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Open AccessArticle

Privacy-Aware Distributed Hypothesis Testing

Department of Electrical and Computer Engineering , Cornell University, Ithaca, NY 14850, USA
The School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 8410501, Israel
Department of Electrical and Electronic Engineering, Imperial College London, London SW72AZ, UK
Author to whom correspondence should be addressed.
This paper is an extended version of our paper published in Proceedings of IEEE Information Theory Workshop (ITW), Guangzhou, 2018.
Entropy 2020, 22(6), 665;
Received: 1 May 2020 / Revised: 11 June 2020 / Accepted: 12 June 2020 / Published: 16 June 2020
(This article belongs to the Special Issue Information Theory, Forecasting, and Hypothesis Testing)
A distributed binary hypothesis testing (HT) problem involving two parties, a remote observer and a detector, is studied. The remote observer has access to a discrete memoryless source, and communicates its observations to the detector via a rate-limited noiseless channel. The detector observes another discrete memoryless source, and performs a binary hypothesis test on the joint distribution of its own observations with those of the observer. While the goal of the observer is to maximize the type II error exponent of the test for a given type I error probability constraint, it also wants to keep a private part of its observations as oblivious to the detector as possible. Considering both equivocation and average distortion under a causal disclosure assumption as possible measures of privacy, the trade-off between the communication rate from the observer to the detector, the type II error exponent, and privacy is studied. For the general HT problem, we establish single-letter inner bounds on both the rate-error exponent-equivocation and rate-error exponent-distortion trade-offs. Subsequently, single-letter characterizations for both trade-offs are obtained (i) for testing against conditional independence of the observer’s observations from those of the detector, given some additional side information at the detector; and (ii) when the communication rate constraint over the channel is zero. Finally, we show by providing a counter-example where the strong converse which holds for distributed HT without a privacy constraint does not hold when a privacy constraint is imposed. This implies that in general, the rate-error exponent-equivocation and rate-error exponent-distortion trade-offs are not independent of the type I error probability constraint. View Full-Text
Keywords: Hypothesis testing; privacy; testing against conditional independence; error exponent; equivocation; distortion; causal disclosure Hypothesis testing; privacy; testing against conditional independence; error exponent; equivocation; distortion; causal disclosure
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Sreekumar, S.; Cohen, A.; Gündüz, D. Privacy-Aware Distributed Hypothesis Testing. Entropy 2020, 22, 665.

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