Locally Private Bayesian Inference for Count Models

Aaron Schein, Zhiwei Steven Wu, Alexandra Schofield, Mingyuan Zhou, Hanna Wallach
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:5638-5648, 2019.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-schein19a, title = {Locally Private {B}ayesian Inference for Count Models}, author = {Schein, Aaron and Wu, Zhiwei Steven and Schofield, Alexandra and Zhou, Mingyuan and Wallach, Hanna}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {5638--5648}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/schein19a/schein19a.pdf}, url = {https://proceedings.mlr.press/v97/schein19a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Locally Private Bayesian Inference for Count Models %A Aaron Schein %A Zhiwei Steven Wu %A Alexandra Schofield %A Mingyuan Zhou %A Hanna Wallach %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-schein19a %I PMLR %P 5638--5648 %U https://proceedings.mlr.press/v97/schein19a.html %V 97 %X 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.
APA
Schein, A., Wu, Z.S., Schofield, A., Zhou, M. & Wallach, H.. (2019). Locally Private Bayesian Inference for Count Models. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:5638-5648 Available from https://proceedings.mlr.press/v97/schein19a.html.

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