Ridge Regression Learning Algorithm in Dual Variables

By Craig John Saunders, A. Gammerman, Vladimir G Vovk. 1998

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Citations in the corpus

On the Error of Random Fourier Features (2015, methodology): “We first consider kernel ridge regression (KRR; Saunders et al. 1998).”
Domain Adaptation: Learning Bounds and Algorithms (2009, methodology): “This family of algorithms includes support vector machines (SVM) (Cortes & Vapnik, 1995), support vector regression (SVR) (Vapnik, 1998), kernel ridge regression (Saunders et al., 1998), and other algorithms such as those based on the relative entropy regularization (Bousquet & Elisseeff, 2002).”
Divide and conquer kernel ridge regression: a distributed algorithm with minimax optimal rates (2013, background): “In a standard implementation [25], the kernel matrix must be inverted, which requires costs O(N3) and O(N2) in time and”
Feature Mining for Localised Crowd Counting (2012, methodology): “Comparative Evaluation – We compared the following models • Single global model with global feature (1) ridge regression (RR) [22], and (2) Gaussian processes regression (GPR) with linear + RBF kernel as in [6].”
Learning with Support Vector Machines (2011, methodology): “Further reading: Ridge regression was initially discussed by Hoerl and Kennard [1970] with the dual form later introduced by Saunders et al. [1998]. -SV regression was originally proposed by (Vapnik [1995], Vapnik [1998]).”
Least Squares Support Vector Machine Classifiers (1999, methodology): “For the function estimation problem a support vector interpretation of ridge regression (Golub & Van Loan, 1989) has been given in (Saunders et al., 1998), which considers equality type constraints instead of inequalities from the classical SVM approach.”
Kernel Partial Least Squares Regression in Reproducing Kernel Hilbert Space (2002, methodology): “…the kernel principal components regression (PCR) technique and we also made theoretical and experimental comparison to kernel ridge regression (RR) (Saunders et al., 1998, Cristianini Kernel Partial Least Squares Regression in RKHS In Section 2 a basic definition of a RKHS and formulation of the…”
Feature selection methods for big data bioinformatics: A survey from the search perspective. (2016, methodology): “Mohapatra et al. [87] proposed two variations of kernel ridge regression (KRR) [88,89,90], namely wavelet kernel ridge regression (WKRR) and radial basis kernel ridge regression (RKRR) for classification of microarray medical datasets.”
On Over-fitting in Model Selection and Subsequent Selection Bias in Performance Evaluation (2010, methodology): “Kernel Ridge Regression In this section, we provide a brief overview of the Kernel Ridge Regression (KRR) classifier (Saunders et al., 1998), also known as the Least-Squares Support Vector Machine (Suykens et al.”
Optimal control by least squares support vector machines (2001, methodology): “For the sequel we employ a least squares version of the support vector method, which has been investigated by Saunders et al. (1998) and Suykens and Vandewalle (1999b), for function estimation and classi®cation problems, respectively.”
Domain Adaptation under Target and Conditional Shift (2013, methodology): “We compare our approaches to correction for TarS (Section 3) and for LS-GeTarS (Section 5) with the baseline (unweighted) least squares KRR or SVM, the importance weighting approach to correction for covariate shift (CovS) proposed in Huang et al. (2007); Gretton et al. (2008), as well as two " orac”
A Survey of Modern Questions and Challenges in Feature Extraction (2015, unknown): “For example, in the case of kernel ridge regression (Saunders et al., 1998), if a linear combination of kernels is learned jointly, then the resulting supervised coupled problem requires solving following minimax problem min‖μ‖q≤1 maxα L(μ,α) = −λαTα− ∑p k=1 μkα Kkα+ 2α T y (Cortes et al.”
Multilabel Classification with Principal Label Space Transformation (2012, methodology): “gif" mimetype="image" xlink:type="simple"> , the approach performs kernel ridge regression (Saunders, Gammerman, & Vovk, 1998 ) from x to h [m] to get a regressor r m ( x ).”
Bayesian Framework for Least-Squares Support Vector Machine Classifiers, Gaussian Processes, and Kernel Fisher Discriminant Analysis (2002, methodology): “When one uses no bias term b in the regression formulation (Cristianini & Shawe-Taylor, 2000; Saunders et al., 1998) the support values α * are obtained from the linear system (Ω + µ ζ I N )α * = Y. (23) The output of the LS-SVM regressor for a new input x is given by .”