论文标题
用于聚合鹰派过程的参数估计的蒙特卡洛EM算法
A Monte Carlo EM Algorithm for the Parameter Estimation of Aggregated Hawkes Processes
论文作者
论文摘要
实际事件数据引起的关键难度是记录事件时间戳记的不精确。在许多情况下，由于活动量的庞大，保留较高精度的事件时间很昂贵。结合测量准确性的实际限制，汇总数据很常见。为了使用点过程对此类事件数据进行建模，用于处理参数估计的工具至关重要。在这里，我们考虑了霍克斯过程的参数估计，这是一种自我激发点过程，它在金融股票市场，地震和社交媒体级联的建模中发现了应用。我们开发了一种新型的优化方法，用于使用蒙特卡洛期望最大化（MC-EM）算法的汇总霍克斯过程的参数估计。通过详细的仿真研究，我们证明了现有方法能够产生严重偏见且高度可变的参数估计值，并且我们的新型MC-EM方法在所有研究的情况下都显着优于它们。这些结果突出了正确处理汇总数据的重要性。
A key difficulty that arises from real event data is imprecision in the recording of event time-stamps. In many cases, retaining event times with a high precision is expensive due to the sheer volume of activity. Combined with practical limits on the accuracy of measurements, aggregated data is common. In order to use point processes to model such event data, tools for handling parameter estimation are essential. Here we consider parameter estimation of the Hawkes process, a type of self-exciting point process that has found application in the modeling of financial stock markets, earthquakes and social media cascades. We develop a novel optimization approach to parameter estimation of aggregated Hawkes processes using a Monte Carlo Expectation-Maximization (MC-EM) algorithm. Through a detailed simulation study, we demonstrate that existing methods are capable of producing severely biased and highly variable parameter estimates and that our novel MC-EM method significantly outperforms them in all studied circumstances. These results highlight the importance of correct handling of aggregated data.
