Privacy-preserving statistical estimation with optimal convergence rates

Adam Davison Smith

Research output: Chapter in Book/Report/Conference proceedingConference contribution

89 Scopus citations

Abstract

Consider an analyst who wants to release aggregate statistics about a data set containing sensitive information. Using differentially private algorithms guarantees that the released statistics reveal very little about any particular record in the data set. In this paper we study the asymptotic properties of differentially private algorithms for statistical inference. We show that for a large class of statistical estimators T and input distributions P, there is a differentially private estimator AT with the same asymptotic distribution as T. That is, the random variables AT(X) and T(X) converge in distribution when X consists of an i.i.d. sample from P of increasing size. This implies that AT(X) is essentially as good as the original statistic T(X) for statistical inference, for sufficiently large samples. Our technique applies to (almost) any pair T,P such that T is asymptotically normal on i.i.d. samples from P - -in particular, to parametric maximum likelihood estimators and estimators for logistic and linear regression under standard regularity conditions. A consequence of our techniques is the existence of low-space streaming algorithms whose output converges to the same asymptotic distribution as a given estimator T (for the same class of estimators and input distributions as above).

Original languageEnglish (US)
Title of host publicationSTOC'11 - Proceedings of the 43rd ACM Symposium on Theory of Computing
Pages813-821
Number of pages9
DOIs
StatePublished - Jul 4 2011
Event43rd ACM Symposium on Theory of Computing, STOC'11 - San Jose, CA, United States
Duration: Jun 6 2011Jun 8 2011

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Other

Other43rd ACM Symposium on Theory of Computing, STOC'11
CountryUnited States
CitySan Jose, CA
Period6/6/116/8/11

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All Science Journal Classification (ASJC) codes

  • Software

Cite this

Smith, A. D. (2011). Privacy-preserving statistical estimation with optimal convergence rates. In STOC'11 - Proceedings of the 43rd ACM Symposium on Theory of Computing (pp. 813-821). (Proceedings of the Annual ACM Symposium on Theory of Computing). https://doi.org/10.1145/1993636.1993743