# Causal Message Passing for Experiments with Unknown and General Network Interference

arXiv: https://arxiv.org/abs/2311.08340 · HTML: https://mlsanity.com/paper/2311.08340/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 80 references that are in the map.
- First posted on arXiv 14 Nov 2023.

## Builds on (most cited first, 16 of 16)

- [Statistical physics of inference: Thresholds and algorithms](https://mlsanity.com/paper/1511.02476/) (2015)
- [A unifying tutorial on Approximate Message Passing](https://mlsanity.com/paper/2105.02180/) (2021)
- [Graph cluster randomization: network exposure to multiple universes](https://mlsanity.com/paper/1305.6979/) (2013)
- [Design and analysis of experiments in networks: Reducing bias from interference](https://mlsanity.com/paper/1404.7530/) (2014)
- [Experimental Design in Two-Sided Platforms: An Analysis of Bias](https://mlsanity.com/paper/2002.05670/) (2020)
- [Markovian Interference in Experiments](https://mlsanity.com/paper/2206.02371/) (2022)
- [Approximate Message Passing for orthogonally invariant ensembles: Multivariate non-linearities and spectral initialization](https://mlsanity.com/paper/2110.02318/) (2021)
- [Estimating Total Treatment Effect in Randomized Experiments with Unknown Network Structure](https://mlsanity.com/paper/2205.12803/) (2022)
- [Experimenting in Equilibrium](https://mlsanity.com/paper/1903.02124/) (2019)
- [Randomized Graph Cluster Randomization](https://mlsanity.com/paper/2009.02297/) (2020)
- [Optimal Experimental Design for Staggered Rollouts](https://mlsanity.com/paper/1911.03764/) (2019)
- [Reducing Interference Bias in Online Marketplace Pricing Experiments](https://mlsanity.com/paper/2004.12489/) (2020)
- [Regression adjustments for estimating the global treatment effect in experiments with interference](https://mlsanity.com/paper/1808.08683/) (2018)
- [Model-assisted design of experiments in the presence of network correlated outcomes](https://mlsanity.com/paper/1507.00803/) (2015)
- [Testing for arbitrary interference on experimentation platforms](https://mlsanity.com/paper/1704.01190/) (2017)
- [Limitations of design-based causal inference and A/B testing under arbitrary and network interference](https://mlsanity.com/paper/1705.05752/) (2017)

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

- [Unraveling the Interplay between Carryover Effects and Reward Autocorrelations in Switchback Experiments](https://mlsanity.com/paper/2403.17285/) (2024)
- [Higher-Order Causal Message Passing for Experimentation with Complex Interference](https://mlsanity.com/paper/2411.00945/) (2024)
- [Simulating and Experimenting with Social Media Mobilization Using LLM Agents](https://mlsanity.com/paper/2510.26494/) (2025)
- [Differences-in-Neighbors for Network Interference in Experiments](https://mlsanity.com/paper/2503.02271/) (2025)
- [Bayesian Estimation of Causal Effects Using Proxies of a Latent Interference Network](https://mlsanity.com/paper/2505.08395/) (2025)
- [On Evolution-Based Models for Experimentation Under Interference](https://mlsanity.com/paper/2511.21675/) (2025)
- [Causal Effects with Unobserved Unit Types in Interacting Human-AI Systems](https://mlsanity.com/paper/2603.01339/) (2026)

## Abstract (arXiv)

Randomized experiments are a powerful methodology for data-driven evaluation of decisions or interventions. Yet, their validity may be undermined by network interference. This occurs when the treatment of one unit impacts not only its outcome but also that of connected units, biasing traditional treatment effect estimations. Our study introduces a new framework to accommodate complex and unknown network interference, moving beyond specialized models in the existing literature. Our framework, termed causal message-passing, is grounded in high-dimensional approximate message passing methodology. It is tailored for multi-period experiments and is particularly effective in settings with many units and prevalent network interference. The framework models causal effects as a dynamic process where a treated unit's impact propagates through the network via neighboring units until equilibrium is reached. This approach allows us to approximate the dynamics of potential outcomes over time, enabling the extraction of valuable information before treatment effects reach equilibrium. Utilizing causal message-passing, we introduce a practical algorithm to estimate the total treatment effect, defined as the impact observed when all units are treated compared to the scenario where no unit receives treatment. We demonstrate the effectiveness of this approach across five numerical scenarios, each characterized by a distinct interference structure.