Cyclic Causal Models with Discrete Variables: Markov Chain Equilibrium Semantics and Sample Ordering
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.
Cite
Text
Poole and Crowley. "Cyclic Causal Models with Discrete Variables: Markov Chain Equilibrium Semantics and Sample Ordering." International Joint Conference on Artificial Intelligence, 2013.Markdown
[Poole and Crowley. "Cyclic Causal Models with Discrete Variables: Markov Chain Equilibrium Semantics and Sample Ordering." International Joint Conference on Artificial Intelligence, 2013.](https://mlanthology.org/ijcai/2013/poole2013ijcai-cyclic/)BibTeX
@inproceedings{poole2013ijcai-cyclic,
title = {{Cyclic Causal Models with Discrete Variables: Markov Chain Equilibrium Semantics and Sample Ordering}},
author = {Poole, David and Crowley, Mark},
booktitle = {International Joint Conference on Artificial Intelligence},
year = {2013},
pages = {1060-1068},
url = {https://mlanthology.org/ijcai/2013/poole2013ijcai-cyclic/}
}