Pólya Urn Latent Dirichlet Allocation: a doubly sparse massively parallel sampler

Abstract

Latent Dirichlet Allocation (LDA) is a topic model widely used in natural language processing and machine learning. Most approaches to training the model rely on iterative algorithms, which makes it difficult to run LDA on big corpora that are best analyzed in parallel and distributed computational environments. Indeed, current approaches to parallel inference either don't converge to the correct posterior or require storage of large dense matrices in memory. We present a novel sampler that overcomes both problems, and we show that this sampler is faster, both empirically and theoretically, than previous Gibbs samplers for LDA. We do so by employing a novel Pólya-urn-based approximation in the sparse partially collapsed sampler for LDA. We prove that the approximation error vanishes with data size, making our algorithm asymptotically exact, a property of importance for large-scale topic models. In addition, we show, via an explicit example, that - contrary to popular belief in the topic modeling literature - partially collapsed samplers can be more efficient than fully collapsed samplers. We conclude by comparing the performance of our algorithm with that of other approaches on well-known corpora.

References in corpus (3)

• A Spectral Algorithm for Latent Dirichlet Allocation
• Bayes Shrinkage at GWAS scale: Convergence and Approximation Theory of a Scalable MCMC Algorithm for the Horseshoe Prior
• Approximations of Geometrically Ergodic Reversible Markov Chains

Cited by in corpus (4)

• A Survey of Monte Carlo Methods for Parameter Estimation
• A Noninformative Prior on a Space of Distribution Functions
• Bayesian Allocation Model: Inference by Sequential Monte Carlo for Nonnegative Tensor Factorizations and Topic Models using Polya Urns
• Techniques for proving Asynchronous Convergence results for Markov Chain Monte Carlo methods