Fitting Autoregressive Graph Generative Models through Maximum Likelihood Estimation
Xu Han, Xiaohui Chen, Francisco J. R. Ruiz, Li-Ping Liu; 24(97):1−30, 2023.
Abstract
The objective of this study is to address the problem of fitting autoregressive graph generative models using maximum likelihood estimation (MLE). MLE is challenging for graph autoregressive models due to the possible arbitrary rearrangement of nodes in a graph. Consequently, the exact likelihood computation requires summing over all possible node orders that result in the same graph. To overcome this, we propose fitting the graph models by maximizing a variational bound. This is achieved by first deriving the joint probability over the graph and the node order of the autoregressive process. The advantage of this approach is that it eliminates the need for specifying ad-hoc node orders, as an inference network learns the most probable node sequences responsible for generating a given graph. We enhance this approach by developing a graph generative model based on attention mechanisms and an inference network based on routing search. Empirical evidence demonstrates that fitting autoregressive graph models through variational inference enhances their qualitative and quantitative performance, and the improved model and inference network further enhance performance.
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