{"paper":{"title":"On learning k-parities with and without noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.LG"],"primary_cat":"cs.DS","authors_text":"Ameet Gadekar, Arnab Bhattacharyya, Ninad Rajgopal","submitted_at":"2015-02-18T20:36:19Z","abstract_excerpt":"We first consider the problem of learning $k$-parities in the on-line mistake-bound model: given a hidden vector $x \\in \\{0,1\\}^n$ with $|x|=k$ and a sequence of \"questions\" $a_1, a_2, ...\\in \\{0,1\\}^n$, where the algorithm must reply to each question with $< a_i, x> \\pmod 2$, what is the best tradeoff between the number of mistakes made by the algorithm and its time complexity? We improve the previous best result of Buhrman et al. by an $\\exp(k)$ factor in the time complexity.\n  Second, we consider the problem of learning $k$-parities in the presence of classification noise of rate $\\eta \\in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05375","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"}