TY - GEN
T1 - On theoretical pProperties of sum-product networks
AU - Peharz, Robert
AU - Tschiatschek, Sebastian
AU - Pernkopf, Franz
AU - Domingos, Pedro
PY - 2015
Y1 - 2015
N2 - Sum-product networks (SPNs) are a promising avenue for probabilistic modeling and have been successfully applied to various tasks. However, some theoretic properties about SPNs are not yet well understood. In this paper we fill some gaps in the theoretic foundation of SPNs. First, we show that the weights of any complete and consistent SPN can be transformed into locally normalized weights without changing the SPN distribution. Second, we show that consistent SPNs cannot model distributions significantly (exponentially) more compactly than decomposable SPNs. As a third contribution, we extend the inference mechanisms known for SPNs with finite states to generalized SPNs with arbitrary input distributions.
AB - Sum-product networks (SPNs) are a promising avenue for probabilistic modeling and have been successfully applied to various tasks. However, some theoretic properties about SPNs are not yet well understood. In this paper we fill some gaps in the theoretic foundation of SPNs. First, we show that the weights of any complete and consistent SPN can be transformed into locally normalized weights without changing the SPN distribution. Second, we show that consistent SPNs cannot model distributions significantly (exponentially) more compactly than decomposable SPNs. As a third contribution, we extend the inference mechanisms known for SPNs with finite states to generalized SPNs with arbitrary input distributions.
M3 - Conference contribution
T3 - Proceedings of Machine Learning Research
SP - 744
EP - 752
BT - Proceedings of the Conference on Artificial Intelligence and Statistics (AISTATS)
T2 - 18th International Conference on Artificial Intelligence and Statistics (AISTATS 2015)
Y2 - 9 May 2015 through 12 May 2015
ER -