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Conference Paper

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

##### External Resource

https://www.elen.ucl.ac.be/esann/proceedings/papers.php?ann=2007

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##### Fulltext (public)

ESANN-2007-Sun-Janzing.pdf

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##### Citation

Sun, X., & Janzing, D. (2007). Exploring the causal order of binary variables via
exponential hierarchies of Markov kernels. In M. Verleysen (*Advances
in computational intelligence and learning: 15th European Symposium on Artificial Neural Networks: ESANN 2007* (pp.
465-470). Evere, Belgium: D-Side.

Cite as: https://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.