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.
['Subramani Mani', 'Constantin F. Aliferis', 'Alexander Statnikov']
Bayesian algorithms for causal data mining