A Bayesian Approach to Causal Discovery

We examine the Bayesian approach to the discovery of directed acyclic causal models and compare it to the constraint-based approach. Both approaches rely on the Causal Markov assumption, but the two di er signi cantly in theory and practice. An important di erence between the approaches is that the constraint-based approach uses categorical information about conditional-independence constraints in the domain, whereas the Bayesian approach weighs the degree to which such constraints hold. As a result, the Bayesian approach has three distinct advantages over its constraint-based counterpart. One, conclusions derived from the Bayesian approach are not susceptible to incorrect categorical decisions about independence facts that can occur with data sets of nite size. Two, using the Bayesian approach, ner distinctions among model structures|both quantitative and qualitative|can be made. Three, information from several models can be combined to make better inferences and to better account for modeling uncertainty. In addition to describing the general Bayesian approach to causal discovery, we review approximationmethods for missing data and hidden variables, and illustrate di erences between the Bayesian and constraint-based methods using arti cial and real examples.