Vector causal inference between two groups of variables

TL;DR

This paper introduces a novel non-parametric, constraint-based method for inferring causal relationships between vector-valued variables, extending causal discovery to complex, multi-dimensional data.

Contribution

It proposes new principles and algorithms for groupwise causal inference between vectors, justified within Pearl's graphical models, and demonstrates effectiveness through simulations.

Findings

Accurately infers causal direction in vector variables

Performs reliably with nonlinear interactions

Outperforms existing state-of-the-art methods

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 relationship 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 principles for groupwise causal reasoning that we justify theoretically 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.