  We lay theoretical foundations for new database release mechanisms that allow
third-parties to construct consistent estimators of population statistics,
while ensuring that the privacy of each individual contributing to the database
is protected. The proposed framework rests on two main ideas. First, releasing
(an estimate of) the kernel mean embedding of the data generating random
variable instead of the database itself still allows third-parties to construct
consistent estimators of a wide class of population statistics. Second, the
algorithm can satisfy the definition of differential privacy by basing the
released kernel mean embedding on entirely synthetic data points, while
controlling accuracy through the metric available in a Reproducing Kernel
Hilbert Space. We describe two instantiations of the proposed framework,
suitable under different scenarios, and prove theoretical results guaranteeing
differential privacy of the resulting algorithms and the consistency of
estimators constructed from their outputs.
