Regression on Ice: Function approximation for the mathematically-inclined glaciologist
Modern satellite-based analysis of the ice sheets presents a profound statistical-geometric problem: how do we make sense of scattered, noisy measurements of vast, steadily evolving surfaces like the Greenland and Antarctic ice sheets? In these lecture notes, I attempt to providethe mathematical fou...
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ftzenodo:oai:zenodo.org:8363976 2024-09-15T17:48:13+00:00 Regression on Ice: Function approximation for the mathematically-inclined glaciologist Noah Bergam 2023-09-20 https://doi.org/10.5281/zenodo.8363976 unknown Zenodo https://zenodo.org/communities/ghub https://doi.org/10.5281/zenodo.8363975 https://doi.org/10.5281/zenodo.8363976 oai:zenodo.org:8363976 info:eu-repo/semantics/openAccess Creative Commons Attribution 4.0 International https://creativecommons.org/licenses/by/4.0/legalcode info:eu-repo/semantics/lecture 2023 ftzenodo https://doi.org/10.5281/zenodo.836397610.5281/zenodo.8363975 2024-07-25T17:20:50Z Modern satellite-based analysis of the ice sheets presents a profound statistical-geometric problem: how do we make sense of scattered, noisy measurements of vast, steadily evolving surfaces like the Greenland and Antarctic ice sheets? In these lecture notes, I attempt to providethe mathematical foundations of function approximation techniques that may aid the reader in appreciating and tackling this problem. The main topics include non-parametric regression , linear models , Gaussian processes , and reproducing Kernel Hilbert spaces . Each chapter features both examples from recent glaciology research and mathematical “curios” which invoke more niche remarks, such as the duality of Voronoi and Delaunay graphs and the intimate relationship between free knot linear splines and ReLu neural networks. Code demos and lecture notes are available at The Ghub. Code is also available in a GitHub repository . Lecture Antarc* Antarctic Greenland Zenodo |
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Modern satellite-based analysis of the ice sheets presents a profound statistical-geometric problem: how do we make sense of scattered, noisy measurements of vast, steadily evolving surfaces like the Greenland and Antarctic ice sheets? In these lecture notes, I attempt to providethe mathematical foundations of function approximation techniques that may aid the reader in appreciating and tackling this problem. The main topics include non-parametric regression , linear models , Gaussian processes , and reproducing Kernel Hilbert spaces . Each chapter features both examples from recent glaciology research and mathematical “curios” which invoke more niche remarks, such as the duality of Voronoi and Delaunay graphs and the intimate relationship between free knot linear splines and ReLu neural networks. Code demos and lecture notes are available at The Ghub. Code is also available in a GitHub repository . |
format |
Lecture |
author |
Noah Bergam |
spellingShingle |
Noah Bergam Regression on Ice: Function approximation for the mathematically-inclined glaciologist |
author_facet |
Noah Bergam |
author_sort |
Noah Bergam |
title |
Regression on Ice: Function approximation for the mathematically-inclined glaciologist |
title_short |
Regression on Ice: Function approximation for the mathematically-inclined glaciologist |
title_full |
Regression on Ice: Function approximation for the mathematically-inclined glaciologist |
title_fullStr |
Regression on Ice: Function approximation for the mathematically-inclined glaciologist |
title_full_unstemmed |
Regression on Ice: Function approximation for the mathematically-inclined glaciologist |
title_sort |
regression on ice: function approximation for the mathematically-inclined glaciologist |
publisher |
Zenodo |
publishDate |
2023 |
url |
https://doi.org/10.5281/zenodo.8363976 |
genre |
Antarc* Antarctic Greenland |
genre_facet |
Antarc* Antarctic Greenland |
op_relation |
https://zenodo.org/communities/ghub https://doi.org/10.5281/zenodo.8363975 https://doi.org/10.5281/zenodo.8363976 oai:zenodo.org:8363976 |
op_rights |
info:eu-repo/semantics/openAccess Creative Commons Attribution 4.0 International https://creativecommons.org/licenses/by/4.0/legalcode |
op_doi |
https://doi.org/10.5281/zenodo.836397610.5281/zenodo.8363975 |
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1810289368875663360 |