Vector Causal Inference between Two Groups of Variables

Urmi Ninad, Jonas Wahl, Jakob Runge

Abstract:

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