The spectral condition number plot for regularization parameter evaluation

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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.
Original languageEnglish
JournalComputational Statistics
DOIs
Publication statusE-pub ahead of print - 12 Jul 2019

Cite this

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title = "The spectral condition number plot for regularization parameter evaluation",
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.",
keywords = "Eigenvalues, High-dimensional covariance (precision) estimation, Matrix condition number, ℓ -Penalization",
author = "Peeters, {Carel F. W.} and {van de Wiel}, {Mark A.} and {van Wieringen}, {Wessel N.}",
year = "2019",
month = "7",
day = "12",
doi = "10.1007/s00180-019-00912-z",
language = "English",
journal = "Computational Statistics",
issn = "0943-4062",

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T1 - The spectral condition number plot for regularization parameter evaluation

AU - Peeters, Carel F. W.

AU - van de Wiel, Mark A.

AU - van Wieringen, Wessel N.

PY - 2019/7/12

Y1 - 2019/7/12

N2 - 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.

AB - 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.

KW - Eigenvalues

KW - High-dimensional covariance (precision) estimation

KW - Matrix condition number

KW - ℓ -Penalization

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DO - 10.1007/s00180-019-00912-z

M3 - Article

JO - Computational Statistics

JF - Computational Statistics

SN - 0943-4062

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