Heavy hitters and the structure of local privacy

Mark Bun, Jelani Nelson, Uri Stemmer

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


We present a new locally differentially private algorithm for the heavy hitters problem which achieves optimal worst-case error as a function of all standardly considered parameters. Prior work obtained error rates which depend optimally on the number of users, the size of the domain, and the privacy parameter, but depend sub-optimally on the failure probability. We strengthen existing lower bounds on the error to incorporate the failure probability, and show that our new upper bound is tight with respect to this parameter as well. Our lower bound is based on a new understanding of the structure of locally private protocols. We further develop these ideas to obtain the following general results beyond heavy hitters. • Advanced Grouposition: In the local model, group privacy for k users degrades proportionally to ≈ k, instead of linearly in k as in the central model. Stronger group privacy yields improved max-information guarantees, as well as stronger lower bounds (via “packing arguments”), over the central model. • Building on a transformation of Bassily and Smith (STOC 2015), we give a generic transformation from any non interactive approximate-private local protocol into a pure-private local protocol. Again in contrast with the central model, this shows that we cannot obtain more accurate algorithms by moving from pure to approximate local privacy.

Original languageEnglish
Title of host publicationPODS 2018 - Proceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems
EditorsJan Van den Bussche, Mart�n Ugarte, Marcelo Arenas
PublisherAssociation for Computing Machinery
Number of pages13
ISBN (Electronic)9781450347068
StatePublished - 27 May 2018
Externally publishedYes
Event37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS 2018 - Houston, United States
Duration: 10 Jun 201815 Jun 2018

Publication series

NameProceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems


Conference37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS 2018
Country/TerritoryUnited States


  • Differential privacy
  • Heavy hitters
  • Local model

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