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Information 2016, 7(1), 15; doi:10.3390/info7010015

Information Extraction Under Privacy Constraints

Department of Mathematics and Statistics, Queen’s University, Kingston, Canada
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].
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Academic Editors: Mikael Skoglund, Lars K. Rasmussen and Tobias Oechtering
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)
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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. 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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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Asoodeh, S.; Diaz, M.; Alajaji, F.; Linder, T. Information Extraction Under Privacy Constraints. Information 2016, 7, 15.

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