Differential Semantics of Intervention in Bayesian Networks

Differentiation is an important inference method in Bayesian networks and intervention is a basic notion in causal Bayesian networks. In this paper, we reveal the connection between differentiation and intervention in Bayesian networks. We first encode an intervention as changing a conditional probabilistic table into a partial intervention table. We next introduce a jointree algorithm to compute the full atomic interventions of all nodes with respect to evidence in a Bayesian network. We further discover that an intervention has differential semantics if the intervention variables can reach the evidence in Bayesian networks and the output of the state-of-the-art algorithm is not the differentiation but the intervention of a Bayesian network if the differential nodes cannot reach any one of the evidence nodes. Finally, we present experimental results to demonstrate the efficiency of our algorithm to infer the causal effect in Bayesian networks.