  Guaranteeing a certain level of user privacy in an arbitrary piece of text is
a challenging issue. However, with this challenge comes the potential of
unlocking access to vast data stores for training machine learning models and
supporting data driven decisions. We address this problem through the lens of
dx-privacy, a generalization of Differential Privacy to non Hamming distance
metrics. In this work, we explore word representations in Hyperbolic space as a
means of preserving privacy in text. We provide a proof satisfying dx-privacy,
then we define a probability distribution in Hyperbolic space and describe a
way to sample from it in high dimensions. Privacy is provided by perturbing
vector representations of words in high dimensional Hyperbolic space to obtain
a semantic generalization. We conduct a series of experiments to demonstrate
the tradeoff between privacy and utility. Our privacy experiments illustrate
protections against an authorship attribution algorithm while our utility
experiments highlight the minimal impact of our perturbations on several
downstream machine learning models. Compared to the Euclidean baseline, we
observe > 20x greater guarantees on expected privacy against comparable worst
case statistics.
