This paper studies semi-supervised object classification in relational data, which is a fundamental problem in relational data modeling. The problem has been extensively studied in the literature of both statistical relational learning (e.g. relational Markov networks) and graph neural networks (e.g. graph convolutional networks). Statistical relational learning methods can effectively model the dependency of object labels through conditional random fields for collective classification, whereas graph neural networks learn effective object representations for classification through end-to-end training. In this paper, we propose the Graph Markov Neural Network (GMNN) that combines the advantages of both worlds. A GMNN models the joint distribution of object labels with a conditional random field, which can be effectively trained with the variational EM algorithm. In the E-step, one graph neural network learns effective object representations for approximating the posterior distributions of object labels. In the M-step, another graph neural network is used to model the local label dependency. Experiments on object classification, link classification, and unsupervised node representation learning show that GMNN achieves state-of-the-art results.

本研究提出了 Graph Markov Neural Network (GMNN) 模型，将统计关系学习和图神经网络的优势相结合，通过有条件随机场建模对象标签的联合分布，并利用变分 EM 算法进行有效训练，在目标分类、链接分类和无监督节点表示学习等任务中实现了最先进的结果。

GMNN: 图马尔可夫神经网络