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Methods to identify cause-effect relationships currently mostly assume thevariables to be scalar random variables. However, in many fields the objects ofinterest are vectors or groups of scalar variables. We present a newconstraint-based non-parametric approach for inferring the causal relationshipbetween two vector-valued random variables from observational data. Our methodemploys sparsity estimates of directed and undirected graphs and is based ontwo new principles for groupwise causal reasoning that we justify theoreticallyin Pearl's graphical model-based causality framework. Our theoreticalconsiderations are complemented by two new causal discovery algorithms forcausal interactions between two random vectors which find the correct causaldirection reliably in simulations even if interactions are nonlinear. Weevaluate our methods empirically and compare them to other state-of-the-arttechniques.

Vector causal inference between two groups of variables