Speaker: Fredrik Lindsten, Linköping University
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)
Deep Gaussian Markov Random Fields
Scalable Deep Gaussian Markov Random Fields for General Graphs