple local binning median step can effectively remove the adversary noise and this median estimator is minimax optimal up to absolute constants over the H\\\"{o}lder function class with smoothness parameters smaller than or equal to 1. Furthermore, when the underlying function has higher smoothness, we show that using local binning median as pre-preprocessing step to remove the adversaria"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10406","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"}