Title: Convergence Rates of Latent Topic Models Under Relaxed Identifiability Conditions,
Abstract: In this paper we study the frequentist convergence rate for the Latent
Dirichlet Allocation (Blei et al., 2003) topic models. We show that the maximum
likelihood estimator converges to one of the finitely many equivalent
parameters in Wasserstein's distance metric at a rate of $n^{-1/4}$ without
assuming separability or non-degeneracy of the underlying topics and/or the
existence of more than three words per document, thus generalizing the previous
works of Anandkumar et al. (2012, 2014) from an information-theoretical
perspective. We also show that the $n^{-1/4}$ convergence rate is optimal in
the worst case.