In our previously published work, we introduced a supervised deep learning method for event detection in multivariate time series data, employing regression instead of binary classification. This simplification avoids the need for point-wise labels throughout the entire dataset, relying solely on ground truth events defined as time points or intervals. In this paper, we establish mathematically that our method is universal, and capable of detecting any type of event with arbitrary precision under mild continuity assumptions on the time series. These events may encompass change points, frauds, anomalies, physical occurrences, and more. We substantiate our theoretical results using the universal approximation theorem for feed-forward neural networks (FFN). Additionally, we provide empirical validations that confirm our claims, demonstrating that our method, with a limited number of parameters, outperforms other deep learning approaches, particularly for rare events and imbalanced datasets from different domains.

翻译：在我们之前发表的工作中，我们提出了一种用于多变量时间序列数据事件检测的监督深度学习方法，该方法采用回归替代二分类。这种简化避免了在整个数据集中使用逐点标注的需求，仅依赖定义为时间点或时间间隔的真实事件。本文从数学上证明了我们的方法具有通用性，能够在时间序列的弱连续性假设下以任意精度检测任何类型的事件。这些事件可能包括变化点、欺诈、异常、物理事件等。我们利用前馈神经网络（FFN）的通用近似定理为理论结果提供了支撑。此外，我们通过实证验证确认了我们的主张，表明在参数数量有限的情况下，我们的方法优于其他深度学习方法，尤其在处理不同领域的罕见事件和不平衡数据集时表现突出。