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Abstract: Vapnik-Chervonenkis (VC) dimension appears as one of the central concepts in Statistical Learning Theory (Vapnik 1995, 1998). Though it led to some important mathematical results and contributed to the development of a new class of very efficient algorithms, the Support Vector Machines, there are few attempts (Vapnik et al., 1994, Vapnik 1995) to turn VC dimension into a practical notion that could be measured or observed in particular learning problems. In the presentpaper,we review some... (Update)
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BibTeX entry: (Update)
@misc{ vayatis-how,
author = "Nicolas Vayatis and Robert Azencott",
title = "How to Estimate the Vapnik-Chervonenkis Dimension of Support Vector Machines
Through Simulations?",
url = "citeseer.ist.psu.edu/279153.html" }
Citations (may not include all citations):1291 The Nature of Statistical Learning Theory (context) - Vapnik - 1995
947 StatisticalLearning Theory (context) - Vapnik - 1998
348 Estimation of Dependences Based on Empirical Data (context) - Vapnik - 1982
93 Learning from Data - Concepts (context) - Cherkassky, Mulier - 1998
51 Sharper Bounds for Gaussian and Empirical Processes (context) - Talagrand - 1994
47 Rigorous Learning Curve Bounds from Statistical Mechanics - Haussler, Kearns et al. - 1996
31 Necessary and Sufficient Conditions for the Uniform Converge.. (context) - Vapnik, Ya - 1981
29 Measuring the VC-Dimension of a Learning Machine - Vapnik, Levin et al. - 1994
14 Prediction of GeneralizationAbility in Learning Machines (context) - Cortes - 1995
4 Grandes D'eviations (context) - Azencott - 1978
4 AProbabilistic Theory of Pattern Recognition (context) - Devroye, Gyorfi et al. - 1996
3 the Uniform ConvergenceofRelative Frequencies of Events to t.. (context) - Vapnik, Ya et al. - 1971
2 Distribution-DependentVapnik-Chervonenkis Bounds - Vayatis, Azencott - 1999
2 Learning Complexity and Pattern Recognition (context) - Vayatis - 1999
1 Large Deviations Bounds for Empirical Processes - Azencott, Vayatis - 1999
1 Nonlinear Principal Component Analysis as a Kernel Eigenvalu.. (context) - Scholkopf, Smolla et al. - 1998
1 How Tight Are the Vapnik-ChervonenkisBounds (context) - Cohn, Tesauro - 1992
1 Separating Formal Bounds from Practicval PerformanceinLearni.. (context) - Cohn - 1992
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