Vector Causal Inference between Two Groups of Variables

Methods to identify cause-effect relationships currently mostly assume the variables be scalar random variables. However, in many fields objects of interest are vectors or groups We present a new constraint-based non-parametric approach for inferring causal relationship between two vector-valued from observational data. Our method employs sparsity estimates directed and undirected graphs is based on principles groupwise reasoning that we justify theoretically Pearl's graphical model-based causality framework. theoretical considerations complemented by discovery algorithms interactions which find correct direction reliably simulations even if nonlinear. evaluate our methods empirically compare them other state-of-the-art techniques.