Learning Discrete Structures for Graph Neural Networks

TL;DR

This paper introduces a method to jointly learn graph structures and GCN parameters, enabling the use of graph neural networks even when the original graph data is noisy, incomplete, or unavailable.

Contribution

It proposes a bilevel optimization approach to learn a discrete probability distribution over edges, allowing GCNs to operate without pre-existing reliable graphs.

Findings

Outperforms related methods significantly

Effective in scenarios with noisy or missing graph data

Enables GCN application without a pre-defined graph

Abstract

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.