{"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/exactly-minimax-optimal-locally","title":"Exactly Minimax-Optimal Locally Differentially Private Sampling","arxiv_id":"2410.22699","date":"2024-10-30","proceeding":null,"authors":["Hyun-Young Park","Shahab Asoodeh","Si-Hyeon Lee"],"abstract":"The sampling problem under local differential privacy has recently been studied with potential applications to generative models, but a fundamental analysis of its privacy-utility trade-off (PUT) remains incomplete. In this work, we define the fundamental PUT of private sampling in the minimax sense, using the f-divergence between original and sampling distributions as the utility measure. We characterize the exact PUT for both finite and continuous data spaces under some mild conditions on the data distributions, and propose sampling mechanisms that are universally optimal for all f-divergences. Our numerical experiments demonstrate the superiority of our mechanisms over baselines, in terms of theoretical utilities for finite data space and of empirical utilities for continuous data space.","url_abs":"https://arxiv.org/abs/2410.22699v1","url_pdf":"https://arxiv.org/pdf/2410.22699v1.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":"exactly-minimax-optimal-locally","repo_url":"https://github.com/phy811/Optimal-LDP-Sampling","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2410.22699","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2410.22699"}},"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/phy811/Optimal-LDP-Sampling","reach":null}],"summary":{"ran":1,"ran_draft_wrong":1,"unverified":2},"by_repo_kind":{"official":{"samples":4,"ran":2,"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":4,"samples":[{"code_sha256_prefix":"eee1f8be31d6bce0","entry":"ContinuousMeasure","repo":"phy811/Optimal-LDP-Sampling","repo_kind":"official","path":"propMech.py","file_url":"https://github.com/phy811/Optimal-LDP-Sampling/blob/HEAD/propMech.py","link_basis":"first_harvest_node","language":"python","status":"ran","verification_level":1,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"eee1f8be31d6bce0"}},{"code_sha256_prefix":"091889f9ede3ac1a","entry":"truncation","repo":"phy811/Optimal-LDP-Sampling","repo_kind":"official","path":"propMech.py","file_url":"https://github.com/phy811/Optimal-LDP-Sampling/blob/HEAD/propMech.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"091889f9ede3ac1a"}},{"code_sha256_prefix":"e55b0b243ef479c1","entry":"ProposedMech_Continuous","repo":"phy811/Optimal-LDP-Sampling","repo_kind":"official","path":"propMech.py","file_url":"https://github.com/phy811/Optimal-LDP-Sampling/blob/HEAD/propMech.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"e55b0b243ef479c1"}},{"code_sha256_prefix":"ece12369a3e0d09b","entry":"perturb_discrete","repo":"phy811/optimal-ldp-sampling","repo_kind":"official","path":"visualize_finiteSpace.py","file_url":"https://github.com/phy811/optimal-ldp-sampling/blob/HEAD/visualize_finiteSpace.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":"TIMEOUT","metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"NONE","inline_ok":false,"mcp_get_code":{"code_sha256":"ece12369a3e0d09b"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}