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The GeometricKernels Package: Heat and Mat\'ern Kernels for Geometric Learning on Manifolds, Meshes, and Graphs
Paper Details
Published: 2024/07/10
DOI: 10.48550/arXiv.2407.08086
ARXIV ID: 2407.08086v1
Kernels are a fundamental technical primitive in machine learning. In recent years, kernel-based methods such as Gaussian processes are becoming increasingly important in applications where quantifying uncertainty is of key interest. In settings that involve structured data defined on graphs, meshes, manifolds, or other related spaces, defining kernels with good uncertainty-quantification behavior, and computing their value numerically, is less straightforward than in the Euclidean setting. To address this difficulty, the authors present GeometricKernels, a software package which implements the geometric analogs of classical Euclidean squared exponential - also known as heat - and Mat’ern kernels, which are widely-used in settings where uncertainty is of key interest. As a byproduct, the authors obtain the ability to compute Fourier-feature-type expansions, which are widely used in their own right, on a wide set of geometric spaces
Authors
P. Mostowsky
V. Dutordoir
I. Azangulov
N. Jaquier
M.J. Hutchinson
L. Rozo
A. Terenin