Parallelizing LDA using Partially Collapsed Gibbs Sampling

Latent dirichlet allocation (LDA) is a model widely used for unsupervised probabilistic modeling of text and images. MCMC sampling from the posterior distribution is typically performed using a collapsed Gibbs sampler that integrates out all model parameters except the topic indicators for each word. The topic indicators are Gibbs sampled iteratively by drawing each topic from its conditional posterior. The popularity of this sampler stems from its balanced combination of simplicity and efficiency, but its inherently sequential nature is an obstacle for parallel implementations. Growing corpus sizes and increasing model complexity are making inference in LDA models computationally infeasible without parallel sampling. We propose a parallel implementation of LDA that only collapses over the topic proportions in each document and therefore allows independent sampling of the topic indicators in different documents. We develop several modifications of the basic algorithm that exploits sparsity and structure to further improve the performance of the partially collapsed sampler. Contrary to other parallel LDA implementations, the partially collapsed sampler guarantees convergence to the true posterior. We show on several well-known corpora that the expected increase in statistical inefficiency from only partial collapsing is smaller than commonly assumed, and can be more than compensated by the speed-up from parallelization for larger corpora.