Hypothesis Testing under Mutual Information Privacy Constraints in the High Privacy Regime

Jiachun Liao, Lalitha Sankar, Vincent Y.F. Tan, Flavio du Pin Calmon

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

Hypothesis testing is a statistical inference framework for determining the true distribution among a set of possible distributions for a given data set. Privacy restrictions may require the curator of the data or the respondents themselves to share data with the test only after applying a randomizing privacy mechanism. This work considers mutual information (MI) as the privacy metric for measuring leakage. In addition, motivated by the Chernoff-Stein lemma, the relative entropy between pairs of distributions of the output (generated by the privacy mechanism) is chosen as the utility metric. For these metrics, the goal is to find the optimal privacy-utility tradeoff (PUT) and the corresponding optimal privacy mechanism for both binary and m -ary hypothesis testing. Focusing on the high privacy regime, Euclidean information-theoretic approximations of the binary and m -ary PUT problems are developed. The solutions for the approximation problems clarify that an MI-based privacy metric preserves the privacy of the source symbols in inverse proportion to their likelihoods.

Original languageEnglish (US)
Article number8125176
Pages (from-to)1058-1071
Number of pages14
JournalIEEE Transactions on Information Forensics and Security
Volume13
Issue number4
DOIs
StatePublished - Apr 2018

Keywords

  • Hypothesis testing
  • Rényi divergence
  • euclidean information theory
  • mutual information
  • privacy mechanism
  • privacy-guaranteed data publishing
  • relative entropy

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Computer Networks and Communications

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