Exact Bayesian structure learning from uncertain interventions

We show how to apply the dynamic program- ming algorithm of Koivisto and Sood (KS04, Koi06), which computes the exact posterior marginal edge probabilities p(Gij = 1|D) of a DAGG given data D, to the case where the data is obtained by interventions (experiments). In particular, we consider the case where the targets of the interventions are a priori unknown. We show that it is possible to learn the targets of in- tervention at the same time as learning the causal structure. We apply our exact technique to a bio- logical data set that had previously been analyzed using MCMC (SPP+05, EW06, WGH06).