Poisson Sum-Product Networks: A Deep Architecture for Tractable Multivariate Poisson Distributions

Multivariate count data are pervasive in science in the form of histograms, contingency tables and others. Previous work on modeling this type of distributions do not allow for fast and tractable inference. In this paper we present a novel Poisson graphical model, the first based on sum product networks, called PSPN, allowing for positive as well as negative dependencies. We present algorithms for learning tree PSPNs from data as well as for tractable inference via symbolic evaluation. With these, information-theoretic measures such as entropy, mutual information, and distances among count variables can be computed without resorting to approximations. Additionally, we show a connection between PSPNs and LDA, linking the structure of tree PSPNs to a hierarchy of topics. The experimental results on several synthetic and real world datasets demonstrate that PSPN often outperform state-of-the-art while remaining tractable.