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

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.