  With the wide-spread availability of complex relational data, semi-supervised
node classification in graphs has become a central machine learning problem.
Graph neural networks are a recent class of easy-to-train and accurate methods
for this problem that map the features in the neighborhood of a node to its
label, but they ignore label correlation during inference and their predictions
are difficult to interpret. On the other hand, collective classification is a
traditional approach based on interpretable graphical models that explicitly
model label correlations. Here, we introduce a model that combines the
advantages of these two approaches, where we compute the marginal probabilities
in a conditional random field, similar to collective classification, and the
potentials in the random field are learned through end-to-end training, akin to
graph neural networks. In our model, potentials on each node only depend on
that node's features, and edge potentials are learned via a coupling matrix.
This structure enables simple training with interpretable parameters, scales to
large networks, naturally incorporates training labels at inference, and is
often more accurate than related approaches. Our approach can be viewed as
either an interpretable message-passing graph neural network or a collective
classification method with higher capacity and modernized training.
