Linearly Constrained Gaussian Processes with Boundary Conditions

Markus Lange-Hegermann
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:1090-1098, 2021.

Abstract

One goal in Bayesian machine learning is to encode prior knowledge into prior distributions, to model data efficiently. We consider prior knowledge from systems of linear partial differential equations together with their boundary conditions. We construct multi-output Gaussian process priors with realizations in the solution set of such systems, in particular only such solutions can be represented by Gaussian process regression. The construction is fully algorithmic via Gröbner bases and it does not employ any approximation. It builds these priors combining two parametrizations via a pullback: the first parametrizes the solutions for the system of differential equations and the second parametrizes all functions adhering to the boundary conditions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-lange-hegermann21a, title = { Linearly Constrained Gaussian Processes with Boundary Conditions }, author = {Lange-Hegermann, Markus}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {1090--1098}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/lange-hegermann21a/lange-hegermann21a.pdf}, url = {https://proceedings.mlr.press/v130/lange-hegermann21a.html}, abstract = { One goal in Bayesian machine learning is to encode prior knowledge into prior distributions, to model data efficiently. We consider prior knowledge from systems of linear partial differential equations together with their boundary conditions. We construct multi-output Gaussian process priors with realizations in the solution set of such systems, in particular only such solutions can be represented by Gaussian process regression. The construction is fully algorithmic via Gröbner bases and it does not employ any approximation. It builds these priors combining two parametrizations via a pullback: the first parametrizes the solutions for the system of differential equations and the second parametrizes all functions adhering to the boundary conditions. } }
Endnote
%0 Conference Paper %T Linearly Constrained Gaussian Processes with Boundary Conditions %A Markus Lange-Hegermann %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-lange-hegermann21a %I PMLR %P 1090--1098 %U https://proceedings.mlr.press/v130/lange-hegermann21a.html %V 130 %X One goal in Bayesian machine learning is to encode prior knowledge into prior distributions, to model data efficiently. We consider prior knowledge from systems of linear partial differential equations together with their boundary conditions. We construct multi-output Gaussian process priors with realizations in the solution set of such systems, in particular only such solutions can be represented by Gaussian process regression. The construction is fully algorithmic via Gröbner bases and it does not employ any approximation. It builds these priors combining two parametrizations via a pullback: the first parametrizes the solutions for the system of differential equations and the second parametrizes all functions adhering to the boundary conditions.
APA
Lange-Hegermann, M.. (2021). Linearly Constrained Gaussian Processes with Boundary Conditions . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:1090-1098 Available from https://proceedings.mlr.press/v130/lange-hegermann21a.html.

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