# Differentially Private High Dimensional Sparse Covariance Matrix Estimation

arXiv: https://arxiv.org/abs/1901.06413 · HTML: https://mlsanity.com/paper/1901.06413/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jan 2019.

## Built on by (most cited first, 7 of 7)

- [Private High-Dimensional Hypothesis Testing](https://mlsanity.com/paper/2203.01537/) (2022)
- [Differentially private sliced inverse regression in the federated paradigm](https://mlsanity.com/paper/2306.06324/) (2023)
- [Nonparametric spectral density estimation using interactive mechanisms under local differential privacy](https://mlsanity.com/paper/2504.00919/) (2025)
- [High-Dimensional Differentially Private Quantile Regression: Distributed Estimation and Statistical Inference](https://mlsanity.com/paper/2508.05212/) (2025)
- [On the Curse of Dimensionality in Private Sparse Covariance Estimation and PCA](https://mlsanity.com/paper/2606.21951/) (2026)
- [Private Adaptive Covariance Estimation via Gaussian Graphical Models](https://mlsanity.com/paper/2605.24295/) (2026)
- [Improved Private Sparse Covariance Estimation with Multiscale Threshold Tests](https://mlsanity.com/paper/2609.22783/) (2026)

## Abstract (arXiv)

In this paper, we study the problem of estimating the covariance matrix under differential privacy, where the underlying covariance matrix is assumed to be sparse and of high dimensions. We propose a new method, called DP-Thresholding, to achieve a non-trivial ℓ2-norm based error bound, which is significantly better than the existing ones from adding noise directly to the empirical covariance matrix. We also extend the ℓ2-norm based error bound to a general ℓw-norm based one for any 1≤ w≤ ∞, and show that they share the same upper bound asymptotically. Our approach can be easily extended to local differential privacy. Experiments on the synthetic datasets show consistent results with our theoretical claims.