Probabilistic Generating Circuits

Honghua Zhang, Brendan Juba, Guy Van Den Broeck
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:12447-12457, 2021.

Abstract

Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose probabilistic generating circuits (PGCs) for their efficient representation. PGCs are strictly more expressive efficient than many existing tractable probabilistic models, including determinantal point processes (DPPs), probabilistic circuits (PCs) such as sum-product networks, and tractable graphical models. We contend that PGCs are not just a theoretical framework that unifies vastly different existing models, but also show great potential in modeling realistic data. We exhibit a simple class of PGCs that are not trivially subsumed by simple combinations of PCs and DPPs, and obtain competitive performance on a suite of density estimation benchmarks. We also highlight PGCs’ connection to the theory of strongly Rayleigh distributions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-zhang21i, title = {Probabilistic Generating Circuits}, author = {Zhang, Honghua and Juba, Brendan and Van Den Broeck, Guy}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {12447--12457}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/zhang21i/zhang21i.pdf}, url = {https://proceedings.mlr.press/v139/zhang21i.html}, abstract = {Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose probabilistic generating circuits (PGCs) for their efficient representation. PGCs are strictly more expressive efficient than many existing tractable probabilistic models, including determinantal point processes (DPPs), probabilistic circuits (PCs) such as sum-product networks, and tractable graphical models. We contend that PGCs are not just a theoretical framework that unifies vastly different existing models, but also show great potential in modeling realistic data. We exhibit a simple class of PGCs that are not trivially subsumed by simple combinations of PCs and DPPs, and obtain competitive performance on a suite of density estimation benchmarks. We also highlight PGCs’ connection to the theory of strongly Rayleigh distributions.} }
Endnote
%0 Conference Paper %T Probabilistic Generating Circuits %A Honghua Zhang %A Brendan Juba %A Guy Van Den Broeck %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-zhang21i %I PMLR %P 12447--12457 %U https://proceedings.mlr.press/v139/zhang21i.html %V 139 %X Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose probabilistic generating circuits (PGCs) for their efficient representation. PGCs are strictly more expressive efficient than many existing tractable probabilistic models, including determinantal point processes (DPPs), probabilistic circuits (PCs) such as sum-product networks, and tractable graphical models. We contend that PGCs are not just a theoretical framework that unifies vastly different existing models, but also show great potential in modeling realistic data. We exhibit a simple class of PGCs that are not trivially subsumed by simple combinations of PCs and DPPs, and obtain competitive performance on a suite of density estimation benchmarks. We also highlight PGCs’ connection to the theory of strongly Rayleigh distributions.
APA
Zhang, H., Juba, B. & Van Den Broeck, G.. (2021). Probabilistic Generating Circuits. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:12447-12457 Available from https://proceedings.mlr.press/v139/zhang21i.html.

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