25 October 2022
Fredrik Lindsten
#### Deep Gaussian Markov Random Fields Date: 25-10-2022 14:00-1500 Central European Summer time 
Speaker: **Fredrik Lindsten**, Linköping University **Abstract:**
Machine learning methods on graphs are relevant for many application domains due to their ability to model complex dependencies and structures. Gaussian Markov Random Fields (GMRFs) provide a principled way to define Gaussian models on graphs by utilizing their sparsity structure. In this talk I will show how we can use graph neural networks (GNNs) and convolutional neural networks (CNNs) do design scalable and flexible GMRFs. Starting with lattice graphs, we establish a formal connection between CNNs and GMRFs, by showing that 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. I will also discuss how this Deep GMRF can be generalized to arbitrary graphs using a specialized GNN layer. Well-established tools, such as autodiff and variational inference, can be used for simple and efficient inference and learning of the Deep GMRF, and for a Gaussian likelihood, close to exact Bayesian inference is available for the latent field. I demonstrate the flexibility of the proposed model and show that it compares favorably to other methods, both Bayesian and deep-learning-based, on spatial and non-spatial data. Joint work with Joel Oskarsson (LiU) and Per Sidén (LiU/Qualcomm Arriver) Papers: [Deep Gaussian Markov Random Fields][10] [Scalable Deep Gaussian Markov Random Fields for General Graphs][11] [1]: https://bereau.group/ [2]: /blog/ [9]: /contact/ [3]:https://github.com/undark-lab/swyft [4]:https://arxiv.org/abs/2011.13951 [5]:http://www.mathben.com/ [6]:https://pubs.acs.org/doi/10.1021/acs.jctc.0c00981 [7]:https://github.com/Ensing-Laboratory/FABULOUS [8]:www.evozyne.com [10]:https://arxiv.org/abs/2002.07467 [11]:https://arxiv.org/abs/2206.05032
Speaker: **Fredrik Lindsten**, Linköping University **Abstract:** Machine learning methods on graphs are relevant for many application domains due to their ability to model complex dependencies and structures. Gaussian Markov Random Fields (GMRFs) provide a principled way to define Gaussian models on graphs by utilizing their sparsity structure. In this talk I will show how we can use graph neural networks (GNNs) and convolutional neural networks (CNNs) do design scalable and flexible GMRFs. Starting with lattice graphs, we establish a formal connection between CNNs and GMRFs, by showing that 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. I will also discuss how this Deep GMRF can be generalized to arbitrary graphs using a specialized GNN layer. Well-established tools, such as autodiff and variational inference, can be used for simple and efficient inference and learning of the Deep GMRF, and for a Gaussian likelihood, close to exact Bayesian inference is available for the latent field. I demonstrate the flexibility of the proposed model and show that it compares favorably to other methods, both Bayesian and deep-learning-based, on spatial and non-spatial data. Joint work with Joel Oskarsson (LiU) and Per Sidén (LiU/Qualcomm Arriver) Papers: [Deep Gaussian Markov Random Fields][10] [Scalable Deep Gaussian Markov Random Fields for General Graphs][11] [1]: https://bereau.group/ [2]: /blog/ [9]: /contact/ [3]:https://github.com/undark-lab/swyft [4]:https://arxiv.org/abs/2011.13951 [5]:http://www.mathben.com/ [6]:https://pubs.acs.org/doi/10.1021/acs.jctc.0c00981 [7]:https://github.com/Ensing-Laboratory/FABULOUS [8]:www.evozyne.com [10]:https://arxiv.org/abs/2002.07467 [11]:https://arxiv.org/abs/2206.05032
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