Discriminating between causal structures in Bayesian Networks given partial observations

Given an observed subset Y1, . . . , Yk of variables in a fixed Bayesian network G, our main result is a tight bound on the generalized mutual information Ic(Y1, . . . , Yk) = ￿k j=1 H(Yj)/c −H(Y1, . . . , Yk) over all probability distributions satisfying G. Our bound depends on the ancestral structure of the nodes in the network. It makes it possible to discriminate between different causal models for a probability distribution, as we show from numerical experiments.