# Enhancing Differentially Private Mechanisms via Empirical Bayes

arXiv: https://arxiv.org/abs/2606.21107 · HTML: https://mlsanity.com/paper/2606.21107/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 46 references that are in the map.
- First posted on arXiv 19 Jun 2026.

## Builds on (most cited first, 20 of 20)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising](https://mlsanity.com/paper/1805.06530/) (2018)
- [Understanding Gradient Clipping in Private SGD: A Geometric Perspective](https://mlsanity.com/paper/2006.15429/) (2020)
- [Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain](https://mlsanity.com/paper/1803.02596/) (2018)
- [The Noisy Power Method: A Meta Algorithm with Applications](https://mlsanity.com/paper/1311.2495/) (2013)
- [Rate-Optimal Perturbation Bounds for Singular Subspaces with Applications to High-Dimensional Statistics](https://mlsanity.com/paper/1605.00353/) (2016)
- [Improving Deep Learning with Differential Privacy using Gradient Encoding and Denoising](https://mlsanity.com/paper/2007.11524/) (2020)
- [From Robustness to Privacy and Back](https://mlsanity.com/paper/2302.01855/) (2023)
- [DP-PCA: Statistically Optimal and Differentially Private PCA](https://mlsanity.com/paper/2205.13709/) (2022)
- [Easy Differentially Private Linear Regression](https://mlsanity.com/paper/2208.07353/) (2022)
- [Private Gradient Descent for Linear Regression: Tighter Error Bounds and Instance-Specific Uncertainty Estimation](https://mlsanity.com/paper/2402.13531/) (2024)
- [Optimal Differentially Private PCA and Estimation for Spiked Covariance Matrices](https://mlsanity.com/paper/2401.03820/) (2024)
- [DPlis: Boosting Utility of Differentially Private Deep Learning via Randomized Smoothing](https://mlsanity.com/paper/2103.01496/) (2021)
- [Lognormal Distributions and Geometric Averages of Positive Definite Matrices](https://mlsanity.com/paper/1407.6383/) (2014)
- [Differentially Private Learning of Undirected Graphical Models using Collective Graphical Models](https://mlsanity.com/paper/1706.04646/) (2017)
- [Improved Differentially Private Regression via Gradient Boosting](https://mlsanity.com/paper/2303.03451/) (2023)
- [Stochastic and Private Nonconvex Outlier-Robust PCA](https://mlsanity.com/paper/2203.09276/) (2022)
- [Differentially Private Multivariate Statistics with an Application to Contingency Table Analysis](https://mlsanity.com/paper/2211.15019/) (2022)
- [On the Utility Gain of Iterative Bayesian Update for Locally Differentially Private Mechanisms](https://mlsanity.com/paper/2307.07744/) (2023)

## Abstract (arXiv)

Differential privacy (DP) has become the gold standard for ensuring the privacy protection of machine learning and statistical algorithms in recent decades. A plethora of algorithms and methods have been developed to enhance the utility of DP algorithms while maintaining the same level of DP. However, these are often overly complex or computationally ineffective. We propose a novel approach focusing on denoising the output of the simple additive Gaussian mechanism by adopting the idea of textitempirical Bayes estimation. We highlight that the empirical Bayes approach can reduce the mean-squared error solely by taking the output of the Gaussian mechanism as input. Our numerical studies show that this simple yet powerful approach can be applied to improve upon various statistical problems, including histogram release, principal component analysis, and linear regression, often outperforming existing private algorithms.