{"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/tight-approximate-differential-privacy-for","title":"Tight Differential Privacy for Discrete-Valued Mechanisms and for the Subsampled Gaussian Mechanism Using FFT","arxiv_id":"2006.07134","date":"2020-06-12","proceeding":null,"authors":["Antti Koskela","Joonas Jälkö","Lukas Prediger","Antti Honkela"],"abstract":"We propose a numerical accountant for evaluating the tight $(\\varepsilon,\\delta)$-privacy loss for algorithms with discrete one dimensional output. The method is based on the privacy loss distribution formalism and it uses the recently introduced fast Fourier transform based accounting technique. We carry out an error analysis of the method in terms of moment bounds of the privacy loss distribution which leads to rigorous lower and upper bounds for the true $(\\varepsilon,\\delta)$-values. As an application, we present a novel approach to accurate privacy accounting of the subsampled Gaussian mechanism. This completes the previously proposed analysis by giving strict lower and upper bounds for the privacy parameters. We demonstrate the performance of the accountant on the binomial mechanism and show that our approach allows decreasing noise variance up to 75 percent at equal privacy compared to existing bounds in the literature. We also illustrate how to compute tight bounds for the exponential mechanism applied to counting queries.","url_abs":"https://arxiv.org/abs/2006.07134v3","url_pdf":"https://arxiv.org/pdf/2006.07134v3.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":"tight-approximate-differential-privacy-for","repo_url":"https://github.com/DPBayes/PLD-Accountant","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2006.07134","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2006.07134"}},"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/DPBayes/PLD-Accountant","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":7},"by_repo_kind":{"official":{"samples":7,"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":"d90ae7ca45fead6d","entry":"df","repo":"DPBayes/PLD-Accountant","repo_kind":"official","path":"fourier_accountant/experimental/subsampled_gaussian_bounds.py","file_url":"https://github.com/DPBayes/PLD-Accountant/blob/HEAD/fourier_accountant/experimental/subsampled_gaussian_bounds.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"d90ae7ca45fead6d"}},{"code_sha256_prefix":"2df6e3aed39035e5","entry":"f","repo":"DPBayes/PLD-Accountant","repo_kind":"official","path":"fourier_accountant/experimental/subsampled_gaussian_bounds.py","file_url":"https://github.com/DPBayes/PLD-Accountant/blob/HEAD/fourier_accountant/experimental/subsampled_gaussian_bounds.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"2df6e3aed39035e5"}},{"code_sha256_prefix":"31fb5847e2b7de82","entry":"get_L","repo":"DPBayes/PLD-Accountant","repo_kind":"official","path":"fourier_accountant/experimental/adaptive_discrete_DP.py","file_url":"https://github.com/DPBayes/PLD-Accountant/blob/HEAD/fourier_accountant/experimental/adaptive_discrete_DP.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"31fb5847e2b7de82"}},{"code_sha256_prefix":"fec641c792292cb5","entry":"get_delta_lower","repo":"DPBayes/PLD-Accountant","repo_kind":"official","path":"fourier_accountant/experimental/adaptive_discrete_DP.py","file_url":"https://github.com/DPBayes/PLD-Accountant/blob/HEAD/fourier_accountant/experimental/adaptive_discrete_DP.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"fec641c792292cb5"}},{"code_sha256_prefix":"afc443cccf602f46","entry":"get_delta_max","repo":"DPBayes/PLD-Accountant","repo_kind":"official","path":"fourier_accountant/experimental/subsampled_gaussian_bounds.py","file_url":"https://github.com/DPBayes/PLD-Accountant/blob/HEAD/fourier_accountant/experimental/subsampled_gaussian_bounds.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"afc443cccf602f46"}},{"code_sha256_prefix":"f82b5046949ce03c","entry":"get_delta_upper","repo":"DPBayes/PLD-Accountant","repo_kind":"official","path":"fourier_accountant/experimental/adaptive_discrete_DP.py","file_url":"https://github.com/DPBayes/PLD-Accountant/blob/HEAD/fourier_accountant/experimental/adaptive_discrete_DP.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"f82b5046949ce03c"}},{"code_sha256_prefix":"ff04203c9035f8c5","entry":"get_epsilon","repo":"DPBayes/PLD-Accountant","repo_kind":"official","path":"fourier_accountant/experimental/binomial_mechanism.py","file_url":"https://github.com/DPBayes/PLD-Accountant/blob/HEAD/fourier_accountant/experimental/binomial_mechanism.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"ff04203c9035f8c5"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}