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Machine learning methods on graphs have proven useful in many applicationsdue to their ability to handle generally structured data. The framework ofGaussian Markov Random Fields (GMRFs) provides a principled way to defineGaussian models on graphs by utilizing their sparsity structure. We propose aflexible GMRF model for general graphs built on the multi-layer structure ofDeep GMRFs, originally proposed for lattice graphs only. By designing a newtype of layer we enable the model to scale to large graphs. The layer isconstructed to allow for efficient training using variational inference andexisting software frameworks for Graph Neural Networks. For a Gaussianlikelihood, close to exact Bayesian inference is available for the latentfield. This allows for making predictions with accompanying uncertaintyestimates. The usefulness of the proposed model is verified by experiments on anumber of synthetic and real world datasets, where it compares favorably toother both Bayesian and deep learning methods.

Scalable Deep Gaussian Markov Random Fields for General Graphs