Locally Differentially Private Bayesian Inference
This work addresses the privacy-utility trade-off in LDP for researchers and practitioners needing trustworthy Bayesian methods in scenarios with untrustworthy aggregators, representing an incremental improvement by adapting existing Bayesian frameworks to LDP constraints.
The paper tackles the problem of accurate uncertainty quantification in Bayesian inference under local differential privacy (LDP), where noise added for privacy complicates statistical analysis, and demonstrates efficacy in parameter estimation for distributions and regression tasks.
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.