Max-Information, Differential Privacy, and Post-selection Hypothesis Testing

Ryan Rogers, Aaron Roth, Adam Smith, Om Thakkar

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

28 Scopus citations

Abstract

In this paper, we initiate a principled study of how the generalization properties of approximate differential privacy can be used to perform adaptive hypothesis testing, while giving statistically valid p-value corrections. We do this by observing that the guarantees of algorithms with bounded approximate max-information are sufficient to correct the p-values of adaptively chosen hypotheses, and then by proving that algorithms that satisfy (ϵ,δ)-differential privacy have bounded approximate max information when their inputs are drawn from a product distribution. This substantially extends the known connection between differential privacy and max-information, which previously was only known to hold for (pure) (ϵ,0)-differential privacy. It also extends our understanding of max-information as a partially unifying measure controlling the generalization properties of adaptive data analyses. We also show a lower bound, proving that (despite the strong composition properties of max-information), when data is drawn from a product distribution, (ϵ,δ)-differentially private algorithms can come first in a composition with other algorithms satisfying max-information bounds, but not necessarily second if the composition is required to itself satisfy a nontrivial max-information bound. This, in particular, implies that the connection between (ϵ,δ)-differential privacy and max-information holds only for inputs drawn from product distributions, unlike the connection between (ϵ,0)-differential privacy and max-information.

Original languageEnglish (US)
Title of host publicationProceedings - 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016
PublisherIEEE Computer Society
Pages487-494
Number of pages8
ISBN (Electronic)9781509039333
DOIs
StatePublished - Dec 14 2016
Event57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016 - New Brunswick, United States
Duration: Oct 9 2016Oct 11 2016

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2016-December
ISSN (Print)0272-5428

Other

Other57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016
CountryUnited States
CityNew Brunswick
Period10/9/1610/11/16

All Science Journal Classification (ASJC) codes

  • Computer Science(all)

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