77 research outputs found
Information Extraction Under Privacy Constraints
A privacy-constrained information extraction problem is considered where for
a pair of correlated discrete random variables governed by a given
joint distribution, an agent observes and wants to convey to a potentially
public user as much information about as possible without compromising the
amount of information revealed about . To this end, the so-called {\em
rate-privacy function} is introduced to quantify the maximal amount of
information (measured in terms of mutual information) that can be extracted
from under a privacy constraint between and the extracted information,
where privacy is measured using either mutual information or maximal
correlation. Properties of the rate-privacy function are analyzed and
information-theoretic and estimation-theoretic interpretations of it 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 . Finally, the
rate-privacy function under the mutual information privacy measure is
considered for the case where has a joint probability density function
by studying the problem where the extracted information is a uniform
quantization of 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.Comment: 55 pages, 6 figures. Improved the organization and added detailed
literature revie
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