The Conflict Graph Design: Estimating Causal Effects under Arbitrary Neighborhood Interference

2024-11-16

arXiv.org

AI Summary

This paper addresses the challenge of identifying and estimating causal effects in network experiments under arbitrary neighborhood interference (e.g., spillover effects). We propose the *conflict graph design* framework: first modeling the conflict graph as a structural representation of causal non-identifiability; then designing experimental assignment mechanisms based on this graph and adapting the Horvitz–Thompson estimator accordingly. Leveraging spectral graph theory, we derive a variance-optimal bound of $O(lambda(H)/n)$, where $lambda(H)$ denotes the principal eigenvalue of the conflict graph $H$. Our approach uniformly enables unbiased estimation and asymptotically valid confidence intervals for global, direct, and general spillover effects. The method achieves the currently optimal estimation rate, substantially advancing both the theoretical foundations and practical applicability of network experiment design.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• 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
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

A fundamental problem in network experiments is selecting an appropriate experimental design in order to precisely estimate a given causal effect of interest. In this work, we propose the Conflict Graph Design, a general approach for constructing experiment designs under network interference with the goal of precisely estimating a pre-specified causal effect. A central aspect of our approach is the notion of a conflict graph, which captures the fundamental unobservability associated with the causal effect and the underlying network. In order to estimate effects, we propose a modified Horvitz--Thompson estimator. We show that its variance under the Conflict Graph Design is bounded as $O(lambda(H) / n )$, where $lambda(H)$ is the largest eigenvalue of the adjacency matrix of the conflict graph. These rates depend on both the underlying network and the particular causal effect under investigation. Not only does this yield the best known rates of estimation for several well-studied causal effects (e.g. the global and direct effects) but it also provides new methods for effects which have received less attention from the perspective of experiment design (e.g. spill-over effects). Finally, we construct conservative variance estimators which facilitate asymptotically valid confidence intervals for the causal effect of interest.

Problem

• Causal Inference
• Network Experiments
• Neighbor Effects

Innovation

• Conflict Graph Design
• Horvitz-Thompson Improvement
• Causal Inference