Unveiling Environmental Sensitivity of Individual Gains in Influence Maximization

Abstract: Influence Maximization (IM) is to identify the 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 the node's importance. Prevailing literature typically assumes such individual gains remain constant throughout the cascade process and are solvable through explicit formulas based on the node's characteristics and network topology. However, this assumption is not always feasible for two reasons: 1)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)Environmental sensitivity: In addition to the node's inherent properties, individual gains are also sensitive to the activation status of surrounding nodes, which is dynamic during iteration even when the network topology remains static. To address these challenges, we extend the consideration of IM to a broader scenario with dynamic node individual gains, leveraging causality techniques. In our paper, we introduce a Causal Influence Maximization (CauIM) framework and develop 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, in synthetic and real-world experiments, we demonstrate the effectiveness and robustness of our algorithms.