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Published in:
In Hindsight: Doklady Akademii Nauk SSSR, 181(4), 1968 Read chapter Read first chapter

2013 | OriginalPaper | Chapter

6. On the Relations and Differences Between Popper Dimension, Exclusion Dimension and VC-Dimension

Authors : Yevgeny Seldin, Bernhard Schölkopf

Published in: Empirical Inference

Publisher: Springer Berlin Heidelberg

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Abstract

A high-level relationPopper dimension—( Exclusion dimension—( VC dimension—( between Karl Popper’s ideas on “falsifiability of scientific theories” and the notion of “overfitting”Overfitting in statistical learning theory can be easily traced. However, it was pointed out that at the level of technical details the two concepts are significantly different. One possible explanation that we suggest is that the process of falsification is an active process, whereas statistical learning theory is mainly concerned with supervised learningSupervised learning, which is a passive process of learning from examples arriving from a stationary distribution. We show that concepts that are closer (although still distant) to Karl Popper’s definitions of falsifiability can be found in the domain of learning using membership queries, and derive relations between Popper’s dimension, exclusion dimension, and the VC-dimensionVC dimension.

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Corfield, D., Schölkopf, B., Vapnik, V.N.: Falsification and statistical learning theory: comparing the Popper and Vapnik-Chervonenkis dimensions. J. Gen. Philos. Sci. 40, 51–58 (2009)CrossRef
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Metadata
Title
On the Relations and Differences Between Popper Dimension, Exclusion Dimension and VC-Dimension
Authors
Yevgeny Seldin
Bernhard Schölkopf
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_6

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