## Title data

Köhler, Hannes ; Christmann, Andreas:

**Total Stability of SVMs and Localized SVMs.**

*In:* Journal of Machine Learning Research.
Vol. 23
(2022)
Issue 100
.
- pp. 1-41.

ISSN 1533-7928

## Abstract in another language

Regularized kernel-based methods such as support vector machines (SVMs) typically depend on the underlying probability measure P (respectively an empirical measure Dn in applications) as well as on the regularization parameter λ and the kernel k. Whereas classical statistical robustness only considers the effect of small perturbations in P, the present paper investigates the influence of simultaneous slight variations in the whole triple (P,λ,k), respectively (Dn,λn,k), on the resulting predictor. Existing results from the literature are considerably generalized and improved. In order to also make them applicable to big data, where regular SVMs suffer from their super-linear computational requirements, we show how our results can be transferred to the context of localized learning. Here, the effect of slight variations in the applied regionalization, which might for example stem from changes in P respectively Dn, is considered as well.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Keywords: | statistical robustness; stability; localized learning; kernel methods; big data |

Institutions of the University: | Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics VII - Stochastics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics VII - Stochastics > Chair Mathematics VII - Stochastics - Univ.-Prof. Dr. Andreas Christmann |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 12 May 2022 06:27 |

Last Modified: | 12 May 2022 06:27 |

URI: | https://eref.uni-bayreuth.de/id/eprint/69576 |