Efficient methods for Gaussian Markov random fields under sparse linear constraints
(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:
https://lup.lub.lu.se/record/087c8b24-2eb3-4dff-afee-d1e229b98f6c
- author
- Bolin, David LU and Wallin, Jonas LU
- organization
- publishing date
- 2021
- 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}}, }