On the Relationship Between Probabilistic Circuits and Determinantal Point Processes

Honghua Zhang, Steven Holtzen, Guy Broeck
Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), PMLR 124:1188-1197, 2020.

Abstract

Scaling probabilistic models to large realistic problems and datasets is a key challenge in machine learning. Central to this effort is the development of tractable probabilistic models (TPMs): models whose structure guarantees efficient probabilistic inference algorithms. The current landscape of TPMs is fragmented: there exist various kinds of TPMs with different strengths and weaknesses. Two of the most prominent classes of TPMs are determinantal point processes (DPPs) and probabilistic circuits (PCs). This paper provides the first systematic study of their relationship. We propose a unified analysis and shared language for discussing DPPs and PCs. Then we establish theoretical barriers for the unification of these two families, and prove that there are cases where DPPs have no compact representation as a class of PCs. We close with a perspective on the central problem of unifying these tractable models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v124-zhang20c, title = {On the Relationship Between Probabilistic Circuits and Determinantal Point Processes}, author = {Zhang, Honghua and Holtzen, Steven and Van den Broeck, Guy}, booktitle = {Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI)}, pages = {1188--1197}, year = {2020}, editor = {Peters, Jonas and Sontag, David}, volume = {124}, series = {Proceedings of Machine Learning Research}, month = {03--06 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v124/zhang20c/zhang20c.pdf}, url = {https://proceedings.mlr.press/v124/zhang20c.html}, abstract = {Scaling probabilistic models to large realistic problems and datasets is a key challenge in machine learning. Central to this effort is the development of tractable probabilistic models (TPMs): models whose structure guarantees efficient probabilistic inference algorithms. The current landscape of TPMs is fragmented: there exist various kinds of TPMs with different strengths and weaknesses. Two of the most prominent classes of TPMs are determinantal point processes (DPPs) and probabilistic circuits (PCs). This paper provides the first systematic study of their relationship. We propose a unified analysis and shared language for discussing DPPs and PCs. Then we establish theoretical barriers for the unification of these two families, and prove that there are cases where DPPs have no compact representation as a class of PCs. We close with a perspective on the central problem of unifying these tractable models.} }
Endnote
%0 Conference Paper %T On the Relationship Between Probabilistic Circuits and Determinantal Point Processes %A Honghua Zhang %A Steven Holtzen %A Guy Broeck %B Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI) %C Proceedings of Machine Learning Research %D 2020 %E Jonas Peters %E David Sontag %F pmlr-v124-zhang20c %I PMLR %P 1188--1197 %U https://proceedings.mlr.press/v124/zhang20c.html %V 124 %X Scaling probabilistic models to large realistic problems and datasets is a key challenge in machine learning. Central to this effort is the development of tractable probabilistic models (TPMs): models whose structure guarantees efficient probabilistic inference algorithms. The current landscape of TPMs is fragmented: there exist various kinds of TPMs with different strengths and weaknesses. Two of the most prominent classes of TPMs are determinantal point processes (DPPs) and probabilistic circuits (PCs). This paper provides the first systematic study of their relationship. We propose a unified analysis and shared language for discussing DPPs and PCs. Then we establish theoretical barriers for the unification of these two families, and prove that there are cases where DPPs have no compact representation as a class of PCs. We close with a perspective on the central problem of unifying these tractable models.
APA
Zhang, H., Holtzen, S. & Broeck, G.. (2020). On the Relationship Between Probabilistic Circuits and Determinantal Point Processes. Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), in Proceedings of Machine Learning Research 124:1188-1197 Available from https://proceedings.mlr.press/v124/zhang20c.html.

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