Guaranteed Model Order Estimation and Sample Complexity Bounds for LDA

The question of how to determine the number of independent latent factors, or topics, in Latent Dirichlet Allocation (LDA) is of great practical importance. In most applications, the exact number of topics is unknown, and depends on the application and the size of the data set. We introduce a spectral model selection procedure for topic number estimation that does not require learning the model's latent parameters beforehand and comes with probabilistic guarantees. The procedure is motivated by the spectral learning approach and relies on adaptations of results from random matrix theory. In a simulation experiment taken from the nonparametric Bayesian literature, this procedure outperforms the nonparametric Bayesian approach in both accuracy and speed. We also discuss some implications of our results for the sample complexity and accuracy of popular spectral learning algorithms for LDA. The principles underlying the procedure can be extended to spectral learning algorithms for other exchangeable mixture models with similar conditional independence properties.