  In this paper, we propose guaranteed spectral methods for learning a broad
range of topic models, which generalize the popular Latent Dirichlet Allocation
(LDA). We overcome the limitation of LDA to incorporate arbitrary topic
correlations, by assuming that the hidden topic proportions are drawn from a
flexible class of Normalized Infinitely Divisible (NID) distributions. NID
distributions are generated through the process of normalizing a family of
independent Infinitely Divisible (ID) random variables. The Dirichlet
distribution is a special case obtained by normalizing a set of Gamma random
variables. We prove that this flexible topic model class can be learned via
spectral methods using only moments up to the third order, with (low order)
polynomial sample and computational complexity. The proof is based on a key new
technique derived here that allows us to diagonalize the moments of the NID
distribution through an efficient procedure that requires evaluating only
univariate integrals, despite the fact that we are handling high dimensional
multivariate moments. In order to assess the performance of our proposed Latent
NID topic model, we use two real datasets of articles collected from New York
Times and Pubmed. Our experiments yield improved perplexity on both datasets
compared with the baseline.
