  Nested Chinese Restaurant Process (nCRP) topic models are powerful
nonparametric Bayesian methods to extract a topic hierarchy from a given text
corpus, where the hierarchical structure is automatically determined by the
data. Hierarchical Latent Dirichlet Allocation (hLDA) is a popular instance of
nCRP topic models. However, hLDA has only been evaluated at small scale,
because the existing collapsed Gibbs sampling and instantiated weight
variational inference algorithms either are not scalable or sacrifice inference
quality with mean-field assumptions. Moreover, an efficient distributed
implementation of the data structures, such as dynamically growing count
matrices and trees, is challenging.
  In this paper, we propose a novel partially collapsed Gibbs sampling (PCGS)
algorithm, which combines the advantages of collapsed and instantiated weight
algorithms to achieve good scalability as well as high model quality. An
initialization strategy is presented to further improve the model quality.
Finally, we propose an efficient distributed implementation of PCGS through
vectorization, pre-processing, and a careful design of the concurrent data
structures and communication strategy.
  Empirical studies show that our algorithm is 111 times more efficient than
the previous open-source implementation for hLDA, with comparable or even
better model quality. Our distributed implementation can extract 1,722 topics
from a 131-million-document corpus with 28 billion tokens, which is 4-5 orders
of magnitude larger than the previous largest corpus, with 50 machines in 7
hours.
