{"title":"差分私有匿名直方图的紧边界","authors":"Pasin Manurangsi","doi":"10.1137/1.9781611977066.14","DOIUrl":null,"url":null,"abstract":"In this note, we consider the problem of differentially privately (DP) computing an anonymized histogram, which is defined as the multiset of counts of the input dataset (without bucket labels). In the low-privacy regime $\\epsilon \\geq 1$, we give an $\\epsilon$-DP algorithm with an expected $\\ell_1$-error bound of $O(\\sqrt{n} / e^\\epsilon)$. In the high-privacy regime $\\epsilon<1$, we give an $\\Omega(\\sqrt{n \\log(1/\\epsilon) / \\epsilon})$ lower bound on the expected $\\ell_1$ error. In both cases, our bounds asymptotically match the previously known lower/upper bounds due to [Suresh, NeurIPS 2019].","PeriodicalId":93491,"journal":{"name":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","volume":"17 1","pages":"203-213"},"PeriodicalIF":0.0000,"publicationDate":"2021-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Tight Bounds for Differentially Private Anonymized Histograms\",\"authors\":\"Pasin Manurangsi\",\"doi\":\"10.1137/1.9781611977066.14\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note, we consider the problem of differentially privately (DP) computing an anonymized histogram, which is defined as the multiset of counts of the input dataset (without bucket labels). In the low-privacy regime $\\\\epsilon \\\\geq 1$, we give an $\\\\epsilon$-DP algorithm with an expected $\\\\ell_1$-error bound of $O(\\\\sqrt{n} / e^\\\\epsilon)$. In the high-privacy regime $\\\\epsilon<1$, we give an $\\\\Omega(\\\\sqrt{n \\\\log(1/\\\\epsilon) / \\\\epsilon})$ lower bound on the expected $\\\\ell_1$ error. In both cases, our bounds asymptotically match the previously known lower/upper bounds due to [Suresh, NeurIPS 2019].\",\"PeriodicalId\":93491,\"journal\":{\"name\":\"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)\",\"volume\":\"17 1\",\"pages\":\"203-213\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-11-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/1.9781611977066.14\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the SIAM Symposium on Simplicity in Algorithms (SOSA)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/1.9781611977066.14","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Tight Bounds for Differentially Private Anonymized Histograms
In this note, we consider the problem of differentially privately (DP) computing an anonymized histogram, which is defined as the multiset of counts of the input dataset (without bucket labels). In the low-privacy regime $\epsilon \geq 1$, we give an $\epsilon$-DP algorithm with an expected $\ell_1$-error bound of $O(\sqrt{n} / e^\epsilon)$. In the high-privacy regime $\epsilon<1$, we give an $\Omega(\sqrt{n \log(1/\epsilon) / \epsilon})$ lower bound on the expected $\ell_1$ error. In both cases, our bounds asymptotically match the previously known lower/upper bounds due to [Suresh, NeurIPS 2019].