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

TL;DR

This paper introduces the Conflict Graph Design, a novel method for constructing network experiment designs that accurately estimate causal effects under arbitrary neighborhood interference, using a conflict graph framework and a modified Horvitz--Thompson estimator.

Contribution

The paper proposes a general conflict graph approach for experimental design in network settings, providing new variance bounds and methods for estimating diverse causal effects.

Findings

Variance of estimator bounded by $O(rac{ ext{largest eigenvalue of conflict graph}}{n})$

Achieves best known rates for global and direct effects

Provides new methods for spill-over effects estimation

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.