Integrating Locally Learned Causal Structures with Overlapping Variables

In many domains, data are distributed among datasets that share only some variables; other recorded variables may occur in only one dataset. There are several asymptotically correct, informative algorithms that search for causal information given a single dataset, even with missing values and hidden variables. There are, however, no such reliable procedures for distributed data with overlapping variables, and only a single heuristic procedure (Structural EM). This paper describes an asymptotically correct procedure, ION, that provides all the information about structure obtainable from the marginal independence relations. Using simulated and real data, the accuracy of ION is compared with that of Structural EM, and with inference on complete, unified data.