Sound and complete causal identification with latent variables given local background knowledge

Great efforts have been devoted to causal discovery from observational data, and it is well known that introducing some background knowledge attained from experiments or human expertise can be very helpful. However, it remains unknown that what causal relations are identifiable given background knowledge in the presence of latent confounders. In this paper, we solve the problem with sound and complete orientation rules when the background knowledge is given in a local form. Furthermore, based on the solution to the problem, this paper proposes two applications that are of independent interests. One is that we give a maximal ancestral graph (MAG) listing algorithm, to output all the MAGs consistent to the observational data in the presence of latent variables. The other application is that we present a general active learning framework for causal discovery in the presence of latent confounders, where we propose a baseline criterion to select the intervention variable with a Metropolis-Hastings MAG-sampling method. Experiments validate the efficiency of the proposed MAG listing method and the effectiveness of the active learning framework.& COPY; 2023 Elsevier B.V. All rights reserved.