Generalized cross-validation as a method for choosing a good ridge parameter

By Gene H. Golub, Michael T. Heath, Grace Wahba. 1979

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

An evaluation of adaptive surrogate modeling based optimization with two benchmark problems (2014, methodology): “MARS chooses the best model with less GCV. Random forests Random forests (Breiman, 2001) are one of ensemble methods.”
Multi-Step Regression Learning for Compositional Distributional Semantics (2013, methodology): “For each verb matrix or tensor to be learned, we tuned the parameter λ by generalized cross-validation (Golub et al., 1979).”
Just Interpolate: Kernel "Ridgeless" Regression Can Generalize (2018, background): “The parameter is either chosen to reﬂect the knowledge of the spectral decay at the population level (De Vito et al., 2005) (typically unknown to statistician), or by the means of cross-validation (Golub et al., 1979).”
Robust smoothing of gridded data in one and higher dimensions with missing values (2010, unknown): “Assuming that one wants to solve the smoothing linear systemˆy = H(s)y, where H is the so-called hat matrix, the GCV method chooses the parameter s that minimizes the GCV score (Craven and Wahba, 1978; Golub et al., 1979) , where Tr denotes the matrix trace.”
WGSQuikr: Fast Whole-Genome Shotgun Metagenomic Classification (2014, methodology): “Two common methods include Generalized Cross Validation [11] and the L-Curve method [12].”
Asymptotic Equivalence between Cross-Validations and Akaike Information Criteria in Mixed-Effects Models (2021, unknown): “As Golub et al. (1979), replacing hkk in (2.9) by tr(H1)/N leads to GCV = 1 N m∑ i=1 ni∑ j=1 [ yij − xTij β̂ − zTij b̂i 1 − tr(H1)/N ]2 .”
Surprises in High-Dimensional Ridgeless Least Squares Interpolation (2019, unknown): “The key implication of Theorem 7, in the context of the current paper and its central focus, is that the CV-tuned or GCV-tuned ridge estimator has the same asymptotic performance as the optimally-tuned ridge estimator.”
A novel computational inverse technique for load identification using the shape function method of moving least square fitting (2014, methodology): “(16) is chosen through minimizing the Generalized Cross-Validation (GCV) function [32]:”
Automatic Parameter Selection for Denoising Algorithms Using a No-Reference Measure of Image Content (2010, methodology): “A canonical example is the regularization parameter in MAP-based restoration algorithms [5], [8].”
Representational models: A common framework for understanding encoding, pattern-component, and representational-similarity analysis (2017, background): “This can be done again by nested cross-validation [12], generalized cross454 validation [43], or restricted maximum-likelihood estimation (Eq.”