Smoothing noisy data with spline functions

By Peter Craven, Grace Wahba. 1978

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Citations in the corpus

Deep learning in neural networks: An overview (2014, neutral): “ Other weight priors are implicit in additional penalty terms (MacKay, 1992) or in methods based on validation sets (Mosteller and Tukey, 1968; Stone, 1974; Eubank, 1988; Hastie and Tibshirani, 1990; Craven and Wahba, 1979; Golub et al., 1979), ﬁnal prediction error (Akaike, 1970), generalized predi”
Component selection and smoothing in multivariate nonparametric regression (2006, methodology): “The generalized cross-validation proposed by Craven and Wahba [4] is one of the most popular methods for choosing smoothing parameters in the smoothing spline method.”
Estimating option implied risk‐neutral densities using spline and hypergeometric functions (2007, unknown): “The most popular class of these methods is based on cross validation (CV) proposed by Craven and Wahba (1979).”
Constructive algorithms for structure learning in feedforward neural networks for regression problems (1997, background): “Alternatively, it may be obtained from a number of information criteria like Akaike's information criterion (AIC) [40], Bayesian information criterion (BIC) [41], final prediction error (FPE) [42], generalized cross-validation (GCV) [43], predicted square error (PSE) [44], minimum description length”
Fréchet regression for random objects with Euclidean predictors (2016, methodology): “For the special case Ω = R, various nonparametric regression methods have been developed which are based on kernel or local linear polynomial fitting (Fan and Gijbels 1996), splines (Craven and Wahba 1979; Marx and Eilers 1996) or other smoothers.”
Adaptive computation and machine learning (1998, background): “, 1997; Vapnik, 1998), risk inflation criterion (RIC) (Foster and George, 1994), Shibata’s model selector (SMS) (Shibata, 1981), generalized cross-validation (GCV) (Craven and Wahba, 1979), Bayesian information criterion (BIC) (Schwarz, 1978), Akaike information criterion (AIC) (Akaike, 1974), Mallo”
Variable Selection using MM Algorithms. (2005, methodology): “For SCAD, p (cid:4) λ ( 0 + ) = λ , and this tuning parameter λ is chosen using generalized cross-validation, or GCV [5].”
Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models (2009, methodology): “(3.20), which is chosen by the GCV criterion with all λ j = λ.”
Confidence Intervals for Nonparametric Curve Estimates (2001, background): “The relationship (7) was shown in Craven and Wahba (1979), and in the same paper an approximation to (6), called the generalized cross-validation function, was proposed:”