6 papers
Gaussian Processes with Sample Paths in Reproducing Kernel Banach Spaces
Toni Karvonen, Rasmus Kleist Hørlyck Sørensen
We investigate the connection between Gaussian processes and Gaussian random elements in reproducing kernel Banach spaces. We show that the covariance operator of a weak second-ord…
Piecewise linear interpolation via kernels
Toni Karvonen, Gabriele Santin, Tizian Wenzel
We consider piecewise linear interpolation from the perspective of kernel interpolation and quadrature. If the Sobolev space is equipped with a suitable inner product…
Maximum mean discrepancies of Farey sequences
Toni Karvonen, Anatoly Zhigljavsky
We identify a large class of positive-semidefinite kernels for which a certain polynomial rate of convergence of maximum mean discrepancies of Farey sequences is equivalent to the…
A debiased Bernoulli factory and unbiased estimation of a probability
Jere Koskela, Toni Karvonen, Krzysztof ÅatuszyÅski +1
Given a known function and a random but almost surely finite number of independent, Ber-distributed random variables with unknown , w…
Smoothness Estimation for Whittle-Matérn Processes on Closed Riemannian Manifolds
Moritz Korte-Stapff, Toni Karvonen, Eric Moulines
The family of Matérn kernels are often used in spatial statistics, function approximation and Gaussian process methods in machine learning. One reason for their popularity is the…
General superconvergence for kernel-based approximation
Toni Karvonen, Gabriele Santin, Tizian Wenzel
Kernel interpolation is a fundamental technique for approximating functions from scattered data, with a well-understood convergence theory when interpolating elements of a reproduc…