Hybrid Smoothing for Anomaly Detection in Time Series
用于时间序列异常检测的混合平滑方法AI 解读 ↓
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用于时间序列异常检测的混合平滑方法
- 研究问题
- 如何从具有平滑趋势的工业时间序列中分离稀疏异常，并在趋势拟合、异常识别和误报漏报之间取得可检验的平衡？
- 方法与思路
- 作者对两组基函数分别施加 L2 与 L1 惩罚，结合三次平滑样条和 LASSO，并构建对应的贝叶斯层次模型及调参方法。
- 材料陈述的贡献
- 摘要称，研究提出两种基于有效自由度的惩罚选择方法和后验采样改进，并在水处理应用及模拟中获得较低误报与漏报。
- 阅读关注点
- 应核对趋势与异常基函数能否区分、惩罚参数选择及异常判定规则，并检查模拟中的异常形态、误报漏报定义和比较公平性。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收均未核实；摘要未报告错误率数值及条件，离线监测表现也不能直接推广到实时检测。
原文摘要
Many industrial and engineering processes monitored as times series have smooth trends that indicate normal behavior and occasionally anomalous patterns that can indicate a problem. This kind of behavior can be modeled by a smooth trend, such as a spline or Gaussian process, and a disruption based on a sparser representation. Our approach is to expand the process signal into two sets of basis functions: one set uses L2 penalties on the coefficients, and the other set uses L1 penalties to control sparsity. From a frequentist perspective, this results in a hybrid smoother that combines cubic smoothing splines and the LASSO. As a Bayesian hierarchical model (BHM), this is equivalent to priors giving a Gaussian process and a Laplace distribution for anomaly coefficients. For the hybrid smoother, we propose two new ways of determining the penalty parameters that use effective degrees of freedom and contrast this with the BHM that uses loosely informative inverse gamma priors. Several reformulations are used to make sampling the BHM posterior more efficient, including some novel features in orthogonalizing and regularizing the model basis functions. This methodology is motivated by a substantive application, offline monitoring of a water treatment process for municipal water filtration. We also test the robustness of these methods with a Monte Carlo study designed to inspect a range trended time series under an array of conditions and compare this new approach to multiple existing modern methods. Both the hybrid smoother and the full BHM give comparable results with small false positive and false negative rates. Besides being successful in the water treatment application, this work can be easily extended to other Gaussian process models and other features that represent process disruptions in offline data.