Tractable Mode-Finding in Sum-Product Networks with Gaussian Leaves

In this work, we leverage the relation between Sum-Product Networks (SPNs) and Gaussian mixtures to propose an algorithm that adapts the Expectation-Maximization method to efficiently find the modes of SPNs with Gaussian leaves. We discuss how the algorithm can be used to perform Maximum-A-Posteriori inference in SPNs learned from continuous data with theoretical advantages over the existing methods in the literature, and how it can be used to shrink the size of learned models. As an additional example of the use of the algorithm, we perform an SPN-based hierarchical clustering of digit images. Thus, our proposed algorithm can be used for model analysis, model compression, and exploratory data analysis.