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Learning and Testing Exposure Mappings of Interference using Graph Convolutional Autoencoder

Martin Huber, Jannis Kueck, Mara Mattes

TL;DR

This paper tackles identifying direct treatment effects under network interference by learning exposure mappings from network data using a graph convolutional autoencoder (GCA) and validating them with a machine learning–based conditional independence test. It integrates a double machine learning (DML) framework to estimate average direct effects, using a learned exposure $\tilde{Z}_i$ as an instrument to validate a researcher-specified exposure $\dot{Z}_i$. The main contributions are a data-driven method to uncover complex exposure mappings, a tractable testing procedure for exposure-mapping validity, and finite-sample evidence that the approach yields consistent direct-effect estimates when the mapping is correctly specified, with a principled alternative when it is not. Overall, the work advances causal representation learning for network-based interference and provides practical tools for robust inference in graph-structured causal settings.

Abstract

Interference or spillover effects arise when an individual's outcome (e.g., health) is influenced not only by their own treatment (e.g., vaccination) but also by the treatment of others, creating challenges for evaluating treatment effects. Exposure mappings provide a framework to study such interference by explicitly modeling how the treatment statuses of contacts within an individual's network affect their outcome. Most existing research relies on a priori exposure mappings of limited complexity, which may fail to capture the full range of interference effects. In contrast, this study applies a graph convolutional autoencoder to learn exposure mappings in a data-driven way, which exploit dependencies and relations within a network to more accurately capture interference effects. As our main contribution, we introduce a machine learning-based test for the validity of exposure mappings and thus test the identification of the direct effect. In this testing approach, the learned exposure mapping is used as an instrument to test the validity of a simple, user-defined exposure mapping. The test leverages the fact that, if the user-defined exposure mapping is valid (so that all interference operates through it), then the learned exposure mapping is statistically independent of any individual's outcome, conditional on the user-defined exposure mapping. We assess the finite-sample performance of this proposed validity test through a simulation study.

Learning and Testing Exposure Mappings of Interference using Graph Convolutional Autoencoder

TL;DR

This paper tackles identifying direct treatment effects under network interference by learning exposure mappings from network data using a graph convolutional autoencoder (GCA) and validating them with a machine learning–based conditional independence test. It integrates a double machine learning (DML) framework to estimate average direct effects, using a learned exposure as an instrument to validate a researcher-specified exposure . The main contributions are a data-driven method to uncover complex exposure mappings, a tractable testing procedure for exposure-mapping validity, and finite-sample evidence that the approach yields consistent direct-effect estimates when the mapping is correctly specified, with a principled alternative when it is not. Overall, the work advances causal representation learning for network-based interference and provides practical tools for robust inference in graph-structured causal settings.

Abstract

Interference or spillover effects arise when an individual's outcome (e.g., health) is influenced not only by their own treatment (e.g., vaccination) but also by the treatment of others, creating challenges for evaluating treatment effects. Exposure mappings provide a framework to study such interference by explicitly modeling how the treatment statuses of contacts within an individual's network affect their outcome. Most existing research relies on a priori exposure mappings of limited complexity, which may fail to capture the full range of interference effects. In contrast, this study applies a graph convolutional autoencoder to learn exposure mappings in a data-driven way, which exploit dependencies and relations within a network to more accurately capture interference effects. As our main contribution, we introduce a machine learning-based test for the validity of exposure mappings and thus test the identification of the direct effect. In this testing approach, the learned exposure mapping is used as an instrument to test the validity of a simple, user-defined exposure mapping. The test leverages the fact that, if the user-defined exposure mapping is valid (so that all interference operates through it), then the learned exposure mapping is statistically independent of any individual's outcome, conditional on the user-defined exposure mapping. We assess the finite-sample performance of this proposed validity test through a simulation study.
Paper Structure (9 sections, 1 theorem, 21 equations, 3 figures, 2 tables)

This paper contains 9 sections, 1 theorem, 21 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Causal effects and identification
  3. Learning exposure mappings
  4. Testing the validity of exposure mappings
  5. Estimation of causal effects
  6. Simulation
  7. Conclusion
  8. Graph convolutional autoencoder
  9. Details on the testing approach described in Section \ref{['testability']}

Key Result

Theorem 1

Conditional on Assumptions ass4 and ass6, it holds that Conditional on Assumptions ass4 and ass6, the testable implication $Y_i \perp\!\!\!\perp \tilde{Z}_i | \dot{Z}_i=\dot{z}$ is necessary and sufficient for the joint satisfaction of $Y_i(d,\dot{z}) \perp\!\!\!\perp \dot{Z}_i$ and $Y_i(d,\dot{z}) \perp\!\!\!\perp \tilde{Z}_i$ when considering potenti

Figures (3)

  • Figure 1: Causal diagram satisfying Assumption \ref{['ass1']}.
  • Figure 2: Causal diagram underlying the testing method
  • Figure 3: Graph convolutional autoencoder architecture

Theorems & Definitions (1)

  • Theorem 1