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2013 | OriginalPaper | Chapter

1. In Hindsight: Doklady Akademii Nauk SSSR, 181(4), 1968

Author : Léon Bottou

Published in: Empirical Inference

Publisher: Springer Berlin Heidelberg

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Abstract

This short contribution presents the first paper in which Vapnik and Chervonenkis describe the foundations of Statistical Learning Theory (Vapnik, Chervonenkis (1968) Proc USSR Acad Sci 181(4): 781–783).

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next chapter On the Uniform Convergence of the Frequencies of Occurrence of Events to Their Probabilities
Footnotes
1
A slightly modified version of this English translation of the 1968 paper follows this brief introduction.
 
2
Sauer motivates his work with a single sentence, “P. Erdös transmitted to me in Nice the following question: is it true that [statement of the theorem]”, without attributing the conjecture to anyone. Sauer kindly replied to my questions with interesting details: “When I proved that Lemma, I was very young, and have since moved my interest more towards model theoretic type questions. Erdös visited Calgary and told me at that occasion that this question had come up. But I do not remember the context in which he claimed that it did come up. I then produced a proof and submitted it as a paper. I did not know about that question before the visit by Erdös,” and “the only thing I can contribute is that I believe Weiss in Israel told me that Shelah had asked Perles to prove such a Lemma, which he did, and subsequently both forgot about it and Shelah then asked Perles again to prove that Lemma.”
 
3
In fact, Sauer gives the optimal bound (Dudley, personal communication).
 
Literature
1.
Aizerman, M.A., Braverman, É.M., Rozonoér, L.I.: Theoretical foundations of the potential function method in pattern recognition learning. Autom. Remote Control 25, 821–837 (1964)
2.
Cantelli, F.P.: Sulla determinazione empirica della legi di probabilita. Giornale dell’Istituto Italiano degli Attuari 4, 421–424 (1933)MATH
3.
Dudley, R.M.: Mathematical Reviews MR0231431 (37#6986) (1969)
4.
Fel’dbaum, A.A.: Optimal Control Systems. Nauka, Moscow (1963). English translation: Academic, New York, 1965
5.
6.
Shelah, S.: A combinatorial problem: stability and order for models and theories in infinitary languages. Pac. J. Math. 41, 247–261 (1972)CrossRefMATH
7.
Tsypkin, Y.: Adaptation and Learning in Automatic Systems. Nauka, Moscow (1969). English translation: Academic, New York, 1971
8.
Tsypkin, Y.: Foundations of the Theory of Learning Systems. Nauka, Moscow (1970). English translation: Academic, New York, 1973
9.
Vapnik, V.N.: Estimation of Dependences Based on Empirical Data. Information Science and Statistics. Springer, Berlin/New York (1982)MATH
10.
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: Soviet Math. Dokl. 9, 915–918 (1968)
11.
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)MathSciNetCrossRefMATH
12.
Vapnik, V.N., Chervonenkis, A.Y.: Theory of pattern recognition. Nauka, Moscow (1974). German translation: Akademie-Verlag, Berlin, 1979
Metadata
Title
In Hindsight: Doklady Akademii Nauk SSSR, 181(4), 1968
Author
Léon Bottou
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Empirical Inference

Print ISBN: 978-3-642-41135-9

Electronic ISBN: 978-3-642-41136-6

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-41136-6_1

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