用生存分析方法精准评估异常检测模型在短序列下的表现。
Accurate Evaluation of Quickest Changepoint Detectors via Non-parametric Survival Analysis
- 借鉴生存分析思想，构建非参数化估计算法
- 在有限和不规则序列中仍保持无偏估计
- 适合实际数据中样本不完整场景的模型评估
我们提出了非参数化估计方法，用于在有限且不规则序列长度下估算快速变点检测（QCD）中的平均运行长度（ARL）和平均检测延迟（ADD）。尽管ARL与ADD广泛用于理论和仿真研究，但在真实数据中因序列长度受限且不规则而难以应用。为此，我们通过将QCD类比为生存分析，提出基于Kaplan-Meier的非参数估计器——KM-ARL与KM-ADD，以建模序列截断下的检测概率。我们推导了估计偏差的边界，并证明其在无需外推时为渐近无偏。在模拟与真实数据集上的实验表明，该方法能有效提升对短序列和不规则长度的鲁棒性，增强可解释性，并支持直观的模型选择。代码已开源于https://github.com/TaikiMiyagawa/Kaplan-Meier-Average-Run-Length，供实践者直接使用。
原文摘要 · Abstract (English)
We propose non-parametric estimators for the average run length (ARL) and average detection delay (ADD) in quickest changepoint detection (QCD) under finite and irregular sequence lengths. Although ARL and ADD are widely used as optimality criteria in theoretical and simulation studies, their application to real-world datasets is hindered by limited and irregular sequence lengths. To address this issue, we propose non-parametric estimators for the ARL and ADD, termed KM-ARL and KM-ADD, by drawing an analogy between QCD and survival analysis to model detection probabilities under sequence truncation. We derive estimation bias bounds and prove that they are asymptotically unbiased unless extrapolation is required. Experiments on simulated and real-world datasets demonstrate their practical utility, enhancing robustness against limited and irregular sequence lengths, improving interpretability, and facilitating empirical, intuitive model selection. Our Python code is provided at https://github.com/TaikiMiyagawa/Kaplan-Meier-Average-Run-Length, offering ready-to-use implementations for practitioners.
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