Graph Neural Networks with a Distribution of Parametrized Graphs
This addresses graph uncertainty issues in applications like chemistry and heterogeneous networks, but it is incremental as it builds on existing graph neural network methods with a probabilistic extension.
The paper tackles the problem of graph neural networks relying on a single observed graph, which may have uncertainties like missing edges, by introducing latent variables to generate multiple graphs and estimating parameters via an EM framework with MCMC and PAC-Bayesian theory. It shows performance improvements in node classification for heterogeneous graphs and graph regression on chemistry datasets.
Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having erroneous or missing edges, as well as edge weights that provide little informative value. To address these challenges and capture additional information previously absent in the observed graph, we introduce latent variables to parameterize and generate multiple graphs. We obtain the maximum likelihood estimate of the network parameters in an Expectation-Maximization (EM) framework based on the multiple graphs. Specifically, we iteratively determine the distribution of the graphs using a Markov Chain Monte Carlo (MCMC) method, incorporating the principles of PAC-Bayesian theory. Numerical experiments demonstrate improvements in performance against baseline models on node classification for heterogeneous graphs and graph regression on chemistry datasets.