Parameter Estimation of Binned Hawkes Processes
针对事件时间戳记录不精确导致的分箱数据，提出一种改进的期望最大化算法（BH-EM）来估计霍克斯过程参数，模拟和真实网络数据表明该方法优于现有方法。
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, binned 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 binned Hawkes processes using a modified Expectation-Maximization algorithm, referred to as Binned Hawkes Expectation Maximization (BH-EM). 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 BH-EM method significantly outperforms them in all studied circumstances. We further illustrate the performance on network flow (NetFlow) data between devices in a real large-scale computer network, to characterize triggering behavior. These results highlight the importance of correct handling of binned data.