Hypothesis testing in the high privacy limit

Liao, Jiachun; Sankar, Lalitha; Tan, Vincent Y. F.; Calmon, Flávio P.

doi:10.1109/allerton.2016.7852293

Cited by 22 publications

(13 citation statements)

References 11 publications

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“…For example, Asoodeh et al [14] and Calmon et al [16] used estimation-theoretic tools to characterize fundamental limits of privacy. Liao et al [37,38] explored the PUT within a hypothesis testing framework. Issa et al [12,39] introduced maximal leakage as an information leakage metric.…”

Section: Related Workmentioning

confidence: 99%

Privacy With Estimation Guarantees

Wang

Calmon

et al. 2019

IEEE Trans. Inform. Theory

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We study the central problem in data privacy: how to share data with an analyst while providing both privacy and utility guarantees to the user that owns the data. In this setting, we present an estimation-theoretic analysis of the privacy-utility trade-off (PUT). Here, an analyst is allowed to reconstruct (in a mean-squared error sense) certain functions of the data (utility), while other private functions should not be reconstructed with distortion below a certain threshold (privacy). We demonstrate how χ 2 -information captures the fundamental PUT in this case and provide bounds for the best PUT. We propose a convex program to compute privacy-assuring mappings when the functions to be disclosed and hidden are known a priori and the data distribution is known. We derive lower bounds on the minimum mean-squared error of estimating a target function from the disclosed data and evaluate the robustness of our approach when an empirical distribution is used to compute the privacy-assuring mappings instead of the true data distribution. We illustrate the proposed approach through two numerical experiments.Index Terms-Estimation, privacy-utility trade-off, minimum mean-squared error.

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Section: Related Workmentioning

confidence: 99%

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Wang

Calmon

et al. 2019

IEEE Trans. Inform. Theory

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“…A variety of problems related to privacy and networked estimation and control have been studied in the literature. The privacy aspect of the hypothesis testing problem as well as various solutions for privacy-aware hypothesis testing have been studied in the literature, e.g., [2], [3], [4], [5]. The authors in [6] considered a multi-sensor hypothesis testing problem wherein a fusion center receives the decisions of a set of sensors and an adversary overhears the local decisions of a subset of sensors.…”

Section: B Related Workmentioning

confidence: 99%

A Model Randomization Approach to Statistical Parameter Privacy

Nekouei¹,

Skoglund²,

Johansson³

2021

Preprint

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In this paper, we study a privacy filter design problem for a sequence of sensor measurements whose joint probability density function (p.d.f.) depends on a private parameter. To ensure parameter privacy, we propose a filter design framework which consists of two components: a randomizer and a nonlinear transformation. The randomizer takes the private parameter as input and randomly generates a pseudo parameter. The nonlinear mapping transforms the measurements such that the joint p.d.f. of the filter's output depends on the pseudo parameter rather than the private parameter. It also ensures that the joint p.d.f. of the filter's output belongs to the same family of distributions as that of the measurements. The nonlinear transformation has a feedforward-feedback structure that allows real-time and causal generation of the disguised measurements with low complexity using a recursive structure.The design of the randomizer is formulated as an optimization problem subject to a privacy constraint, in terms of mutual information, and it is shown that the optimal randomizer is the solution of a convex optimization problem. Using information-theoretic inequalities, we show that the performance of any estimator of the private parameter, based on the output of the privacy filter, is limited by the privacy constraint. The structure of the nonlinear transformation is studied in the special cases of independent and identically distributed, Markovian, and Gauss-Markov measurements. Our results show that the privacy filter in the Gauss-Markov case can be implemented as two one-step ahead Kalman predictors and a set of minimum mean square error predictors. The Kalman predictors significantly reduce the complexity of computing the disguised measurements. A numerical example on occupancy privacy in a building automation system illustrates the approach.

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“…In [5], the authors considered a binary hypothesis test problem with a private hypothesis. They studied the optimal randomized privacy mechanisms for maximizing the type-II error exponent subject to privacy constraints.…”

Section: Related Workmentioning

confidence: 99%

Privacy of Information Sharing Schemes in a Cloud-based Multi-sensor Estimation Problem

Nekouei

Skoglund

Johansson

2018

2018 Annual American Control Conference (ACC)

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In this paper, we consider a multi-sensor estimation problem wherein each sensor collects noisy information about its local process, which is only observed by that sensor, and a common process, which is simultaneously observed by all sensors. The objective is to assess the privacy level of (the local process of) each sensor while the common process is estimated using cloud computing technology. The privacy level of a sensor is defined as the conditional entropy of its local process given the shared information with the cloud. Two information sharing schemes are considered: a local scheme, and a global scheme. Under the local scheme, each sensor estimates the common process based on its the measurement and transmits its estimate to a cloud. Under the global scheme, the cloud receives the sum of sensors' measurements. It is shown that, in the local scheme, the privacy level of each sensor is always above a certain level which is characterized using Shannon's mutual information. It is also proved that this result becomes tight as the number of sensors increases. We also show that the global scheme is asymptotically private, i.e., the privacy loss of the global scheme decreases to zero at the rate of O (1/M ) where M is the number of sensors.

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Hypothesis testing in the high privacy limit

Cited by 22 publications

References 11 publications

Privacy With Estimation Guarantees

Privacy With Estimation Guarantees

A Model Randomization Approach to Statistical Parameter Privacy

Privacy of Information Sharing Schemes in a Cloud-based Multi-sensor Estimation Problem

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