Quantifying intrinsic causal contributions via structure preserving interventions

TL;DR

This paper introduces a new method to quantify the intrinsic causal influence of nodes in a DAG using structure-preserving interventions and Shapley symmetrization, applicable to variance and entropy.

Contribution

It presents a novel framework for measuring intrinsic causal contributions in DAGs through structure-preserving interventions and Shapley-based symmetrization, extending to multiple target metrics.

Findings

Intrinsic causal influence can be separated from ancestral effects.

Shapley symmetrization ensures relabeling invariance.

Method reduces to ANOVA in linear cases.

Abstract

We propose a notion of causal influence that describes the `intrinsic' part of the contribution of a node on a target node in a DAG. By recursively writing each node as a function of the upstream noise terms, we separate the intrinsic information added by each node from the one obtained from its ancestors. To interpret the intrinsic information as a {\it causal} contribution, we consider `structure-preserving interventions' that randomize each node in a way that mimics the usual dependence on the parents and does not perturb the observed joint distribution. To get a measure that is invariant with respect to relabelling nodes we use Shapley based symmetrization and show that it reduces in the linear case to simple ANOVA after resolving the target node into noise variables. We describe our contribution analysis for variance and entropy, but contributions for other target metrics can be defined analogously. The code is available in the package gcm of the open source library DoWhy.