Identifying Best Interventions through Online Importance Sampling

A causal graph G(V, E) specifies causal relationships among the random variables representing the vertices of the graph V . The relationships are specified by the directed edges E ; an edge Vi ! Vj implies that Vi 2 V is a direct parental cause for the effect Vj 2 V . With some abuse of notation, we will denote the random variable associated with a node V 2 V by V itself. We will denote the parents of a node V by pa(V ). The causal dependence implies that V = fV (U 2 pa(V ), ✏V ), where ✏V is an independent exogenous noise variable. One does not get to measure the functions fV in practice. The noise variable and the above functional dependence induce a conditional probability distribution P(V |pa(V )). Further, the joint distribution of {V }V 2V decomposes into product of conditional distributions according to G viewed as a Bayesian Network, i.e. P({V }V 2V) = Q