Guaranteed Model Order Estimation and Sample Complexity Bounds for LDA
This addresses the practical issue of topic number selection in mixture models for applications like text analysis, offering a faster and more reliable alternative to Bayesian nonparametric methods.
The paper tackles the problem of determining the number of topics in Latent Dirichlet Allocation (LDA) without learning latent parameters, developing a guaranteed procedure based on random matrix theory that outperforms nonparametric methods like hLDA.
The question of how to determine the number of independent latent factors (topics) in mixture models such as 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. Bayesian nonparametric methods can avoid the problem of topic number selection, but they can be impracticably slow for large sample sizes and are subject to local optima. We develop a guaranteed procedure for topic number recovery that does not necessitate learning the model's latent parameters beforehand. Our procedure relies on adapting results from random matrix theory. Performance of our topic number recovery procedure is superior to hLDA, a nonparametric method. We also discuss some implications of our results on the sample complexity and accuracy of popular spectral learning algorithms for LDA. Our results and procedure can be extended to spectral learning algorithms for other exchangeable mixture models as well as Hidden Markov Models.