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Cyclic Causal Models with Discrete Variables: Markov Chain Equilibrium Semantics and Sample Ordering

2019-11-08 | |  50 |   48 |   0
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.

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