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Open AccessArticle

Information Extraction Under Privacy Constraints

Department of Mathematics and Statistics, Queen’s University, Kingston, Canada
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Author to whom correspondence should be addressed.
Parts of the results in this paper were presented at the 52nd Allerton Conference on Communications, Control and Computing [1] and the 14th Canadian Workshop on Information Theory [2].
Academic Editors: Mikael Skoglund, Lars K. Rasmussen and Tobias Oechtering
Information 2016, 7(1), 15; https://doi.org/10.3390/info7010015
Received: 1 November 2015 / Revised: 24 February 2016 / Accepted: 3 March 2016 / Published: 10 March 2016
(This article belongs to the Special Issue Communication Theory)
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. View Full-Text
Keywords: data privacy; equivocation; rate-privacy function; information theory; minimum mean-squared error estimation; additive channels; mutual information; maximal correlation data privacy; equivocation; rate-privacy function; information theory; minimum mean-squared error estimation; additive channels; mutual information; maximal correlation
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Asoodeh, S.; Diaz, M.; Alajaji, F.; Linder, T. Information Extraction Under Privacy Constraints. Information 2016, 7, 15.

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