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Treatment Effect Estimation for Graph-Structured Targets

Shonosuke Harada, Ryosuke Yoneda, Hisashi Kashima

TL;DR

The paper tackles treatment effect estimation when targets are graphs, where observational bias concentrates on a small set of confounding nodes. It introduces GraphTEE, a two-step framework that first identifies confounding nodes via GNNs and SAG pooling, then estimates graph-level treatment effects with a TARNet-based predictor augmented by an IPM-based bias-regularizer that leverages the confounding/non-confounding node decomposition. Theoretical analysis shows that focusing bias mitigation on the smaller confounding subspace yields tighter generalization bounds and more efficient computation, and experiments on synthetic and semi-synthetic data demonstrate that GraphTEE outperforms baselines in both accuracy and robustness to bias. The approach offers a practical, graph-aware solution for causal inference at the graph level, with implications for graph-based decision-making in domains like influencer marketing and group recommendations.

Abstract

Treatment effect estimation, which helps understand the causality between treatment and outcome variable, is a central task in decision-making across various domains. While most studies focus on treatment effect estimation on individual targets, in specific contexts, there is a necessity to comprehend the treatment effect on a group of targets, especially those that have relationships represented as a graph structure between them. In such cases, the focus of treatment assignment is prone to depend on a particular node of the graph, such as the one with the highest degree, thus resulting in an observational bias from a small part of the entire graph. Whereas a bias tends to be caused by the small part, straightforward extensions of previous studies cannot provide efficient bias mitigation owing to the use of the entire graph information. In this study, we propose Graph-target Treatment Effect Estimation (GraphTEE), a framework designed to estimate treatment effects specifically on graph-structured targets. GraphTEE aims to mitigate observational bias by focusing on confounding variable sets and consider a new regularization framework. Additionally, we provide a theoretical analysis on how GraphTEE performs better in terms of bias mitigation. Experiments on synthetic and semi-synthetic datasets demonstrate the effectiveness of our proposed method.

Treatment Effect Estimation for Graph-Structured Targets

TL;DR

The paper tackles treatment effect estimation when targets are graphs, where observational bias concentrates on a small set of confounding nodes. It introduces GraphTEE, a two-step framework that first identifies confounding nodes via GNNs and SAG pooling, then estimates graph-level treatment effects with a TARNet-based predictor augmented by an IPM-based bias-regularizer that leverages the confounding/non-confounding node decomposition. Theoretical analysis shows that focusing bias mitigation on the smaller confounding subspace yields tighter generalization bounds and more efficient computation, and experiments on synthetic and semi-synthetic data demonstrate that GraphTEE outperforms baselines in both accuracy and robustness to bias. The approach offers a practical, graph-aware solution for causal inference at the graph level, with implications for graph-based decision-making in domains like influencer marketing and group recommendations.

Abstract

Treatment effect estimation, which helps understand the causality between treatment and outcome variable, is a central task in decision-making across various domains. While most studies focus on treatment effect estimation on individual targets, in specific contexts, there is a necessity to comprehend the treatment effect on a group of targets, especially those that have relationships represented as a graph structure between them. In such cases, the focus of treatment assignment is prone to depend on a particular node of the graph, such as the one with the highest degree, thus resulting in an observational bias from a small part of the entire graph. Whereas a bias tends to be caused by the small part, straightforward extensions of previous studies cannot provide efficient bias mitigation owing to the use of the entire graph information. In this study, we propose Graph-target Treatment Effect Estimation (GraphTEE), a framework designed to estimate treatment effects specifically on graph-structured targets. GraphTEE aims to mitigate observational bias by focusing on confounding variable sets and consider a new regularization framework. Additionally, we provide a theoretical analysis on how GraphTEE performs better in terms of bias mitigation. Experiments on synthetic and semi-synthetic datasets demonstrate the effectiveness of our proposed method.
Paper Structure (14 sections, 3 theorems, 11 equations, 4 figures, 1 table)

This paper contains 14 sections, 3 theorems, 11 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Treatment effect estimation
  4. Representation learning on graph-structured data
  5. Problem statement
  6. Methodology
  7. Confounding nodes selecting step
  8. Outcome prediction step
  9. Theoretical analysis
  10. Experiments
  11. Datasets
  12. Experimental settings
  13. Results
  14. Conclusion

Key Result

Proposition 1

sriperumbudur2009integral Given $m$, $n$ samples from $p,q$ respectively and for any $\mathcal{F}$ such that $\nu\coloneqq\underset{{x\in\mathcal{X}}}{\sup}f(x)<\infty$, we have with a probability at least $1-\delta$, where $R_m(\mathcal{F})\coloneqq\mathbb{E}\underset{f\in\mathcal{F}}{\sup}\Bigl| \frac{1}{m}\Sigma^{m}_{i=1}\rho_if(x_i) \Bigr|$ and $\{\rho_{i}\}_{i=1}^{m}$ is the Rademacher compl

Figures (4)

  • Figure 1: An illustrative example of treatment effect estimation on graph-structured targets like a social network. The shaded outcome is a counterfactual outcome and never observed. For example, if a central user promotes a product, the entire graph may have positive impression on the product, i.g., the majority of users ($5$ users) may buy it; however, if no-advertisement is given, only $1$ user may have interests in the product and the others may not buy it. In this example, the treatment effect on this network is $4$. Our interest is to understand how interventions affect on entire graphs.
  • Figure 2: Overview of the proposed algorithm. An input graph is first mapped into representations using GNNs $\Phi$ and then decomposed into two types of nodes using $\phi$:(i) confounding and (ii) other nodes. Outcome prediction is conducted using the entire nodes' representations with TARNet-based feedforward neural networks as Eq. (\ref{['eq:supervised_loss']}). Representations of nodes of each type are used for bias mitigation as Eq. (\ref{['eq:ipm_loss']}).
  • Figure 3: Sensitivity of the results to the strength of observational bias $\alpha$. The proposed method shows the robustness against the observational bias and consistently perform better than the baseline methods. Lower values are better.
  • Figure 4: Sensitivity of the results to the strength of hyper-parameter $\lambda$. Although we need to exercise discretion in selecting the hyper-parameter, the proposed method consistently demonstrates the better results than the baseline methods. Lower values are better.

Theorems & Definitions (8)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Proposition 1
  • Proposition 2
  • Theorem 1
  • Remark 1