Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond

By Christopher K. I. Williams. 2003

9,804 citations recorded by the source corpus.

Subfields: Optimization & Training, Statistical Learning Theory

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Citations in the corpus

Deep Models Under the GAN: Information Leakage from Collaborative Deep Learning (2017, background): “Supervised learning algorithms like Support Vector Machines (SVMs) [74], Random Forests [10], Gaussian Processes (GPs) [69] and, of course, deep neural networks [28] can be depicted by this general framework.”
Machine Learning Methods That Economists Should Know About (2019, methodology): “2 Support Vector Machines and Kernels Support Vector Machines (SVMs, Vapnik [1998], Scholkopf and Smola [2001]) are another flexible set of methods for classification analyses.”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “The kernel mean has appeared in the literature since the beginning of the field of kernel methods itself (Schölkopf et al. 1998, Schölkopf and Smola 2002).”
Security Evaluation of Support Vector Machines in Adversarial Environments (2014, background): “, the VC dimension, which is not always possible to control, and for the RBF kernel SVM is infinite) [61].”
Black-Box vs. White-Box: Understanding Their Advantages and Weaknesses From a Practical Point of View (2019, methodology): “a kernel) for separating those non-linear problems have been proposed [22].”
Explaining nonlinear classification decisions with deep Taylor decomposition (2015, methodology): “They include, for example, graphical models [1], kernels [2, 3], Gaussian processes [4], neu-”
Learning Fair Classifiers (2015, neutral): “3The CV score suffers from similar limitations.”
Fast Conditional Independence Test for Vector Variables with Large Sample Sizes (2018, methodology): “For continuous variables, extant non-parametric CITs have largely focused on kernel meth-ods [Schölkopf and Smola, 2002].”
Prototypal Analysis and Prototypal Regression (2017, methodology): “Kernel methods and reproducing kernel Hilbert space (RKHS) are widely used in machine learning to extend algorithms where only inner products among data points are required (Schölkopf and Smola, 2002; Shawe-Taylor and Cristianini, 2004; Hofmann et al., 2008).”
Consistent Kernel Mean Estimation for Functions of Random Variables (2016, methodology): “The algorithms for constructing such expansions are known as reduced set methods and have been studied by the machine learning community (Schölkopf and Smola, 2002, Chapter 18).”
Bayesian Learning of Kernel Embeddings (2016, background): “A large class of popular and successful machine learning methods rely on kernels (positive semidefinite functions), including support vector machines, kernel ridge regression, kernel PCA (Schölkopf and Smola, 2002), Gaussian processes (Rasmussen and Williams, 2006), and kernel-based hypothesis testi”
Optimal Rates for Random Fourier Features (2015, neutral): “ar X iv :1 50 6.”
Kernel-Based Just-In-Time Learning for Passing Expectation Propagation Messages (2015, methodology): “In principle, during the initial batch training, the operator can perform cross validation or type-II maximum likelihood esti- mation for parameter selection; however for computational simplicity we set the kernel parameters according to the median heuristic (Schölkopf and Smola, 2002).”
K2-ABC: Approximate Bayesian Computation with Infinite Dimensional Summary Statistics via Kernel Embeddings (2015, background): “Computing a distance in the feature space without forming an explicit feature vector is known as the kernel trick (Schölkopf & Smola, 2001).”
FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Test (2014, background): “…of the big data era, it has become a hot trend to enhancing the efficiency of kernel-based learning methods, such as support vector machines and Gaussian process (Cortes & Vapnik, 1995; Schölkopf & Smola, 2002), throughout machine learning, computer vision, pattern recognition and data mining.”
One-Class Support Measure Machines for Group Anomaly Detection (2013, background): “The existence and uniqueness of the hyperplane then follows from the supporting hyperplane theorem (Schölkopf and Smola 2001).”
Nonparametric kernel estimators for image classification (2012, background): “The dual form of the “soft margin Support Vector Machine” can be described as follows [26]:”
Random Feature Maps for Dot Product Kernels (2012, methodology): “To see that this suﬃces we make use of some well known facts regarding positive deﬁnite kernels (for example refer to Sch¨olkopf and Smola, 2002).”