具有缺失或噪声事件时间的Hawkes过程的ABC学习
ABC Learning of Hawkes Processes with Missing or Noisy Event Times
摘要：
自激Hawkes过程被广泛用于模拟爆发事件。然而，许多真实世界的数据集包含丢失的事件和/或噪声观测的事件时间，我们称之为数据失真。这种失真的存在会严重影响霍克斯过程参数的学习。为了避免这一点，我们建议明确建模的失真函数。这导致了一个模型，一个棘手的似然函数，这使得它难以部署标准的参数估计技术。因此，我们开发了ABC-Hawkes算法，这是一种基于近似贝叶斯计算（ABC）和马尔可夫链蒙特卡罗的新方法。这使得霍克斯过程的参数可以在常规方法引起实质性偏差或不适用的设置中学习。所提出的方法被证明是执行良好的真实和模拟数据。
英文摘要：
The self-exciting Hawkes process is widely used to model events which occur in bursts. However, many real world data sets contain missing events and/or noisily observed event times, which we refer to as data distortion. The presence of such distortion can severely bias the learning of the Hawkes process parameters. To circumvent this, we propose modeling the distortion function explicitly. This leads to a model with an intractable likelihood function which makes it difficult to deploy standard parameter estimation techniques. As such, we develop the ABC-Hawkes algorithm which is a novel approach to estimation based on Approximate Bayesian Computation (ABC) and Markov Chain Monte Carlo. This allows the parameters of the Hawkes process to be learned in settings where conventional methods induce substantial bias or are inapplicable. The proposed approach is shown to perform well on both real and simulated data.
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