Zuxing Li

Parallel distributed Neyman-Pearson detection with privacy constraints

In this paper, the privacy problem of a parallel distributed detection system vulnerable to an eavesdropper is proposed and studied in the Neyman-Pearson formulation. The privacy leakage is evaluated by a metric related to the Neyman-Pearson criterion. We will show that it is sufficient to consider a deterministic likelihood-ratio test for the optimal detection strategy at the eavesdropped sensor. This fundamental insight helps to simplify the problem to find the optimal privacy-constrained distributed detection system design. The trade-off between the detection performance and privacy leakage is illustrated in a numerical example.

Privacy-Aware Distributed Bayesian Detection

We study the eavesdropping problem in the remotely distributed sensing of a privacy-sensible hypothesis from the Bayesian detection perspective. We consider a parallel distributed detection network where remote decision makers independently make local decisions defined on finite domains and forward them to the fusion center which makes the final decision. An eavesdropper is assumed to intercept a specific set of local decisions to make also a guess on the hypothesis. We propose a novel Bayesian detection-operational privacy metric given by the minimal achievable Bayesian risk of the eavesdropper. Further, we introduce two privacy-aware distributed Bayesian detection formulations, namely the privacy-constrained distributed Bayesian detection problem and the privacy-concerned distributed Bayesian detection problem where the detection performance is optimized under a privacy guarantee constraint and a weighted sum objective of the detection performance and privacy risk is minimized respectively. For an optimal privacy-aware distributed Bayesian detection design, the optimal decision strategy of employing a deterministic likelihood test or a randomized strategy thereof is identified. Further, it is shown that equivalent problems of different formulations always exist and lead to the same optimal privacy-aware distributed Bayesian detection design. The results are illustrated and discussed by numerical examples. The idea of privacy-aware distributed Bayesian detection design provides a novel solution to realize future trustworthy Internet of Things applications.

Parallel distributed Bayesian detection with privacy constraints

In this paper, the privacy problem of a parallel distributed detection system vulnerable to an eavesdropper is proposed and studied in the Bayesian formulation. The privacy risk is evaluated by the detection cost of the eavesdropper which is assumed to be informed and greedy. It is shown that the optimal detection strategy of the sensor whose decision is eavesdropped on is a likelihood-ratio test. This fundamental insight allows for the optimization to reuse known algorithms extended to incorporate the privacy constraint. The trade-off between the detection performance and privacy risk is illustrated in a numerical example. The incorporation of physical layer privacy in the system design will lead to trustworthy sensor networks in future.

Tandem Distributed Bayesian Detection with Privacy Constraints

In this paper, the privacy problem of a tandem distributed detection system vulnerable to an eavesdropper is proposed and studied in the Bayesian formulation. The privacy risk is evaluated by the detection cost of the eavesdropper which is assumed to be informed and greedy. For the sensors whose operations are constrained to suppress the privacy risk, it is shown that the optimal detection strategies are likelihood-ratio tests. This fundamental insight allows for the optimization to reuse known algorithms extended to incorporate the privacy constraint. The trade-off between the detection performance and privacy risk is illustrated in an example.

Privacy on hypothesis testing in smart grids

In this paper, we study the problem of privacy information leakage in a smart grid. The privacy risk is assumed to be caused by an unauthorized binary hypothesis testing of the consumers behaviour based on the smart meter readings of energy supplies from the energy provider. Another energy supplies are produced by an alternative energy source. A controller equipped with an energy storage device manages the energy inflows to satisfy the energy demand of the consumer. We study the optimal energy control strategy which minimizes the asymptotic exponential decay rate of the minimum Type II error probability in the unauthorized hypothesis testing to suppress the privacy risk. Our study shows that the cardinality of the energy supplies from the energy provider for the optimal control strategy is no more than two. This result implies a simple objective of the optimal energy control strategy. When additional side information is available for the adversary, the optimal control strategy and privacy risk are compared with the case of leaking smart meter readings to the adversary only.

Smart meter privacy based on adversarial hypothesis testing

Privacy-preserving energy management is studied in the presence of a renewable energy source. It is assumed that the energy demand/supply from the energy provider is tracked by a smart meter. The resulting privacy leakage is measured through the probabilities of error in a binary hypothesis test, which tries to detect the consumer behavior based on the meter readings. An optimal privacy-preserving energy management policy maximizes the minimal Type II probability of error subject to a constraint on the Type I probability of error. When the privacy-preserving energy management policy is based on all the available information of energy demands, energy supplies, and hypothesis, the asymptotic exponential decay rate of the maximum minimal Type II probability of error is characterized by a divergence rate expression. Two special privacy-preserving energy management policies, the memoryless hypothesis-aware policy and the hypothesis-unaware policy with memory, are then considered and their performances are compared. Further, it is shown that the energy supply alphabet can be constrained to the energy demand alphabet without loss of optimality for the evaluation of a single-letter-divergence privacy-preserving guarantee.

Privacy-Constrained Parallel Distributed Neyman-Pearson Test

In this paper, the privacy leakage problem in an eavesdropped parallel distributed binary hypothesis test network is considered. A novel Neyman–Pearson test-operational privacy leakage measure is proposed and a privacy-constrained distributed Neyman–Pearson test problem is formulated. Such privacy-constrained distributed Neyman–Pearson test network is designed to optimize the Neyman–Pearson test performance and meanwhile to satisfy a desired suppression constraint on the privacy leakage. This study characterizes the privacy-constrained distributed Neyman–Pearson test network design and particularly identifies the sufficiency of deterministic likelihood-ratio test for optimality. These results help to simplify the optimal design problem of a privacy-constrained distributed Neyman–Pearson test network. Numerical results are presented to show the trade-off between the test performance and privacy leakage in privacy-constrained distributed Neyman–Pearson test networks.

Privacy-preserving energy flow control in smart grids

In this paper, an energy flow control strategy to reduce the smart meter privacy leakage is studied. The considered smart grid is equipped with an energy storage device. The privacy leakage is modeled as optimal Bayesian detections on the behaviors of the consumer made by an authorized adversary. To evaluate the privacy risk, a Bayesian detection-operational privacy leakage metric is proposed. The design of an optimal privacy-preserving energy control strategy can be formulated as a belief state MDP problem. Therefore, standard methods and algorithms can be utilized to obtain or to approximate the optimal control strategy. A simplified problem to design an instantaneous optimal privacy-preserving control strategy is also considered. It is shown that the problem of the instantaneous optimal control strategy design can be formulated as a set of linear programmings.

Privacy-concerned parallel distributed Bayesian sequential detection

In this paper, eavesdropping in parallel distributed sequential detections is considered. The privacy risk is evaluated by the minimal achievable Bayesian risk of a greedy and informed eavesdropper who is curious about the hypothesis realization. We propose a novel metric based on Bayesian risk to take the detection performance and privacy risk with different weights into account. We formulate and study the privacy-concerned parallel distributed Bayesian sequential detection problem under a finite time-horizon assumption. Solving this problem will lead to the optimal distributed sequential detection design which achieves the minimal privacy-concerned Bayesian risk. The study shows that it is not sufficient to consider a deterministic likelihood-ratio test for a remote decision maker at an active time index in the optimal privacy-concerned system design. However, properties of the optimal design indicate that the standard method can be extended to solve the proposed problem.