# Locally Private Bayesian Inference for Count Models

arXiv: https://arxiv.org/abs/1803.08471 · HTML: https://mlsanity.com/paper/1803.08471/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2018.

## Built on by (most cited first, 9 of 9)

- [How to DP-fy ML: A Practical Guide to Machine Learning with Differential Privacy](https://mlsanity.com/paper/2303.00654/) (2023)
- [The Skellam Mechanism for Differentially Private Federated Learning](https://mlsanity.com/paper/2110.04995/) (2021)
- [Differential privacy for medical deep learning: methods, tradeoffs, and deployment implications](https://mlsanity.com/paper/2506.00660/) (2025)
- [Differentially Private Bayesian Neural Networks on Accuracy, Privacy and Reliability](https://mlsanity.com/paper/2107.08461/) (2021)
- [Technical and Legal Aspects of Federated Learning in Bioinformatics: Applications, Challenges and Opportunities](https://mlsanity.com/paper/2503.09649/) (2025)
- [Doubly Non-Central Beta Matrix Factorization for DNA Methylation Data](https://mlsanity.com/paper/2106.06691/) (2021)
- [Locally Differentially Private Bayesian Inference](https://mlsanity.com/paper/2110.14426/) (2021)
- [Scaling up Dynamic Edge Partition Models via Stochastic Gradient MCMC](https://mlsanity.com/paper/2403.00044/) (2024)
- [Optimal Survey Design for Private Mean Estimation](https://mlsanity.com/paper/2501.18121/) (2025)

## Abstract (arXiv)

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.