  We present the \textit{hierarchical Dirichlet scaling process} (HDSP), a
Bayesian nonparametric mixed membership model. The HDSP generalizes the
hierarchical Dirichlet process (HDP) to model the correlation structure between
metadata in the corpus and mixture components. We construct the HDSP based on
the normalized gamma representation of the Dirichlet process, and this
construction allows incorporating a scaling function that controls the
membership probabilities of the mixture components. We develop two scaling
methods to demonstrate that different modeling assumptions can be expressed in
the HDSP. We also derive the corresponding approximate posterior inference
algorithms using variational Bayes. Through experiments on datasets of
newswire, medical journal articles, conference proceedings, and product
reviews, we show that the HDSP results in a better predictive performance than
labeled LDA, partially labeled LDA, and author topic model and a better
negative review classification performance than the supervised topic model and
SVM.
