Random matrix improved covariance estimation for a large class of metrics*

2019/02/07 by Malik Tiomoko, Florent Bouchard, Guillaume Ginolhac +2
Computer Science · Mathematics · #Covariance #Covariance function #Covariance matrix #Estimation of covariance matrices #Gaussian Processes and Bayesian Inference #Matrix (chemical analysis) #Matérn covariance function #Quadratic equation #Random Matrices and Applications #Random matrix #Sample mean and sample covariance #Scatter matrix #Stochastic Gradient Optimization Techniques #cs.LG #stat.ML

paper · pdf · doi:10.1088/1742-5468/abcaf2

arxiv created 2019/02/07 · openalex created_date 2019/02/21 · openalex publication_date 2020/12/01 · arxiv updated 2021/02/03 · openalex updated_date 2026/08/05

Abstract

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.

Citations

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