Explain Influence Maximization with Sobol Indices

Due to its vast application on online social networks, Influence Maximization (IM) has garnered considerable attention over the last couple of decades. Current IM research lacks human-comprehensible explanations of how the seed set results in the influence effect, hence reducing the trustworthiness of existing solutions despite their applicability. Due to the intricacy of IM, the majority of current research concentrate on estimating first-order spreading power and often is regard the interplay between flows dispersed from different seeds. This study uses Sobol indices, the cornerstone of variance-based sensitivity analysis, to decompose the influence effect to individual seeds and their interactions. The Sobol indices are tailored for IM contexts by modeling the seed selection as binary variables. This explanation method is universally applicable to all network types, IM techniques, and diffusion models. Based on the explanation method, a general framework dubbed SobolIM is proposed to improve the performance of current IM studies by over-selecting nodes followed by an elimination strategy. Experiments on synthetic and real-world graphs demonstrate that the explanation of the impact effect can dependably identify the key high-order interaction between seeds across a variety of networks and IM methods. SobolIM is empirically proved to be superior on effectiveness and competitive on efficiency.