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Abstract: : We give an analysis of the generalization error of cross validation in terms of two natural measures of the difficulty of the problem under consideration: the approximation rate (the accuracy to which the target function can be ideally approximated as a function of the number of hypothesis parameters), and the estimation rate (the deviation between the training and generalization errors as a function of the number of hypothesis parameters). The approximation rate captures the complexity of... (Update)
Context of citations to this paper: More
...of model selection which has be widely studied and criticized. Foundational papers include [2, 3, 4] and recent contributions include [5, 6]. In this paper, our emphasis is on exhibiting a simple and general scaling law which can guide experimentalists in pattern recognition:...
...with k = n l decreasing. The optimal choice of l and k depend on the learner L, the hypothesis space H, and the learning task Pr( x; y) [Kearns, 1996]. Nevertheless, there are good heuristics for selecting reasonable values for l and k [Kearns, 1996] Let s nally also look at...
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9: An Experimental and Theoretical Comparison of Model Selection Methods - Kearns, Mansour et al.
6: Statistical Learning Theory (context) - Vapnik
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BibTeX entry: (Update)
Kearns, M. J. (1996). A bound on the error of Cross Validation using the approximation and estimation rates, with consequences for the training-test split. In Advances in Neural Information Processing Systems 8, pages 183--189. Morgan Kaufmann. http://citeseer.ist.psu.edu/article/kearns96bound.html More
@inproceedings{ kearns96bound,
author = "Michael Kearns",
title = "A Bound on the Error of Cross Validation Using the Approximation and Estimation Rates, with Consequences for the Training-Test Split",
booktitle = "Advances in Neural Information Processing Systems",
volume = "8",
publisher = "The {MIT} Press",
editor = "David S. Touretzky and Michael C. Mozer and Michael E. Hasselmo",
pages = "183--189",
year = "1996",
url = "citeseer.ist.psu.edu/article/kearns96bound.html" }
Citations (may not include all citations):454 the uniform convergence of relative frequencies of events to.. (context) - Vapnik, Chervonenkis - 1971
417 Stochastic Complexity in Statistical Inquiry (context) - Rissanen - 1989
348 Estimation of Dependences Based on Empirical Data (context) - Vapnik - 1982
258 Cross-validatory choice and assessment of statistical predic.. (context) - Stone - 1974
214 Universal approximation bounds for superpositions of a sigmo.. (context) - Barron - 1991
101 Minimum complexity density estimation (context) - Barron, Cover - 1991
66 An experimental and theoretical comparison of model selectio.. - Kearns, Mansour et al. - 1995
58 Statistical mechanics of learning from examples (context) - Seung, Sompolinsky et al. - 1992
23 Asymptotics for and against cross-validation (context) - Stone - 1977
8 Rigourous learning curve bounds from statistical mechanics (context) - Haussler, Kearns et al. - 1994
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