Provable Algorithms for Inference in Topic Models


Sanjeev Arora, Rong Ge, Frederic Koehler, Tengyu Ma, Ankur Moitra ;
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:2859-2867, 2016.


Recently, there has been considerable progress on designing algorithms with provable guarantees —typically using linear algebraic methods—for parameter learning in latent variable models. Designing provable algorithms for inference has proved more difficult. 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 single iteration of Gibbs sampling.

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