检测高维自激Poisson过程的突变
Detecting Abrupt Changes in High-Dimensional Self-Exciting Poisson Processes
摘要：
高维自激点过程已被广泛应用于许多应用领域，以模拟过去和当前事件影响未来事件可能性的离散事件数据。在本文中，我们关注的是检测离散时间高维自激泊松过程中的系数矩阵的突变，这还没有被研究在现有的文献中，由于理论和计算的挑战植根于非平稳和高维的基本过程的性质。我们提出了一个惩罚的动态规划方法，这是支持的理论率分析和数值证据。
英文摘要：
High-dimensional self-exciting point processes have been widely used in many application areas to model discrete event data in which past and current events affect the likelihood of future events. In this paper, we are concerned with detecting abrupt changes of the coefficient matrices in discrete-time high-dimensional self-exciting Poisson processes, which have yet to be studied in the existing literature due to both theoretical and computational challenges rooted in the non-stationary and high-dimensional nature of the underlying process. We propose a penalized dynamic programming approach which is supported by a theoretical rate analysis and numerical evidence.
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