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.

本文提出了一种使用差分隐私技术保证贝叶斯学习个体隐私安全的算法，采样自后验分布得出的估计符合要求，同时随机梯度下降方法也可以达到类似效果，是较好的解决贝叶斯学习隐私问题的方法。

免费隐私: 后验采样和随机梯度 Monte Carlo