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# Bayesian Algorithms for Causal Data Mining

*Proceedings of Workshop on Causality: Objectives and Assessment at NIPS 2008*, PMLR 6:121-136, 2010.

#### Abstract

We present two Bayesian algorithms CD-B and CD-H for discovering unconfounded cause and effect relationships from observational data without assuming causal sufficiency which precludes hidden common causes for the observed variables. The CD-B algorithm first estimates the Markov blanket of a node $X$ using a Bayesian greedy search method and then applies Bayesian scoring methods to discriminate the parents and children of $X$. Using the set of parents and set of children CD-B constructs a global Bayesian network and outputs the causal effects of a node $X$ based on the identification of $Y$ arcs. Recall that if a node $X$ has two parent nodes $A, B$ and a child node $C$ such that there is no arc between $A, B$ and $A, B$ are not parents of $C$, then the arc from $X$ to $C$ is called a $Y$ arc. The CD-H algorithm uses the MMPC algorithm to estimate the union of parents and children of a target node $X$. The subsequent steps are similar to those of CD-B. We evaluated the CD-B and CD-H algorithms empirically based on simulated data from four different Bayesian networks. We also present comparative results based on the identification of $Y$ structures and $Y$ arcs from the output of the PC, MMHC and FCI algorithms. The results appear promising for mining causal relationships that are unconfounded by hidden variables from observational data.