Locally Differentially Private Bayesian Inference

TL;DR

This paper introduces a noise-aware Bayesian inference framework that accounts for local differential privacy noise, enabling accurate parameter estimation while respecting privacy constraints in data collection.

Contribution

It presents a novel probabilistic modeling approach that incorporates LDP noise into Bayesian inference, addressing computational and statistical challenges for improved uncertainty quantification.

Findings

Effective parameter estimation for various distributions.

Improved Bayesian inference under LDP constraints.

Demonstrated applicability to regression models.

Abstract

In recent years, local differential privacy (LDP) has emerged as a technique of choice for privacy-preserving data collection in several scenarios when the aggregator is not trustworthy. LDP provides client-side privacy by adding noise at the user's end. Thus, clients need not rely on the trustworthiness of the aggregator. In this work, we provide a noise-aware probabilistic modeling framework, which allows Bayesian inference to take into account the noise added for privacy under LDP, conditioned on locally perturbed observations. Stronger privacy protection (compared to the central model) provided by LDP protocols comes at a much harsher privacy-utility trade-off. Our framework tackles several computational and statistical challenges posed by LDP for accurate uncertainty quantification under Bayesian settings. We demonstrate the efficacy of our framework in parameter estimation for univariate and multi-variate distributions as well as logistic and linear regression.