{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/hadamard-response-estimating-distributions","title":"Hadamard Response: Estimating Distributions Privately, Efficiently, and with Little Communication","arxiv_id":"1802.04705","date":"2018-02-13","proceeding":null,"authors":["Jayadev Acharya","Ziteng Sun","Huanyu Zhang"],"abstract":"We study the problem of estimating $k$-ary distributions under\n$\\varepsilon$-local differential privacy. $n$ samples are distributed across\nusers who send privatized versions of their sample to a central server. All\npreviously known sample optimal algorithms require linear (in $k$)\ncommunication from each user in the high privacy regime $(\\varepsilon=O(1))$,\nand run in time that grows as $n\\cdot k$, which can be prohibitive for large\ndomain size $k$.\n  We propose Hadamard Response (HR}, a local privatization scheme that requires\nno shared randomness and is symmetric with respect to the users. Our scheme has\norder optimal sample complexity for all $\\varepsilon$, a communication of at\nmost $\\log k+2$ bits per user, and nearly linear running time of $\\tilde{O}(n +\nk)$.\n  Our encoding and decoding are based on Hadamard matrices, and are simple to\nimplement. The statistical performance relies on the coding theoretic aspects\nof Hadamard matrices, ie, the large Hamming distance between the rows. An\nefficient implementation of the algorithm using the Fast Walsh-Hadamard\ntransform gives the computational gains.\n  We compare our approach with Randomized Response (RR), RAPPOR, and\nsubset-selection mechanisms (SS), both theoretically, and experimentally. For\n$k=10000$, our algorithm runs about 100x faster than SS, and RAPPOR.","url_abs":"http://arxiv.org/abs/1802.04705v2","url_pdf":"http://arxiv.org/pdf/1802.04705v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"hadamard-response-estimating-distributions","repo_url":"https://github.com/jlyx417353617/hadamard_response","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"hadamard-response-estimating-distributions","repo_url":"https://github.com/Samuel-Maddock/pure-LDP","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"hadamard-response-estimating-distributions","repo_url":"https://github.com/zitengsun/hadamard_response","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1802.04705","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}