Kernel Approximation and Gaussian Processes: Integrating and Expanding Perspectives (26w5635)

The Banff International Research Station will host the "Kernel Approximation and Gaussian Processes: Integrating and Expanding Perspectives" workshop in Banff from September 13 - 18, 2026.

The fields of kernel approximation and Gaussian processes have evolved, mostly independently, over the past few decades
to become mature subjects in numerical analysis and statistics/applied probability,
respectively.
The two fields have natural affinities, both by relying on a common mathematical machinery of reproducing kernel Hilbert spaces and positive definite functions,
and by treating a diverse assortment of scientific applications.
A hallmark problem for kernels is the modeling of irregularly sampled, deterministic data,
but kernels are also heavily employed in the simulation of a range of phenomena from atmospheric flows to financial forecasting.;
a key feature of kernel approximation is the ability to deliver solutions to computational problems without requiring costly underlying geometric structures like meshing.
Gaussian processes have traditionally focused on regression, classification, and learning of the underlying probability distribution from random samples, although recent activity has focused on
successful undertakings in interpretable and explainable machine learning,
inverse problems and partial differential equations with stochastic parameters.
Despite their different languages and different objects of interest,
the fields share a similar collection of important, challenging theoretical and computational problems.

This workshop will bring together experts from both fields
to exchange ideas, to present new developments to theory, applications,
computational problems and software, to promote research synergies, and to tackle open problems fundamental to both subjects and with wide applications to other fields in science and engineering.
A key aspect is to provide a segue between
fields which is suitable to researchers who are
unfamiliar with the core problems of their counterparts.
This will be especially helpful to students and early career researchers who wish to be connected to other problems and approaches. In addition to providing a much needed synergistic network between these fields, this exchange will result in future research being more cross-accessible between the communities.