Order Matters: Probabilistic Modeling of Node Sequence for Graph Generation [article]

Xiaohui Chen, Xu Han, Jiajing Hu, Francisco J. R. Ruiz, Liping Liu
<span title="2021-06-14">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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
more &raquo; ... 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 [https://github.com/tufts-ml/graph-generation-vi]https://github.com/tufts-ml/graph-generation-vi.
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