Locally private bayesian inference for count models

Aaron Schein, Zhiwei Steven Wu, Alexandra Schofield, Mingyuan Zhou, Hanna Wallachs

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We present a general and modular method for privacy-preserving Bayesian inference for Pois-son 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.

Original languageEnglish (US)
Title of host publication36th International Conference on Machine Learning, ICML 2019
PublisherInternational Machine Learning Society (IMLS)
Pages9924-9938
Number of pages15
ISBN (Electronic)9781510886988
StatePublished - Jan 1 2019
Event36th International Conference on Machine Learning, ICML 2019 - Long Beach, United States
Duration: Jun 9 2019Jun 15 2019

Publication series

Name36th International Conference on Machine Learning, ICML 2019
Volume2019-June

Conference

Conference36th International Conference on Machine Learning, ICML 2019
CountryUnited States
CityLong Beach
Period6/9/196/15/19

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Schein, A., Wu, Z. S., Schofield, A., Zhou, M., & Wallachs, H. (2019). Locally private bayesian inference for count models. In 36th International Conference on Machine Learning, ICML 2019 (pp. 9924-9938). (36th International Conference on Machine Learning, ICML 2019; Vol. 2019-June). International Machine Learning Society (IMLS).