  Information about people's movements and the locations they visit enables an
increasing number of mobility analytics applications, e.g., in the context of
urban and transportation planning, In this setting, rather than collecting or
sharing raw data, entities often use aggregation as a privacy protection
mechanism, aiming to hide individual users' location traces. Furthermore, to
bound information leakage from the aggregates, they can perturb the input of
the aggregation or its output to ensure that these are differentially private.
  In this paper, we set to evaluate the impact of releasing aggregate location
time-series on the privacy of individuals contributing to the aggregation. We
introduce a framework allowing us to reason about privacy against an adversary
attempting to predict users' locations or recover their mobility patterns. We
formalize these attacks as inference problems, and discuss a few strategies to
model the adversary's prior knowledge based on the information she may have
access to. We then use the framework to quantify the privacy loss stemming from
aggregate location data, with and without the protection of differential
privacy, using two real-world mobility datasets. We find that aggregates do
leak information about individuals' punctual locations and mobility profiles.
The density of the observations, as well as timing, play important roles, e.g.,
regular patterns during peak hours are better protected than sporadic
movements. Finally, our evaluation shows that both output and input
perturbation offer little additional protection, unless they introduce large
amounts of noise ultimately destroying the utility of the data.
