# MVG Mechanism: Differential Privacy under Matrix-Valued Query

arXiv: https://arxiv.org/abs/1801.00823 · HTML: https://mlsanity.com/paper/1801.00823/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jan 2018.

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

- [DP-Forward: Fine-tuning and Inference on Language Models with Differential Privacy in Forward Pass](https://mlsanity.com/paper/2309.06746/) (2023)
- [Photonic Differential Privacy with Direct Feedback Alignment](https://mlsanity.com/paper/2106.03645/) (2021)
- [Improved Matrix Gaussian Mechanism for Differential Privacy](https://mlsanity.com/paper/2104.14808/) (2021)
- [Privacy Risk for anisotropic Langevin dynamics using relative entropy bounds](https://mlsanity.com/paper/2302.00766/) (2023)
- [Universally Harmonizing Differential Privacy Mechanisms for Federated Learning: Boosting Accuracy and Convergence](https://mlsanity.com/paper/2407.14710/) (2024)
- [The Normal Distributions Indistinguishability Spectrum and its Application to Privacy-Preserving Machine Learning](https://mlsanity.com/paper/2309.01243/) (2023)
- [S-BDT: Distributed Differentially Private Boosted Decision Trees](https://mlsanity.com/paper/2309.12041/) (2023)

## Abstract (arXiv)

Differential privacy mechanism design has traditionally been tailored for a scalar-valued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrix-valued query function by adding i.i.d. noise to each element of the matrix, this method is often suboptimal as it forfeits an opportunity to exploit the structural characteristics typically associated with matrix analysis. To address this challenge, we propose a novel differential privacy mechanism called the Matrix-Variate Gaussian (MVG) mechanism, which adds a matrix-valued noise drawn from a matrix-variate Gaussian distribution, and we rigorously prove that the MVG mechanism preserves (ε,δ)-differential privacy. Furthermore, we introduce the concept of directional noise made possible by the design of the MVG mechanism. Directional noise allows the impact of the noise on the utility of the matrix-valued query function to be moderated. Finally, we experimentally demonstrate the performance of our mechanism using three matrix-valued queries on three privacy-sensitive datasets. We find that the MVG mechanism notably outperforms four previous state-of-the-art approaches, and provides comparable utility to the non-private baseline.