  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.
