156 research outputs found
Notes on Information-Theoretic Privacy
We investigate the tradeoff between privacy and utility in a situation where
both privacy and utility are measured in terms of mutual information. For the
binary case, we fully characterize this tradeoff in case of perfect privacy and
also give an upper-bound for the case where some privacy leakage is allowed. We
then introduce a new quantity which quantifies the amount of private
information contained in the observable data and then connect it to the optimal
tradeoff between privacy and utility.Comment: The corrected version of a paper appeared in Allerton 201
Privacy-Aware MMSE Estimation
We investigate the problem of the predictability of random variable under
a privacy constraint dictated by random variable , correlated with ,
where both predictability and privacy are assessed in terms of the minimum
mean-squared error (MMSE). Given that and are connected via a
binary-input symmetric-output (BISO) channel, we derive the \emph{optimal}
random mapping such that the MMSE of given is minimized while
the MMSE of given is greater than for a
given . We also consider the case where are continuous
and is restricted to be an additive noise channel.Comment: 9 pages, 3 figure
Privacy-Aware Guessing Efficiency
We investigate the problem of guessing a discrete random variable under a
privacy constraint dictated by another correlated discrete random variable ,
where both guessing efficiency and privacy are assessed in terms of the
probability of correct guessing. We define as the maximum
probability of correctly guessing given an auxiliary random variable ,
where the maximization is taken over all ensuring that the
probability of correctly guessing given does not exceed . We
show that the map is strictly increasing,
concave, and piecewise linear, which allows us to derive a closed form
expression for when and are connected via a
binary-input binary-output channel. For being pairs of independent
and identically distributed binary random vectors, we similarly define
under the assumption that is also
a binary vector. Then we obtain a closed form expression for
for sufficiently large, but nontrivial
values of .Comment: ISIT 201
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