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Locally Private Bayesian Inference for Count Models
Aaron Schein · Steven Wu · Alexandra Schofield · Mingyuan Zhou · Hanna Wallach

Tue Jun 11 06:30 PM -- 09:00 PM (PDT) @ Pacific Ballroom #175

We present a general and modular method for privacy-preserving Bayesian inference for Poisson factorization, a broad class of models that includes some of the most widely used models in the social sciences. Our method satisfies limited-precision local privacy, a generalization of local differential privacy that we introduce to formulate appropriate privacy guarantees for sparse count data. We present an MCMC algorithm that approximates the posterior distribution over the latent variables conditioned on data that has been locally privatized by the geometric mechanism. Our method is based on two insights: 1) a novel reinterpretation of the geometric mechanism in terms of the Skellam distribution and 2) a general theorem that relates the Skellam and Bessel distributions. We demonstrate our method's utility using two case studies that involve real-world email data. We show that our method consistently outperforms the commonly used naive approach, wherein inference proceeds as usual, treating the locally privatized data as if it were not privatized.

Author Information

Aaron Schein (UMass Amherst)
Steven Wu (University of Minnesota)
Xanda Schofield (Cornell University)
Mingyuan Zhou (University of Texas at Austin)
Hanna Wallach (Microsoft Research)

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