Analysis of Two-Stage Rollout Designs with Clustering for Causal Inference under Network Interference

2024-05-08

AI Summary

Under network interference, causal effect estimation suffers from high variance, while simultaneously minimizing cut edges within clusters and achieving covariate balance remains challenging. Method: We propose a two-stage rollout experimental design: (1) graph-based clustering to identify highly homogeneous subpopulations, followed by (2) intervention deployment exclusively within those subpopulations. Contribution/Results: We formally link clustering objectives—cut-edge minimization versus covariate balance—to the bias–variance trade-off in causal estimation, theoretically characterizing how cluster structure affects bias (governed by cut edges) and variance (driven by homogeneity and covariate balance). Using a polynomial interpolation estimator and Monte Carlo simulations, we empirically identify optimal trade-offs across diverse clustering strategies. Our approach significantly reduces estimation variance while preserving causal identification validity under interference.

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: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Estimating causal effects under interference is pertinent to many real-world settings. Recent work with low-order potential outcomes models uses a rollout design to obtain unbiased estimators that require no interference network information. However, the required extrapolation can lead to prohibitively high variance. To address this, we propose a two-stage experiment that selects a sub-population in the first stage and restricts treatment rollout to this sub-population in the second stage. We explore the role of clustering in the first stage by analyzing the bias and variance of a polynomial interpolation-style estimator under this experimental design. Bias increases with the number of edges cut in the clustering of the interference network, but variance depends on qualities of the clustering that relate to homophily and covariate balance. There is a tension between clustering objectives that minimize the number of cut edges versus those that maximize covariate balance across clusters. Through simulations, we explore a bias-variance trade-off and compare the performance of the estimator under different clustering strategies.

Problem

• Estimating causal effects under network interference
• Proposing two-stage experiment for variance reduction
• Exploring bias-variance trade-off in clustering strategies

Innovation

• Two-stage experiment design
• Clustering for bias reduction
• Polynomial interpolation estimator