Scaling up Hybrid Probabilistic Inference with Logical and Arithmetic Constraints via Message Passing

Zhe Zeng, Paolo Morettin, Fanqi Yan, Antonio Vergari, Guy Van Den Broeck
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:10990-11000, 2020.

Abstract

Weighted model integration (WMI) is an appealing framework for probabilistic inference: it allows for expressing the complex dependencies in real-world problems, where variables are both continuous and discrete, via the language of Satisfiability Modulo Theories (SMT), as well as to compute probabilistic queries with complex logical and arithmetic constraints. Yet, existing WMI solvers are not ready to scale to these problems. They either ignore the intrinsic dependency structure of the problem entirely, or they are limited to overly restrictive structures. To narrow this gap, we derive a factorized WMI computation enabling us to devise a scalable WMI solver based on message passing, called MP-WMI. Namely, MP-WMI is the first WMI solver that can (i) perform exact inference on the full class of tree-structured WMI problems, and (ii) perform inter-query amortization, e.g., to compute all marginal densities simultaneously. Experimental results show that our solver dramatically outperforms the existingWMI solvers on a large set of benchmarks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-zeng20a, title = {Scaling up Hybrid Probabilistic Inference with Logical and Arithmetic Constraints via Message Passing}, author = {Zeng, Zhe and Morettin, Paolo and Yan, Fanqi and Vergari, Antonio and Van Den Broeck, Guy}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {10990--11000}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/zeng20a/zeng20a.pdf}, url = {https://proceedings.mlr.press/v119/zeng20a.html}, abstract = {Weighted model integration (WMI) is an appealing framework for probabilistic inference: it allows for expressing the complex dependencies in real-world problems, where variables are both continuous and discrete, via the language of Satisfiability Modulo Theories (SMT), as well as to compute probabilistic queries with complex logical and arithmetic constraints. Yet, existing WMI solvers are not ready to scale to these problems. They either ignore the intrinsic dependency structure of the problem entirely, or they are limited to overly restrictive structures. To narrow this gap, we derive a factorized WMI computation enabling us to devise a scalable WMI solver based on message passing, called MP-WMI. Namely, MP-WMI is the first WMI solver that can (i) perform exact inference on the full class of tree-structured WMI problems, and (ii) perform inter-query amortization, e.g., to compute all marginal densities simultaneously. Experimental results show that our solver dramatically outperforms the existingWMI solvers on a large set of benchmarks.} }
Endnote
%0 Conference Paper %T Scaling up Hybrid Probabilistic Inference with Logical and Arithmetic Constraints via Message Passing %A Zhe Zeng %A Paolo Morettin %A Fanqi Yan %A Antonio Vergari %A Guy Van Den Broeck %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-zeng20a %I PMLR %P 10990--11000 %U https://proceedings.mlr.press/v119/zeng20a.html %V 119 %X Weighted model integration (WMI) is an appealing framework for probabilistic inference: it allows for expressing the complex dependencies in real-world problems, where variables are both continuous and discrete, via the language of Satisfiability Modulo Theories (SMT), as well as to compute probabilistic queries with complex logical and arithmetic constraints. Yet, existing WMI solvers are not ready to scale to these problems. They either ignore the intrinsic dependency structure of the problem entirely, or they are limited to overly restrictive structures. To narrow this gap, we derive a factorized WMI computation enabling us to devise a scalable WMI solver based on message passing, called MP-WMI. Namely, MP-WMI is the first WMI solver that can (i) perform exact inference on the full class of tree-structured WMI problems, and (ii) perform inter-query amortization, e.g., to compute all marginal densities simultaneously. Experimental results show that our solver dramatically outperforms the existingWMI solvers on a large set of benchmarks.
APA
Zeng, Z., Morettin, P., Yan, F., Vergari, A. & Van Den Broeck, G.. (2020). Scaling up Hybrid Probabilistic Inference with Logical and Arithmetic Constraints via Message Passing. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:10990-11000 Available from https://proceedings.mlr.press/v119/zeng20a.html.

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