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The question of how to determine the number of independent latent factors(topics) in mixture models such as Latent Dirichlet Allocation (LDA) is ofgreat practical importance. In most applications, the exact number of topics isunknown, and depends on the application and the size of the data set. Bayesiannonparametric methods can avoid the problem of topic number selection, but theycan be impracticably slow for large sample sizes and are subject to localoptima. We develop a guaranteed procedure for topic number recovery that doesnot necessitate learning the model's latent parameters beforehand. Ourprocedure relies on adapting results from random matrix theory. Performance ofour topic number recovery procedure is superior to hLDA, a nonparametricmethod. We also discuss some implications of our results on the samplecomplexity and accuracy of popular spectral learning algorithms for LDA. Ourresults and procedure can be extended to spectral learning algorithms for otherexchangeable mixture models as well as Hidden Markov Models.

Guaranteed Model Order Estimation and Sample Complexity Bounds for LDA