Online nonparametric regression with Sobolev kernels

Autor:	Zadorozhnyi, Oleksandr, Gaillard, Pierre, Gerschinovitz, Sebastien, Rudi, Alessandro
Rok vydání:	2021
Předmět:	Mathematics - Statistics Theory Computer Science - Machine Learning Statistics - Machine Learning
Druh dokumentu:	Working Paper
Popis:	In this work we investigate the variation of the online kernelized ridge regression algorithm in the setting of $d-$dimensional adversarial nonparametric regression. We derive the regret upper bounds on the classes of Sobolev spaces $W_{p}^{\beta}(\mathcal{X})$, $p\geq 2, \beta>\frac{d}{p}$. The upper bounds are supported by the minimax regret analysis, which reveals that in the cases $\beta> \frac{d}{2}$ or $p=\infty$ these rates are (essentially) optimal. Finally, we compare the performance of the kernelized ridge regression forecaster to the known non-parametric forecasters in terms of the regret rates and their computational complexity as well as to the excess risk rates in the setting of statistical (i.i.d.) nonparametric regression. Comment: 40 pages, 5 figures, 3 tables (version 2)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2102.03594 Zobrazit plný text záznamu View this record from Arxiv