Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo

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.

References in corpus (5)

• Stochastic Gradient Hamiltonian Monte Carlo
• Bayesian Posterior Sampling via Stochastic Gradient Fisher Scoring
• Efficient, Differentially Private Point Estimators
• (Non-) asymptotic properties of Stochastic Gradient Langevin Dynamics
• Bayesian inference under differential privacy

Cited by in corpus (57)

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• Comparative Study of Differentially Private Data Synthesis Methods
• The Cost of Privacy: Rates of Convergence for Parameter Estimation with Differential Privacy
• Privacy-preserving parametric inference: a case for robust statistics
• Federated Learning via Posterior Averaging: A New Perspective and Practical Algorithms
• Stochastic Quasi-Newton Langevin Monte Carlo
• Generalization in Generative Adversarial Networks: A Novel Perspective from Privacy Protection
• Differentially Private Summation with Multi-Message Shuffling
• On the Theory and Practice of Privacy-Preserving Bayesian Data Analysis
• Reviewing and Improving the Gaussian Mechanism for Differential Privacy
• Private Approximations of the 2nd-Moment Matrix Using Existing Techniques in Linear Regression
• On-Average KL-Privacy and its equivalence to Generalization for Max-Entropy Mechanisms
• Bayesian Inference for Large Scale Image Classification
• Optimal Accounting of Differential Privacy via Characteristic Function
• Computing Tight Differential Privacy Guarantees Using FFT
• Parametric Bootstrap for Differentially Private Confidence Intervals
• Network Shuffling: Privacy Amplification via Random Walks
• Learning Rate Adaptation for Federated and Differentially Private Learning
• Data-dependent PAC-Bayes priors via differential privacy
• Concentrated Differentially Private Gradient Descent with Adaptive per-Iteration Privacy Budget
• Bayesian Pseudo Posterior Mechanism under Asymptotic Differential Privacy
• On the Convergence and Calibration of Deep Learning with Differential Privacy
• Structure and Sensitivity in Differential Privacy: Comparing K-Norm Mechanisms
• Differential privacy and robust statistics in high dimensions
• Tighter Generalization Bounds for Iterative Differentially Private Learning Algorithms
• Latent Dirichlet Allocation Model Training with Differential Privacy
• Model-Agnostic Private Learning via Stability
• On the Differential Privacy of Bayesian Inference
• Differentially Private Bayesian Inference for Generalized Linear Models
• KNG: The K-Norm Gradient Mechanism
• Differentially Private Convex Optimization with Feasibility Guarantees
• Differentially Private Bayesian Neural Networks on Accuracy, Privacy and Reliability
• Differential Privacy Dynamics of Langevin Diffusion and Noisy Gradient Descent
• Model-based Differentially Private Data Synthesis and Statistical Inference in Multiply Synthetic Differentially Private Data
• Differentially Private Online Bayesian Estimation With Adaptive Truncation
• Revisiting Model-Agnostic Private Learning: Faster Rates and Active Learning
• Privacy-Preserving Multiple Tensor Factorization for Synthesizing Large-Scale Location Traces with Cluster-Specific Features
• Faster Differentially Private Samplers via Rényi Divergence Analysis of Discretized Langevin MCMC
• Re-weighting of Vector-weighted Mechanisms for Utility Maximization under Differential Privacy
• PD-ML-Lite: Private Distributed Machine Learning from Lighweight Cryptography
• Integral Privacy for Sampling
• Privacy-Aware Rejection Sampling
• Entropy-SGD optimizes the prior of a PAC-Bayes bound: Generalization properties of Entropy-SGD and data-dependent priors
• Per-instance Differential Privacy
• Differentially Private Hamiltonian Monte Carlo
• Locally Differentially Private Bayesian Inference
• N-grams Bayesian Differential Privacy
• Secure and Differentially Private Bayesian Learning on Distributed Data
• Differentially private training of neural networks with Langevin dynamics for calibrated predictive uncertainty
• Learning Games and Rademacher Observations Losses
• Stability Enhanced Privacy and Applications in Private Stochastic Gradient Descent
• Designing a Location Trace Anonymization Contest
• On Privacy Protection of Latent Dirichlet Allocation Model Training
• On the Use of Penalty MCMC for Differential Privacy
• Pufferfish Privacy Mechanisms for Correlated Data