# Random Matrix Improved Covariance Estimation for a Large Class of Metrics

arXiv: https://arxiv.org/abs/1902.02554 · HTML: https://mlsanity.com/paper/1902.02554/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2019.

## Built on by (most cited first, 3 of 3)

- [Random matrix theory improved Fr'echet mean of symmetric positive definite matrices](https://mlsanity.com/paper/2405.06558/) (2024)
- [A Random Matrix Theory Perspective on the Learning Dynamics of Multi-head Latent Attention](https://mlsanity.com/paper/2507.09394/) (2025)
- [Consistent Estimation of a Class of Distances Between Covariance Matrices](https://mlsanity.com/paper/2409.11761/) (2024)

## Abstract (arXiv)

Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to largely outperform the sample covariance matrix estimate and to compete with state-of-the-art methods, while at the same time being computationally simpler. Applications to linear and quadratic discriminant analyses also demonstrate significant gains, therefore suggesting practical interest to statistical machine learning.