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Matematicheskie Zametki, 2012, Volume 91, Issue 6, Pages 853–860
DOI: https://doi.org/10.4213/mzm9388 (Mi mzm9388) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Bracketing Entropy and VC-Dimension

Yu. V. Malykhin

Steklov Mathematical Institute of the Russian Academy of Sciences
Full-text PDF (478 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm9388
Abstract: We study the relationship between two characteristics of functional classes, pseudodimension and bracketing entropy. (Pseudodimension is a generalization of VC-dimension to classes of functions. Bracket entropy characterizes the $L_1$-error of one-sided approximation of a class by finite sets.) It is shown that classes of continuous functions with finite pseudodimension possess a finite bracketing $\varepsilon$-entropy for any $\varepsilon>0$. We establish a general result concerning the relationship between the VC-dimension of classes of sets and their bracketing entropy.
Keywords: bracketing entropy, pseudodimension, VC-dimension, measurable function, bracketing compactness of sets, random variable, probability space.
Funding agency Grant number
Russian Foundation for Basic Research 09-01-12173-офи-м
Received: 18.11.2010
English version:
Mathematical Notes, 2012, Volume 91, Issue 6, Pages 800–807
DOI: https://doi.org/10.1134/S0001434612050264
Bibliographic databases:
Document Type: Article
UDC: 517.518.8
Language: Russian
Citation: Yu. V. Malykhin, “Bracketing Entropy and VC-Dimension”, Mat. Zametki, 91:6 (2012), 853–860; Math. Notes, 91:6 (2012), 800–807
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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