ML Anthology

On the Vgamma Dimension for Regression in Reproducing Kernel Hilbert Spaces

Theodoros Evgeniou, Massimiliano Pontil
ALT 1999 pp. 106-117
doi:10.1007/3-540-46769-6_9 /alt/1999/evgeniou1999alt-vgamma/

Abstract

This paper presents a computation of the V _γ dimension for regression in bounded subspaces of Reproducing Kernel Hilbert Spaces (RKHS) for the Support Vector Machine (SVM) regression ε -insensitive loss function L _ε, and general L _p loss functions. Finiteness of the V _γ dimension is shown, which also proves uniform convergence in probability for regression machines in RKHS subspaces that use the L _ε or general L _p loss functions. This paper presents a novel proof of this result. It also presents a computation of an upper bound of the V _γ dimension under some conditions, that leads to an approach for the estimation of the empirical V _γ dimension given a set of training data.

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Cite

Text

Evgeniou and Pontil. "On the Vgamma Dimension for Regression in Reproducing Kernel Hilbert Spaces." International Conference on Algorithmic Learning Theory, 1999. doi:10.1007/3-540-46769-6_9

Markdown

[Evgeniou and Pontil. "On the Vgamma Dimension for Regression in Reproducing Kernel Hilbert Spaces." International Conference on Algorithmic Learning Theory, 1999.](https://mlanthology.org/alt/1999/evgeniou1999alt-vgamma/) doi:10.1007/3-540-46769-6_9

BibTeX

@inproceedings{evgeniou1999alt-vgamma,
  title     = {{On the Vgamma Dimension for Regression in Reproducing Kernel Hilbert Spaces}},
  author    = {Evgeniou, Theodoros and Pontil, Massimiliano},
  booktitle = {International Conference on Algorithmic Learning Theory},
  year      = {1999},
  pages     = {106-117},
  doi       = {10.1007/3-540-46769-6_9},
  url       = {https://mlanthology.org/alt/1999/evgeniou1999alt-vgamma/}
}