[Paper Review] Distributed Hypothesis Testing With a Privacy Constraint

Sreejith Sreekumar, Asaf Cohen+1 more|arXiv (Cornell University)|Jul 8, 2018

Wireless Communication Security Techniques49 references3 citations

TL;DR

This paper studies distributed binary hypothesis testing with privacy constraints, where a remote observer transmits data to a detector over a rate-limited channel while minimizing disclosure of private information. It establishes single-letter inner bounds and exact characterizations for rate-error exponent-equivocation and rate-error exponent-distortion trade-offs under conditional independence and zero-rate settings, showing the strong converse does not hold under privacy constraints.

ABSTRACT

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 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 counterexample that, 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.

Motivation & Objective

• To model a distributed binary hypothesis testing scenario where a remote observer communicates with a detector under a communication rate constraint.
• To incorporate privacy constraints by minimizing information leakage (equivocation) or distortion of private observations from the detector’s view.
• To analyze the trade-off between communication rate, type II error exponent, and privacy metrics (equivocation or distortion).
• To determine whether the strong converse property—valid in standard distributed HT—persists under privacy constraints.
• To provide single-letter characterizations of the rate-error exponent-privacy trade-off in specific cases, including conditional independence and zero-rate communication.

Proposed method

• Formalizing the problem using a discrete memoryless source at the observer and another at the detector, with a rate-limited noiseless channel for communication.
• Defining the hypothesis test as a binary test on the joint distribution of the observer’s and detector’s observations.
• Using equivocation and average distortion as privacy metrics to quantify the observer’s private part’s secrecy and distortion from the detector’s perspective.
• Deriving single-letter inner bounds on the rate-error exponent-equivocation and rate-error exponent-distortion trade-offs using information-theoretic techniques.
• Establishing exact single-letter characterizations under two conditions: (i) testing against conditional independence given side information, and (ii) zero communication rate.
• Constructing a counterexample to show the strong converse does not hold when privacy constraints are introduced, implying dependence on the type I error probability constraint.

Experimental results

Research questions

• RQ1 What is the fundamental trade-off between communication rate, type II error exponent, and privacy (measured via equivocation or distortion) in distributed hypothesis testing?
• RQ2 How do the rate-error exponent-equivocation and rate-error exponent-distortion trade-offs behave under conditional independence of the observer’s observations from the detector’s given side information?
• RQ3 What happens to the trade-off when the communication rate is zero—can privacy and detection performance still be balanced?
• RQ4 Does the strong converse property, valid in standard distributed HT, still hold when privacy constraints are imposed?
• RQ5 How does the type I error probability constraint affect the achievable rate-error exponent-privacy trade-offs under privacy constraints?

Key findings

• Single-letter inner bounds are established for the rate-error exponent-equivocation and rate-error exponent-distortion trade-offs in the general distributed HT problem with privacy constraints.
• Exact single-letter characterizations are obtained for the rate-error exponent-equivocation and rate-error exponent-distortion trade-offs when the observer’s observations are conditionally independent of the detector’s given side information.
• Exact characterizations are also derived in the case of zero communication rate, showing that privacy and detection performance can still be balanced without transmission.
• A counterexample is provided demonstrating that the strong converse does not hold in the presence of privacy constraints, implying that the trade-offs depend on the type I error probability constraint.
• The results show that privacy constraints fundamentally alter the behavior of the system, making the rate-error exponent-privacy trade-offs dependent on the type I error probability, unlike in the unconstrained case.