Abstract
These recollections about the origins of VC theory were written by Alexey Chervonenkis in 2004 for several colleagues and not intended for publication. They are now published for the first time. (Eds.) Translated by Vladimir Vovk.
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Notes
- 1.
In fact, in the setting of the problem as described here it is also true that
$$\begin{aligned} N&\le 2^{l}\\ l&\ge \log _2N \end{aligned}$$(\(\log _2\) standing for base 2 logarithm). Alexey’s weaker (but sufficient for his purpose) bound \((\log _2N)/(n+1)\) also holds in a situation that is easier for the learner: he knows the true decision rule, and his goal is to choose a training sequence \(x_1,\ldots ,x_l\) proving that the known decision rule is indeed the true one (in the sense that the observed \(\omega _1,\ldots ,\omega _l\) is compatible with only one rule). (Eds.)
- 2.
Here Alexey jokingly refers to Aizerman, Braverman, and Rozonoer (members of Aizerman’s laboratory at the Institute of Control Sciences) as the Aizermans. (Eds.)
- 3.
The Third All-Union Conference on the Theory of Automatic Control, Odessa, September 20–26, 1965. (Eds.)
- 4.
Alexey means the method of conformal prediction; the first monograph [5] on the subject was being prepared by his colleagues at that time. (Eds.)
References
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Vapnik, V.N., Chervonenkis, A.Y.: Algorithms with complete memory and recurrent algorithms in pattern recognition learning. Autom. Remote Control 29, 606–616 (1968)
Vapnik, V.N., Chervonenkis, A.Y.: On the uniform convergence of the frequencies of occurrence of events to their probabilities. Dokl. Akad. Nauk SSSR 181, 781–783 (1968) (Sov. Math. Dokl. 9, 915–918)
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)
Vovk, V., Gammerman, A., Shafer, G.: Algorithmic Learning in a Random World. Springer, New York (2005)
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Chervonenkis, A. (2015). Chervonenkis’s Recollections. In: Vovk, V., Papadopoulos, H., Gammerman, A. (eds) Measures of Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-21852-6_1
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