Causal Inference for Network Data with Endogenous Peer Effect: A Targeted Minimum Loss Estimation Approach

2025-11-10

AI Summary

This paper addresses estimation of the average treatment effect (ATE) in observational network data under interference, relaxing the conventional finite-order interference assumption. It permits distance-decaying spillover effects induced by endogenous peer influence modeled via spatial autoregression (SAR). We propose a targeted minimum loss–based estimation (TMLE) method leveraging the network autoregressive structure, incorporating heterogeneous network weights and constructing diverging-order V-statistics. A novel asymptotic theory is developed for weakly dependent networks, ensuring asymptotic normality and variance efficiency of the estimator. Theoretically, under i.i.d. covariates, our estimator achieves strictly smaller asymptotic variance than standard alternatives and admits a consistent variance estimator. Extensive numerical simulations and empirical analysis on real-world live-streaming platform data confirm its superior finite-sample performance and robustness.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We study estimation of the average treatment effect (ATE) from a single network in observational settings with interference. The weak cross-unit dependence is modeled via an endogenous peer-effect (spatial autoregressive) term that induces distance-decaying spillover effects, relaxing the common finite-order interference assumption. We propose a targeted minimum loss estimation (TMLE) procedure that removes plug-in bias from an initial estimator. The targeting step yields an adjustment direction that incorporates the network autoregressive structure and assigns heterogeneous, network-dependent weights to units. We find that the asymptotic leading term related to the covariates $mathbf{X}_i$ can be formulated into a $V$-statistic whose order diverges with the network degrees. A novel limit theory is developed to establish the asymptotic normality under such complex network dependent scenarios. We show that our method can achieve smaller asymptotic variance than existing methods when $mathbf{X}_i$ is i.i.d. generated and estimated with empirical distribution, and provide theoretical guarantee for estimating the variance. Extensive numerical studies and a live-streaming data analysis are presented to illustrate the advantages of the proposed method.

Problem

• Estimating average treatment effects under network interference with endogenous peer effects
• Addressing plug-in bias in network causal inference using targeted minimum loss estimation
• Developing asymptotic theory for network-dependent data with diverging degree statistics

Innovation

• Targeted minimum loss estimation removes plug-in bias
• Adjustment direction incorporates network autoregressive structure
• Novel limit theory establishes asymptotic normality