  Topic models, and more specifically the class of Latent Dirichlet Allocation
(LDA), are widely used for probabilistic modeling of text. MCMC sampling from
the posterior distribution is typically performed using a collapsed Gibbs
sampler. We propose a parallel sparse partially collapsed Gibbs sampler and
compare its speed and efficiency to state-of-the-art samplers for topic models
on five well-known text corpora of differing sizes and properties. In
particular, we propose and compare two different strategies for sampling the
parameter block with latent topic indicators. The experiments show that the
increase in statistical inefficiency from only partial collapsing is smaller
than commonly assumed, and can be more than compensated by the speedup from
parallelization and sparsity on larger corpora. We also prove that the
partially collapsed samplers scale well with the size of the corpus. The
proposed algorithm is fast, efficient, exact, and can be used in more modeling
situations than the ordinary collapsed sampler.
