Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo (1502.07645v2)

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.

• The paper demonstrates that a single posterior sample can inherently guarantee differential privacy under bounded log-likelihood conditions while achieving statistical consistency and optimality.
• It extends these findings to stochastic gradient methods, proving that integrating inherent noise in techniques like SGLD maintains privacy without extra computational cost.
• Empirical evaluations confirm that the approach outperforms state-of-the-art DP methods, offering practical, privacy-preserving benefits for sensitive data analytics.

Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo

The paper "Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo," authored by Yu-Xiang Wang, Stephen E. Fienberg, and Alex Smola, addresses the intersection of Bayesian learning and differential privacy (DP). The authors present notable findings on how these seemingly disparate areas can be aligned to achieve privacy in data analyses, which is paramount when handling sensitive datasets. This summary aims to dissect the primary contributions and implications of their research.

The central premise of the paper revolves around two significant discoveries:

1. Single Posterior Sampling and Differential Privacy: Under conventional assumptions, the authors demonstrate that obtaining a single sample from a posterior distribution inherently provides differential privacy. This derivation arises when the log-likelihood is bounded. Furthermore, the sampled posterior is shown to be statistically consistent, asymptotically optimal, and notably computationally feasible, given the Bayesian model's own consistency and tractability. This insight implies that Bayesian posterior sampling can function as a valid DP mechanism without necessitating alterations to existing algorithms or systems, especially when utilizing closed-form scenarios.
2. Stochastic Gradient Monte Carlo and Differential Privacy: The paper extends its findings to stochastic gradient-based methods, particularly emphasizing Stochastic Gradient Langevin Dynamics (SGLD). By integrating noise comparable in scale to inherent algorithmic randomness, these stochastic gradient methods maintain differential privacy without requiring substantive modifications. This facilitates the development of "anytime" algorithms for Bayesian inference that respect privacy constraints, useful in iterative or streaming data scenarios.

Implementation and Empirical Evaluation

The authors present empirical evidence to validate the proposed methodologies. Their experiments show that the single posterior sampling outperforms state-of-the-art DP empirical risk minimization methods, such as objective perturbation. They demonstrate efficacy on several benchmark datasets, confirming that the methods developed are competitive in performance while ensuring privacy.

Implications and Future Work

The paper's findings have broader implications in both theoretical and practical realms of computer science and data privacy:

• Theoretical Contribution: The results bridge Bayesian inferential methodologies with cryptographic-based privacy approaches, suggesting potential for extensive research into other inherent privacy characteristics of randomized algorithms. This integration paves a path toward understanding the intrinsic privacy properties of stochastic processes in machine learning and promoting methods with dual functional values.
• Practical Applications: The potential to apply these findings extends richly into secure data analytics, particularly in domains such as healthcare, finance, and any other areas managing sensitive information. The ability to leverage existing Bayesian models and algorithms to achieve privacy enhances their applicability without incurring additional computational costs or redesign.
• Speculation on Future Developments: The authors suggest further exploration into other machine learning algorithms and randomization techniques, such as hashing and dropout, to identify undiscovered privacy properties. Moreover, they propose the possibility of harnessing these privacy-preserving features in sectors like movie recommendations, thereby aligning industry practices with ethical data-handling norms.

In conclusion, the paper offers a compelling examination of how Bayesian sampling and stochastic gradient algorithms can contribute to maintaining data privacy. By efficiently intertwining statistical methods and privacy constraints, the authors illuminate a path forward for developing private-by-design data analytic tools that do more with less. This represents a significant step toward making differential privacy more accessible and applicable in real-world scenarios.