Vapnik-Chervonenkis Dimension of Axis-Parallel Cuts

Servane Gey (1)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

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.

Mots clés: Vapnik-Chervonenkis dimension; axis-parallel cuts

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Servane Gey. Vapnik-Chervonenkis Dimension of Axis-Parallel Cuts. 2012. ⟨hal-00675553v3⟩