2015/02/26 by Yu-Xiang Wang, Stephen E. Fienberg, Wang, Yu-Xiang +3 · 5 citations
Computer Science · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Privacy-Preserving Technologies in Data #Statistical Methods and Bayesian Inference
paper · pdf · doi:10.48550/arxiv.1502.07645
openalex publication_date 2015/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of Bayesian learning on sensitive datasets and present two simple but somewhat surprising results that connect Bayesian learning to "differential privacy:, a cryptographic approach to protect individual-level privacy while permiting database-level utility. Specifically, we show that that under standard assumptions, getting one single sample from a posterior distribution is differentially private "for free". We will see that estimator is statistically consistent, near optimal and computationally tractable whenever the Bayesian model of interest is consistent, optimal and tractable. Similarly but separately, we show that a recent line of works that use stochastic gradient for Hybrid Monte Carlo (HMC) sampling also preserve differentially privacy with minor or no modifications of the algorithmic procedure at all, these observations lead to an "anytime" algorithm for Bayesian learning under privacy constraint. We demonstrate that it performs much better than the state-of-the-art differential private methods on synthetic and real datasets.