The VC-dimension of axis-parallel boxes on the Torus

The VC-dimension of axis-parallel boxes on the Torus

We show in this paper that the VC-dimension of the family of d-dimensional axis-parallel boxes and cubes on the d-dimensional torus are both asymptotically dlog2⁡d. This is especially surprising as in most other examples the VC-dimension usually grows linearly with d in similar settings.

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of Complexity 2022-02, Vol.68, p.101600, Article 101600
Hauptverfasser: Gillibert, P., Lachmann, T., Müllner, C.
Format: Artikel
Sprache:eng
Schlagworte:
Discrepancy Theory
Machine Learning
Measure Theory
Points on the Torus
Sample Compression
VC-dimension
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We show in this paper that the VC-dimension of the family of d-dimensional axis-parallel boxes and cubes on the d-dimensional torus are both asymptotically dlog2⁡d. This is especially surprising as in most other examples the VC-dimension usually grows linearly with d in similar settings.
ISSN:0885-064X
1090-2708
DOI:10.1016/j.jco.2021.101600