A Design-Based Minimax Theory for Network Experiments

2026-08-05

AI Summary

This work addresses the fundamental statistical limits in causal inference under interference in network experiments, where existing methods lack a theoretical characterization of optimal estimation accuracy. The authors develop a minimax risk theory grounded in experimental design, establishing the optimal precision for estimating causal effects under arbitrary neighborhood interference models. They uniquely connect minimax risk to both local and global connectivity properties of the conflict graph, revealing the graph-theoretic nature of unobservability in potential outcomes. By integrating design-based inference, the potential outcomes framework, and tools from graph theory, they derive minimax optimal convergence rates for both direct treatment effects and global average treatment effects, and precisely quantify the intrinsic limitations on estimation accuracy through structural properties of the conflict graph.

Abstract

Network experiments are used throughout the social and medical sciences to investigate causal effects under the presence of interference. While a large body of work has developed improved statistical procedures, the fundamental limits of statistical estimation in these settings is less well understood. In this paper, we develop and investigate a design-based theory of minimax risk for network experiments under an arbitrary neighborhood interference model. Our notion of minimax risk describes the optimal precision among all statistical procedures for investigating a particular causal effect on the observed interference network. We show that the minimax risk is a function of the corresponding conflict graph, which captures inherent unobservability of estimand-relevant potential outcomes given the observed interference network. Our main contribution is a series of upper and lower bounds on the minimax rate in terms of local and global connectivity properties of the conflict graph. To illustrate their utility, we apply these general results to obtain minimax analyses for two commonly studied effects: the direct treatment effect and global average treatment effect.

Problem

• network experiments
• interference
• minimax risk
• causal inference
• conflict graph

Innovation

• minimax risk
• network experiments
• interference
• conflict graph
• causal inference