Deep Gaussian Markov Random Fields

Per Sidén, Fredrik Lindsten
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:8916-8926, 2020.

Abstract

Gaussian Markov random fields (GMRFs) are probabilistic graphical models widely used in spatial statistics and related fields to model dependencies over spatial structures. We establish a formal connection between GMRFs and convolutional neural networks (CNNs). Common GMRFs are special cases of a generative model where the inverse mapping from data to latent variables is given by a 1-layer linear CNN. This connection allows us to generalize GMRFs to multi-layer CNN architectures, effectively increasing the order of the corresponding GMRF in a way which has favorable computational scaling. We describe how well-established tools, such as autodiff and variational inference, can be used for simple and efficient inference and learning of the deep GMRF. We demonstrate the flexibility of the proposed model and show that it outperforms the state-of-the-art on a dataset of satellite temperatures, in terms of prediction and predictive uncertainty.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-siden20a, title = {Deep {G}aussian {M}arkov Random Fields}, author = {Sid{\'e}n, Per and Lindsten, Fredrik}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {8916--8926}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/siden20a/siden20a.pdf}, url = {https://proceedings.mlr.press/v119/siden20a.html}, abstract = {Gaussian Markov random fields (GMRFs) are probabilistic graphical models widely used in spatial statistics and related fields to model dependencies over spatial structures. We establish a formal connection between GMRFs and convolutional neural networks (CNNs). Common GMRFs are special cases of a generative model where the inverse mapping from data to latent variables is given by a 1-layer linear CNN. This connection allows us to generalize GMRFs to multi-layer CNN architectures, effectively increasing the order of the corresponding GMRF in a way which has favorable computational scaling. We describe how well-established tools, such as autodiff and variational inference, can be used for simple and efficient inference and learning of the deep GMRF. We demonstrate the flexibility of the proposed model and show that it outperforms the state-of-the-art on a dataset of satellite temperatures, in terms of prediction and predictive uncertainty.} }
Endnote
%0 Conference Paper %T Deep Gaussian Markov Random Fields %A Per Sidén %A Fredrik Lindsten %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-siden20a %I PMLR %P 8916--8926 %U https://proceedings.mlr.press/v119/siden20a.html %V 119 %X Gaussian Markov random fields (GMRFs) are probabilistic graphical models widely used in spatial statistics and related fields to model dependencies over spatial structures. We establish a formal connection between GMRFs and convolutional neural networks (CNNs). Common GMRFs are special cases of a generative model where the inverse mapping from data to latent variables is given by a 1-layer linear CNN. This connection allows us to generalize GMRFs to multi-layer CNN architectures, effectively increasing the order of the corresponding GMRF in a way which has favorable computational scaling. We describe how well-established tools, such as autodiff and variational inference, can be used for simple and efficient inference and learning of the deep GMRF. We demonstrate the flexibility of the proposed model and show that it outperforms the state-of-the-art on a dataset of satellite temperatures, in terms of prediction and predictive uncertainty.
APA
Sidén, P. & Lindsten, F.. (2020). Deep Gaussian Markov Random Fields. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:8916-8926 Available from https://proceedings.mlr.press/v119/siden20a.html.

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