Tractability in Structured Probability Spaces

Recently, the Probabilistic Sentential Decision Diagram (PSDD) has been proposed as a framework for systematically inducing and learning distributions over structured objects, including combinatorial objects such as permutations and rankings, paths and matchings on a graph, etc. In this paper, we study the scalability of such models in the context of representing and learning distributions over routes on a map. In particular, we introduce the notion of a hierarchical route distribution and show how they can be leveraged to construct tractable PSDDs over route distributions, allowing them to scale to larger maps. We illustrate the utility of our model empirically, in a route prediction task, showing how accuracy can be increased significantly compared to Markov models.