Smoothing Spline Anova Models

By Chong Gu. 2002

1,128 citations recorded by the source corpus.

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In Statistics and Probability

Citations in the corpus

Sharp analysis of low-rank kernel matrix approximations (2012, positive): “Following classical results from the statistics literature (see, e.g., Wahba, 1990; Hastie and Tibshirani, 1990; Gu, 2002), we obtain the following expected prediction error: 1 which may be classically decomposed in two terms: Note that the bias term is a matrix-decreasing function of K/λ (and thus ”
Variance-based Regularization with Convex Objectives (2016, background): “= exp(−1 2 kx−x′k 2 2) generates a class of smooth functions for which the eigenvalues λj decay exponentially, as λj .e−j 2. Kernel operators underlying Sobolev spaces with diﬀerent smoothness orders [9, 23] typically have eigenvalues scaling as λj .j−2α for some α>1 2. As a concrete example, the”
Breaking the Curse of Dimensionality with Convex Neural Networks (2014, methodology): “, convex optimization for convex loss es). (c) Nonparametric ANOVA models: f(x) = P A∈A fA(xA) for a set A of subsets of {1,...,d}, and non-linear functionsfA : RA → R. The set A may be either given (Gu, 2013) or learned from data (Lin and Zhang, 2006; Bach,2008b). Multi-way interactions are explici”
Divide and conquer kernel ridge regression: a distributed algorithm with minimax optimal rates (2013, background): “We provide only a very brief coverage of the basics here, referring the reader to one of the many books on the topic (Wahba, 1990; Shawe-Taylor and Cristianini, 2004; Berlinet and Thomas-Agnan, 2004; Gu, 2002) for further details.”
Component selection and smoothing in multivariate nonparametric regression (2006, neutral): “A popular model for high-dimensional problems is the smoothing spline analysis of variance (SS-ANOVA) model [10, 19, 20].”
Numerical assessment of metamodelling strategies in computationally intensive optimization (2012, methodology): “Some examples of such techniques include: polynomials (Crestaux et al., 2009; Fen et al., 2009; Hussain et al., 2002; Sudret, 2008), kriging which is sometimes called design and analysis of computer experiment (DACE) in the metamodelling context (Kleijnen, 2005; Sacks et al., 1989; Sakata et al., 20”
Generalized Functional ANOVA Diagnostics for High-Dimensional Functions of Dependent Variables (2007, methodology): “The functional ANOVA decomposition has been studied in many contexts and appears in the literature as far back as Hoeffding (1948). Modern applications have been in the study of Quasi Monte Carlo methods for integration in Owen (2003). It has been used directly in a machine learning context and stud”
Minimax-Optimal Rates For Sparse Additive Models Over Kernel Classes Via Convex Programming (2010, background): “Various types of Sobolev/Besov classes exhibit this type of metric entropy decay [5, 13].”
A simple approach for varying-coefficient model selection (2009, methodology): “See Wahba (1990) and Gu (2002) for detailed”
Component selection and smoothing in smoothing spline analysis of variance models -- COSSO (2003, methodology): “S is a RKHS with the reproducing kernel ¯ K(s, t) = k1(s)k1(t)+k2(s)k2(t) −k4(|s −t|), with k1(t) = t −1/2, k2(t) = {k2 1(t) −1/12}/2, and k4(t) = {k4 1(t) − k2 1(t)/2 + 7/240}/24. See Wahba (1990), Gu (2002) .”
Local and global asymptotic inference in smoothing spline models (2012, methodology): “9 of [13] when the null space Nm ≡ {g ∈ H :J (g, g) = 0} is finite dimensional and (y;a) is concave and continuous w.”
Estimating residual variance in nonparametric regression using least squares (2005, methodology): “We use the generalized cross-validation (GCV) and generalized maximum likelihood method (GML) to estimate the smoothing parameters (Wahba 1990, Gu 2002, Wang and Ke 2002).”
Coverage Properties of Confidence Intervals for Generalized Additive Model Components (2012, background): “Wahba/Silverman type intervals are straightforward to extend to non-Gaussian settings and GAM components (e.g. Gu, 1992, 2002; Gu & Wahba, 1993; Ruppert et al., 2003; Wood, 2006b).”
P-spline ANOVA-type interaction models for spatio-temporal smoothing (2011, methodology): “These models have been considered in the literature in the context of Smoothing Splines, as SS-ANOVA models (see Chen, 1993; Gu, 2002).”
DECIDING THE DIMENSION OF EFFECTIVE DIMENSION REDUCTION SPACE FOR FUNCTIONAL AND HIGH-DIMENSIONAL DATA (2010, methodology): “be the sample mean function and the sample covariance operator, respectively. Let ω̂j and ψ̂j be the j th sample eigenvalue and eigenfunction of ̂X . By Dauxois, Pousse and Romain (1982), ω̂j and ψ̂j are root-n consistent under (C1).”
Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models (2004, methodology): “For maximal computational efficiency the “performance-iteration” method of Gu (e.g., Gu 2002) is appealing: Smoothing parameter selection is performed on the weighted penalized least squares problem produced at each iteration of the P–IRLS algorithm.”
Estimation of a semiparametric recursive bivariate probit model in the presence of endogeneity (2011, background): “…(1983) or Silverman (1985) in the univariate spline model context, and then generalized to the componentwise case when dealing with Gaussian and non-Gaussian data (e.g., Gu 2002; Ruppert, Wand & Carroll 2003; Wood 2006), are typically used to reliably represent the uncertainty of smooth terms.”