Detecting responsible nodes in differential Bayesian networks

To study the roles that different nodes play in differentiating Bayesian networks under two states, such as control versus disease, we formulate two node-specific scores to facilitate such assessment. The first score is motivated by the prediction invariance property of a causal model. The second score results from modifying an existing score constructed for differential analysis of undirected networks. We develop strategies based on these scores to identify nodes responsible for topological differences between two Bayesian networks. Synthetic data and real-life data from designed experiments are used to demonstrate the efficacy of the proposed methods in detecting responsible nodes.