Provable Algorithms for Inference in Topic Models
This addresses the problem of efficient and reliable inference in topic models for researchers and practitioners in machine learning, representing an incremental step toward provable methods.
The paper tackles the challenge of designing provable algorithms for inference in topic models, which has been more difficult than parameter learning, by constructing simple linear estimators for topic proportions that work with short documents and have small variance. The result is an algorithm that yields good solutions on synthetic data and runs in time comparable to a single iteration of Gibbs sampling.
Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference has proven to be more challenging. Here we take a first step towards provable inference in topic models. We leverage a property of topic models that enables us to construct simple linear estimators for the unknown topic proportions that have small variance, and consequently can work with short documents. Our estimators also correspond to finding an estimate around which the posterior is well-concentrated. We show lower bounds that for shorter documents it can be information theoretically impossible to find the hidden topics. Finally, we give empirical results that demonstrate that our algorithm works on realistic topic models. It yields good solutions on synthetic data and runs in time comparable to a {\em single} iteration of Gibbs sampling.