Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernels

Authors: Michael Hutchinson, Alexander Terenin, Viacheslav Borovitskiy, So Takao, Yee Teh, Marc Deisenroth

NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental We demonstrate our techniques on a series of examples in modeling dynamical systems and weather science, and show that incorporating geometric structural bias into probabilistic modeling is beneficial in these settings to obtain coherent predictions and uncertainties.
Researcher Affiliation Collaboration 1University of Oxford 2University of Cambridge 3Imperial College London 4St. Petersburg State University 5Centre for Artificial Intelligence, University College London ... We also acknowledge support from Huawei Research.
Pseudocode No The paper does not include any figures, blocks, or sections explicitly labeled as 'Pseudocode' or 'Algorithm'.
Open Source Code Yes Code: https://github.com/MJHutchinson/Extrinsic Gauge Independant Vector GPs. For a general implementation, see https://github.com/GPflow/Geometric Kernels/.
Open Datasets Yes We use hourly wind data (10 m above ground) from the Weather Bench dataset [35], available from 1979 2018.
Dataset Splits No The paper mentions collecting data points for training and evaluating models but does not specify explicit train/validation/test splits by percentage or count. For instance, in Appendix B.1, it states, 'We sample 100 data points from the initial conditions' but provides no further split details.
Hardware Specification No The paper does not provide specific hardware details such as CPU or GPU models used for running experiments.
Software Dependencies No The paper does not list specific software dependencies with version numbers (e.g., Python 3.8, PyTorch 1.9).
Experiment Setup Yes B.1 Dynamical Systems: We consider a pendulum with length l = 1m and mass m = 1kg. The friction parameter b = 0.5kg/s. The gravitational acceleration g = 9.8m/s2. We use the initial conditions of (q, p) = (0.5π, 0) and (q, p) = (0.75π, 0). ... We sample 100 data points from the initial conditions. We train a sparse GP with 20 inducing points. We use a RBF kernel with lengthscale 1 and variance 1. B.2 Weather Modeling: ... We used a Matérn-3/2 kernel with lengthscale 1 and variance 1. We trained a sparse GP with 100 inducing points.