Causal discovery of linear cyclic models from multiple experimental data sets with overlapping variables

Much of scientific data is collected as randomized experiments intervening on some and observing other variables of interest. Quite often, a given phenomenon is investigated in several studies, and different sets of variables are involved in each study. In this article we consider the problem of integrating such knowledge, inferring as much as possible concerning the underlying causal structure with respect to the union of observed variables from such experimental or passive observational overlapping data sets. We do not assume acyclicity or joint causal sufficiency of the underlying data generating model, but we do restrict the causal relationships to be linear and use only second order statistics of the data. We derive conditions for full model identifiability in the most generic case, and provide novel techniques for incorporating an assumption of faithfulness to aid in inference. In each case we seek to establish what is and what is not determined by the data at hand.