The study of continuous-time information diffusion has been an important area of research for many applications in recent years. When only the diffusion traces (cascades) are accessible, cascade-based network inference and influence estimation are two essential problems to explore. Alas, existing methods exhibit limited capability to infer and process networks with more than a few thousand nodes, suffering from scalability issues. In this paper, we view the diffusion process as a continuous-time dynamical system, based on which we establish a continuous-time diffusion model. Subsequently, we instantiate the model to a scalable and effective framework (FIM) to approximate the diffusion propagation from available cascades, thereby inferring the underlying network structure. Furthermore, we undertake an analysis of the approximation error of FIM for network inference. To achieve the desired scalability for influence estimation, we devise an advanced sampling technique and significantly boost the efficiency. We also quantify the effect of the approximation error on influence estimation theoretically. Experimental results showcase the effectiveness and superior scalability of FIM on network inference and influence estimation.

翻译：近年来，连续时间信息扩散研究已成为众多应用领域的重要研究方向。当仅有扩散轨迹（级联）可观测时，基于级联的网络推断与影响力估计是亟待探索的两个核心问题。然而，现有方法在处理节点数超过数千的网络时表现出有限能力，存在可扩展性瓶颈。本文将扩散过程视为连续时间动态系统，基于此构建连续时间扩散模型，进而将该模型实例化为可扩展的通用框架FIM，通过近似从可用级联中提取的扩散传播过程来推断底层网络结构。进一步，我们分析了FIM在网络推断中的近似误差。为实现影响力估计所需的可扩展性，我们设计了先进的采样技术，显著提升了计算效率。同时从理论上量化了近似误差对影响力估计的影响。实验结果表明，FIM在网络推断与影响力估计任务中展现出卓越的有效性与可扩展性。