Lifted reasoning meets weighted model integration

Jonathan Feldstein, Vaishak Belle
Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, PMLR 161:322-332, 2021.

Abstract

Exact inference in probabilistic graphical models is particularly challenging in the presence of relational and other deterministic constraints. For discrete domains, weighted model counting has emerged as an effective and general approach in a variety of formalisms. Weighted first-order model counting, which allows relational atoms and function-free first order logic has pushed the envelope further, by exploiting symmetry properties over indistinguishable groups of objects, and by extension avoids the need to perform inference on the exponential ground theory. Given the limitation to discrete domains, the formulation of weighted model integration was proposed as an extension to weighted model counting for mixed discrete-continuous domains over both symbolic and numeric weight functions. While that formulation has enjoyed considerable attention in recent years, there is very little understanding on whether the task can be solved at a lifted level, that is, whether we can reason with relational models by avoiding grounding. In this paper, we consider this question. We show how to generalize algorithmic ideas known in the circuit compilation for function-free lifted inference to functions with a continuous range.

Cite this Paper

BibTeX
@InProceedings{pmlr-v161-feldstein21a, title = {Lifted reasoning meets weighted model integration}, author = {Feldstein, Jonathan and Belle, Vaishak}, booktitle = {Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence}, pages = {322--332}, year = {2021}, editor = {de Campos, Cassio and Maathuis, Marloes H.}, volume = {161}, series = {Proceedings of Machine Learning Research}, month = {27--30 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v161/feldstein21a/feldstein21a.pdf}, url = {https://proceedings.mlr.press/v161/feldstein21a.html}, abstract = {Exact inference in probabilistic graphical models is particularly challenging in the presence of relational and other deterministic constraints. For discrete domains, weighted model counting has emerged as an effective and general approach in a variety of formalisms. Weighted first-order model counting, which allows relational atoms and function-free first order logic has pushed the envelope further, by exploiting symmetry properties over indistinguishable groups of objects, and by extension avoids the need to perform inference on the exponential ground theory. Given the limitation to discrete domains, the formulation of weighted model integration was proposed as an extension to weighted model counting for mixed discrete-continuous domains over both symbolic and numeric weight functions. While that formulation has enjoyed considerable attention in recent years, there is very little understanding on whether the task can be solved at a lifted level, that is, whether we can reason with relational models by avoiding grounding. In this paper, we consider this question. We show how to generalize algorithmic ideas known in the circuit compilation for function-free lifted inference to functions with a continuous range.} }
Endnote
%0 Conference Paper %T Lifted reasoning meets weighted model integration %A Jonathan Feldstein %A Vaishak Belle %B Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2021 %E Cassio de Campos %E Marloes H. Maathuis %F pmlr-v161-feldstein21a %I PMLR %P 322--332 %U https://proceedings.mlr.press/v161/feldstein21a.html %V 161 %X Exact inference in probabilistic graphical models is particularly challenging in the presence of relational and other deterministic constraints. For discrete domains, weighted model counting has emerged as an effective and general approach in a variety of formalisms. Weighted first-order model counting, which allows relational atoms and function-free first order logic has pushed the envelope further, by exploiting symmetry properties over indistinguishable groups of objects, and by extension avoids the need to perform inference on the exponential ground theory. Given the limitation to discrete domains, the formulation of weighted model integration was proposed as an extension to weighted model counting for mixed discrete-continuous domains over both symbolic and numeric weight functions. While that formulation has enjoyed considerable attention in recent years, there is very little understanding on whether the task can be solved at a lifted level, that is, whether we can reason with relational models by avoiding grounding. In this paper, we consider this question. We show how to generalize algorithmic ideas known in the circuit compilation for function-free lifted inference to functions with a continuous range.
APA
Feldstein, J. & Belle, V.. (2021). Lifted reasoning meets weighted model integration. Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 161:322-332 Available from https://proceedings.mlr.press/v161/feldstein21a.html.

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