I cannot help but notice that the discussions of changing probabilistic domain, and unusual assumptions about exchangability are reminiscent of inference on social graphs. Connections?
See the big book.
Braz, Rodrigo de Salvo, Eyal Amir, and Dan Roth. 2008. “A Survey of First-Order Probabilistic Models.” In Innovations in Bayesian Networks, edited by Dawn E. Holmes and Lakhmi C. Jain, 156:289–317. Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-85066-3_12.
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.
Getoor, Lise, Daphne Koller, and Avi Pfeffer. n.d. “Learning Probabilistic Relational Models,” 8.
Getoor, Lise, and Ben Taskar, eds. 2007. Introduction to Statistical Relational Learning. Adaptive Computation and Machine Learning. Cambridge, Mass: MIT Press.
Jaeger, Manfred, and Oliver Schulte. 2020. “A Complete Characterization of Projectivity for Statistical Relational Models.” arXiv:2004.10984 [cs, Stat], April. http://arxiv.org/abs/2004.10984.
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. https://doi.org/10.1007/978-3-642-13059-5_25.
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. https://doi.org/10.1007/978-0-387-30164-8_786.