Non-Parametric Bayesian Sum-Product Networks

We define two non-parametric models for Sum-Product Networks (SPNs) (Poon & Domingos, 2011). The first is a tree structure of Dirichlet Processes; the second is a dag of hierarchical Dirichlet Processes. These generative models for data implicitly define a prior distribution on SPN of tree and of dag structure. They allow MCMC fitting of data to SPN models, and the learning of SPN structure from data.