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Scalable Deep Gaussian Markov Random Fields for General Graphs
Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-8201-0282
Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering. Arriver Software AB, Sweden.
Linköping University, Faculty of Science & Engineering. Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning.
2022 (English)In: Proceedings of the 39th International Conference on Machine Learning / [ed] Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesvari, Gang Niu, Sivan Sabato, 2022, p. 17117-17137Conference paper, Published paper (Refereed)
Abstract [en]

Machine learning methods on graphs have proven useful in many applications due to their ability to handle generally structured data. The framework of Gaussian Markov Random Fields (GMRFs) provides a principled way to define Gaussian models on graphs by utilizing their sparsity structure. We propose a flexible GMRF model for general graphs built on the multi-layer structure of Deep GMRFs, originally proposed for lattice graphs only. By designing a new type of layer we enable the model to scale to large graphs. The layer is constructed to allow for efficient training using variational inference and existing software frameworks for Graph Neural Networks. For a Gaussian likelihood, close to exact Bayesian inference is available for the latent field. This allows for making predictions with accompanying uncertainty estimates. The usefulness of the proposed model is verified by experiments on a number of synthetic and real world datasets, where it compares favorably to other both Bayesian and deep learning methods.

Place, publisher, year, edition, pages
2022. p. 17117-17137
Series
Proceedings of Machine Learning Research, ISSN 2640-3498 ; 162
Keywords [en]
machine learning, graphs, gmrf, deep gmrf, variational inference, gaussian, markov random field
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-187178ISI: 000900064907012OAI: oai:DiVA.org:liu-187178DiVA, id: diva2:1686544
Conference
The 39th International Conference on Machine Learning, ICML, 17-23 July 2022, Baltimore, Maryland, USA
Funder
Wallenberg AI, Autonomous Systems and Software Program (WASP)ELLIIT - The Linköping‐Lund Initiative on IT and Mobile CommunicationsSwedish Research Council, 2020-04122Available from: 2022-08-10 Created: 2022-08-10 Last updated: 2023-05-10

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Oskarsson, JoelSidén, PerLindsten, Fredrik

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