A Spectral Analysis of Dot-product Kernels

Meyer Scetbon, Zaid Harchaoui
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:3394-3402, 2021.

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 this Paper

BibTeX
@InProceedings{pmlr-v130-scetbon21b, title = { A Spectral Analysis of Dot-product Kernels }, author = {Scetbon, Meyer and Harchaoui, Zaid}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {3394--3402}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/scetbon21b/scetbon21b.pdf}, url = {https://proceedings.mlr.press/v130/scetbon21b.html}, 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. } }
Endnote
%0 Conference Paper %T A Spectral Analysis of Dot-product Kernels %A Meyer Scetbon %A Zaid Harchaoui %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-scetbon21b %I PMLR %P 3394--3402 %U https://proceedings.mlr.press/v130/scetbon21b.html %V 130 %X 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.
APA
Scetbon, M. & Harchaoui, Z.. (2021). A Spectral Analysis of Dot-product Kernels . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:3394-3402 Available from https://proceedings.mlr.press/v130/scetbon21b.html.

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