{"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/private-frequency-estimation-via-projective","title":"Private Frequency Estimation via Projective Geometry","arxiv_id":"2203.00194","date":"2022-03-01","proceeding":null,"authors":["Vitaly Feldman","Jelani Nelson","Huy Lê Nguyen","Kunal Talwar"],"abstract":"In this work, we propose a new algorithm ProjectiveGeometryResponse (PGR) for locally differentially private (LDP) frequency estimation. For a universe size of $k$ and with $n$ users, our $\\varepsilon$-LDP algorithm has communication cost $\\lceil\\log_2k\\rceil$ bits in the private coin setting and $\\varepsilon\\log_2 e + O(1)$ in the public coin setting, and has computation cost $O(n + k\\exp(\\varepsilon) \\log k)$ for the server to approximately reconstruct the frequency histogram, while achieving the state-of-the-art privacy-utility tradeoff. In many parameter settings used in practice this is a significant improvement over the $ O(n+k^2)$ computation cost that is achieved by the recent PI-RAPPOR algorithm (Feldman and Talwar; 2021). Our empirical evaluation shows a speedup of over 50x over PI-RAPPOR while using approximately 75x less memory for practically relevant parameter settings. In addition, the running time of our algorithm is within an order of magnitude of HadamardResponse (Acharya, Sun, and Zhang; 2019) and RecursiveHadamardResponse (Chen, Kairouz, and Ozgur; 2020) which have significantly worse reconstruction error. The error of our algorithm essentially matches that of the communication- and time-inefficient but utility-optimal SubsetSelection (SS) algorithm (Ye and Barg; 2017). Our new algorithm is based on using Projective Planes over a finite field to define a small collection of sets that are close to being pairwise independent and a dynamic programming algorithm for approximate histogram reconstruction on the server side. We also give an extension of PGR, which we call HybridProjectiveGeometryResponse, that allows trading off computation time with utility smoothly.","url_abs":"https://arxiv.org/abs/2203.00194v1","url_pdf":"https://arxiv.org/pdf/2203.00194v1.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":"private-frequency-estimation-via-projective","repo_url":"https://github.com/minilek/private_frequency_oracles","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2203.00194","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2203.00194"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/minilek/private_frequency_oracles","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"summary":{"unverified":2},"by_repo_kind":{"official":{"samples":2,"ran":0,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"a894a8c292ffae71","entry":"extract_base_filename","repo":"minilek/private_frequency_oracles","repo_kind":"official","path":"generate_figures.py","file_url":"https://github.com/minilek/private_frequency_oracles/blob/HEAD/generate_figures.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"a894a8c292ffae71"}},{"code_sha256_prefix":"83605e36cc4029ea","entry":"zipfian","repo":"minilek/private_frequency_oracles","repo_kind":"official","path":"run_all_experiments.py","file_url":"https://github.com/minilek/private_frequency_oracles/blob/HEAD/run_all_experiments.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"83605e36cc4029ea"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}