Abstract
A privacy-constrained information extraction problem is considered where for a pair of correlated discrete random variables (X,Y) governed by a given joint distribution, an agent observes Y and wants to convey to a potentially public user as much information about Y as possible while limiting the amount of information revealed about X. To this end, the so-called rate-privacy function is investigated to quantify the maximal amount of information (measured in terms of mutual information) that can be extracted from Y under a privacy constraint between X and the extracted information, where privacy is measured using either mutual information or maximal correlation. Properties of the rate-privacy function are analyzed and its information-theoretic and estimation-theoretic interpretations are presented for both the mutual information and maximal correlation privacy measures. It is also shown that the rate-privacy function admits a closed-form expression for a large family of joint distributions of (X,Y). Finally, the rate-privacy function under the mutual information privacy measure is considered for the case where (X,Y) has a joint probability density function by studying the problem where the extracted information is a uniform quantization of Y corrupted by additive Gaussian noise. The asymptotic behavior of the rate-privacy function is studied as the quantization resolution grows without bound and it is observed that not all of the properties of the rate-privacy function carry over from the discrete to the continuous case.
Highlights
With the emergence of user-customized services, there is an increasing desire to balance between the need to share data and the need to protect sensitive and private information
Using mutual information as measure of both utility and privacy, we formulate the corresponding privacy-utility tradeoff for discrete random variables X and Y via the rate-privacy function, gε ( X; Y ), in which the mutual information between Y and displayed data, Z, is maximized over all channels PZ|Y such that the mutual information between Z and X is no larger than a given ε
Adopting mutual information as a measure of both privacy and utility, we are interested in characterizing the following quantity, which we call the rate-privacy function, gε ( X; Y ) :=
Summary
With the emergence of user-customized services, there is an increasing desire to balance between the need to share data and the need to protect sensitive and private information. Information 2016, 7, 15 conditional security, see, e.g., [4,5,6], the randomized response model assumes that the adversary can have unlimited computational power and it provides unconditional privacy This model, in which the control of private data remains in the users’ hands, has been extensively studied since Warner. In all above examples of randomized response models, given a private source, denoted by X, the mechanism generates Z which can be publicly displayed without breaching the desired privacy level. Alice collects all her measurements from an observation into a random variable Y and wants to reveal this information to Bob in order to receive a payoff She is worried about her private data, represented by X, which is correlated with Y. While in secrecy problems the aim is to keep information secret only from wiretappers, in privacy problems the aim is to keep the private information (not necessarily all the information) secret from everyone including the intended receiver
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