Private coresets

Dan Feldman, Amos Fiat, Haim Kaplan, Kobbi Nissim

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A coreset of a point set P is a small weighted set of points that captures some geometric properties of P. Coresets have found use in a vast host of geometric settings. We forge a link between coresets, and differentially private sanitizations that can answer any number of queries without compromising privacy. We define the notion of private coresets, which are simultaneously both coresets and differentially private, and show how they may be constructed. We first show that the existence of a small coreset with low generalized sensitivity (i.e., replacing a single point in the original point set slightly affects the quality of the coreset) implies (in an inefficient manner) the existence of a private coreset for the same queries. This greatly extends the works of Blum, Ligett, and Roth [STOC 2008] and McSherry and Talwar [FOCS 2007]. We also give an efficient algorithm to compute private coresets for k-median and k-mean queries in R d, immediately implying efficient differentially private sanitizations for such queries. Following McSherry and Talwar, this construction also gives efficient coalition proof (approximately dominant strategy) mechanisms for location problems. Unlike coresets which only have a multiplicative approximation factor, we prove that private coresets must exhibit additive error. We present a new technique for showing lower bounds on this error.

Original languageEnglish
Title of host publicationSTOC'09 - Proceedings of the 2009 ACM International Symposium on Theory of Computing
Pages361-370
Number of pages10
DOIs
StatePublished - 2009
Externally publishedYes
Event41st Annual ACM Symposium on Theory of Computing, STOC '09 - Bethesda, MD, United States
Duration: 31 May 20092 Jun 2009

Publication series

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

Conference

Conference41st Annual ACM Symposium on Theory of Computing, STOC '09
Country/TerritoryUnited States
CityBethesda, MD
Period31/05/092/06/09

Keywords

  • Coresets
  • Differential privacy
  • Privacy

ASJC Scopus subject areas

  • Software

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