Online nonparametric regression with Sobolev kernels
- University of Potsdam（波茨坦大学）
- Centre de Recherche INRIA de Paris（法国国家信息与自动化研究所巴黎研究中心）
- IRT Saint Exupéry（圣埃克苏佩里技术研究院）
- Institut de Mathématiques de Toulouse（图卢兹数学研究所）
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英文摘要：
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 $W_{p}^β(\mathcal{X})$, $p\geq 2, β>\frac{d}{p}$. The upper bounds are supported by the minimax regret analysis, which reveals that in the cases $β> \frac{d}{2}$ 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.
