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Published in:
Chervonenkis’s Recollections Read chapter Read first chapter

2015 | OriginalPaper | Chapter

9. Making Vapnik–Chervonenkis Bounds Accurate

Author : Léon Bottou

Published in: Measures of Complexity

Publisher: Springer International Publishing

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Abstract

This chapter shows how returning to the combinatorial nature of the Vapnik–Chervonenkis bounds provides simple ways to increase their accuracy, take into account properties of the data and of the learning algorithm, and provide empirically accurate estimates of the deviation between training error and test error.

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previous chapter Predictive Complexity for Games with Finite Outcome Spaces
next chapter Comment: TransductiveTransduction PAC-Bayes Bounds Seen as a Generalization of Vapnik–Chervonenkis Bounds
Literature
1.
Bloom, D.: A birthday problem. Am. Math. Mon. 80, 1141–1142 (1973)
2.
Bottou, L., Cortes, C., Denker, J.S., Drucker, H., Guyon, I., Jackel, L.D., LeCun, Y., Muller, U.A., Säckinger, E., Simard, P., Vapnik, V.N.: Comparison of classifier methods: a case study in handwritten digit recognition. In: Proceedings of the 12th IAPR International Conference on Pattern Recognition, vol. 2, pp. 77–82. IEEE (1994)
3.
4.
5.
Bousquet, O.: Concentration inequalities and empirical processes theory applied to the analysis of learning algorithms. Ph.D. thesis, École Polytechnique (2002)
6.
Dudley, R.M.: The sizes of compact subsets of Hilbert space and continuity of Gaussian processes. J. Funct. Anal. 1(3), 290–330 (1967)MATHMathSciNetCrossRef
7.
8.
Haussler, D.: Sphere packing numbers for subsets of the boolean \(n\)-cube with bounded Vapnik-Chervonenkis dimension. J. Comb. Theory Ser. A 69(2), 217–232 (1995)MATHMathSciNetCrossRef
9.
Kanerva, P.: Sparse Distributed Memory. MIT Press, Cambridge (1988)MATH
10.
LeCun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient based learning applied to document recognition. Proc. IEEE 86(11), 2278–2324 (1998)CrossRef
11.
LeCun, Y., Bottou, L., Orr, G.B., Müller, K.R.: Efficient backprop. In: Orr, G.B., Müller, K.R. (eds.) Neural Networks, Tricks of the Trade. Lecture Notes in Computer Science, vol. 1524. Springer, Berlin (1998)
12.
Shawe-Taylor, J., Bartlett, P., Williamson, R., Anthony, M.: Structural risk minimization over data-dependent hierarchies. IEEE Trans. Inf. Theory 44(5), 1926–1940 (1998)MATHMathSciNetCrossRef
13.
Talagrand, M.: The Generic Chaining: Upper and Lower Bounds of Stochastic Processes. Springer, Berlin (2005)
14.
15.
Vapnik, V.N.: Estimation of Dependences based on Empirical Data. Springer Series in Statistics. Springer, Berlin (1982)
16.
Vapnik, V.N.: Statistical Learning Theory. Wiley, New York (1998)MATH
17.
Vapnik, V.N., Chervonenkis, A.Y.: A note on one class of perceptrons. Autom. Remote Control 25(1), 774–780 (1964)
18.
Vapnik, V.N., Chervonenkis, A.Y.: On the uniform convergence of relative frequencies of events to their probabilities. Proc. USSR Acad. Sci. 181(4), 781–783 (1968) (English translation: Sov. Math. Dokl. 9(4), 915–918 (1968))
19.
Vapnik, V.N., Chervonenkis, A.Y.: On the uniform convergence of relative frequencies of events to their probabilities. Theory Probab. Appl. 16(2), 264–281 (1971) (This volume, Chap. 3)
20.
Vapnik, V.N., Chervonenkis, A.Y.: Теория распознавания образов: Статистические проблемы обучения (Theory of Pattern Recognition: Statistical Problems of Learning: in Russian). Nauka, Moscow (1974). German translation: Theorie der Zeichenerkennung, transl. K.G. Stöckel and B. Schneider, ed. S. Unger and B. Fritzsch, Akademie Verlag, Berlin (1979)
21.
Vapnik, V.N., Lerner, A.Y.: Pattern recognition using generalized portrait method. Autom. Remote Control 24(6), 774–780 (1963)
22.
Vapnik, V.N., Levin, E., LeCun, Y.: Measuring the VC-dimension of a learning machine. Neural Comput. 6(5), 851–876 (1994)CrossRef
23.
Vorontsov, K.V.: Combinatorial substantiation of learning algorithms. Comput. Math. Math. Phys. 44(11), 1997–2009 (2004)MathSciNet
24.
Vorontsov, K.V.: Exact combinatorial bounds on the probability of overfitting for empirical risk minimization. Pattern Recognit. Image Anal. Adv. Math. Theory Appl. 20(3), 269–285 (2010)
Metadata
Title
Making Vapnik–Chervonenkis Bounds Accurate
Author
Léon Bottou
Copyright Year
2015
Book
Measures of Complexity

Print ISBN: 978-3-319-21851-9

Electronic ISBN: 978-3-319-21852-6

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-21852-6_9

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