We propose a novel problem formulation of continuous-time information propagation on heterogeneous networks based on jump stochastic differential equations (JSDE). The structure of the network and activation rates between nodes are naturally taken into account in the JSDE. This new formulation allows for efficient and stable algorithms for a variety of challenging information propagation problems, including estimations of individual activation probability and influence level, by solving the JSDE numerically. In particular, we develop an efficient numerical algorithm for solving the JSDE by incorporating variance reduction; and furthermore, we provide theoretical bounds for its sample complexity. Numerical experiments on a variety of propagation networks show that the proposed method is more accurate and efficient compared with the state-of-the-art methods, and more importantly it can be applied to solve other critical information propagation problems to which existing methods cannot be applied.

中文翻译：

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异质网络影响预测的跳跃随机微分方程方法

我们提出了一种基于跳跃随机微分方程（JSDE）的异构网络上连续时间信息传播的新问题公式。在JSDE中自然会考虑网络的结构和节点之间的激活率。这种新的公式允许通过数值求解JSDE来解决各种挑战性的信息传播问题的有效且稳定的算法，包括对单个激活概率和影响程度的估计。特别是，我们开发了一种有效的数值算法，通过结合方差减少来求解JSDE。而且，我们为其样本的复杂性提供了理论上的界限。