# Wishart Mechanism for Differentially Private Principal Components Analysis

arXiv: https://arxiv.org/abs/1511.05680 · HTML: https://mlsanity.com/paper/1511.05680/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2015.

## Built on by (most cited first, 9 of 9)

- [Differential Private Knowledge Transfer for Privacy-Preserving Cross-Domain Recommendation](https://mlsanity.com/paper/2202.04893/) (2022)
- [Differentially private Riemannian optimization](https://mlsanity.com/paper/2205.09494/) (2022)
- [Shape And Structure Preserving Differential Privacy](https://mlsanity.com/paper/2209.12667/) (2022)
- [Stochastic and Private Nonconvex Outlier-Robust PCA](https://mlsanity.com/paper/2203.09276/) (2022)
- [Differentially Private Low-dimensional Synthetic Data from High-dimensional Datasets](https://mlsanity.com/paper/2305.17148/) (2023)
- [A Survey on Differential Privacy with Machine Learning and Future Outlook](https://mlsanity.com/paper/2211.10708/) (2022)
- [On the Optimal Regret of Locally Private Linear Contextual Bandit](https://mlsanity.com/paper/2404.09413/) (2024)
- [Differentially private sliced inverse regression in the federated paradigm](https://mlsanity.com/paper/2306.06324/) (2023)
- [Differentially Private Distribution Release of Gaussian Mixture Models via KL-Divergence Minimization](https://mlsanity.com/paper/2506.03467/) (2025)

## Abstract (arXiv)

We propose a new input perturbation mechanism for publishing a covariance matrix to achieve (ε,0)-differential privacy. Our mechanism uses a Wishart distribution to generate matrix noise. In particular, We apply this mechanism to principal component analysis. Our mechanism is able to keep the positive semi-definiteness of the published covariance matrix. Thus, our approach gives rise to a general publishing framework for input perturbation of a symmetric positive semidefinite matrix. Moreover, compared with the classic Laplace mechanism, our method has better utility guarantee. To the best of our knowledge, Wishart mechanism is the best input perturbation approach for (ε,0)-differentially private PCA. We also compare our work with previous exponential mechanism algorithms in the literature and provide near optimal bound while having more flexibility and less computational intractability.