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The spectral condition number plot for regularization parameter evaluation

Published version
Peer-reviewed

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Authors

Peeters, Carel F. W. 
van de Wiel, Mark A. 
van Wieringen, Wessel N. 

Abstract

Abstract: Many modern statistical applications ask for the estimation of a covariance (or precision) matrix in settings where the number of variables is larger than the number of observations. There exists a broad class of ridge-type estimators that employs regularization to cope with the subsequent singularity of the sample covariance matrix. These estimators depend on a penalty parameter and choosing its value can be hard, in terms of being computationally unfeasible or tenable only for a restricted set of ridge-type estimators. Here we introduce a simple graphical tool, the spectral condition number plot, for informed heuristic penalty parameter assessment. The proposed tool is computationally friendly and can be employed for the full class of ridge-type covariance (precision) estimators.

Description

Keywords

Original Paper, Eigenvalues, High-dimensional covariance (precision) estimation, ℓ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _2$$\end{document}-Penalization, Matrix condition number

Journal Title

Computational Statistics

Conference Name

Journal ISSN

0943-4062
1613-9658

Volume Title

35

Publisher

Springer Berlin Heidelberg
Sponsorship
FP7 Research infrastructures (269553)