An approach to the Gaussian RBF kernels via Fock spaces

Abstract: In this talk we use methods from the Fock spaces theory in order to prove several results on the Gaussian RBF kernels in the complex case. The latter is one of the most used kernels in modern machine learning kernel methods, and support vector machines (SVMs) classification algorithms. It turns out that complex analysis techniques allow us to consider several notions linked to the RBF kernels like the feature space and the feature map, using the so-called Segal-Bargmann transform. We show also that the RBF kernels can be related to some important operators in quantum mechanics and time frequency analysis, specifically, we prove different connections of such kernels with creation, annihilation, Fourier, translation, modulation and Weyl operators. A semi-group property will be proved in the case of Weyl operators. This is a joint work with Daniel Alpay, Fabrizio Colombo and Irene Sabadini.

analysis of PDEsclassical analysis and ODEscomplex variablesdifferential geometrydynamical systemsfunctional analysismetric geometry

Audience: researchers in the topic

Analysis and Geometry Seminar