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

## TL;DR

This paper introduces an improved covariance estimation method using random matrix theory that outperforms traditional estimates and is computationally efficient, with demonstrated benefits in machine learning classification tasks.

## Contribution

It proposes a novel covariance estimation technique based on random matrix theory applicable to a broad class of metrics, improving accuracy and computational simplicity.

## Key findings

- Outperforms sample covariance matrix estimates in various metrics.
- Competes with state-of-the-art methods while being simpler to compute.
- Enhances classification performance in discriminant analysis.

## Abstract

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.