Structure Inference in Sum-Product Networks using Infinite Sum-Product Trees

Sum-Product Networks (SPNs) are a highly efficient type of a deep probabilistic
model that allows exact inference in time linear in the size of the network. In
previous work, several heuristic structure learning approaches for SPNs have been
developed, which are prone to overfitting compared to a purely Bayesian model.
In this work, we propose a principled approach to structure learning in SPNs by
introducing infinite Sum-Product Trees (SPTs). Our approach is the first correct and
successful extension of SPNs to a Bayesian nonparametric model. We show that
infinite SPTs can be used successfully to discover SPN structures and outperform
infinite Gaussian mixture models in the task of density estimation.