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 language||English (US)|
|Title of host publication||36th International Conference on Machine Learning, ICML 2019|
|Publisher||International Machine Learning Society (IMLS)|
|Number of pages||15|
|State||Published - 2019|
|Event||36th International Conference on Machine Learning, ICML 2019 - Long Beach, United States|
Duration: Jun 9 2019 → Jun 15 2019
|Name||36th International Conference on Machine Learning, ICML 2019|
|Conference||36th International Conference on Machine Learning, ICML 2019|
|Period||6/9/19 → 6/15/19|
Bibliographical noteFunding Information:
We acknowledge the support of NSF awards #1812699 and #1652536. We also thank Dan Sheldon, David Mimno, and Antti Honkela. This research was partially conducted while Alexandra Schofield was a summer intern at Microsoft.