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Abstract: This paper focuses on a general setup for obtaining sample size lower bounds for learning concept classes under fixed distribution laws in an extended PAC learning framework. These bounds do not depend on the running time of learning procedures and are informationtheoretic in nature. They are based on incompressibility methods drawn from Kolmogorov Complexity and Algorithmic Probability theories. 1 INTRODUCTION In recent years the job of algorithmically understanding data, above and beyond... (Update)
Context of citations to this paper: More
.... space [Hof90] whereas Apolloni and Gentile suggest to measure the complexity of a concept class by the complexity of its covers [AG98]. These notions are closely related to the Vapnik Chervonenkis dimension which captures somehow the capacity of a concept class and thus...
...13) Remark 2.1. Left inequality can be improved using the VC complexity index and related information theory results; see for instance [2]. Furthermore, note that fairly strong surjectivity requirements are not a heavy limitation to the learning algorithms; they essentially...
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2: A formal theory of inductive inference (context) - Solomono - 1964
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BibTeX entry: (Update)
B. Apolloni and C. Gentile, Sample size lower bounds in pac learning by algorithmic complexity theory, 1998. http://citeseer.ist.psu.edu/apolloni98sample.html More
@article{ apolloni98sample,
author = "B. Apolloni and C. Gentile",
title = "Sample size lower bounds in {PAC} learning by {Algorithmic Complexity Theory}",
journal = "Theoretical Computer Science",
volume = "209",
number = "1--2",
pages = "141--162",
year = "1998",
url = "citeseer.ist.psu.edu/apolloni98sample.html" }
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