2026-08-10T15:59:53Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8089 2024-03-06T10:40:51Z ddc:004 open_access

A Formal Semantics of Influence in Bayesian Reasoning Jacobs, Bart Zanasi, Fabio probability distribution Bayesian network influence This paper proposes a formal definition of influence in Bayesian reasoning, based on the notions of state (as probability distribution), predicate, validity and conditioning. Our approach highlights how conditioning a joint entwined/entangled state with a predicate on one of its components has 'crossover' influence on the other components. We use the total variation metric on probability distributions to quantitatively measure such influence. These insights are applied to give a rigorous explanation of the fundamental concept of d-separation in Bayesian networks. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Bart Jacobs and Fabio Zanasi 2017 Is Part Of LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2017.21 urn:nbn:de:0030-drops-80896 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.21 eng https://creativecommons.org/licenses/by/3.0/legalcode