Learning Graph Structure from Convolutional Mixtures

TL;DR

This paper introduces Graph Deconvolution Networks (GDNs), a neural architecture for inferring and learning latent graph structures from data, applicable to noisy, unobserved, or dynamic graphs, with demonstrated superior performance on synthetic and real datasets.

Contribution

The paper proposes GDNs, a novel neural network architecture for graph structure learning that unrolls proximal gradient iterations, enabling effective inference of latent graphs in various settings.

Findings

GDN outperforms spectral and iterative methods in graph recovery.

GDN generalizes well to larger graphs in synthetic experiments.

GDN demonstrates robustness and effectiveness on neuroimaging and social network data.

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, 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.