Inferring the graph structure from observed data is a key task in graph machine learning to capture the intrinsic relationship between data entities. While significant advancements have been made in learning the structure of homogeneous graphs, many real-world graphs exhibit heterogeneous patterns where nodes and edges have multiple types. This paper fills this gap by introducing the first approach for heterogeneous graph structure learning (HGSL). To this end, we first propose a novel statistical model for the data-generating process (DGP) of heterogeneous graph data, namely hidden Markov networks for heterogeneous graphs (H2MN). Then we formalize HGSL as a maximum a-posterior estimation problem parameterized by such DGP and derive an alternating optimization method to obtain a solution together with a theoretical justification of the optimization conditions. Finally, we conduct extensive experiments on both synthetic and real-world datasets to demonstrate that our proposed method excels in learning structure on heterogeneous graphs in terms of edge type identification and edge weight recovery.

本文解决了从观察数据中推断异构图结构的问题，该结构在真实世界中普遍存在。研究提出了一种新的统计模型，即适用于异构图的隐马尔可夫网络（H2MN），并将异构图结构学习形式化为最大后验估计问题。实验表明，所提方法在边类型识别和边权恢复方面表现优异，展示了其在异构图学习中的重要价值。

通过数据生成过程视角进行异构图结构学习