  It is often necessary to disclose training data to the public domain, while
protecting privacy of certain sensitive labels. We use information theoretic
measures to develop such privacy preserving data disclosure mechanisms. Our
mechanism involves perturbing the data vectors in a manner that strikes a
balance in the privacy-utility trade-off. We use maximal information leakage
between the output data vector and the confidential label as our privacy
metric. We first study the theoretical Bernoulli-Gaussian model and study the
privacy-utility trade-off when only the mean of the Gaussian distributions can
be perturbed. We show that the optimal solution is the same as the case when
the utility is measured using probability of error at the adversary. We then
consider an application of this framework to a data driven setting and provide
an empirical approximation to the Sibson mutual information. By performing
experiments on the MNIST and FERG data-sets, we show that our proposed
framework achieves equivalent or better privacy than previous methods based on
mutual information.
