Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo

TL;DR

This paper reveals that sampling from Bayesian posteriors and using stochastic gradient Monte Carlo methods inherently provide differential privacy, enabling private Bayesian learning with minimal modifications and strong utility guarantees.

Contribution

It establishes that single posterior samples are differentially private for free and that stochastic gradient Monte Carlo methods preserve privacy without significant changes, advancing private Bayesian inference.

Findings

Single posterior samples are differentially private without extra effort.

Stochastic gradient Monte Carlo methods inherently preserve privacy.

Proposed methods outperform existing private Bayesian techniques on datasets.

Abstract

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.