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Estimating Treatment Effects in Networks using Domain Adversarial Training

Daan Caljon, Jente Van Belle, Wouter Verbeke

TL;DR

The paper tackles estimating heterogeneous treatment effects in networks with interference when the exposure mapping is unknown. It introduces HINet, a two-branch graph neural network that learns exposure mappings with a Graph Isomorphism Network and enforces treatment-invariant representations via domain adversarial training to counter network-level covariate shift. The approach yields two new evaluation metrics, PEHNE and CNEE, and demonstrates superior performance across (semi-)synthetic and real-network datasets, especially under homophily and exposure-mapping misspecification. This enables more accurate, robust treatment effect estimation in interconnected settings with realistic, unknown spillover mechanisms, with practical implications for policy and personalized decision-making in networks.

Abstract

Estimating heterogeneous treatment effects in network settings is complicated by interference, meaning that the outcome of an instance can be influenced by the treatment status of others. Existing causal machine learning approaches usually assume a known exposure mapping that summarizes how the outcome of a given instance is influenced by others' treatment, a simplification that is often unrealistic. Furthermore, the interaction between homophily -- the tendency of similar instances to connect -- and the treatment assignment mechanism can induce a network-level covariate shift that may lead to inaccurate treatment effect estimates, a phenomenon that has not yet been explicitly studied. To address these challenges, we propose HINet, a novel method that integrates graph neural networks with domain adversarial training. This combination allows estimating treatment effects under unknown exposure mappings while mitigating the impact of (network-level) covariate shift. An extensive empirical evaluation on synthetic and semi-synthetic network datasets demonstrates the effectiveness of our approach.

Estimating Treatment Effects in Networks using Domain Adversarial Training

TL;DR

The paper tackles estimating heterogeneous treatment effects in networks with interference when the exposure mapping is unknown. It introduces HINet, a two-branch graph neural network that learns exposure mappings with a Graph Isomorphism Network and enforces treatment-invariant representations via domain adversarial training to counter network-level covariate shift. The approach yields two new evaluation metrics, PEHNE and CNEE, and demonstrates superior performance across (semi-)synthetic and real-network datasets, especially under homophily and exposure-mapping misspecification. This enables more accurate, robust treatment effect estimation in interconnected settings with realistic, unknown spillover mechanisms, with practical implications for policy and personalized decision-making in networks.

Abstract

Estimating heterogeneous treatment effects in network settings is complicated by interference, meaning that the outcome of an instance can be influenced by the treatment status of others. Existing causal machine learning approaches usually assume a known exposure mapping that summarizes how the outcome of a given instance is influenced by others' treatment, a simplification that is often unrealistic. Furthermore, the interaction between homophily -- the tendency of similar instances to connect -- and the treatment assignment mechanism can induce a network-level covariate shift that may lead to inaccurate treatment effect estimates, a phenomenon that has not yet been explicitly studied. To address these challenges, we propose HINet, a novel method that integrates graph neural networks with domain adversarial training. This combination allows estimating treatment effects under unknown exposure mappings while mitigating the impact of (network-level) covariate shift. An extensive empirical evaluation on synthetic and semi-synthetic network datasets demonstrates the effectiveness of our approach.
Paper Structure (24 sections, 1 theorem, 27 equations, 7 figures, 11 tables, 2 algorithms)

This paper contains 24 sections, 1 theorem, 27 equations, 7 figures, 11 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related work
  3. Problem Setup
  4. Methodology
  5. Experiments and Discussion
  6. Performance on (semi-)synthetic data
  7. Impact of homophily
  8. Learning exposure mappings
  9. Ablation study
  10. Conclusion
  11. Proof of balanced representations with respect to treatments of neighbors
  12. Homophily and interference
  13. Causal diagram
  14. Balanced representations with respect to treatments of neighbors
  15. Performance metrics
  16. ...and 9 more sections

Key Result

Proposition 1

If the hidden representations $(\boldsymbol{\phi}_i,\boldsymbol{\phi}_{\mathcal{N}_i})$ are treatment-invariant with respect to $T_i$, i.e., $p(\boldsymbol{\phi}_i,\boldsymbol{\phi}_{\mathcal{N}_i}\mid T_i)=p(\boldsymbol{\phi}_{i},\boldsymbol{\phi}_{\mathcal{N}_i})$, then these representations are a

Figures (7)

  • Figure 1: Homophily and the treatment assignment mechanism interact to create clusters of treated and untreated nodes within the network, i.e., network-level covariate shift. When there is no homophily, the treatment is allocated randomly with respect to network topology.
  • Figure 2: DAG of the assumed causal structure.
  • Figure 3: HINet architecture.
  • Figure 4: Impact of balancing node representations on test CNEE (mean $\pm$ SD over five different initializations). The two rows correspond to the BA and Homophily Sim datasets. The columns correspond to different DGPs. The x-axis shows increasing treatment assignment mechanism strength $\beta_{XT}$. Lower values indicate better performance.
  • Figure 5: CNEE across datasets with increasing treatment assignment mechanism strength $\beta_{XT}$.
  • ...and 2 more figures

Theorems & Definitions (2)

  • Proposition 1
  • proof