Unveiling Environmental Sensitivity of Individual Gains in Influence Maximization

Influence Maximization (IM) seeks a seed set to maximize information dissemination in a network. Elegant IM algorithms could naturally extend to cases where each node is equipped with a specific weight, reflecting individual gains to measure its importance. In prevailing literature, these gains are typically assumed to remain constant throughout diffusion and are solvable through explicit formulas based on node characteristics and network topology. However, this assumption is not always feasible due to two key challenges: 1) \textit{Unobservability}: The individual gains of each node are primarily evaluated by the difference between the outputs in the activated and non-activated states. In practice, we can only observe one of these states, with the other remaining unobservable post-propagation. 2) \textit{Environmental sensitivity}: Beyond nodes’ inherent properties, individual gains are also sensitive to the activation status of surrounding nodes, which change dynamically during propagation even when the network topology is fixed. To address these uncertainties, we introduce a Causal Influence Maximization (CauIM) framework, leveraging causal inference techniques to model dynamic individual gains. We propose two algorithms, G-CauIM and A-CauIM, where the latter incorporates a novel acceleration technique. Theoretically, we establish the generalized lower bound of influence spread and provide robustness analysis. Empirically, experiments on synthetic and real-world datasets validate the effectiveness and reliability of our approach.