# Private Adaptive Covariance Estimation via Gaussian Graphical Models

arXiv: https://arxiv.org/abs/2605.24295 · HTML: https://mlsanity.com/paper/2605.24295/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 31 references that are in the map.
- First posted on arXiv 22 May 2026.

## Builds on (most cited first, 16 of 16)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Privately Learning High-Dimensional Distributions](https://mlsanity.com/paper/1805.00216/) (2018)
- [AIM: An Adaptive and Iterative Mechanism for Differentially Private Synthetic Data](https://mlsanity.com/paper/2201.12677/) (2022)
- [CoinPress: Practical Private Mean and Covariance Estimation](https://mlsanity.com/paper/2006.06618/) (2020)
- [Revisiting differentially private linear regression: optimal and adaptive prediction & estimation in unbounded domain](https://mlsanity.com/paper/1803.02596/) (2018)
- [Iterative Methods for Private Synthetic Data: Unifying Framework and New Methods](https://mlsanity.com/paper/2106.07153/) (2021)
- [Differentially Private Query Release Through Adaptive Projection](https://mlsanity.com/paper/2103.06641/) (2021)
- [Differentially Private Ordinary Least Squares](https://mlsanity.com/paper/1507.02482/) (2015)
- [Differentially Private Simple Linear Regression](https://mlsanity.com/paper/2007.05157/) (2020)
- [Fully Adaptive Composition in Differential Privacy](https://mlsanity.com/paper/2203.05481/) (2022)
- [Differentially Private Covariance Revisited](https://mlsanity.com/paper/2205.14324/) (2022)
- [HDMM: Optimizing error of high-dimensional statistical queries under differential privacy](https://mlsanity.com/paper/2106.12118/) (2021)
- [Differentially Private High Dimensional Sparse Covariance Matrix Estimation](https://mlsanity.com/paper/1901.06413/) (2019)
- [Differentially Private Linear Regression with Linked Data](https://mlsanity.com/paper/2308.00836/) (2023)
- [Fast Private Adaptive Query Answering for Large Data Domains](https://mlsanity.com/paper/2602.05674/) (2026)

## Abstract (arXiv)

We propose PACE-GGM, a data-adaptive differentially private method for covariance estimation that concentrates its privacy budget on the most informative entries of the empirical covariance matrix, rather than perturbing all entries. This applies in the natural setting where the modeler supplies separate bounds for each variable, so that individual entries can be measured with less noise than the full matrix. In each round, our method selects a poorly approximated entry, measures it using the Gaussian mechanism, and then reconstructs a full covariance matrix using a maximum-entropy reconstruction objective, leading to a Gaussian graphical model structure. Experiments on diverse real-world datasets demonstrate consistent improvements in estimation error with respect to the Gaussian mechanism and other baselines, particularly in high-dimensional and low-to-moderate privacy regimes.