<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Poole, David</style></author><author><style face="normal" font="default" size="100%">Crowley, Mark</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Cyclic causal models with discrete variables: Markov chain equilibrium semantics and sample ordering</style></title><secondary-title><style face="normal" font="default" size="100%">IJCAI International Joint Conference on Artificial Intelligence</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Causality</style></keyword><keyword><style  face="normal" font="default" size="100%">probabilistic inference</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2013</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://dl.acm.org/citation.cfm?id=2540281</style></url></web-urls></urls><pub-location><style face="normal" font="default" size="100%">Beijing, China</style></pub-location><pages><style face="normal" font="default" size="100%">1060–1068</style></pages><isbn><style face="normal" font="default" size="100%">9781577356332</style></isbn><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">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.</style></abstract></record></records></xml>