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

TL;DR

This paper investigates the optimal balance between privacy and utility in hypothesis testing when using mutual information as a privacy measure, especially under high privacy constraints, and derives approximations to guide mechanism design.

Contribution

It introduces Euclidean information-theoretic approximations for the privacy-utility trade-off in high privacy regimes, enhancing understanding of MI-based privacy mechanisms in hypothesis testing.

Findings

MI-based privacy preserves source privacy inversely proportional to symbol likelihoods

Derived Euclidean approximations simplify the analysis of privacy-utility trade-offs

Provided insights into optimal privacy mechanisms under high privacy constraints

Abstract

Hypothesis testing is a statistical inference framework for determining the true distribution among a set of possible distributions for a given dataset. 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 trade-off (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.