A Bottom-up Hidden Tree Markov Model

Hidden Tree Markov Models describe probability distributions over tree-structured data by defining a top-down generative process from the root to the leaves of the tree. We provide a novel compositional hidden tree Markov model that inverts the generative process, allowing hidden states to better correlate and model the co-occurrence of substructures among the child subtrees of internal nodes. To this end, we introduce a mixed memory approximation that factorizes the joint children-to-parent state transition matrix as a mixture of pairwise transitions. This Technical Report provides and in-depth introduction to the Bottom-Up Hidden Tree Markov Model, including the details of the learning and inference procedures.