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. (21st December 2020) - Tiomoko, Malik; Bouchard, Florent; Ginolhac, Guillaume; Couillet, Romain
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 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.