  This paper proposes a model of information cascades as directed spanning
trees (DSTs) over observed documents. In addition, we propose a contrastive
training procedure that exploits partial temporal ordering of node infections
in lieu of labeled training links. This combination of model and unsupervised
training makes it possible to improve on models that use infection times alone
and to exploit arbitrary features of the nodes and of the text content of
messages in information cascades. With only basic node and time lag features
similar to previous models, the DST model achieves performance with
unsupervised training comparable to strong baselines on a blog network
inference task. Unsupervised training with additional content features achieves
significantly better results, reaching half the accuracy of a fully supervised
model.
