  We focus on the privacy-utility trade-off encountered by users who wish to
disclose some information to an analyst, that is correlated with their private
data, in the hope of receiving some utility. We rely on a general privacy
statistical inference framework, under which data is transformed before it is
disclosed, according to a probabilistic privacy mapping. We show that when the
log-loss is introduced in this framework in both the privacy metric and the
distortion metric, the privacy leakage and the utility constraint can be
reduced to the mutual information between private data and disclosed data, and
between non-private data and disclosed data respectively. We justify the
relevance and generality of the privacy metric under the log-loss by proving
that the inference threat under any bounded cost function can be upper-bounded
by an explicit function of the mutual information between private data and
disclosed data. We then show that the privacy-utility tradeoff under the
log-loss can be cast as the non-convex Privacy Funnel optimization, and we
leverage its connection to the Information Bottleneck, to provide a greedy
algorithm that is locally optimal. We evaluate its performance on the US census
dataset.
