Distributed Hypothesis Testing with Privacy Constraints

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.

Strong Converse for Hypothesis Testing Against Independence over a Two-Hop Network

“…Thus, in the future, one may refine the proof in the current paper by deriving secondorder converse or exact second-order asymptotics. Furthermore, one may also consider deriving strong converse theorems or simplifying existing strong converse proofs for hypothesis testing problems with both communication and privacy constraints such as that in [21] by using the techniques in the current paper. It is also interesting to explore whether the current techniques can be applied to obtain strong converse theorems for hypothesis testing with zero-rate compression problems [3].…”

A Strong Converse Theorem for Hypothesis Testing Against Independence over a Two-Hop Network

“…Thus, in the future, one may refine the proof in the current paper by deriving second-order converse or exact second-order asymptotics. Furthermore, one may also consider deriving strong converse theorems or simplifying existing strong converse proofs for hypothesis testing problems with both communication and privacy constraints such as that in [ 23 ] by using the techniques in the current paper. It is also interesting to explore whether current techniques can be applied to obtain strong converse theorems for hypothesis testing with zero-rate compression problems [ 3 ].…”

Privacy-Aware Distributed Hypothesis Testing

“…The detector performs HT on the probability distribution of the observer’s data, and the optimal privacy mechanism that maximizes the error exponent while satisfying the privacy constraint is analyzed. Recently, a distributed version of this problem has been studied in [ 27 ], where the observer applies a privacy mechanism to its observed data prior to further coding for compression, and the goal at the detector is to perform a HT on the joint distribution of its own observations with those of the observer. In contrast with [ 25 , 26 , 27 ], we study DHT with a privacy constraint , but without considering a separate privacy mechanism at the observer.…”

“…Recently, a distributed version of this problem has been studied in [ 27 ], where the observer applies a privacy mechanism to its observed data prior to further coding for compression, and the goal at the detector is to perform a HT on the joint distribution of its own observations with those of the observer. In contrast with [ 25 , 26 , 27 ], we study DHT with a privacy constraint , but without considering a separate privacy mechanism at the observer. In Section 2 , we will further discuss the differences between the system model considered here and that of [ 27 ].…”

“…In contrast with [ 25 , 26 , 27 ], we study DHT with a privacy constraint , but without considering a separate privacy mechanism at the observer. In Section 2 , we will further discuss the differences between the system model considered here and that of [ 27 ].…”