{"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/privit-private-and-sample-efficient-identity","title":"Priv'IT: Private and Sample Efficient Identity Testing","arxiv_id":"1703.10127","date":"2017-03-29","proceeding":null,"authors":["Bryan Cai","Constantinos Daskalakis","Gautam Kamath"],"abstract":"We develop differentially private hypothesis testing methods for the small\nsample regime. Given a sample $\\cal D$ from a categorical distribution $p$ over\nsome domain $\\Sigma$, an explicitly described distribution $q$ over $\\Sigma$,\nsome privacy parameter $\\varepsilon$, accuracy parameter $\\alpha$, and\nrequirements $\\beta_{\\rm I}$ and $\\beta_{\\rm II}$ for the type I and type II\nerrors of our test, the goal is to distinguish between $p=q$ and\n$d_{\\rm{TV}}(p,q) \\geq \\alpha$.\n  We provide theoretical bounds for the sample size $|{\\cal D}|$ so that our\nmethod both satisfies $(\\varepsilon,0)$-differential privacy, and guarantees\n$\\beta_{\\rm I}$ and $\\beta_{\\rm II}$ type I and type II errors. We show that\ndifferential privacy may come for free in some regimes of parameters, and we\nalways beat the sample complexity resulting from running the $\\chi^2$-test with\nnoisy counts, or standard approaches such as repetition for endowing\nnon-private $\\chi^2$-style statistics with differential privacy guarantees. We\nexperimentally compare the sample complexity of our method to that of recently\nproposed methods for private hypothesis testing.","url_abs":"http://arxiv.org/abs/1703.10127v3","url_pdf":"http://arxiv.org/pdf/1703.10127v3.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":"privit-private-and-sample-efficient-identity","repo_url":"https://github.com/hoonose/privit","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"hypothesis-testing","task_name":"Two-sample testing"},{"task_slug":"type","task_name":"Vocal Bursts Type Prediction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1703.10127","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1703.10127"}},"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. 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