{"paper":{"title":"Hadamard Response: Estimating Distributions Privately, Efficiently, and with Little Communication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.IT","math.IT"],"primary_cat":"cs.LG","authors_text":"Huanyu Zhang, Jayadev Acharya, Ziteng Sun","submitted_at":"2018-02-13T16:20:56Z","abstract_excerpt":"We study the problem of estimating $k$-ary distributions under $\\varepsilon$-local differential privacy. $n$ samples are distributed across users who send privatized versions of their sample to a central server. All previously known sample optimal algorithms require linear (in $k$) communication from each user in the high privacy regime $(\\varepsilon=O(1))$, and run in time that grows as $n\\cdot k$, which can be prohibitive for large domain size $k$.\n  We propose Hadamard Response (HR}, a local privatization scheme that requires no shared randomness and is symmetric with respect to the users. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04705","kind":"arxiv","version":2},"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"}