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Handling Overlaps When Lifting Gaussian Bayesian Networks

Mattis Hartwig; Tanya Braun; Ralf Möller
In: Proceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI 2021). International Joint Conference on Artificial Intelligence (IJCAI-2021), August 19-27, Montreal, Quebec, Canada, Pages 4228-4234, ISBN 978-0-9992411-9-6, IJCAI Organization, 8/2021.


Gaussian Bayesian networks are widely used for modeling the behavior of continuous random variables. Lifting exploits symmetries when dealing with large numbers of isomorphic random variables. It provides a more compact representation for more efficient query answering by encoding the symmetries using logical variables. This paper improves on an existing lifted representationof the joint distribution represented by a Gaussian Bayesian network (lifted joint), allowing overlaps between the logical variables. Handling overlaps without grounding a model is critical for modelling real-world scenarios. Specifically, this paper contributes (i) a lifted joint that allows overlaps in logical variables and (ii) a lifted query answering algorithm using the lifted joint. Complexity analyses and experimental results show that — despite overlaps — constructing a lifted joint and answering queries on the lifted joint outperform their grounded counterparts significantly.