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Higher-Order Causal Message Passing for Experimentation with Complex Interference
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Proposes HO-CMP, a learned state-evolution estimator that uses higher-order moments (mean and variance) of outcomes over a multi-stage rollout to estimate total treatment effect dynamics under unknown network interference.
Problem
Estimating total treatment effects over time in randomized experiments under pervasive, unknown network interference, where the interference structure is unobserved and outcomes may be off-equilibrium.
Approach
Extends first-order causal message passing by learning, via linear regression on non-linear features of sample mean, sample variance, and treatment means, the state-evolution update map for both outcome mean and variance across a multi-stage staggered rollout, so that off-equilibrium data and higher moments are used to predict counterfactual TTE without knowing the network.
Key results
- In the Non-LinearInMeans setting, HO-CMP achieves substantially lower estimation error than FO-CMP across random geometric and Twitch graphs.
- DM and HT estimators show significant bias across all simulated cases because they ignore network interference.
- PolyFit shows large bias when T=40 because off-equilibrium sample averages are used, whereas FO-CMP and HO-CMP remain accurate in both LinearInMeans settings.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add higher-order treatment and outcome-variance features (ablation) | FO-CMP, yielding HO-CMP · Non-LinearInMeans | TTE estimation error | Helped |
| Add higher-order treatment and outcome-variance features (ablation) | FO-CMP, yielding HO-CMP · LinearInMeans | TTE estimation error | No clear effect |
| Use FO-CMP instead of HO-CMP, omitting outcome variance and squared treatment features (ablation) | HO-CMP · Non-LinearInMeans | TTE estimation error | Hurt |
| Use difference-in-means without accounting for network interference | TTE estimation · All cases | TTE estimation bias | Hurt |
| Use Horvitz-Thompson without accounting for network interference | TTE estimation · All cases | TTE estimation bias | Hurt |
| Use PolyFit with a short experiment horizon | PolyFit · LinearInMeans, T=40 | TTE estimation bias | Hurt |
| Use degree-L polynomial interpolation | PolyFit · LinearInMeans, T=200 | TTE estimation variance | Hurt |
Surprising findings
- PolyFit's bias with short horizons is driven by outcomes that have not yet reached equilibrium, which the message-passing estimators handle by design.
Limitations
- Framework applicability may be limited when multiple outcome observations over time are unavailable.
- PolyFit-style polynomial fitting has high variance as the number of treatment levels grows; HO-CMP's learned mapping depends on feature choice made heuristically.
- Evaluation is limited to simulated outcome models and two graphs.
Experimental setup
Datasets: simulated random geometric graph Twitch social network graph
Benchmarks: simulated random geometric graph experiments Twitch network experiments
Metrics: estimation bias variance of TTE estimates over time
Baselines: difference-in-means Horvitz-Thompson estimator PolyFit FO-CMP
Builds on: causal message passing approximate message passing PolyFit
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