Title: Learning Graph Structure from Convolutional Mixtures. Abstract: Machine learning frameworks such as graph neural networks typically rely on a given, fixed graph to exploit relational inductive biases and thus effectively learn from network data. However, assuming the knowledge of said graphs may be untenable in practice, which motivates the problem of inferring graph structure from data. In this paper, we postulate a graph convolutional relationship between the observed and latent graphs, and formulate the graph learning task as a network inverse (deconvolution) problem. In lieu of eigendecomposition-based spectral methods or iterative optimization solutions, we unroll and truncate proximal gradient iterations to arrive at a parameterized neural network architecture that we call a Graph Deconvolution Network (GDN). GDNs can learn a distribution of graphs in a supervised fashion, and perform link-prediction or edge-weight regression tasks by adapting the loss function. Since layers directly operate on, combine, and refine graph objects (instead of node features), GDNs are inherently inductive and can generalize to larger-sized graphs after training.
Algorithm unrolling offers an explicit handle on computational complexity; we trade-off training time in return for quick approximations to the inverse problem solution, obtained via a forward pass through the learnt model. We corroborate GDN's superior graph recovery performance using synthetic data in supervised settings, as well as its ability to generalize to graphs orders of magnitude larger that those seen in training. Using the Human Connectome Project-Young Adult neuroimaging dataset, we demonstrate the robustness and representation power of our model by inferring structural brain networks from functional connectivity estimated using fMRI signals.