Support Vector Machines and the Bayes Rule in Classification

By Yi Lin. 2002

270 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Computer Vision and Pattern Recognition, Statistics and Probability

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Citations in the corpus

Estimating treatment effect heterogeneity in randomized program evaluation (2013, methodology): “In addition, the group LASSO introduced by Yuan and Lin (2006) groups different levels of the same factor together so that all levels of a factor are selected without sacrificing rotational invariance.”
Theory of classification : a survey of some recent advances (2005, background): “The study of universal approximation properties of kernels and statistical consistency of Support Vector Machines is due to Steinwart [203–205], Lin [140,141], Zhou [243], and Blanchard, Bousquet, and Massart [39].”
Using AUC and accuracy in evaluating learning algorithms (2005, methodology): “SVM over other learning algorithms [25], [ 19 ], [4], [16] We think that one major difference is”
Learning the coordinate gradients (2011, methodology): “Secondly, gradient learning aims at estimating the gradient rf⁄ of the target function f⁄. When the SVM hinge loss is used the target function is known to be the Bayes rule [ 20 ,41] which is usually not continuous.”
Robust Truncated Hinge Loss Support Vector Machines (2007, background): “Then Fisher consistency requires that the minimizer of E[ (Yf (X))|X = x] has the same sign as p(x) − 1/2 (Lin 2004). Fisher consistency, also known as classification-calibration (Bartlett, Jordan, and McAuliffe 2006), is a desirable property for a loss function. For the binary SVM, Lin (2002) showe”
Multicategory Support Vector Machines, Theory, and Application to the Classiﬁcation of Microarray Data and Satellite Radiance Data (2002, methodology): “With some abuse of notation, let K be now the n by n matrix with ijth entry K(xi,xj).”
Covariate Shift Adaptation by Importance Weighted Cross Validation (2007, methodology): “SVM (Vapnik, 1998; Schölkopf and Smola, 2002) is a popular classification technique and is shown to converge to the Bayes optimal classifier as the number of training samples tends to infinity (Lin, 2002).”
Reinforcement learning design for cancer clinical trials (2009, unknown): “Kaelbling LP, Littman ML, Moore AW.”
Compound facial expressions of emotion (2014, background): “It has been shown (45) that for some kernels (e.”
Estimating Individualized Treatment Rules Using Outcome Weighted Learning (2012, methodology): “The proposition is analogous to results for SVM (e.g., Lin 2002).”
Statistical performance of support vector machines (2008, background): “Part (i) of the Lemma can be found in [ 12 ] and part (ii) in [26], but we give a proof in Appendix B for completeness.”
A Review of Machine Learning Algorithms for Text-Documents Classification (2010, methodology): “The SVM classification method is outstanding from the others with its outstanding classification effectiveness [99] [111] [112] [110] [113] [70].”
How to Compare Different Loss Functions and Their Risks (2007, background): “[18, 19, 37, 27, 1]), and for margin-based loss functions L2, i.”
Finite-Dimensional Projection for Classification and Statistical Learning (2008, unknown): “The main reason for this choice is that the bounds in [23] have a very similar ’oracle-type’ form involving approximation properties of models (in the case of SVMs, these models are ellipsoids) for the excess hinge risk.”
Comparing naive Bayes, decision trees, and SVM with AUC and accuracy (2003, result): “Our results on SVM may be inconsistent with some other comparisons involving SVM which showed superiority of SVM over other learning algorithms [17, 13, 3].”
In Defense of One-Vs-All Classification (2004, background): “Using arguments along the same lines of those in Lin (1999), it is shown that the asymptotic solution to this regularization problem (again ignoring the λ term and the fact that the functions must live in the RKHS) is fi(x) = 1 if i = arg maxj=1,.”