Information-Theoretic Causal Discovery and Intervention Detection over Multiple Environments

Given multiple datasets over a fixed set of random variables, each collected from a different environment, we are interested in discovering the shared underlying causal network and the local interventions per environment, without assuming prior knowledge on which datasets are observational or interventional, and without assuming the shape of the causal dependencies. We formalize this problem using the Algorithmic Model of Causation, instantiate a consistent score via the Minimum Description Length principle, and show under which conditions the network and interventions are identifiable. To efficiently discover causal networks and intervention targets in practice, we introduce the ORION algorithm, which through extensive experiments we show outperforms the state of the art in causal inference over multiple environments.