SangWoo Lee and ByoungTak Zhang
Abstract
Designing efficient deep probabilistic models with powerful representation is a challenging problem in various academic fields including computational cognitive science. We propose sumproduct graphical models (SPGM), which are novel probabilistic models generalizing sumproduct networks and other classical probabilistic graphical models. Previous probabilistic graphical models mainly focused on finding only directed connections between nodes (e.g. Bayesian networks, Markov random fields) or only undirected connections (e.g. mixture models, sumproduct networks). Our approach considers both directed and undirected interactions on probabilistic graphical models. Sumproduct graphical models can be explained as an ensemble of exponential number of classical probabilistic models, whereas sumproduct networks consist of naïve Bayes. Allowing leaves in a sumproduct network to be directly related to each other, a sumproduct graphical model has a powerful representation beyond not only sumproduct networks but also Bayesian networks and Markov random fields. In addition, we propose treeaugmented sumproduct networks (TASPN), a kind of sumproduct graphical models which allows for efficient and exact inference. Treeaugmented sumproduct networks are special ensembles of exponential number of ChowLiu trees (1968). In experiments on various benchmark datasets and a visiolinguistic dataset in cartoon video, we measure performance of our model and discover usefulness of the novel framework.
