# Quantifying intrinsic causal contributions via structure preserving interventions

arXiv: https://arxiv.org/abs/2007.00714 · HTML: https://mlsanity.com/paper/2007.00714/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2020.

## Built on by (most cited first, 12 of 12)

- [DoWhy-GCM: An extension of DoWhy for causal inference in graphical causal models](https://mlsanity.com/paper/2206.06821/) (2022)
- [Root Cause Analysis of Outliers with Missing Structural Knowledge](https://mlsanity.com/paper/2406.05014/) (2024)
- [Backtracking Counterfactuals](https://mlsanity.com/paper/2211.00472/) (2022)
- [Counterfactual Effect Decomposition in Multi-Agent Sequential Decision Making](https://mlsanity.com/paper/2410.12539/) (2024)
- [Multiply-Robust Causal Change Attribution](https://mlsanity.com/paper/2404.08839/) (2024)
- [Causal-discovery-based root-cause analysis and its application in time-series prediction error diagnosis](https://mlsanity.com/paper/2411.06990/) (2024)
- [Beyond Single-Feature Importance with ICECREAM](https://mlsanity.com/paper/2307.09779/) (2023)
- [Counterfactual explainability and analysis of variance](https://mlsanity.com/paper/2411.01625/) (2024)
- [On Measuring Intrinsic Causal Attributions in Deep Neural Networks](https://mlsanity.com/paper/2505.09660/) (2025)
- [Scaling Causal Mediation for Complex Systems: A Framework for Root Cause Analysis](https://mlsanity.com/paper/2512.14764/) (2025)
- [cc-Shapley: Measuring Multivariate Feature Importance Needs Causal Context](https://mlsanity.com/paper/2602.20396/) (2026)
- [Feature Attribution in Directed Acyclic Graphs Using Edge Intervention](https://mlsanity.com/paper/2606.15273/) (2026)

## Abstract (arXiv)

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.