We used the maximal seating assignment (Wallach, 2008) for propagating counts through the Dirichlet hierarchy.
if the word v appeared B l,u,v times in label l following a preceding word u, S l,v times in label l, T c,v times in category c, and G v times in total, we estimate the probability of a word v appearing in label k, category t, and after word u as p where we use • to represent marginalization, e.g.