Random Matrix Improved Covariance Estimation for a Large Class of Metrics
This addresses covariance estimation for statistical machine learning, though it appears incremental as it builds on existing random matrix theory advances.
The paper tackles the problem of covariance and precision matrix estimation by proposing a method based on random matrix theory that outperforms sample covariance estimates and competes with state-of-the-art approaches while being computationally simpler, with applications showing significant gains in linear and quadratic discriminant analyses.
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.