Title: Locally Private Bayesian Inference for Count Models,
Abstract: As more aspects of social interaction are digitally recorded, there is a
growing need to develop privacy-preserving data analysis methods. Social
scientists will be more likely to adopt these methods if doing so entails
minimal change to their current methodology. Toward that end, we present a
general and modular method for privatizing Bayesian inference for Poisson
factorization, a broad class of models that contains some of the most widely
used models in the social sciences. Our method satisfies local differential
privacy, which ensures that no single centralized server need ever store the
non-privatized data. To formulate our local-privacy guarantees, we introduce
and focus on limited-precision local privacy---the local privacy analog of
limited-precision differential privacy (Flood et al., 2013). We present two
case studies, one involving social networks and one involving text corpora,
that test our method's ability to form the posterior distribution over latent
variables under different levels of noise, and demonstrate our method's utility
over a naïve approach, wherein inference proceeds as usual, treating the
privatized data as if it were not privatized.