A Spectral Analysis of Dot-Product Kernels
Abstract
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.
Cite
Text
Scetbon and Harchaoui. "A Spectral Analysis of Dot-Product Kernels." Artificial Intelligence and Statistics, 2021.Markdown
[Scetbon and Harchaoui. "A Spectral Analysis of Dot-Product Kernels." Artificial Intelligence and Statistics, 2021.](https://mlanthology.org/aistats/2021/scetbon2021aistats-spectral/)BibTeX
@inproceedings{scetbon2021aistats-spectral,
title = {{A Spectral Analysis of Dot-Product Kernels}},
author = {Scetbon, Meyer and Harchaoui, Zaid},
booktitle = {Artificial Intelligence and Statistics},
year = {2021},
pages = {3394-3402},
volume = {130},
url = {https://mlanthology.org/aistats/2021/scetbon2021aistats-spectral/}
}