  Consider a data publishing setting for a data set with public and private
features. The objective of the publisher is to maximize the amount of
information about the public features in a revealed data set, while keeping the
information leaked about the private features bounded. The goal of this paper
is to analyze the performance of privacy mechanisms that are constructed to
match the distribution learned from the data set. Two distinct scenarios are
considered: (i) mechanisms are designed to provide a privacy guarantee for the
learned distribution; and (ii) mechanisms are designed to provide a privacy
guarantee for every distribution in a given neighborhood of the learned
distribution. For the first scenario, given any privacy mechanism, upper bounds
on the difference between the privacy-utility guarantees for the learned and
true distributions are presented. In the second scenario, upper bounds on the
reduction in utility incurred by providing a uniform privacy guarantee are
developed.
