流行动态预测模型中的不确定性量化
Quantifying Uncertainty in a Predictive Model for Popularity Dynamics
摘要：
近年来，霍克斯过程因其适用于描述在线信息级联的行为而受到关注。在这里，我们提出了一个完全易于处理的方法来分析描述霍克斯过程中的事件数量的分布，这与纯粹的经验研究或基于模拟的模型，使级联动力学的过程参数的影响进行分析。我们表明，所提出的理论还允许预测事件的未来分布后，在一个时间窗口内观察到给定数量的事件。我们的结果是通过微分方程的方法来获得一般分支过程的控制方程。我们通过对这些过程的广泛模拟证实了我们的理论研究结果。这项工作提供了更完整的分析的自我激励的过程，管理信息通过许多通信平台的传播，包括潜在的预测级联动力学的置信限度内的基础。
英文摘要：
The Hawkes process has garnered attention in recent years for its suitability to describe the behavior of online information cascades. Here, we present a fully tractable approach to analytically describe the distribution of the number of events in a Hawkes process, which, in contrast to purely empirical studies or simulation-based models, enables the effect of process parameters on cascade dynamics to be analyzed. We show that the presented theory also allows predictions regarding the future distribution of events after a given number of events have been observed during a time window. Our results are derived through a differential-equation approach to attain the governing equations of a general branching process. We confirm our theoretical findings through extensive simulations of such processes. This work provides the basis for more complete analyses of the self-exciting processes that govern the spreading of information through many communication platforms, including the potential to predict cascade dynamics within confidence limits.
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