---
_id: '12786'
abstract:
- lang: eng
  text: '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 Grobner 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.'
author:
- first_name: Markus
  full_name: Lange-Hegermann, Markus
  id: '71761'
  last_name: Lange-Hegermann
citation:
  ama: Lange-Hegermann M. <i>Linearly Constrained Gaussian Processes with Boundary
    Conditions</i>. Vol 130. (Banerjee A, Fukumizu K, eds.). MLResearchPress ; 2021.
  apa: Lange-Hegermann, M. (2021). Linearly Constrained Gaussian Processes with Boundary
    Conditions. In A. Banerjee &#38; K. Fukumizu (Eds.), <i>24th International Conference
    on Artificial Intelligence and Statistics (AISTATS)</i> (Vol. 130). MLResearchPress
    .
  bjps: <b>Lange-Hegermann M</b> (2021) <i>Linearly Constrained Gaussian Processes
    with Boundary Conditions</i>, Banerjee A and Fukumizu K (eds). MLResearchPress
    .
  chicago: 'Lange-Hegermann, Markus. <i>Linearly Constrained Gaussian Processes with
    Boundary Conditions</i>. Edited by A. Banerjee and K. Fukumizu. <i>24th International
    Conference on Artificial Intelligence and Statistics (AISTATS)</i>. Vol. 130.
    Proceedings of Machine Learning Research : PMLR . MLResearchPress , 2021.'
  chicago-de: 'Lange-Hegermann, Markus. 2021. <i>Linearly Constrained Gaussian Processes
    with Boundary Conditions</i>. Hg. von A. Banerjee und K. Fukumizu. <i>24th International
    Conference on Artificial Intelligence and Statistics (AISTATS)</i>. Bd. 130. Proceedings
    of machine learning research : PMLR . MLResearchPress .'
  din1505-2-1: '<span style="font-variant:small-caps;">Lange-Hegermann, Markus</span>
    ; <span style="font-variant:small-caps;">Banerjee, A.</span> ; <span style="font-variant:small-caps;">Fukumizu,
    K.</span> (Hrsg.): <i>Linearly Constrained Gaussian Processes with Boundary Conditions</i>,
    <i>Proceedings of machine learning research : PMLR </i>. Bd. 130 : MLResearchPress
    , 2021'
  havard: M. Lange-Hegermann, Linearly Constrained Gaussian Processes with Boundary
    Conditions, MLResearchPress , 2021.
  ieee: M. Lange-Hegermann, <i>Linearly Constrained Gaussian Processes with Boundary
    Conditions</i>, vol. 130. MLResearchPress , 2021.
  mla: Lange-Hegermann, Markus. “Linearly Constrained Gaussian Processes with Boundary
    Conditions.” <i>24th International Conference on Artificial Intelligence and Statistics
    (AISTATS)</i>, edited by A. Banerjee and K. Fukumizu, vol. 130, MLResearchPress
    , 2021.
  short: M. Lange-Hegermann, Linearly Constrained Gaussian Processes with Boundary
    Conditions, MLResearchPress , 2021.
  ufg: '<b>Lange-Hegermann, Markus</b>: Linearly Constrained Gaussian Processes with
    Boundary Conditions, Bd. 130, hg. von Banerjee, A./Fukumizu, K., o. O. 2021 (Proceedings
    of machine learning research : PMLR ).'
  van: 'Lange-Hegermann M. Linearly Constrained Gaussian Processes with Boundary Conditions.
    Banerjee A, Fukumizu K, editors. 24th International Conference on Artificial Intelligence
    and Statistics (AISTATS). MLResearchPress ; 2021. (Proceedings of machine learning
    research : PMLR ; vol. 130).'
conference:
  end_date: 2021-04-15
  location: Virtual
  name: 24th International Conference on Artificial Intelligence and Statistics (AISTATS)
  start_date: 2021-04-13
date_created: 2025-04-14T13:58:16Z
date_updated: 2025-06-26T13:42:36Z
department:
- _id: DEP5000
- _id: DEP5023
editor:
- first_name: A.
  full_name: Banerjee, A.
  last_name: Banerjee
- first_name: K.
  full_name: Fukumizu, K.
  last_name: Fukumizu
intvolume: '       130'
keyword:
- FUNCTIONAL REGRESSION
- PREDICTION
- ALGORITHMS
- COMPLEXITY
- MODELS
language:
- iso: eng
publication: 24th International Conference on Artificial Intelligence and Statistics
  (AISTATS)
publication_identifier:
  issn:
  - 2640-3498
publication_status: published
publisher: 'MLResearchPress '
quality_controlled: '1'
series_title: 'Proceedings of machine learning research : PMLR '
status: public
title: Linearly Constrained Gaussian Processes with Boundary Conditions
type: conference_editor_article
user_id: '83781'
volume: 130
year: '2021'
...