F ¨ Ur Mathematik in Den Naturwissenschaften Leipzig Power Series Kernels Power Series Kernels
نویسنده
چکیده
We introduce a class of analytic positive definite multivariate kernels which includes infinite dot product kernels as sometimes used in machine learning, certain new nonlinearly factorizable kernels and a kernel which is closely related to the Gaussian. Each such kernel reproduces in a certain 'native' Hilbert space of multivariate analytic functions. If functions from this space are interpolated in scattered locations by translates of the kernel, we prove spectral convergence rates of the interpolants and all derivatives. By truncation of the power series of the kernel-based interpolants, we constructively generalize the classical Bernstein theorem concerning polynomial approximation of analytic functions to the multi-variate case. An application to machine learning algorithms is presented.
منابع مشابه
Max - Planck - Institut für Mathematik in den Naturwissenschaften Leipzig Robustness and Conditional Independence Ideals
We study notions of robustness of Markov kernels and probability distribution of a system that is described by n input random variables and one output random variable. Markov kernels can be expanded in a series of potentials that allow to describe the system’s behaviour after knockouts. Robustness imposes structural constraints on these potentials. Robustness of probability distributions is def...
متن کاملF Ur Mathematik in Den Naturwissenschaften Leipzig Interacting Quantum Fields on a Curved Background
متن کامل
F Ur Mathematik in Den Naturwissenschaften Leipzig Dynamical Correlations in a Half--lled Landau Level
متن کامل