2018/03/22 by Aaron Schein, Zhiwei Steven Wu, Schein, Aaron +7 · 3 citations
Computer Science · Mathematics · #Computation and Language (cs.CL) #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Privacy-Preserving Technologies in Data #Random Matrices and Applications #Social and Information Networks (cs.SI) #Statistical Methods and Bayesian Inference #cs.CL #cs.CR #cs.LG #cs.SI #stat.ML
paper · pdf · doi:10.48550/arxiv.1803.08471
openalex publication_date 2018/03/22 · arxiv created 2019/02/21 · arxiv updated 2019/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a general method for privacy-preserving Bayesian inference in 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, which we introduce to formulate privacy guarantees appropriate for sparse count data. We develop an MCMC algorithm that approximates the locally private posterior over model parameters given data that has been locally privatized by the geometric mechanism (Ghosh et al., 2012). Our solution is based on two insights: 1) a novel reinterpretation of the geometric mechanism in terms of the Skellam distribution (Skellam, 1946) and 2) a general theorem that relates the Skellam to the Bessel distribution (Yuan & Kalbfleisch, 2000). We demonstrate our method in two case studies on real-world email data in which we show that our method consistently outperforms the commonly-used naive approach, obtaining higher quality topics in text and more accurate link prediction in networks. On some tasks, our privacy-preserving method even outperforms non-private inference which conditions on the true data.