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}.

中文翻译：

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顺序问题：用于图生成的节点序列的概率建模

图生成模型定义了图上的分布。一种类型的生成模型是由自回归神经网络构建的，它依次添加节点和边以生成图。然而，自回归模型下图的似然性是难以处理的，因为有许多序列导致给定的图；这使得最大似然估计具有挑战性。相反，在这项工作中，我们推导出了图上的精确联合概率和顺序过程的节点排序。从联合中，我们近似边缘化节点排序并使用变分推理计算对数似然的下限。我们通过最大化这个界限来训练图生成模型，而不使用以前方法的临时节点排序。我们的实验表明，对数似然界限明显比以前方案的界限更紧。此外，采用所提出算法的模型可以生成与训练期间未见过的目标图结构相匹配的高质量图。我们已在 \hyperref[https://github.com/tufts-ml/graph-generation-vi]{https://github.com/tufts-ml/graph-generation-vi} 上公开了我们的代码。