  An ongoing challenge in the analysis of document collections is how to
summarize content in terms of a set of inferred themes that can be interpreted
substantively in terms of topics. The current practice of parametrizing the
themes in terms of most frequent words limits interpretability by ignoring the
differential use of words across topics. We argue that words that are both
common and exclusive to a theme are more effective at characterizing topical
content. We consider a setting where professional editors have annotated
documents to a collection of topic categories, organized into a tree, in which
leaf-nodes correspond to the most specific topics. Each document is annotated
to multiple categories, at different levels of the tree. We introduce a
hierarchical Poisson convolution model to analyze annotated documents in this
setting. The model leverages the structure among categories defined by
professional editors to infer a clear semantic description for each topic in
terms of words that are both frequent and exclusive. We carry out a large
randomized experiment on Amazon Turk to demonstrate that topic summaries based
on the FREX score are more interpretable than currently established frequency
based summaries, and that the proposed model produces more efficient estimates
of exclusivity than with currently models. We also develop a parallelized
Hamiltonian Monte Carlo sampler that allows the inference to scale to millions
of documents.
