Combining experiments to discover linear cyclic models with latent variables
We present an algorithm to infer causal relations between a set of measured variables on the basis of experiments on these variables. The algorithm assumes that the causal relations are linear, but is otherwise completely general: It provides consistent estimates when the true causal structure con- tains feedback loops and latent variables, while the experiments can involve surgical or ‘soft’ interventions on one or multiple variables at a time. The algorithm is ‘online’ in the sense that it combines the results from any set of available experiments, can incorporate background knowledge and resolves conflicts that arise from combining results from different experiments. In addition we provide a necessary and sufficient condition that (i) determines when the algorithm can uniquely return the true graph, and (ii) can be used to select the next best experiment until this condition is satisfied. We demonstrate the method by applying it to simulated data and the flow cytometry data of Sachs et al (2005).