Gaussian Processes and Statistical Decision-making in Non-Euclidean Spaces

<table> <tr> <td> <img alt="Torus kernel" src="https://raw.githubusercontent.com/aterenin/phdthesis/main/figures/png/t2_ker.png"> </td> <td> <img alt="Sphere kernel" src="https://raw.githubusercontent.com/aterenin/phdthesis/main/figures/png/s2_ker.png"> </td> <td> <img alt="Dragon manifold kernel" src="https://raw.githubusercontent.com/aterenin/phdthesis/main/figures/png/dr_ker.png"> </td> </tr> </table>

This repository contains the LaTeX source for the PhD thesis written by Alexander Terenin. It also includes the scripts and data used for generating the figures in the thesis, which are created with a combination of TikZ and PGFPlots via the PGFPlotsX.jl Julia interface, as well as Blender. Code for running the experiments presented in the thesis can be found in each respective publication's repository, linked below.

<a href="https://github.com/aterenin/phdthesis/releases/download/corrected/Terenin-A-2022-PhD-Thesis.pdf"><img alt="Download PDF" height="24" src="https://img.shields.io/github/downloads/aterenin/phdthesis/total?label=Download%20PDF"></a>

Publications in this thesis

<table> <tr> <td> <strong>Efficiently Sampling Functions from Gaussian Process Posteriors</strong><br> James T. Wilson,* Viacheslav Borovitskiy,* Alexander Terenin,* Peter Mostowsky,* and Marc Peter Deisenroth<br> ICML 2020<br> <a href="https://arxiv.org/abs/2002.09309"><img alt="Paper" src="https://img.shields.io/badge/-Paper-gray"></a> <a href="https://github.com/j-wilson/GPflowSampling"><img alt="Code" src="https://img.shields.io/badge/-Code-gray" ></a> </td> </tr> <tr> <td> <strong>Pathwise Conditioning of Gaussian Processes</strong><br> James T. Wilson,* Viacheslav Borovitskiy,* Alexander Terenin,* Peter Mostowsky,* and Marc Peter Deisenroth<br> JMLR 2021<br> <a href="https://arxiv.org/abs/2011.04026"><img alt="Paper" src="https://img.shields.io/badge/-Paper-gray"></a> <a href="https://github.com/j-wilson/GPflowSampling"><img alt="Code" src="https://img.shields.io/badge/-Code-gray" ></a> </td> </tr> <tr> <td> <strong>Matérn Gaussian Processes on Riemannian Manifolds</strong><br> Viacheslav Borovitskiy,* Alexander Terenin,* Peter Mostowsky,* and Marc Peter Deisenroth<br> NeurIPS 2020<br> <a href="https://arxiv.org/abs/2006.10160"><img alt="Paper" src="https://img.shields.io/badge/-Paper-gray"></a> <a href="https://github.com/spbu-math-cs/Riemannian-Gaussian-Processes"><img alt="Code" src="https://img.shields.io/badge/-Code-gray" ></a> </td> </tr> <tr> <td> <strong>Matérn Gaussian Processes on Graphs</strong><br> Viacheslav Borovitskiy,* Iskander Azangulov,* Alexander Terenin,* Peter Mostowsky, Marc Peter Deisenroth, and Nicolas Durrande<br> AISTATS 2021<br> <a href="https://arxiv.org/abs/2010.15538"><img alt="Paper" src="https://img.shields.io/badge/-Paper-gray"></a> <a href="https://github.com/spbu-math-cs/Graph-Gaussian-Processes"><img alt="Code" src="https://img.shields.io/badge/-Code-gray" ></a> </td> </tr> <tr> <td> <strong>Geometry-aware Bayesian Optimization in Robotics using Riemannian Matérn Kernels</strong><br> Noémie Jaquier, Viacheslav Borovitskiy, Andrei Smolensky, Alexander Terenin, Tamim Asfour, and Leonel Rozo<br> CoRL 2021<br> <a href="https://arxiv.org/abs/2111.01460"><img alt="Paper" src="https://img.shields.io/badge/-Paper-gray"></a> <a href="https://github.com/NoemieJaquier/MaternGaBO"><img alt="Code" src="https://img.shields.io/badge/-Code-gray" ></a> </td> </tr> <tr> <td> <strong>Vector-valued Gaussian Processes on Riemannian Manifolds via Gauge Independent Projected Kernels</strong><br> Michael John Hutchinson,* Alexander Terenin,* Viacheslav Borovitskiy,* So Takao,* Yee Whye Teh, and Marc Peter Deisenroth<br> NeurIPS 2021<br> <a href="https://arxiv.org/abs/2110.14423"><img alt="Paper" src="https://img.shields.io/badge/-Paper-gray"></a> <a href="https://github.com/MJHutchinson/ExtrinsicGaugeIndependentVectorGPs"><img alt="Code" src="https://img.shields.io/badge/-Code-gray" ></a> </td> </tr> </table>

*Equal contribution

Citation

@phdthesis{terenin22,
    author = {Alexander Terenin},
    school = {Imperial College London},
    title = {Gaussian Processes and Statistical Decision-making in Non-Euclidean Spaces},
    year = {2022}}

<table> <tr> <td> <img alt="Torus kernel" src="https://raw.githubusercontent.com/aterenin/phdthesis/main/figures/png/mvn_pos.png"> </td> <td> <img alt="Sphere kernel" src="https://raw.githubusercontent.com/aterenin/phdthesis/main/figures/png/mvn_neg.png"> </td> <td> <img alt="Dragon manifold kernel" src="https://raw.githubusercontent.com/aterenin/phdthesis/main/figures/png/bayes.png"> </td> </tr> </table>