On some provably correct cases of variational inference for topic models

Variational inference is an efficient, popular heuristic used in the context of latent variable models. We provide the first analysis of instances where variational inference algorithms converge to the global optimum, in the setting of topic models. Our initializations are natural, one of them being used in LDA-c, the most popular implementation of variational inference. In addition to providing intuition into why this heuristic might work in practice, the multiplicative, rather than additive nature of the variational inference updates forces us to use non-standard proof arguments, which we believe might be of general theoretical interest.