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Random Fourier Features for Operator-Valued Kernels

Sujet: Operator-valued kernel, Random Fourier Features, [INFO] Computer Science [cs], [MATH] Mathematics [math]
Auteur: Brault, Romain, d'Alché-Buc, Florence
Résumé: Many problems in Machine Learning can be cast into vector-valued functions approximation. Operator-Valued Kernels Operator-Valued Kernels and vector-valued Reproducing Kernel Hilbert Spaces provide a theoretical and versatile framework to address that issue, extending nicely the well-known setting of scalar-valued kernels. However large scale applications are usually not affordable with these tools that require an important computational power along with a large memory capacity. In this paper, we aim at providing scalable methods that enable efficient regression with Operator-Valued Kernels. To achieve this goal, we extend Random Fourier Features, an approximation technique originally introduced for translation-invariant scalar-valued kernels, to translation-invariant Operator-Valued Kernels. We develop all the machinery in the general context of Locally Compact Abelian groups, allowing for coping with Operator-Valued Kernels. Eventually, the provided approximated operator-valued feature map converts the nonparametric kernel-based model into a linear model in a finite-dimensional space.
Editeur: HAL CCSD