Identifying the Group to Intervene on to Maximise Effect Under Cross-Group Interference

TL;DR

This paper introduces a formal framework and scalable algorithms for identifying the optimal intervention subset in one group to maximize causal effects on another group in networked systems, addressing cross-group interference.

Contribution

It formalizes the cross-group causal influence estimation problem, proves its identifiability from observational data, and develops a graph neural network estimator and scalable algorithms for optimal subset selection.

Findings

CauMax outperforms heuristics and baselines in real-world social networks.

Uncertainty-aware methods improve subset selection.

The framework enables effective intervention targeting in networked systems.

Abstract

In many networked systems, interventions applied to one group of units can induce substantial causal effects on another group through cross-group interference pathways. Despite its practical importance in domains such as public health, digital marketing, and social policy, the problem of identifying which intervention subset in a source group maximizes the benefit on a target group remains largely unaddressed. We formalize this problem as cross-group causal influence estimation and introduce the core-to-group causal effect (Co2G), a formally defined causal estimand that quantifies the contrast in target-group outcomes under intervention versus non-intervention on a candidate source subset. We establish the nonparametric identifiability of Co2G from observational network data using do-calculus under standard causal assumptions, and develop a graph neural network-based estimator that captures cross-group interference patterns. To navigate the combinatorial search space of candidate subsets, we propose CauMax, an uncertainty-aware causal effect maximization framework with two scalable selection algorithms: (i)CauMax-G, an iterative greedy search with Monte Carlo dropout--based lower confidence bounds, and (ii)CauMax-D, a differentiable gradient-based optimization via Gumbel-Softmax relaxation. Extensive experiments on two real-world social networks demonstrate that CauMax achieves an order-of-magnitude reduction in regret compared with structural heuristics and diffusion-based baselines, and that moderate uncertainty penalization consistently improves subset selection quality.