Complex Markov Logic Networks: Expressivity and Liftability

Ondrej Kuzelka
Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), PMLR 124:729-738, 2020.

Abstract

We study expressivity of Markov logic networks (MLNs). We introduce complex MLNs, which use complex-valued weights, and show that, unlike standard MLNs with real-valued weights, complex MLNs are"fully expressive". We then observe that discrete Fourier transform can be computed using weighted first order model counting (WFOMC) with complex weights and use this observation to design an algorithm for computing "relational marginal polytopes" which needs substantially less calls to a WFOMC oracle than an existing recent algorithm.

Cite this Paper


BibTeX
@InProceedings{pmlr-v124-kuzelka20a, title = {Complex Markov Logic Networks: Expressivity and Liftability}, author = {Kuzelka, Ondrej}, booktitle = {Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI)}, pages = {729--738}, year = {2020}, editor = {Jonas Peters and David Sontag}, volume = {124}, series = {Proceedings of Machine Learning Research}, month = {03--06 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v124/kuzelka20a/kuzelka20a.pdf}, url = { http://proceedings.mlr.press/v124/kuzelka20a.html }, abstract = {We study expressivity of Markov logic networks (MLNs). We introduce complex MLNs, which use complex-valued weights, and show that, unlike standard MLNs with real-valued weights, complex MLNs are"fully expressive". We then observe that discrete Fourier transform can be computed using weighted first order model counting (WFOMC) with complex weights and use this observation to design an algorithm for computing "relational marginal polytopes" which needs substantially less calls to a WFOMC oracle than an existing recent algorithm.} }
Endnote
%0 Conference Paper %T Complex Markov Logic Networks: Expressivity and Liftability %A Ondrej Kuzelka %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-kuzelka20a %I PMLR %P 729--738 %U http://proceedings.mlr.press/v124/kuzelka20a.html %V 124 %X We study expressivity of Markov logic networks (MLNs). We introduce complex MLNs, which use complex-valued weights, and show that, unlike standard MLNs with real-valued weights, complex MLNs are"fully expressive". We then observe that discrete Fourier transform can be computed using weighted first order model counting (WFOMC) with complex weights and use this observation to design an algorithm for computing "relational marginal polytopes" which needs substantially less calls to a WFOMC oracle than an existing recent algorithm.
APA
Kuzelka, O.. (2020). Complex Markov Logic Networks: Expressivity and Liftability. Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), in Proceedings of Machine Learning Research 124:729-738 Available from http://proceedings.mlr.press/v124/kuzelka20a.html .

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