mlsanityData to 7 Oct 2026

Differentially Private Bayesian Linear Regression

arXiv 1910.13153 ↗First posted 29 Oct 2019cs.LG stat.MLcited by 24

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Abstract (arXiv)

Linear regression is an important tool across many fields that work with sensitive human-sourced data. Significant prior work has focused on producing differentially private point estimates, which provide a privacy guarantee to individuals while still allowing modelers to draw insights from data by estimating regression coefficients. We investigate the problem of Bayesian linear regression, with the goal of computing posterior distributions that correctly quantify uncertainty given privately released statistics. We show that a naive approach that ignores the noise injected by the privacy mechanism does a poor job in realistic data settings. We then develop noise-aware methods that perform inference over the privacy mechanism and produce correct posteriors across a wide range of scenarios.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Oct 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 5; 2022: 4; 2023: 4; 2024: 5; 2025: 4; 2026: 2.

24 papers.

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  1. 2022Differentially Private Regression with Unbounded Covariatescited by 10
  2. 2024Incentives in Private Collaborative Machine Learningcited by 10
  3. 2022Noise-Aware Statistical Inference with Differentially Private Synthetic Datacited by 9
  4. 2021Non-parametric Differentially Private Confidence Intervals for the Mediancited by 7
  5. 2021Differentially Private Bayesian Neural Networks on Accuracy, Privacy and Reliabilitycited by 6
  6. 2024Private Regression via Data-Dependent Sufficient Statistic Perturbationcited by 4
  7. 2021Gaussian Processes with Differential Privacycited by 3
  8. 2021Differentially Private Nonparametric Regression Under a Growth Conditioncited by 3
  9. 2022Sharper Utility Bounds for Differentially Private Modelscited by 3
  10. 2022DPVIm: Differentially Private Variational Inference Improvedcited by 2
  11. 2024Is merging worth it? Securely evaluating the information gain for causal dataset acquisitioncited by 2
  12. 2021Locally Differentially Private Bayesian Inferencecited by 1
12 more
  1. 2023Differentially Private Distributed Bayesian Linear Regression with MCMCcited by 1
  2. 2023Simulation-based Bayesian Inference from Privacy Protected Datacited by 1
  3. 2024Differentially private Bayesian testscited by 1
  4. 2025Fiducial Matching: Differentially Private Inference for Categorical Datacited by 1
  5. 2026Computation-Utility-Privacy Tradeoffs in Bayesian Estimationcited by 1
  6. 2023Differentially Private Statistical Inference through β-Divergence One Posterior Samplingcited by 0
  7. 2023The Normal Distributions Indistinguishability Spectrum and its Application to Privacy-Preserving Machine Learningcited by 0
  8. 2024Noise-Aware Differentially Private Variational Inferencecited by 0
  9. 2025Optimal Survey Design for Private Mean Estimationcited by 0
  10. 2025On Reconstructing Training Data From Bayesian Posteriors and Trained Modelscited by 0
  11. 2025Differentially Private Two-Stage Gradient Descent for Instrumental Variable Regressioncited by 0
  12. 2026Differentially Private Truncation of Unbounded Data via Public Second Momentscited by 0