A Spectral Analysis of Dot-product Kernels

被引：0

作者：

Scetbon, Meyer ^{[1
]}

Harchaoui, Zaid ^{[2
]}

机构：

[1] CREST, ENSAE, Palaiseau, France

[2] Univ Washington, Seattle, WA 98195 USA

来源：

24TH INTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS (AISTATS) | 2021年 / 130卷

关键词：

INTEGRAL-OPERATORS; REGULARIZATION; CLASSIFICATION;

D O I：

暂无

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

We present eigenvalue decay estimates of integral operators associated with compositional dot-product kernels. The estimates improve on previous ones established for power series kernels on spheres. This allows us to obtain the volumes of balls in the corresponding reproducing kernel Hilbert spaces. We discuss the consequences on statistical estimation with compositional dot product kernels and highlight interesting trade-offs between the approximation error and the statistical error depending on the number of compositions and the smoothness of the kernels.

引用

页数：11

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