The effect of combination functions on the complexity of relational Bayesian networks

Denis Deratani Mauá, Fabio Gagliardi Cozman

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

© 2017 Elsevier Inc. We study the complexity of inference with Relational Bayesian Networks as parameterized by their probability formulas. We show that without combination functions, inference is PP-complete, displaying the same complexity as standard Bayesian networks (this is so even when the domain is succinctly specified in binary notation). Using only maximization as combination function, we obtain inferential complexity that ranges from PP-complete to PSPACE-complete to PEXP-complete. And by combining mean and threshold combination functions, we obtain complexity classes in all levels of the counting hierarchy. We also investigate the use of arbitrary combination functions and obtain that inference is EXP-complete even under a seemingly strong restriction. Finally, we examine the query complexity of Relational Bayesian Networks (i.e., when the relational model is fixed), and we obtain that inference is complete for PP.
Original languageAmerican English
Pages (from-to)178-195
Number of pages18
JournalInternational Journal of Approximate Reasoning
DOIs
StatePublished - 1 Jun 2017
Externally publishedYes

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