Arbitrarily Strong Utility-Privacy Tradeoff in Multi-Agent Systems

Each agent in a network makes a local observation that is linearly related to a set of public and private parameters. The agents send their observations to a fusion center to allow it to estimate the public parameters. To prevent leakage of the private parameters, each agent first sanitizes its local observation using a local privacy mechanism before transmitting it to the fusion center. We investigate the utility-privacy tradeoff in terms of the Cram\'er-Rao lower bounds for estimating the public and private parameters. We study the class of privacy mechanisms given by linear compression and noise perturbation, and derive necessary and sufficient conditions for achieving arbitrarily strong utility-privacy tradeoff in a multi-agent system for both the cases where prior information is available and unavailable, respectively. We also provide a method to find the maximum estimation privacy achievable without compromising the utility and propose an alternating algorithm to optimize the utility-privacy tradeoff in the case where arbitrarily strong utility-privacy tradeoff is not achievable

Asymptotically Optimal Sampling Policy for Quickest Change Detection with Observation-Switching Cost

We consider the problem of quickest change detection (QCD) in a signal where its observations are obtained using a set of actions, and switching from one action to another comes with a cost. The objective is to design a stopping rule consisting of a sampling policy to determine the sequence of actions used to observe the signal and a stopping time to quickly detect for the change, subject to a constraint on the average observation-switching cost. We propose an open-loop sampling policy of finite window size and a generalized likelihood ratio (GLR) Cumulative Sum (CuSum) stopping time for the QCD problem. We show that the GLR CuSum stopping time is asymptotically optimal with a properly designed sampling policy and formulate the design of this sampling policy as a quadratic programming problem. We prove that it is sufficient to consider policies of window size not more than one when designing policies of finite window size and propose several algorithms that solve this optimization problem with theoretical guarantees. For observation-dependent policies, we propose a $2$-threshold stopping time and an observation-dependent sampling policy. We present a method to design the observation-dependent sampling policy based on open-loop sampling policies. Finally, we apply our approach to the problem of QCD of a partially observed graph signal and empirically demonstrate the performance of our proposed stopping times

Quickest Change Detection in the Presence of a Nuisance Change

In the quickest change detection problem in which both nuisance and critical changes may occur, the objective is to detect the critical change as quickly as possible without raising an alarm when either there is no change or a nuisance change has occurred. A window-limited sequential change detection procedure based on the generalized likelihood ratio test statistic is proposed. A recursive update scheme for the proposed test statistic is developed and is shown to be asymptotically optimal under mild technical conditions. In the scenario where the post-change distribution belongs to a parametrized family, a generalized stopping time and a lower bound on its average run length are derived. The proposed stopping rule is compared with the FMA stopping time and the naive 2-stage procedure that detects the nuisance or critical change using separate CuSum stopping procedures for the nuisance and critical changes. Simulations demonstrate that the proposed rule outperforms the FMA stopping time and the 2-stage procedure, and experiments on a real dataset on bearing failure verify the performance of the proposed stopping time

A dynamic Bayesian nonparametric model for blind calibration of sensor networks

We consider the problem of blind calibration of a sensor network, where the sensor gains and offsets are estimated from noisy observations of unknown signals. This is in general a nonidentifiable problem, unless restrictive assumptions on the signal subspace or sensor observations are imposed. We show that if each signal observed by the sensors follows a known dynamic model with additive noise, then the sensor gains and offsets are identifiable. We propose a dynamic Bayesian nonparametric model to infer the sensors’ gains and offsets. Our model allows different sensor clusters to observe different unknown signals, without knowing the sensor clusters a priori . We develop an offline algorithm using block Gibbs sampling and a linearized forward filtering backward sampling method that estimates the sensor clusters, gains, and offsets jointly. Furthermore, for practical implementation, we also propose an online inference algorithm based on particle filtering and local Markov chain Monte Carlo. Simulations using a synthetic dataset, and experiments on two real datasets suggest that our proposed methods perform better than several other blind calibration methods, including a sparse Bayesian learning approach, and methods that first cluster the sensor observations and then estimate the gains and offsets.NRF (Natl Research Foundation, S’pore)MOE (Min. of Education, S’pore)Accepted versio