Transformer Hawkes process models have shown to be successful in modeling event sequence data. However, most of the existing training methods rely on maximizing the likelihood of event sequences, which involves calculating some intractable integral. Moreover, the existing methods fail to provide uncertainty quantification for model predictions, e.g., confidence intervals for the predicted event's arrival time. To address these issues, we propose SMURF-THP, a score-based method for learning Transformer Hawkes process and quantifying prediction uncertainty. Specifically, SMURF-THP learns the score function of events' arrival time based on a score-matching objective that avoids the intractable computation. With such a learned score function, we can sample arrival time of events from the predictive distribution. This naturally allows for the quantification of uncertainty by computing confidence intervals over the generated samples. We conduct extensive experiments in both event type prediction and uncertainty quantification of arrival time. In all the experiments, SMURF-THP outperforms existing likelihood-based methods in confidence calibration while exhibiting comparable prediction accuracy.

翻译：Transformer霍克斯过程模型在事件序列数据建模中已展现出卓越性能。然而，现有训练方法大多依赖最大化事件序列似然，这涉及计算某些难解积分。此外，现有方法无法为模型预测提供不确定性量化（如预测事件到达时间的置信区间）。为解决上述问题，我们提出SMURF-THP——一种基于分数的方法，用于学习Transformer霍克斯过程并量化预测不确定性。具体而言，SMURF-THP基于分数匹配目标学习事件到达时间的分数函数，避免了难解计算问题。借助学习到的分数函数，我们可从预测分布中采样事件到达时间，进而通过计算生成样本的置信区间自然实现不确定性量化。我们在事件类型预测与到达时间不确定性量化两任务上开展广泛实验。在所有实验中，SMURF-THP在置信度校准方面均优于现有基于似然的方法，同时展现出可比的预测精度。