Order Matters: Probabilistic Modeling of Node Sequence for Graph Generation
This addresses a key bottleneck in graph generation for machine learning researchers, offering a more principled approach than previous ad-hoc methods.
The paper tackles the intractability of graph likelihood in autoregressive generative models by deriving an exact joint probability over graphs and node orderings, then using variational inference to compute a lower bound for training, resulting in significantly tighter bounds and high-quality generated graphs.
A graph generative model defines a distribution over graphs. One type of generative model is constructed by autoregressive neural networks, which sequentially add nodes and edges to generate a graph. However, the likelihood of a graph under the autoregressive model is intractable, as there are numerous sequences leading to the given graph; this makes maximum likelihood estimation challenging. Instead, in this work we derive the exact joint probability over the graph and the node ordering of the sequential process. From the joint, we approximately marginalize out the node orderings and compute a lower bound on the log-likelihood using variational inference. We train graph generative models by maximizing this bound, without using the ad-hoc node orderings of previous methods. Our experiments show that the log-likelihood bound is significantly tighter than the bound of previous schemes. Moreover, the models fitted with the proposed algorithm can generate high-quality graphs that match the structures of target graphs not seen during training. We have made our code publicly available at \hyperref[https://github.com/tufts-ml/graph-generation-vi]{https://github.com/tufts-ml/graph-generation-vi}.