# Higher-Order Causal Message Passing for Experimentation with Complex Interference

arXiv: https://arxiv.org/abs/2411.00945 · HTML: https://mlsanity.com/paper/2411.00945/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 67 references that are in the map.
- First posted on arXiv 1 Nov 2024.

## Builds on (most cited first, 29 of 29)

- [Twitch Gamers: a Dataset for Evaluating Proximity Preserving and Structural Role-based Node Embeddings](https://mlsanity.com/paper/2101.03091/) (2021)
- [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)
- [Causal Inference Under Interference And Network Uncertainty](https://mlsanity.com/paper/1907.00221/) (2019)
- [Markovian Interference in Experiments](https://mlsanity.com/paper/2206.02371/) (2022)
- [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)
- [Treatment Effects in Market Equilibrium](https://mlsanity.com/paper/2109.11647/) (2021)
- [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)
- [Elements of estimation theory for causal effects in the presence of network interference](https://mlsanity.com/paper/1702.03578/) (2017)
- [Correcting for Interference in Experiments: A Case Study at Douyin](https://mlsanity.com/paper/2305.02542/) (2023)
- [Causal clustering: design of cluster experiments under network interference](https://mlsanity.com/paper/2310.14983/) (2023)
- [Experimental Design under Network Interference](https://mlsanity.com/paper/2003.08421/) (2020)
- [Design and Analysis of Bipartite Experiments under a Linear Exposure-Response Model](https://mlsanity.com/paper/2103.06392/) (2021)
- [Staggered Rollout Designs Enable Causal Inference Under Interference Without Network Knowledge](https://mlsanity.com/paper/2205.14552/) (2022)
- [Neighborhood Adaptive Estimators for Causal Inference under Network Interference](https://mlsanity.com/paper/2212.03683/) (2022)
- [Network Interference in Micro-Randomized Trials](https://mlsanity.com/paper/2202.05356/) (2022)
- [Causal Message Passing for Experiments with Unknown and General Network Interference](https://mlsanity.com/paper/2311.08340/) (2023)
- [Limitations of design-based causal inference and A/B testing under arbitrary and network interference](https://mlsanity.com/paper/1705.05752/) (2017)
- [The Local Approach to Causal Inference under Network Interference](https://mlsanity.com/paper/2105.03810/) (2021)
- [Policy design in experiments with unknown interference](https://mlsanity.com/paper/2011.08174/) (2020)
- [Reducing Marketplace Interference Bias Via Shadow Prices](https://mlsanity.com/paper/2205.02274/) (2022)
- [Modeling Interference Using Experiment Roll-out](https://mlsanity.com/paper/2305.10728/) (2023)
- [Central limit theorems via Stein's method for randomized experiments under interference](https://mlsanity.com/paper/1804.03105/) (2018)
- [A systematic investigation of classical causal inference strategies under mis-specification due to network interference](https://mlsanity.com/paper/1810.08259/) (2018)
- [Peer Encouragement Designs in Causal Inference with Partial Interference and Identification of Local Average Network Effects](https://mlsanity.com/paper/1609.04464/) (2016)
- [Optimized Covariance Design for AB Test on Social Network under Interference](https://mlsanity.com/paper/2311.14042/) (2023)

## Built on by (most cited first, 4 of 4)

- [Simulating and Experimenting with Social Media Mobilization Using LLM Agents](https://mlsanity.com/paper/2510.26494/) (2025)
- [On Evolution-Based Models for Experimentation Under Interference](https://mlsanity.com/paper/2511.21675/) (2025)
- [Journey to the Centre of Cluster: Harnessing Interior Nodes for A/B Testing under Network Interference](https://mlsanity.com/paper/2602.04457/) (2026)
- [Causal Effects with Unobserved Unit Types in Interacting Human-AI Systems](https://mlsanity.com/paper/2603.01339/) (2026)

## Abstract (arXiv)

Accurate estimation of treatment effects is essential for decision-making across various scientific fields. This task, however, becomes challenging in areas like social sciences and online marketplaces, where treating one experimental unit can influence outcomes for others through direct or indirect interactions. Such interference can lead to biased treatment effect estimates, particularly when the structure of these interactions is unknown. We address this challenge by introducing a new class of estimators based on causal message-passing, specifically designed for settings with pervasive, unknown interference. Our estimator draws on information from the sample mean and variance of unit outcomes and treatments over time, enabling efficient use of observed data to estimate the evolution of the system state. Concretely, we construct non-linear features from the moments of unit outcomes and treatments and then learn a function that maps these features to future mean and variance of unit outcomes. This allows for the estimation of the treatment effect over time. Extensive simulations across multiple domains, using synthetic and real network data, demonstrate the efficacy of our approach in estimating total treatment effect dynamics, even in cases where interference exhibits non-monotonic behavior in the probability of treatment.