Private Adaptive Covariance Estimation via Gaussian Graphical Models

2026-05-22

AI Summary

This work addresses the challenge of high-dimensional covariance estimation under differential privacy, where conventional methods suffer from substantial error due to uniform noise addition. The authors propose PACE-GGM, a novel approach that adaptively allocates the privacy budget to the most informative entries of the empirical covariance matrix. By iteratively identifying entries with the largest approximation errors and perturbing them via the Gaussian mechanism, followed by reconstructing a complete covariance matrix using the principle of maximum entropy, PACE-GGM enables accurate Gaussian graphical model estimation while preserving differential privacy. Empirical evaluations on multiple real-world datasets demonstrate that the method significantly outperforms standard Gaussian mechanisms and other baselines, particularly in high-dimensional settings and under moderate to low privacy budgets.

Abstract

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.

Problem

• differential privacy
• covariance estimation
• Gaussian graphical models
• high-dimensional data
• privacy budget

Innovation

• differentially private
• covariance estimation
• Gaussian graphical models
• adaptive privacy budget
• maximum-entropy reconstruction