Learning Graph Structure from Convolutional Mixtures
This addresses the challenge of graph structure inference for applications like neuroimaging and social networks, though it is an incremental method building on existing graph learning approaches.
The paper tackles the problem of inferring graph structure from data when graphs are unobserved, noisy, or dynamic, by proposing Graph Deconvolution Networks (GDNs) that learn graph distributions in a supervised fashion, achieving superior graph recovery performance on synthetic and real-world datasets.
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, when said graphs are (partially) unobserved, noisy, or dynamic, the problem of inferring graph structure from data becomes relevant. 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, perform link prediction or edge-weight regression tasks by adapting the loss function, and they are inherently inductive. We corroborate GDN's superior graph recovery performance and its generalization to larger graphs using synthetic data in supervised settings. Furthermore, we demonstrate the robustness and representation power of GDNs on real world neuroimaging and social network datasets.