Distributed Hypothesis Testing with Privacy Constraints

TL;DR

This paper studies distributed hypothesis testing under privacy constraints, deriving bounds on error exponents when data is privatized, and provides exact results for testing against independence with practical examples.

Contribution

It introduces a framework for hypothesis testing with privacy constraints, deriving bounds and exact exponents, and applies Euclidean information theory for approximate analysis.

Findings

Lower bound on type-II exponent for general hypotheses

Exact exponent for testing against independence

Strong converse property established

Abstract

We revisit the distributed hypothesis testing (or hypothesis testing with communication constraints) problem from the viewpoint of privacy. Instead of observing the raw data directly, the transmitter observes a sanitized or randomized version of it. We impose an upper bound on the mutual information between the raw and randomized data. Under this scenario, the receiver, which is also provided with side information, is required to make a decision on whether the null or alternative hypothesis is in effect. We first provide a general lower bound on the type-II exponent for an arbitrary pair of hypotheses. Next, we show that if the distribution under the alternative hypothesis is the product of the marginals of the distribution under the null (i.e., testing against independence), then the exponent is known exactly. Moreover, we show that the strong converse property holds. Using ideas from Euclidean information theory, we also provide an approximate expression for the exponent when the communication rate is low and the privacy level is high. Finally, we illustrate our results with a binary and a Gaussian example.