Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

Efficient methods for Gaussian Markov random fields under sparse linear constraints

Bolin, David LU and Wallin, Jonas LU (2021) 35th Conference on Neural Information Processing Systems (NeurIPS 2021) 34.
Abstract
Methods for inference and simulation of linearly constrained Gaussian Markov
Random Fields (GMRF) are computationally prohibitive when the number of
constraints is large. In some cases, such as for intrinsic GMRFs, they may even beunfeasible. We propose a new class of methods to overcome these challenges in the common case of sparse constraints, where one has a large number of constraints and each only involves a few elements. Our methods rely on a basis transformation into blocks of constrained versus non-constrained subspaces, and we show that the methods greatly outperform existing alternatives in terms of computational cost. By combining the proposed methods with the stochastic partial differential equation approach for... (More)
Methods for inference and simulation of linearly constrained Gaussian Markov
Random Fields (GMRF) are computationally prohibitive when the number of
constraints is large. In some cases, such as for intrinsic GMRFs, they may even beunfeasible. We propose a new class of methods to overcome these challenges in the common case of sparse constraints, where one has a large number of constraints and each only involves a few elements. Our methods rely on a basis transformation into blocks of constrained versus non-constrained subspaces, and we show that the methods greatly outperform existing alternatives in terms of computational cost. By combining the proposed methods with the stochastic partial differential equation approach for Gaussian random fields, we also show how to formulate Gaussian process regression with linear constraints in a GMRF setting to reduce computational cost. This is illustrated in two applications with simulated data. (Less)
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Advances in Neural Information Processing Systems
volume
34
conference name
35th Conference on Neural Information Processing Systems (NeurIPS 2021)
conference dates
2021-12-06 - 2021-12-14
external identifiers
  • scopus:85131800800
ISBN
9781713845393
language
English
LU publication?
yes
id
087c8b24-2eb3-4dff-afee-d1e229b98f6c
alternative location
https://proceedings.neurips.cc/paper/2021/file/51e6d6e679953c6311757004d8cbbba9-Paper.pdf
date added to LUP
2022-08-23 11:28:07
date last changed
2022-08-31 13:48:03
@inproceedings{087c8b24-2eb3-4dff-afee-d1e229b98f6c,
  abstract     = {{Methods for inference and simulation of linearly constrained Gaussian Markov<br/>Random Fields (GMRF) are computationally prohibitive when the number of<br/>constraints is large. In some cases, such as for intrinsic GMRFs, they may even beunfeasible. We propose a new class of methods to overcome these challenges in the common case of sparse constraints, where one has a large number of constraints and each only involves a few elements. Our methods rely on a basis transformation into blocks of constrained versus non-constrained subspaces, and we show that the methods greatly outperform existing alternatives in terms of computational cost. By combining the proposed methods with the stochastic partial differential equation approach for Gaussian random fields, we also show how to formulate Gaussian process regression with linear constraints in a GMRF setting to reduce computational cost. This is illustrated in two applications with simulated data.}},
  author       = {{Bolin, David and Wallin, Jonas}},
  booktitle    = {{Advances in Neural Information Processing Systems}},
  isbn         = {{9781713845393}},
  language     = {{eng}},
  title        = {{Efficient methods for Gaussian Markov random fields under sparse linear constraints}},
  url          = {{https://proceedings.neurips.cc/paper/2021/file/51e6d6e679953c6311757004d8cbbba9-Paper.pdf}},
  volume       = {{34}},
  year         = {{2021}},
}