mlsanityData to 14 Oct 2026

On the Theory and Practice of Privacy-Preserving Bayesian Data Analysis

arXiv 1603.07294 ↗First posted 23 Mar 2016cs.LG cs.AI cs.CRcited by 35

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Abstract (arXiv)

Bayesian inference has great promise for the privacy-preserving analysis of sensitive data, as posterior sampling automatically preserves differential privacy, an algorithmic notion of data privacy, under certain conditions (Dimitrakakis et al., 2014; Wang et al., 2015). While this one posterior sample (OPS) approach elegantly provides privacy "for free," it is data inefficient in the sense of asymptotic relative efficiency (ARE). We show that a simple alternative based on the Laplace mechanism, the workhorse of differential privacy, is as asymptotically efficient as non-private posterior inference, under general assumptions. This technique also has practical advantages including efficient use of the privacy budget for MCMC. We demonstrate the practicality of our approach on a time-series analysis of sensitive military records from the Afghanistan and Iraq wars disclosed by the Wikileaks organization.

Key facts. Cited by 35 papers in the map (data through 14 Oct 2026). First posted on arXiv 23 Mar 2016.

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Citing papers per year: 2021: 8; 2022: 3; 2023: 13; 2024: 7; 2025: 1; 2026: 3.

35 papers.

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  1. 2021Differential privacy and robust statistics in high dimensionscited by 64
  2. 2022DP-PCA: Statistically Optimal and Differentially Private PCAcited by 24
  3. 2024Private Gradient Descent for Linear Regression: Tighter Error Bounds and Instance-Specific Uncertainty Estimationcited by 12
  4. 2024Incentives in Private Collaborative Machine Learningcited by 10
  5. 2023Near Optimal Private and Robust Linear Regressioncited by 9
  6. 2021Non-parametric Differentially Private Confidence Intervals for the Mediancited by 7
  7. 2024Insufficient Statistics Perturbation: Stable Estimators for Private Least Squarescited by 7
  8. 2023A Meta-learning Framework for Tuning Parameters of Protection Mechanisms in Trustworthy Federated Learningcited by 6
  9. 2023Protect Your Score: Contact Tracing With Differential Privacy Guaranteescited by 5
  10. 2021Privacy Amplification Via Bernoulli Samplingcited by 4
  11. 2021Mitigating Statistical Bias within Differentially Private Synthetic Datacited by 4
  12. 2024Private Regression via Data-Dependent Sufficient Statistic Perturbationcited by 4
23 more
  1. 2022Statistic Selection and MCMC for Differentially Private Bayesian Estimationcited by 3
  2. 2023Multi-Task Differential Privacy Under Distribution Skewcited by 3
  3. 2023DP-Fast MH: Private, Fast, and Accurate Metropolis-Hastings for Large-Scale Bayesian Inferencecited by 3
  4. 2023Private Matrix Factorization with Public Item Featurescited by 3
  5. 2021Dirichlet Mechanism for Differentially Private KL Divergence Minimizationcited by 2
  6. 2021Can Stochastic Gradient Langevin Dynamics Provide Differential Privacy for Deep Learning?cited by 2
  7. 2022Differentially private partitioned variational inferencecited by 2
  8. 2025Purifying Approximate Differential Privacy with Randomized Post-processingcited by 2
  9. 2021Locally Differentially Private Bayesian Inferencecited by 1
  10. 2021Differentially private stochastic expectation propagation (DP-SEP)cited by 1
  11. 2023Differentially Private Online Bayesian Estimation With Adaptive Truncationcited by 1
  12. 2023Differentially Private Distributed Bayesian Linear Regression with MCMCcited by 1
  13. 2023Differentially Private Statistical Inference through β-Divergence One Posterior Samplingcited by 1
  14. 2023Simulation-based Bayesian Inference from Privacy Protected Datacited by 1
  15. 2024Bridging Privacy and Robustness for Trustworthy Machine Learningcited by 1
  16. 2024Bayesian Frequency Estimation Under Local Differential Privacy With an Adaptive Randomized Response Mechanismcited by 1
  17. 2024Distributed Differentially Private Data Analytics via Secure Sketchingcited by 1
  18. 2026Near-Optimal Private Linear Regression via Iterative Hessian Mixingcited by 1
  19. 2026Computation-Utility-Privacy Tradeoffs in Bayesian Estimationcited by 1
  20. 2023PRIMO: Private Regression in Multiple Outcomescited by 0
  21. 2023The Normal Distributions Indistinguishability Spectrum and its Application to Privacy-Preserving Machine Learningcited by 0
  22. 2023Data Analytics with Differential Privacycited by 0
  23. 2026On Inherent Privacy of Posterior Sampling: A Unified R'enyi-Divergence Frameworkcited by 0