{"paper":{"title":"Private Center Points and Learning of Halfspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CG","cs.CR","stat.ML"],"primary_cat":"cs.LG","authors_text":"Amos Beimel, Kobbi Nissim, Shay Moran, Uri Stemmer","submitted_at":"2019-02-27T19:06:12Z","abstract_excerpt":"We present a private learner for halfspaces over an arbitrary finite domain $X\\subset \\mathbb{R}^d$ with sample complexity $mathrm{poly}(d,2^{\\log^*|X|})$. The building block for this learner is a differentially private algorithm for locating an approximate center point of $m>\\mathrm{poly}(d,2^{\\log^*|X|})$ points -- a high dimensional generalization of the median function. Our construction establishes a relationship between these two problems that is reminiscent of the relation between the median and learning one-dimensional thresholds [Bun et al.\\ FOCS '15]. This relationship suggests that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10731","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"}