  Topic models have achieved significant successes in analyzing large-scale
text corpus. In practical applications, we are always confronted with the
challenge of model selection, i.e., how to appropriately set the number of
topics. Following recent advances in topic model inference via tensor
decomposition, we make a first attempt to provide theoretical analysis on model
selection in latent Dirichlet allocation. Under mild conditions, we derive the
upper bound and lower bound on the number of topics given a text collection of
finite size. Experimental results demonstrate that our bounds are accurate and
tight. Furthermore, using Gaussian mixture model as an example, we show that
our methodology can be easily generalized to model selection analysis for other
latent models.
