Minimizing GCV/GML Scores with Multiple Smoothing Parameters via the Newton Method

By Chong Gu, Grace Wahba. 1991

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Citations in the corpus

Smoothing Parameter and Model Selection for General Smooth Models (2015, unknown): “.5 1.0 1.5 2.0 x0 f 0 (x 0 ) 0.0 0.2 0.4 0.6 0.8 1.0 1 2 3 4 5 6 7 x1 f 1 (x 1 ) 0.0 0.2 0.4 0.6 0.8 1.0 0 2 4 6 8 x2 f 2 (x 2 ) Figure S4: Shapes of the functions used for the simulation study (from Gu and Wahba, 1991). f 3(x 3) = 0. penalized parameter βi of gj dβˆ i/dρj d(RTz)i/dρj ≃ βˆ i (1 +λjΛ”
Smoothing spline Gaussian regression: more scalable computation via efficient approximation (2004, methodology): “Fits with (cid:11) = 1 and q = n by ssanova1 have been checked against (cid:12)ts by the ssanova suite powered by the O ( n 3 ) algorithms of Gu et al. (1989) and Gu and Wahba (1991) for numerical consistency.”
Weak-Lensing Results from the 75 Square Degree Cerro Tololo Inter-American Observatory Survey (2003, methodology): “We instead use a smoothing spline algorithm developed by Gu & Wahba (1991), which is available fromNetLib as Rkpack.7 As noted in x 7.5 by BJ02, the convolution is efficient, because each of the 7 7 kernel components is the result of three successive 3 3 kernel convolutions.”
GAMs with integrated model selection using penalized regression splines and applications to environmental modelling (2002, methodology): “Key words: smoothing, additive, model, selection, GCV Preprint submitted to Elsevier Science 18 May 2002”
Modelling and smoothing parameter estimation with multiple quadratic penalties (2000, methodology): “I will again follow Gu and Wahba (1991) and update the variablesηi = log θi by Newton’s method (see Gillet al. 1981).”
Parsimonious additive models (2007, methodology): “…(used at each step of the backfitting procedure in BRUTO, (Hastie and Tibshirani, 1990), optimized by a Newton method, (Gu and Wahba, 1991; Wood, 2000), or combined with a diagonalization technique for penalized splines, (Ruppert et al., 2003)), Akaike information criteria (Hastie and…”
Asymptotic optimality and efficient computation of the leave-subject-out cross-validation (2012, methodology): “We developed an efficient algorithm to minimizing LsoCV∗(W,λ) with respect to λ for a pre-given W based on the works of Gu and Wahba (1991) and Wood (2004).”