Reviews: Dirichlet belief networks for topic structure learning

This submission proposes a new prior on the topic-word distribution in latent topic models. This model defines a multi-layer feedforward graph, where each layer contains a set of valid multinomial distributions over the vocabulary, and weighted combinations of each layer's "topics" are used as the Dirichlet prior for the "topics" of the next layer. The key purported benefits are sharing of statistical strengh, inference of a hierarchy of interpretable "abstract" topics, and modularity that allows composition with other topic model variants that modify the document-topic distributions. The authors present an efficient fully collapsed Gibbs sampler inference scheme - I did not thoroughly check the derivation but it seems plausible. Although: what is the computational complexity (and relative "wall clock" cost) of the given inference scheme?