Approximate Probabilistic Inference in Hybrid Domains by Hashing

Vaishak Belle KU Leuven, Guy Van den Broeck KU Leuven, Andrea Passerini
Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, PMLR R13:546-555, 2015.

Abstract

In the recent years, there has been considerable progress on fast randomized algorithms that approximate probabilistic inference with tight tolerance and confidence guarantees. The idea here is to formulate inference as a counting task over an annotated propositional theory, called weighted model counting (WMC), which can be partitioned into smaller tasks using universal hashing. An inherent limitation of this approach, however, is that it only admits the inference of discrete probability distributions. In this work, we consider the problem of approximating inference tasks for a probability distribution defined over discrete and continuous random variables. Building on a notion called weighted model integration, which is a strict generalization of WMC and is based on annotating Boolean and arithmetic constraints, we show how probabilistic inference in hybrid domains can be put within reach of hashing-based WMC solvers. Empirical evaluations demonstrate the applicability and promise of the proposal.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR13-leuven15a, title = {Approximate Probabilistic Inference in Hybrid Domains by Hashing}, author = {Leuven, Vaishak Belle KU and Leuven, Guy Van den Broeck KU and Passerini, Andrea}, booktitle = {Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence}, pages = {546--555}, year = {2015}, editor = {Meila, Marina and Heskes, Tom}, volume = {R13}, series = {Proceedings of Machine Learning Research}, month = {12--16 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r13/main/assets/leuven15a/leuven15a.pdf}, url = {https://proceedings.mlr.press/r13/leuven15a.html}, abstract = {In the recent years, there has been considerable progress on fast randomized algorithms that approximate probabilistic inference with tight tolerance and confidence guarantees. The idea here is to formulate inference as a counting task over an annotated propositional theory, called weighted model counting (WMC), which can be partitioned into smaller tasks using universal hashing. An inherent limitation of this approach, however, is that it only admits the inference of discrete probability distributions. In this work, we consider the problem of approximating inference tasks for a probability distribution defined over discrete and continuous random variables. Building on a notion called weighted model integration, which is a strict generalization of WMC and is based on annotating Boolean and arithmetic constraints, we show how probabilistic inference in hybrid domains can be put within reach of hashing-based WMC solvers. Empirical evaluations demonstrate the applicability and promise of the proposal.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Approximate Probabilistic Inference in Hybrid Domains by Hashing %A Vaishak Belle KU Leuven %A Guy Van den Broeck KU Leuven %A Andrea Passerini %B Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2015 %E Marina Meila %E Tom Heskes %F pmlr-vR13-leuven15a %I PMLR %P 546--555 %U https://proceedings.mlr.press/r13/leuven15a.html %V R13 %X In the recent years, there has been considerable progress on fast randomized algorithms that approximate probabilistic inference with tight tolerance and confidence guarantees. The idea here is to formulate inference as a counting task over an annotated propositional theory, called weighted model counting (WMC), which can be partitioned into smaller tasks using universal hashing. An inherent limitation of this approach, however, is that it only admits the inference of discrete probability distributions. In this work, we consider the problem of approximating inference tasks for a probability distribution defined over discrete and continuous random variables. Building on a notion called weighted model integration, which is a strict generalization of WMC and is based on annotating Boolean and arithmetic constraints, we show how probabilistic inference in hybrid domains can be put within reach of hashing-based WMC solvers. Empirical evaluations demonstrate the applicability and promise of the proposal. %Z Reissued by PMLR on 04 October 2026.
APA
Leuven, V.B.K., Leuven, G.V.d.B.K. & Passerini, A.. (2015). Approximate Probabilistic Inference in Hybrid Domains by Hashing. Proceedings of the 31st Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R13:546-555 Available from https://proceedings.mlr.press/r13/leuven15a.html. Reissued by PMLR on 04 October 2026.

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