Bounds on Error Expectation for Support Vector Machines

By Vladimir Naumovich Vapnik, Olivier Chapelle. Neural Computation, 2000

673 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/143bd9651b1f31d8f51a26d6e99ffbbc76deb798

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Citations in the corpus

Feature selection via sensitivity analysis of SVM probabilistic outputs (2008, background): “As suggested by Weston et al. (2001), the idea could also be extended to the span estimate (Vapnik and Chapelle 2000) which is a tighter upper bound on the expected generalization error.”
Combining SVMs with Various Feature Selection Strategies (2006, background): “For a hard-margin SVM, its loo error is bounded by a smoother function [36, 37]: loo ≤ 4‖w‖R, (3.”
Supervised classification and mathematical optimization (2013, background): “The origins of SVMs are found in the literature of Statistical Learning, where it is shown that the probability of misclassifying a forthcoming individual can be bounded by a decreasing function of the margin, this bound being independent of the data distribution, [231].”
Online Machine Learning in Big Data Streams (2018, background): “pport vectors, others need to be discarded ﬁrst, and a i need to be updated. To decide which support vector to discard, the deﬁnition of the span and the Sspan of the support vectors deﬁned by Vapnik [221] can be used. The span of a support vector is the minimum distance of the vector from a certain”
Efficient tuning of SVM hyperparameters using radius/margin bound and iterative algorithms (2002, background): “It was shown by Vapnik and Chapelle [ 14 ] that the following bound holds:”
Analysis of the AutoML Challenge Series 2015-2018 (2019, background): “Other approaches minimize an approximation or an upper bound of the leaveone-out error, instead of its exact form (Opper and Winther, 2000; Vapnik and Chapelle, 2000).”
Exploring the extremes of sequence/structure space with ensemble fold recognition in the program Phyre (2008, methodology): “As an alternative method of circumventing the problem of component selection we also investigate the use of Support Vector Machines (SVMs)30 to classify candidate fold matches as correct or incorrect using information from all the methods simultaneously.”
Automated Machine Learning: Methods, Systems, Challenges (2019, neutral): “As a simple, yet effective baseline that can be trivially included in empirical studies, Jamieson and Recht [68] suggest to compare against different parallelization levels of random search to demonstrate the speedups over regular random search.”
A nested heuristic for parameter tuning in Support Vector Machines (2014, methodology): “Some papers take as surrogate â(·) of the accuracy a(·) a distribution-free, but kernel-specific, bound on the probability of misclassification, see [12, 18, 48].”