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Doubly Robust Causal Effect Estimation under Networked Interference via Targeted Learning
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Proposes TNet, an end-to-end doubly robust estimator for dose-response causal effects under networked interference that adapts targeted maximum likelihood (TMLE) into a neural targeted loss with a B-spline perturbation module.
Problem
Estimating average and individual causal effects (main, spillover, total) from observational networked data where units' outcomes depend on neighbors' treatments; existing parametric and semiparametric estimators are prone to misspecification of nuisance models.
Approach
Generalizes the TMLE efficient influence curve to networked interference with continuous neighborhood exposure and turns the EIC-solving condition into a targeted loss trained jointly with GCN-based propensity, outcome and B-spline perturbation networks, yielding double robustness and a convergence rate that benefits from the product of nuisance rates.
Key results
- On BC(homo) within-sample, TNet reports AME MAE 0.0481 vs 0.0877 for best baseline RRNet; ASE 0.0180 vs 0.0227 (RRNet); ATE 0.0533 vs 0.0284 for NDR being best.
- TNet with the targeted loss L3 outperforms TNet without L3 across average and individual effects on both datasets.
- Hyperparameter sensitivity: TNet keeps MAE below 0.1 for the three average effects across alpha and gamma sweeps.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use TNet instead of the strongest baseline | Causal effect estimation under network interference · BC(homo), Within Sample AME and ASE; Out-of Sample AME, ASE, and ATE | ε_average (MAE) | Helped |
| Use TNet instead of the strongest baseline | Causal effect estimation under network interference · BC(homo), Within Sample ATE | ε_average (MAE) | Hurt |
| Use TNet instead of the strongest baseline | Causal effect estimation under network interference · BC(homo), Within and Out-of Sample IME, ISE, and ITE | ε_individual (RMSE) | Helped |
| Add the L3 perturbation loss (ablation) | TNet · BC(homo), Within Sample and Out-of Sample AME, ASE, and ATE | ε_average (MAE) | Helped |
| Add the L3 perturbation loss (ablation) | TNet · BC(homo), Within Sample and Out-of Sample IME, ISE, and ITE | ε_individual (RMSE) | Helped |
Surprising findings
- On ATE in BC(homo), NDR (0.0284) beats TNet (0.0533) within sample, which the paper does not explain in depth.
- TNet without the targeted loss performs worse than NetEst and RRNet, indicating the gains come mainly from the targeting term.
Limitations
- Evaluation only on semisynthetic outcomes with simple linear-additive DGP on two networks.
- Theory relies on strong assumptions such as bounded densities, sub-Gaussian noise and B-spline dimension growth rates.
- Double robustness relies on the convergence of one nuisance model; no real-world ground-truth causal effects.
Experimental setup
Datasets: BlogCatalog Flickr
Benchmarks: BlogCatalog semisynthetic (homo/hete) Flickr semisynthetic (homo/hete)
Metrics: MAE of AME/ASE/ATE root precision in estimation of heterogeneous effects (IME/I
Baselines: CFR+z ND+z GEst NetEst RRNet NDR
Builds on: targeted maximum likelihood estimation NDR CFR GCN
Closest papers by meaning
- Online Experimental Design With Estimation-Regret Trade-off Under Network Interference (NeurIPS 2025 · similarity 0.89)
- Higher-Order Causal Message Passing for Experimentation with Complex Interference (NeurIPS 2024 · similarity 0.88)
- Learning to target with network interference (NeurIPS 2026 · similarity 0.87)
- Independent-Set Design of Experiments for Estimating Treatment and Spillover Effects under Network Interference (ICLR 2024 · similarity 0.87)
- Doubly Robust Proximal Causal Learning for Continuous Treatments (ICLR 2024 · similarity 0.86)
- Just Ramp-Up: Debiasing Regression-based Estimator for A/B Tests under Network Interference (NeurIPS 2026 · similarity 0.84)
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