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

Scalable Deep Gaussian Markov Random Fields for General Graphs