Privacy-Utility Management of Hypothesis Tests

TL;DR

This paper explores how to balance privacy and utility in hypothesis testing by characterizing error exponents through Chernoff information, proposing an optimal management strategy that ensures privacy protection without sacrificing utility.

Contribution

It introduces a framework for managing privacy-utility trade-offs in hypothesis tests using Chernoff information rates, providing optimal strategies for privacy preservation.

Findings

Error exponent of Bayesian hypothesis test characterized by Chernoff information

Optimal privacy management minimizes privacy error exponent while maintaining utility

Asymptotic privacy guarantees are derived based on Chernoff information bounds

Abstract

The trade-off of hypothesis tests on the correlated privacy hypothesis and utility hypothesis is studied. The error exponent of the Bayesian composite hypothesis test on the privacy or utility hypothesis can be characterized by the corresponding minimal Chernoff information rate. An optimal management protects the privacy by minimizing the error exponent of the privacy hypothesis test and meanwhile guarantees the utility hypothesis testing performance by satisfying a lower bound on the corresponding minimal Chernoff information rate. The asymptotic minimum error exponent of the privacy hypothesis test is shown to be characterized by the infimum of corresponding minimal Chernoff information rates subject to the utility guarantees.