Combining Experiments to Discover Linear Cyclic Models
AbstractWe 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 contains 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 con- ﬂicts 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).
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