Low-count time series describe sparse or intermittent events, which are
prevalent in large-scale online platforms that capture and monitor diverse data
types. Several distinct challenges surface when modelling low-count time
series, particularly low signal-to-noise ratios (when anomaly signatures are
provably undetectable), and non-uniform performance (when average metrics are
not representative of local behaviour). The time series anomaly detection
community currently lacks explicit tooling and processes to model and reliably
detect anomalies in these settings. We address this gap by introducing a novel
generative procedure for creating benchmark datasets comprising of low-count
time series with anomalous segments. Via a mixture of theoretical and empirical
analysis, our work explains how widely-used algorithms struggle with the
distribution overlap between normal and anomalous segments. In order to
mitigate this shortcoming, we then leverage our findings to demonstrate how
anomaly score smoothing consistently improves performance. The practical
utility of our analysis and recommendation is validated on a real-world dataset
containing sales data for retail stores.

我们介绍了一种新颖的生成过程，用于创建包含低计数时间序列和异常片段的基准数据集，通过理论和实证分析，我们解释了现有算法在正常和异常片段之间的分布重叠问题，并展示了异常分数平滑如何提高性能。我们的分析和建议的实际效用在一个包含零售店销售数据的真实世界数据集上得到了验证。