mlsanityData to 14 Oct 2026

Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising

arXiv 1805.06530 ↗First posted 16 May 2018cs.LG stat.MLcited by 218

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Abstract (arXiv)

The Gaussian mechanism is an essential building block used in multitude of differentially private data analysis algorithms. In this paper we revisit the Gaussian mechanism and show that the original analysis has several important limitations. Our analysis reveals that the variance formula for the original mechanism is far from tight in the high privacy regime (varepsilon → 0) and it cannot be extended to the low privacy regime (varepsilon → ∞). We address these limitations by developing an optimal Gaussian mechanism whose variance is calibrated directly using the Gaussian cumulative density function instead of a tail bound approximation. We also propose to equip the Gaussian mechanism with a post-processing step based on adaptive estimation techniques by leveraging that the distribution of the perturbation is known. Our experiments show that analytical calibration removes at least a third of the variance of the noise compared to the classical Gaussian mechanism, and that denoising dramatically improves the accuracy of the Gaussian mechanism in the high-dimensional regime.

Key facts. Cited by 218 papers in the map (data through 14 Oct 2026). First posted on arXiv 16 May 2018.

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Citing papers per year: 2021: 22; 2022: 25; 2023: 41; 2024: 47; 2025: 28; 2026: 55.

218 papers.

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  1. 2021Numerical Composition of Differential Privacycited by 180
  2. 2023How to DP-fy ML: A Practical Guide to Machine Learning with Differential Privacycited by 153
  3. 2023Invisible Image Watermarks Are Provably Removable Using Generative AIcited by 134
  4. 2021The Distributed Discrete Gaussian Mechanism for Federated Learning with Secure Aggregationcited by 128
  5. 2023Privacy Auditing with One (1) Training Runcited by 123
  6. 2023Privacy-Preserving In-Context Learning with Differentially Private Few-Shot Generationcited by 96
  7. 2021Optimal Accounting of Differential Privacy via Characteristic Functioncited by 86
  8. 2024Differentially Private Synthetic Data via Foundation Model APIs 2: Textcited by 76
  9. 2021The Skellam Mechanism for Differentially Private Federated Learningcited by 68
  10. 2023DP-Forward: Fine-tuning and Inference on Language Models with Differential Privacy in Forward Passcited by 67
  11. 2023Differentially Private Synthetic Data via Foundation Model APIs 1: Imagescited by 65
  12. 2022Mixed Differential Privacy in Computer Visioncited by 54
38 more
  1. 2022Private Convex Optimization via Exponential Mechanismcited by 49
  2. 2022Bounding Training Data Reconstruction in Private (Deep) Learningcited by 46
  3. 2022Composition of Differential Privacy & Privacy Amplification by Subsamplingcited by 45
  4. 2024Private Fine-tuning of Large Language Models with Zeroth-order Optimizationcited by 41
  5. 2023One-shot Empirical Privacy Estimation for Federated Learningcited by 36
  6. 2023Split-and-Denoise: Protect large language model inference with local differential privacycited by 32
  7. 2024Towards Certified Unlearning for Deep Neural Networkscited by 31
  8. 2023DP-BART for Privatized Text Rewriting under Local Differential Privacycited by 28
  9. 2024Private prediction for large-scale synthetic text generationcited by 24
  10. 2022Constant matters: Fine-grained Complexity of Differentially Private Continual Observationcited by 23
  11. 2023Privacy Amplification via Compression: Achieving the Optimal Privacy-Accuracy-Communication Trade-off in Distributed Mean Estimationcited by 22
  12. 2023Breaking the Trilemma of Privacy, Utility, Efficiency via Controllable Machine Unlearningcited by 22
  13. 2024How Private are DP-SGD Implementations?cited by 22
  14. 2021A Vertical Federated Learning Framework for Graph Convolutional Networkcited by 21
  15. 2022Individual Privacy Accounting with Gaussian Differential Privacycited by 20
  16. 2021Differentially Private Sliced Wasserstein Distancecited by 19
  17. 2023Differentially Private Image Classification by Learning Priors from Random Processescited by 19
  18. 2024Rewind-to-Delete: Certified Machine Unlearning for Nonconvex Functionscited by 19
  19. 2022Privacy-Aware Compression for Federated Data Analysiscited by 17
  20. 2023Privately Aligning Language Models with Reinforcement Learningcited by 17
  21. 2024Scalable DP-SGD: Shuffling vs. Poisson Subsamplingcited by 16
  22. 2022Bounding Membership Inferencecited by 15
  23. 2025Privacy amplification by random allocationcited by 15
  24. 2022Edgeworth Accountant: An Analytical Approach to Differential Privacy Compositioncited by 14
  25. 2023Fast Optimal Locally Private Mean Estimation via Random Projectionscited by 14
  26. 2024Balls-and-Bins Sampling for DP-SGDcited by 14
  27. 2024Shifted Interpolation for Differential Privacycited by 13
  28. 2024Avoiding Pitfalls for Privacy Accounting of Subsampled Mechanisms under Compositioncited by 13
  29. 2021Privately Publishable Per-instance Privacycited by 12
  30. 2023OPORP: One Permutation + One Random Projectioncited by 12
  31. 2023Improving the Privacy and Practicality of Objective Perturbation for Differentially Private Linear Learnerscited by 12
  32. 2024Subsampling is not Magic: Why Large Batch Sizes Work for Differentially Private Stochastic Optimisationcited by 11
  33. 2024DiSK: Differentially Private Optimizer with Simplified Kalman Filter for Noise Reductioncited by 11
  34. 2021A Coupled Design of Exploiting Record Similarity for Practical Vertical Federated Learningcited by 10
  35. 2021Towards Sparse Federated Analytics: Location Heatmaps under Distributed Differential Privacy with Secure Aggregationcited by 10
  36. 2022Over-the-Air Ensemble Inference with Model Privacycited by 10
  37. 2022Differentially Private Bootstrap: New Privacy Analysis and Inference Strategiescited by 10
  38. 2023DPSUR: Accelerating Differentially Private Stochastic Gradient Descent Using Selective Update and Releasecited by 10

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