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Ego Group Partition: A Novel Framework for Improving Ego Experiments in Social Networks

Lu Deng, JingJing Zhang, Yong Wang, Chuan Chen

TL;DR

The paper tackles the challenge of estimating the global average treatment effect $\tau$ under network interference by introducing Ego Group Partition (EGP), which directly selects an ego sub-population and optimizes alters' treatments to control exposure. It provides a baseline linear-in-means model and an exposure-mapping framework, deriving bias-minimizing rules and a threshold-based solution that can be implemented in parallel. Through simulations on a large social-network graph and a real Weixin case study, EGP demonstrates reduced bias and greater practical power compared to the ego-cluster approach, while highlighting trade-offs between bias and variance under different exposure assumptions. The work offers practical algorithms, theoretical insights, and empirical validations, enabling scalable, ego-centric causal inference in networks with interference, and discusses avenues for future extensions and improvements.

Abstract

Estimating the average treatment effect in social networks is challenging due to individuals influencing each other. One approach to address interference is ego cluster experiments, where each cluster consists of a central individual (ego) and its peers (alters). Clusters are randomized, and only the effects on egos are measured. In this work, we propose an improved framework for ego cluster experiments called ego group partition (EGP), which directly generates two groups and an ego sub-population instead of ego clusters. Under specific model assumptions, we propose two ego group partition algorithms. Compared to the original ego clustering algorithm, our algorithms produce more egos, yield smaller biases, and support parallel computation. The performance of our algorithms is validated through simulation and real-world case studies.

Ego Group Partition: A Novel Framework for Improving Ego Experiments in Social Networks

TL;DR

The paper tackles the challenge of estimating the global average treatment effect under network interference by introducing Ego Group Partition (EGP), which directly selects an ego sub-population and optimizes alters' treatments to control exposure. It provides a baseline linear-in-means model and an exposure-mapping framework, deriving bias-minimizing rules and a threshold-based solution that can be implemented in parallel. Through simulations on a large social-network graph and a real Weixin case study, EGP demonstrates reduced bias and greater practical power compared to the ego-cluster approach, while highlighting trade-offs between bias and variance under different exposure assumptions. The work offers practical algorithms, theoretical insights, and empirical validations, enabling scalable, ego-centric causal inference in networks with interference, and discusses avenues for future extensions and improvements.

Abstract

Estimating the average treatment effect in social networks is challenging due to individuals influencing each other. One approach to address interference is ego cluster experiments, where each cluster consists of a central individual (ego) and its peers (alters). Clusters are randomized, and only the effects on egos are measured. In this work, we propose an improved framework for ego cluster experiments called ego group partition (EGP), which directly generates two groups and an ego sub-population instead of ego clusters. Under specific model assumptions, we propose two ego group partition algorithms. Compared to the original ego clustering algorithm, our algorithms produce more egos, yield smaller biases, and support parallel computation. The performance of our algorithms is validated through simulation and real-world case studies.
Paper Structure (17 sections, 5 theorems, 22 equations, 4 figures, 2 tables, 4 algorithms)

This paper contains 17 sections, 5 theorems, 22 equations, 4 figures, 2 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Network Interference
  4. Ego Cluster Network Experiment
  5. Methodology
  6. Baseline approach
  7. High-level approach
  8. Second neighborhood clustering approach
  9. Numerical Experiments
  10. Simulated data
  11. Real Data
  12. Discussion
  13. Proofs
  14. Proof of Proposition \ref{['prop: basemodelbias']}
  15. Proof of Proposition \ref{['prop: r_ineuqa']}
  16. ...and 2 more sections

Key Result

Proposition 3.1

Given the potential outcome model equa:linearmodel, the bias of ego estimator $\widehat{\tau}_{\text{ego}}$ is

Figures (4)

  • Figure 1: An illustration of ego cluster experiment in saintjacques.
  • Figure 2: Diagram of ego group partition framework.
  • Figure 3: An example of convex function $g_2$. For any $0 < x < y < 1$ and $0 < \delta < 1-y$, $g_2(x+\delta) - g_2(x) \geq g_1(x+\delta) - g_1(x)$.
  • Figure 4: The distribution of $\sigma_i$ of different algorithms, which are Ego cluster, Ego partition(threshold=0), Ego partition(threshold=0.2), Ego partition(threshold=0.5).In every subplot, the blue line describes the $\sigma_i's$ distribution of the treatment group, while the yellow line describes the treatment group. And the gray lines perpendicular to the X-axis are the means of the two distributions, respectively.

Theorems & Definitions (5)

  • Proposition 3.1
  • Proposition 3.2
  • Theorem 3.1
  • Proposition 3.3
  • Theorem 3.2