# Average Direct and Indirect Causal Effects under Interference

arXiv: https://arxiv.org/abs/2104.03802 · HTML: https://mlsanity.com/paper/2104.03802/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2021.

## Built on by (most cited first, 10 of 10)

- [Multi-Armed Bandits with Interference](https://mlsanity.com/paper/2402.01845/) (2024)
- [Individualized Policy Evaluation and Learning under Clustered Network Interference](https://mlsanity.com/paper/2311.02467/) (2023)
- [Balancing Interference and Correlation in Spatial Experimental Designs: A Causal Graph Cut Approach](https://mlsanity.com/paper/2505.20130/) (2025)
- [Graph Machine Learning based Doubly Robust Estimator for Network Causal Effects](https://mlsanity.com/paper/2403.11332/) (2024)
- [A Two-Part Machine Learning Approach to Characterizing Network Interference in A/B Testing](https://mlsanity.com/paper/2308.09790/) (2023)
- [Practical Marketplace Optimization at Uber Using Causally-Informed Machine Learning](https://mlsanity.com/paper/2407.19078/) (2024)
- [A Two-armed Bandit Framework for A/B Testing](https://mlsanity.com/paper/2507.18118/) (2025)
- [Causal Effects with Unobserved Unit Types in Interacting Human-AI Systems](https://mlsanity.com/paper/2603.01339/) (2026)
- [Nonparametric efficient inference for network quantile causal effects under partial interference](https://mlsanity.com/paper/2604.13008/) (2026)
- [Learning to target with network interference](https://mlsanity.com/paper/2605.27794/) (2026)

## Abstract (arXiv)

We propose a definition for the average indirect effect of a binary treatment in the potential outcomes model for causal inference under cross-unit interference. Our definition is analogous to the standard definition of the average direct effect, and can be expressed without needing to compare outcomes across multiple randomized experiments. We show that the proposed indirect effect satisfies a decomposition theorem whereby, in a Bernoulli trial, the sum of the average direct and indirect effects always corresponds to the effect of a policy intervention that infinitesimally increases treatment probabilities. We also consider a number of parametric models for interference, and find that our non-parametric indirect effect remains a natural estimand when re-expressed in the context of these models.