Exploring the causal order of binary variables via exponential hierarchies of Markov kernels
Xiaohai Sun, Dominik Janzing · MPG.PuRe (Max Planck Society) · 2007
Abstract. We propose a new algorithm for estimating the causal structure that underlies the observed dependence among n (n ≥ 4) binary variables X1,..., Xn. Our inference principle states that the factorization of the joint probability into conditional probabilities for Xj given X1,..., Xj−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. 1