Active Learning of Causal Networks with Intervention Experiments and Optimal Designs

The causal discovery from data is important for various scientific investigations. Because we cannot distinguish the different directed acyclic graphs (DAGs) in a Markov equivalence class learned from observational data, we have to collect further information on causal structures from experiments with external interventions. In this paper, we propose an active learning approach for discovering causal structures in which we first find a Markov equivalence class from observational data, and then we orient undirected edges in every chain component via intervention experiments separately. In the experiments, some variables are manipulated through external interventions. We discuss two kinds of intervention experiments, randomized experiment and quasi-experiment. Furthermore, we give two optimal designs of experiments, a batch-intervention design and a sequential-intervention design, to minimize the number of manipulated variables and the set of candidate structures based on the minimax and the maximum entropy criteria. We show theoretically that structural learning can be done locally in subgraphs of chain components without need of checking illegal v-structures and cycles in the whole network and that a Markov equivalence subclass obtained after each intervention can still be depicted as a chain graph.