Gaussian processes are arguably the most important class of spatiotemporal models within
machine learning. They encode prior information about the modeled function and can be …

Data in many applications follows systems of Ordinary Differential Equations (ODEs). This
paper presents a novel algorithmic and symbolic construction for covariance functions of …

Denoising diffusion models have proven to be a flexible and effective paradigm for
generative modelling. Their recent extension to infinite dimensional Euclidean spaces has …

Future NASA lander missions to icy moons will require completely automated, accurate, and
data efficient calibration methods for the robot manipulator arms that sample icy terrains in …

We present Manifold Diffusion Fields (MDF), an approach that unlocks learning of diffusion
models of data in general non-Euclidean geometries. Leveraging insights from spectral …

We propose a principled way to define Gaussian process priors on various sets of
unweighted graphs: directed or undirected, with or without loops. We endow each of these …

Various applications ranging from robotics to climate science require modeling signals on
non-Euclidean domains, such as the sphere. Gaussian process models on manifolds have …

Kernels are a fundamental technical primitive in machine learning. In recent years, kernel-
based methods such as Gaussian processes are becoming increasingly important in …

Positive semidefinite kernels on spheres cross time are on demand in spatial statistics,
machine learning and numerical analysis, motivated by applications in the climate …