  Latent Dirichlet analysis, or topic modeling, is a flexible latent variable
framework for modeling high-dimensional sparse count data. Various learning
algorithms have been developed in recent years, including collapsed Gibbs
sampling, variational inference, and maximum a posteriori estimation, and this
variety motivates the need for careful empirical comparisons. In this paper, we
highlight the close connections between these approaches. We find that the main
differences are attributable to the amount of smoothing applied to the counts.
When the hyperparameters are optimized, the differences in performance among
the algorithms diminish significantly. The ability of these algorithms to
achieve solutions of comparable accuracy gives us the freedom to select
computationally efficient approaches. Using the insights gained from this
comparative study, we show how accurate topic models can be learned in several
seconds on text corpora with thousands of documents.
