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Estimating Peer Direct and Indirect Effects in Observational Network Data

Xiaojing Du, Jiuyong Li, Debo Cheng, Lin Liu, Wentao Gao, Xiongren Chen

TL;DR

A general setting which considers both peer direct effects and peer indirect effects, and the effect of an individual's own treatment, and the effect of an individual's own treatment is proposed, to provide identification conditions of these causal effects and proofs.

Abstract

Estimating causal effects is crucial for decision-makers in many applications, but it is particularly challenging with observational network data due to peer interactions. Many algorithms have been proposed to estimate causal effects involving network data, particularly peer effects, but they often overlook the variety of peer effects. To address this issue, we propose a general setting which considers both peer direct effects and peer indirect effects, and the effect of an individual's own treatment, and provide identification conditions of these causal effects and proofs. To estimate these causal effects, we utilize attention mechanisms to distinguish the influences of different neighbors and explore high-order neighbor effects through multi-layer graph neural networks (GNNs). Additionally, to control the dependency between node features and representations, we incorporate the Hilbert-Schmidt Independence Criterion (HSIC) into the GNN, fully utilizing the structural information of the graph, to enhance the robustness and accuracy of the model. Extensive experiments on two semi-synthetic datasets confirm the effectiveness of our approach. Our theoretical findings have the potential to improve intervention strategies in networked systems, with applications in areas such as social networks and epidemiology.

Estimating Peer Direct and Indirect Effects in Observational Network Data

TL;DR

A general setting which considers both peer direct effects and peer indirect effects, and the effect of an individual's own treatment, and the effect of an individual's own treatment is proposed, to provide identification conditions of these causal effects and proofs.

Abstract

Estimating causal effects is crucial for decision-makers in many applications, but it is particularly challenging with observational network data due to peer interactions. Many algorithms have been proposed to estimate causal effects involving network data, particularly peer effects, but they often overlook the variety of peer effects. To address this issue, we propose a general setting which considers both peer direct effects and peer indirect effects, and the effect of an individual's own treatment, and provide identification conditions of these causal effects and proofs. To estimate these causal effects, we utilize attention mechanisms to distinguish the influences of different neighbors and explore high-order neighbor effects through multi-layer graph neural networks (GNNs). Additionally, to control the dependency between node features and representations, we incorporate the Hilbert-Schmidt Independence Criterion (HSIC) into the GNN, fully utilizing the structural information of the graph, to enhance the robustness and accuracy of the model. Extensive experiments on two semi-synthetic datasets confirm the effectiveness of our approach. Our theoretical findings have the potential to improve intervention strategies in networked systems, with applications in areas such as social networks and epidemiology.
Paper Structure (23 sections, 18 equations, 4 figures, 2 tables)

This paper contains 23 sections, 18 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Notations and Problem Setting
  4. Assumptions
  5. The Proposed gDIS Method
  6. Identifiability of PDE, PIE and STE
  7. Assumption 5
  8. Theorem 1.
  9. Theorem 2.
  10. Implementation
  11. Using attention weights to capture the varying influences of nodes.
  12. HSIC Regularization.
  13. Objective Function.
  14. Experiments
  15. Experiments Setup
  16. ...and 8 more sections

Figures (4)

  • Figure 1: (a) A graph to showing the relationship between individual $i$ and their neighbors in network data. (b) A causal graph illustrating peer direct effects (PDE), peer indirect effects (PIE), and self-treatment effects (STE). In the diagram, $T$ and $Y$ indicate the intervention (e.g., vaccination status and infection condition), the subscript $i$ indicates an individual and ${j \neq i}$ indicates their neighbours.
  • Figure 2: (a) An illustration of the causal relationships considered in our work, for node 2, which has node 1 and 3 as neighbours in the network. The features, treatment, and outcome of node $i$ are represented by $X_i$, $T_i$, and $Y_i$, respectively. (b) The summary causal graph where $W_{x_i}$, $W_{t_i}$, and $W_{y_i}$ represent the aggregated features, treatments, and outcomes of node $i$'s neighbors.
  • Figure 3: The workflow of our gDIS model for estimating PDE, PIE and STE within network data.
  • Figure 4: The results illustrate the relationship between the counterfactual estimation error ($\epsilon_{MSE}$) and the percentage of units with treatment flip.