{"type":"ScholarlyArticle","title":"Cyclic Causal Models with Discrete Variables: Markov Chain Equilibrium Semantics and Sample Ordering","authors":[{"name":"David Poole","slug":"david-poole","given":"David","family":"Poole","affiliation":""},{"name":"Mark Crowley","slug":"mark-crowley","given":"Mark","family":"Crowley","affiliation":""}],"abstract":"We analyze the foundations of cyclic causal models for discrete variables, and compare structural equation models (SEMs) to an alternative semantics as the equilibrium (stationary) distribution of a Markov chain. We show under general conditions, discrete cyclic SEMs cannot have independent noise; even in the simplest case, cyclic structural equation models imply constraints on the noise. We give a formalization of an alternative Markov chain equilibrium semantics which requires not only the causal graph, but also a sample order. We show how the resulting equilibrium is a function of the sample ordering, both theoretically and empirically.","doi":null,"url":"https://ijcai.org/proceedings/2013/161","pdf":"https://ijcai.org/proceedings/2013/0161.pdf","markdown":"https://ijcai.org/proceedings/2013/161.md","bibtex":"https://ijcai.org/proceedings/2013/bibtex/161","volume":{"slug":"2013","title":"Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2013","url":"https://ijcai.org/proceedings/2013/","year":2013,"location":"Beijing, China","dates":"3–9 August 2013","editors":"Francesca Rossi","isbn":"978-1-57735-633-2","publisher":"AAAI Press / International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":161,"pages":{"first":1060,"last":1067},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}