# A Graph-Theoretic Approach to Randomization Tests of Causal Effects Under General Interference

arXiv: https://arxiv.org/abs/1910.10862 · HTML: https://mlsanity.com/paper/1910.10862/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2019.

## Built on by (most cited first, 7 of 7)

- [Policy Evaluation for Temporal and/or Spatial Dependent Experiments](https://mlsanity.com/paper/2202.10887/) (2022)
- [Neighborhood Adaptive Estimators for Causal Inference under Network Interference](https://mlsanity.com/paper/2212.03683/) (2022)
- [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)
- [Causal Deepsets for Off-policy Evaluation under Spatial or Spatio-temporal Interferences](https://mlsanity.com/paper/2407.17910/) (2024)
- [Bayesian Estimation of Causal Effects Using Proxies of a Latent Interference Network](https://mlsanity.com/paper/2505.08395/) (2025)
- [Near-Optimal Experimental Design Under the Budget Constraint in Online Platforms](https://mlsanity.com/paper/2302.05005/) (2023)

## Abstract (arXiv)

Interference exists when a unit's outcome depends on another unit's treatment assignment. For example, intensive policing on one street could have a spillover effect on neighboring streets. Classical randomization tests typically break down in this setting because many null hypotheses of interest are no longer sharp under interference. A promising alternative is to instead construct a conditional randomization test on a subset of units and assignments for which a given null hypothesis is sharp. Finding these subsets is challenging, however, and existing methods are limited to special cases or have limited power. In this paper, we propose valid and easy-to-implement randomization tests for a general class of null hypotheses under arbitrary interference between units. Our key idea is to represent the hypothesis of interest as a bipartite graph between units and assignments, and to find an appropriate biclique of this graph. Importantly, the null hypothesis is sharp within this biclique, enabling conditional randomization-based tests. We also connect the size of the biclique to statistical power. Moreover, we can apply off-the-shelf graph clustering methods to find such bicliques efficiently and at scale. We illustrate our approach in settings with clustered interference and show advantages over methods designed specifically for that setting. We then apply our method to a large-scale policing experiment in Medellin, Colombia, where interference has a spatial structure.