Sample Path Regularity of Gaussian Processes from the Covariance Kernel

no code implementations • 22 Dec 2023 • Nathaël Da Costa, Marvin Pförtner, Lancelot Da Costa, Philipp Hennig

While applications of GPs are myriad, a comprehensive understanding of GP sample paths, i. e. the function spaces over which they define a probability measure, is lacking.

Gaussian Processes

Physics-Informed Gaussian Process Regression Generalizes Linear PDE Solvers

1 code implementation • 23 Dec 2022 • Marvin Pförtner, Ingo Steinwart, Philipp Hennig, Jonathan Wenger

Crucially, this probabilistic viewpoint allows to (1) quantify the inherent discretization error; (2) propagate uncertainty about the model parameters to the solution; and (3) condition on noisy measurements.

Bayesian Inference regression

Posterior and Computational Uncertainty in Gaussian Processes

1 code implementation • 30 May 2022 • Jonathan Wenger, Geoff Pleiss, Marvin Pförtner, Philipp Hennig, John P. Cunningham

For any method in this class, we prove (i) convergence of its posterior mean in the associated RKHS, (ii) decomposability of its combined posterior covariance into mathematical and computational covariances, and (iii) that the combined variance is a tight worst-case bound for the squared error between the method's posterior mean and the latent function.

Gaussian Processes

ProbNum: Probabilistic Numerics in Python

1 code implementation • 3 Dec 2021 • Jonathan Wenger, Nicholas Krämer, Marvin Pförtner, Jonathan Schmidt, Nathanael Bosch, Nina Effenberger, Johannes Zenn, Alexandra Gessner, Toni Karvonen, François-Xavier Briol, Maren Mahsereci, Philipp Hennig

Probabilistic numerical methods (PNMs) solve numerical problems via probabilistic inference.