4 research outputs found
Almost Perfect Privacy for Additive Gaussian Privacy Filters
We study the maximal mutual information about a random variable
(representing non-private information) displayed through an additive Gaussian
channel when guaranteeing that only bits of information is leaked
about a random variable (representing private information) that is
correlated with . Denoting this quantity by , we show that
for perfect privacy, i.e., , one has for any pair of
absolutely continuous random variables and then derive a second-order
approximation for for small . This approximation is
shown to be related to the strong data processing inequality for mutual
information under suitable conditions on the joint distribution . Next,
motivated by an operational interpretation of data privacy, we formulate the
privacy-utility tradeoff in the same setup using estimation-theoretic
quantities and obtain explicit bounds for this tradeoff when is
sufficiently small using the approximation formula derived for
.Comment: 20 pages. To appear in Springer-Verla
On the Inability of Markov Models to Capture Criticality in Human Mobility
We examine the non-Markovian nature of human mobility by exposing the
inability of Markov models to capture criticality in human mobility. In
particular, the assumed Markovian nature of mobility was used to establish a
theoretical upper bound on the predictability of human mobility (expressed as a
minimum error probability limit), based on temporally correlated entropy. Since
its inception, this bound has been widely used and empirically validated using
Markov chains. We show that recurrent-neural architectures can achieve
significantly higher predictability, surpassing this widely used upper bound.
In order to explain this anomaly, we shed light on several underlying
assumptions in previous research works that has resulted in this bias. By
evaluating the mobility predictability on real-world datasets, we show that
human mobility exhibits scale-invariant long-range correlations, bearing
similarity to a power-law decay. This is in contrast to the initial assumption
that human mobility follows an exponential decay. This assumption of
exponential decay coupled with Lempel-Ziv compression in computing Fano's
inequality has led to an inaccurate estimation of the predictability upper
bound. We show that this approach inflates the entropy, consequently lowering
the upper bound on human mobility predictability. We finally highlight that
this approach tends to overlook long-range correlations in human mobility. This
explains why recurrent-neural architectures that are designed to handle
long-range structural correlations surpass the previously computed upper bound
on mobility predictability