# The Correlated Gaussian Sparse Histogram Mechanism

arXiv: https://arxiv.org/abs/2412.10357 · HTML: https://mlsanity.com/paper/2412.10357/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 24 references that are in the map.
- First posted on arXiv 13 Dec 2024.

## Builds on (most cited first, 14 of 14)

- [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)
- [The Discrete Gaussian for Differential Privacy](https://mlsanity.com/paper/2004.00010/) (2020)
- [Practical Differentially Private Top-k Selection with Pay-what-you-get Composition](https://mlsanity.com/paper/1905.04273/) (2019)
- [Simultaneous Private Learning of Multiple Concepts](https://mlsanity.com/paper/1511.08552/) (2015)
- [Differentially Private SQL with Bounded User Contribution](https://mlsanity.com/paper/1909.01917/) (2019)
- [Oneshot Differentially Private Top-k Selection](https://mlsanity.com/paper/2105.08233/) (2021)
- [The Price of Selection in Differential Privacy](https://mlsanity.com/paper/1702.02970/) (2017)
- [Differential Privacy on Finite Computers](https://mlsanity.com/paper/1709.05396/) (2017)
- [Exact Privacy Analysis of the Gaussian Sparse Histogram Mechanism](https://mlsanity.com/paper/2202.01100/) (2022)
- [Better Differentially Private Approximate Histograms and Heavy Hitters using the Misra-Gries Sketch](https://mlsanity.com/paper/2301.02457/) (2023)
- [Better Gaussian Mechanism using Correlated Noise](https://mlsanity.com/paper/2408.06853/) (2024)
- [Faster Differentially Private Top-k Selection: A Joint Exponential Mechanism with Pruning](https://mlsanity.com/paper/2411.09552/) (2024)
- [Some Constructions of Private, Efficient, and Optimal K-Norm and Elliptic Gaussian Noise](https://mlsanity.com/paper/2309.15790/) (2023)

## Built on by (most cited first, 2 of 2)

- [Continual Release Moment Estimation with Differential Privacy](https://mlsanity.com/paper/2502.06597/) (2025)
- [Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees](https://mlsanity.com/paper/2605.22756/) (2026)

## Abstract (arXiv)

We consider the problem of releasing a sparse histogram under (varepsilon, δ)-differential privacy. The stability histogram independently adds noise from a Laplace or Gaussian distribution to the non-zero entries and removes those noisy counts below a threshold. Thereby, the introduction of new non-zero values between neighboring histograms is only revealed with probability at most δ, and typically, the value of the threshold dominates the error of the mechanism. We consider the variant of the stability histogram with Gaussian noise. Recent works ([Joseph and Yu, COLT '24] and [Lebeda, SOSA '25]) reduced the error for private histograms using correlated Gaussian noise. However, these techniques can not be directly applied in the very sparse setting. Instead, we adopt Lebeda's technique and show that adding correlated noise to the non-zero counts only allows us to reduce the magnitude of noise when we have a sparsity bound. This, in turn, allows us to use a lower threshold by up to a factor of 1/2 compared to the non-correlated noise mechanism. We then extend our mechanism to a setting without a known bound on sparsity. Additionally, we show that correlated noise can give a similar improvement for the more practical discrete Gaussian mechanism.