Doubly Robust Causal Effect Estimation under Networked Interference via Targeted Learning

TL;DR

This work tackles causal effect estimation under networked interference, where standard IID assumptions fail. It develops TNet, an end-to-end neural estimator that embeds targeted learning to achieve doubly robust estimates of the average dose–response $\psi(t,z)$ under network interference, with a spline-based perturbation capturing the necessary bias-correction. The authors prove a convergence rate that combines spline-approximation error with a product of nuisance-function errors, ensuring consistency if either the outcome model or the propensity model is correct. Extensive semisynthetic experiments on BlogCatalog and Flickr, plus a real-world NO$_x$ emission study, demonstrate that TNet outperforms existing baselines and remains stable to hyperparameter choices, illustrating the practical impact of DR causal estimation under networked interference.

Abstract

Causal effect estimation under networked interference is an important but challenging problem. Available parametric methods are limited in their model space, while previous semiparametric methods, e.g., leveraging neural networks to fit only one single nuisance function, may still encounter misspecification problems under networked interference without appropriate assumptions on the data generation process. To mitigate bias stemming from misspecification, we propose a novel doubly robust causal effect estimator under networked interference, by adapting the targeted learning technique to the training of neural networks. Specifically, we generalize the targeted learning technique into the networked interference setting and establish the condition under which an estimator achieves double robustness. Based on the condition, we devise an end-to-end causal effect estimator by transforming the identified theoretical condition into a targeted loss. Moreover, we provide a theoretical analysis of our designed estimator, revealing a faster convergence rate compared to a single nuisance model. Extensive experimental results on two real-world networks with semisynthetic data demonstrate the effectiveness of our proposed estimators.

Figures (8)

• Figure 1: A toy example showing networked interference between units. The solid red and dashed green arrows, i.e., $\boldsymbol \rightarrow$ and $\boldsymbol \dashrightarrow$, mean the interaction from one to another unit. Whether the dashed green arrow $\boldsymbol \dashrightarrow$ exists depends on the assumption on DGP.
• Figure 2: Model architecture of our proposed TNet. The feature module aggregates the information of covariates of unit $i$ and its neighbor. The generalized propensity estimator module aims to estimate individual propensity score and neighborhood propensity score respectively. The outcome estimator module aims to estimate potential outcomes of unit $i$. The perturbation estimator module aims to estimate $\epsilon(t,z)$ that is adapted into our estimator to achieve double robustness property.
• Figure 3: Sensitivity analysis results on BC and BC_hete datasets.
• Figure 4: Additional hyperparameter sensitivity experimental results on BC.
• Figure 5: Additional hyperparameter sensitivity experimental results on BC(hete).

Theorems & Definitions (21)

• Definition 3.5: Average Main Effects (AME)
• Definition 3.6: Average Spillover Effects (ASE)
• Definition 3.7: Average Total Effects (ATE)
• Theorem 4.1
• Theorem 4.2
• Lemma 4.3: Double Robustness Property
• Theorem 6.1
• Definition 1.1: Individual Main Effects (IME)
• Definition 1.2: Individual Spillover Effects (ISE)
• Definition 1.3: Individual Total Effects (ITE)