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I cannot help but notice that the discussions of changing probabilistic domain, and unusual assumptions about exchangeability and projectivity are reminiscent of inference on social graphs. Connections?
See the big book of SRL.
Lifted inference
References
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Crane, Harry, and Walter Dempsey. 2019. “Relational Exchangeability.” Journal of Applied Probability 56 (1): 192–208.
De Raedt, Luc, Kristian Kersting, Sriraam Natarajan, and David L. Poole. 2016. Statistical relational artificial intelligence: logic, probability, and computation. Synthesis lectures on artificial intelligence and machine learning #32. San Rafael, California: Morgan & Claypool Publishers.
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Jha, Abhay, Vibhav Gogate, Alexandra Meliou, and Dan Suciu. 2010. “Lifted Inference Seen from the Other Side : The Tractable Features.” In Advances in Neural Information Processing Systems. Vol. 23. Curran Associates, Inc.
Khosravi, Hassan, and Bahareh Bina. 2010. “A Survey on Statistical Relational Learning.” In Advances in Artificial Intelligence, edited by Atefeh Farzindar and Vlado Kešelj, 6085:256–68. Berlin, Heidelberg: Springer Berlin Heidelberg.
Raedt, Luc De, and Kristian Kersting. 2010. “Statistical Relational Learning.” In Encyclopedia of Machine Learning, edited by Claude Sammut and Geoffrey I. Webb, 916–24. Boston, MA: Springer US.
Riguzzi, Fabrizio, Elena Bellodi, Riccardo Zese, Giuseppe Cota, and Evelina Lamma. 2017. “A Survey of Lifted Inference Approaches for Probabilistic Logic Programming Under the Distribution Semantics.” International Journal of Approximate Reasoning 80 (January): 313–33.
Van den Broeck, Guy, Kristian Kersting, Sriraam Natarajan, and David Poole, eds. 2021. An Introduction to Lifted Probabilistic Inference. Cambridge, Massachusetts: The MIT Press.
Van den Broeck, Guy, and Mathias Niepert. 2014. “Lifted Probabilistic Inference for Asymmetric Graphical Models.” arXiv.
Weitkämper, Felix. 2022. “Projectivity Revisited.” arXiv.
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