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#### Exploring the causal order of binary variables via exponential hierarchies of Markov kernels

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##### Citation

Sun, X., & Janzing, D. (2007). Exploring the causal order of binary variables via
exponential hierarchies of Markov kernels.* Proceedings of the 15th European Symposium on Artificial
Neural Networks (ESANN 2007),* 465-470.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-CE1D-4

##### Abstract

We propose a new algorithm for estimating the causal structure that underlies the observed dependence among n (ngt;=4) binary variables X_1,...,X_n. Our inference principle states that the factorization of the joint probability into conditional probabilities for X_j given X_1,...,X_j-1 often leads to simpler terms if the order of variables is compatible with the directed acyclic graph representing the causal structure. We study joint measures of OR/AND gates and show that the complexity of the conditional probabilities (the so-called Markov kernels), defined by a hierarchy of exponential models, depends on the order of the variables. Some toy and real-data experiments support our inference rule.