Compositional Probabilistic and Causal Inference using Tractable Circuit Models

Benjie Wang, Marta Kwiatkowska
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:9488-9498, 2023.

Abstract

Probabilistic circuits (PCs) are a class of tractable probabilistic models, which admit efficient inference routines depending on their structural properties. In this paper, we introduce md-vtrees, a novel structural formulation of (marginal) determinism in structured decomposable PCs, which generalizes previously proposed classes such as probabilistic sentential decision diagrams. Crucially, we show how md-vtrees can be used to derive tractability conditions and efficient algorithms for advanced inference queries expressed as arbitrary compositions of basic probabilistic operations, such as marginalization, multiplication and reciprocals, in a sound and generalizable manner. In particular, we derive the first polytime algorithms for causal inference queries such as backdoor adjustment on PCs. As a practical instantiation of the framework, we propose MDNets, a novel PC architecture using md-vtrees, and empirically demonstrate their application to causal inference.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-wang23o, title = {Compositional Probabilistic and Causal Inference using Tractable Circuit Models}, author = {Wang, Benjie and Kwiatkowska, Marta}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {9488--9498}, year = {2023}, editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}, volume = {206}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v206/wang23o/wang23o.pdf}, url = {https://proceedings.mlr.press/v206/wang23o.html}, abstract = {Probabilistic circuits (PCs) are a class of tractable probabilistic models, which admit efficient inference routines depending on their structural properties. In this paper, we introduce md-vtrees, a novel structural formulation of (marginal) determinism in structured decomposable PCs, which generalizes previously proposed classes such as probabilistic sentential decision diagrams. Crucially, we show how md-vtrees can be used to derive tractability conditions and efficient algorithms for advanced inference queries expressed as arbitrary compositions of basic probabilistic operations, such as marginalization, multiplication and reciprocals, in a sound and generalizable manner. In particular, we derive the first polytime algorithms for causal inference queries such as backdoor adjustment on PCs. As a practical instantiation of the framework, we propose MDNets, a novel PC architecture using md-vtrees, and empirically demonstrate their application to causal inference.} }
Endnote
%0 Conference Paper %T Compositional Probabilistic and Causal Inference using Tractable Circuit Models %A Benjie Wang %A Marta Kwiatkowska %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-wang23o %I PMLR %P 9488--9498 %U https://proceedings.mlr.press/v206/wang23o.html %V 206 %X Probabilistic circuits (PCs) are a class of tractable probabilistic models, which admit efficient inference routines depending on their structural properties. In this paper, we introduce md-vtrees, a novel structural formulation of (marginal) determinism in structured decomposable PCs, which generalizes previously proposed classes such as probabilistic sentential decision diagrams. Crucially, we show how md-vtrees can be used to derive tractability conditions and efficient algorithms for advanced inference queries expressed as arbitrary compositions of basic probabilistic operations, such as marginalization, multiplication and reciprocals, in a sound and generalizable manner. In particular, we derive the first polytime algorithms for causal inference queries such as backdoor adjustment on PCs. As a practical instantiation of the framework, we propose MDNets, a novel PC architecture using md-vtrees, and empirically demonstrate their application to causal inference.
APA
Wang, B. & Kwiatkowska, M.. (2023). Compositional Probabilistic and Causal Inference using Tractable Circuit Models. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:9488-9498 Available from https://proceedings.mlr.press/v206/wang23o.html.

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