论文标题
ABC学习霍克斯流程缺失或嘈杂的事件时间
ABC Learning of Hawkes Processes with Missing or Noisy Event Times
论文作者
论文摘要
自我激发的霍克斯过程被广泛用于建模突发中发生的事件。但是，许多现实世界数据集都包含缺失的事件和/或噪声观察到的事件时间，我们将其称为数据失真。这种失真的存在会严重偏向霍克斯过程参数的学习。为了规避这一点，我们建议明确建模失真函数。这导致了具有棘手的似然函数的模型，这使得很难部署标准参数估计技术。因此，我们开发了ABC-HAWKES算法，这是基于近似贝叶斯计算（ABC）和马尔可夫链蒙特卡洛的一种新型估计方法。这允许在传统方法引起实质性偏见或不适用的设置中学习霍克斯过程的参数。提出的方法显示在真实和模拟数据上表现良好。
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.
