Vapnik-Chervonenkis Dimension of Axis-Parallel Cuts

Abstract : The Vapnik-Chervonenkis (VC) dimension of the set of half-spaces of R^d with frontiers parallel to the axes is computed exactly. It is shown that it is much smaller than the intuitive value of d. A good approximation based on the Stirling's formula proves that it is more likely of the order log_2(d). This result may be used to evaluate the performance of classifiers or regressors based on dyadic partitioning of R^d for instance. Algorithms using axis-parallel cuts to partition R^d are often used to reduce the computational time of such estimators when d is large.
Type de document :
Pré-publication, Document de travail
MAP5 2012-07. 2012
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https://hal.archives-ouvertes.fr/hal-00675553
Contributeur : Servane Gey <>
Soumis le : mercredi 19 octobre 2016 - 17:50:14
Dernière modification le : samedi 22 octobre 2016 - 01:07:02

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VC_CARTv3.pdf
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  • HAL Id : hal-00675553, version 3
  • ARXIV : 1203.0193

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Servane Gey. Vapnik-Chervonenkis Dimension of Axis-Parallel Cuts. MAP5 2012-07. 2012. <hal-00675553v3>

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