On Theoretical Properties of Sum-Product Networks

Robert Peharz, Sebastian Tschiatschek, Franz Pernkopf, Pedro Domingos
Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, PMLR 38:744-752, 2015.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v38-peharz15, title = {{On Theoretical Properties of Sum-Product Networks}}, author = {Peharz, Robert and Tschiatschek, Sebastian and Pernkopf, Franz and Domingos, Pedro}, booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics}, pages = {744--752}, year = {2015}, editor = {Lebanon, Guy and Vishwanathan, S. V. N.}, volume = {38}, series = {Proceedings of Machine Learning Research}, address = {San Diego, California, USA}, month = {09--12 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v38/peharz15.pdf}, url = {https://proceedings.mlr.press/v38/peharz15.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T On Theoretical Properties of Sum-Product Networks %A Robert Peharz %A Sebastian Tschiatschek %A Franz Pernkopf %A Pedro Domingos %B Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2015 %E Guy Lebanon %E S. V. N. Vishwanathan %F pmlr-v38-peharz15 %I PMLR %P 744--752 %U https://proceedings.mlr.press/v38/peharz15.html %V 38 %X 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.
RIS
TY - CPAPER TI - On Theoretical Properties of Sum-Product Networks AU - Robert Peharz AU - Sebastian Tschiatschek AU - Franz Pernkopf AU - Pedro Domingos BT - Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics DA - 2015/02/21 ED - Guy Lebanon ED - S. V. N. Vishwanathan ID - pmlr-v38-peharz15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 38 SP - 744 EP - 752 L1 - http://proceedings.mlr.press/v38/peharz15.pdf UR - https://proceedings.mlr.press/v38/peharz15.html 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. ER -
APA
Peharz, R., Tschiatschek, S., Pernkopf, F. & Domingos, P.. (2015). On Theoretical Properties of Sum-Product Networks. Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 38:744-752 Available from https://proceedings.mlr.press/v38/peharz15.html.

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