Random matrix improved covariance estimation for a large class of metrics This article is an updated version of: Tiomoko M, Couillet R, Bouchard F and Ginolhac G 2019 Random matrix improved covariance estimation for a large class of metrics Proc. Machine Learning Research vol 97 pp 6254-63

• Published in: Journal of statistical mechanics Vol. 2020; no. 12
• Main Authors: Tiomoko, Malik, Bouchard, Florent, Ginolhac, Guillaume, Couillet, Romain
• Format: Journal Article
• Language: English
• Published: IOP Publishing and SISSA 21.12.2020
• Subjects: machine learning
• DOI: 10.1088/1742-5468/abcaf2

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 method for a wide family of metrics. This 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 and faster. Applications to linear and quadratic discriminant analyses also show significant gains, therefore suggesting a practical relevance for statistical machine learning.