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Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernels
Michael Hutchinson · Alexander Terenin · Viacheslav Borovitskiy · So Takao · Yee Teh · Marc Deisenroth

Tue Dec 07 08:30 AM -- 10:00 AM (PST) @

Gaussian processes are machine learning models capable of learning unknown functions in a way that represents uncertainty, thereby facilitating construction of optimal decision-making systems. Motivated by a desire to deploy Gaussian processes in novel areas of science, a rapidly-growing line of research has focused on constructively extending these models to handle non-Euclidean domains, including Riemannian manifolds, such as spheres and tori. We propose techniques that generalize this class to model vector fields on Riemannian manifolds, which are important in a number of application areas in the physical sciences. To do so, we present a general recipe for constructing gauge independent kernels, which induce Gaussian vector fields, i.e. vector-valued Gaussian processes coherent withgeometry, from scalar-valued Riemannian kernels. We extend standard Gaussian process training methods, such as variational inference, to this setting. This enables vector-valued Gaussian processes on Riemannian manifolds to be trained using standard methods and makes them accessible to machine learning practitioners.

Author Information

Michael Hutchinson (University of Oxford)

Hi I'm Michael, a first year DPhil student at Oxford under the supervision of Yee Whye Teh and Max Welling. I'm interested in Probabalistic Machine Leanring in general, with a specific interests in distributed learning, generative modelling and uncertianty at a functional level.

Alexander Terenin (University of Cambridge)
Viacheslav Borovitskiy (St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences (PDMI RAS))
So Takao (University College London)
Yee Teh (DeepMind)
Marc Deisenroth (University College London)
Marc Deisenroth

Professor Marc Deisenroth is the DeepMind Chair in Artificial Intelligence at University College London and the Deputy Director of UCL's Centre for Artificial Intelligence. He also holds a visiting faculty position at the University of Johannesburg and Imperial College London. Marc's research interests center around data-efficient machine learning, probabilistic modeling and autonomous decision making. Marc was Program Chair of EWRL 2012, Workshops Chair of RSS 2013, EXPO-Co-Chair of ICML 2020, and Tutorials Co-Chair of NeurIPS 2021. In 2019, Marc co-organized the Machine Learning Summer School in London. He received Paper Awards at ICRA 2014, ICCAS 2016, and ICML 2020. He is co-author of the book [Mathematics for Machine Learning](https://mml-book.github.io) published by Cambridge University Press (2020).

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