TY - JOUR
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 - 2020/6/1
Y1 - 2020/6/1
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
KW - ℓ-Penalization
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U2 - https://doi.org/10.1007/s00180-019-00912-z
DO - https://doi.org/10.1007/s00180-019-00912-z
M3 - Article
SN - 0943-4062
VL - 35
SP - 629
EP - 646
JO - Computational Statistics
JF - Computational Statistics
IS - 2
ER -