Segmented Confidence Sequences and Multi-Scale Adaptive Confidence Segments for Anomaly Detection in Nonstationary Time Series

2025-08-08

AI Summary

Traditional static thresholds fail in nonstationary time-series anomaly detection due to concept drift, regime shifts, and multiscale dynamics. To address this, we propose two adaptive thresholding frameworks. Our method integrates statistical online learning with sequential segmentation, employing a context-sensitive dynamic threshold adjustment strategy. Key contributions include: (1) a piecewise confidence sequence that enables online modeling of local statistical properties; and (2) a multiscale adaptive confidence segment mechanism that rigorously controls the false positive rate under distributional evolution—backed by theoretical guarantees and offering full interpretability. Evaluated on the Wafer Manufacturing benchmark dataset, our approach achieves significantly higher F1 scores than percentile- and rolling-percentile-based baselines, demonstrating superior robustness and practical efficacy in real-world nonstationary settings.

Technology Category

Data Mining & Knowledge Management: Anomaly/Outlier DetectionMachine Learning: Online Learning & BanditsReasoning under Uncertainty: Sequential Decision Making

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsWeb Mining and Content Analysis: Robustness and generalizability of Web mining methodsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

As time series data become increasingly prevalent in domains such as manufacturing, IT, and infrastructure monitoring, anomaly detection must adapt to nonstationary environments where statistical properties shift over time. Traditional static thresholds are easily rendered obsolete by regime shifts, concept drift, or multi-scale changes. To address these challenges, we introduce and empirically evaluate two novel adaptive thresholding frameworks: Segmented Confidence Sequences (SCS) and Multi-Scale Adaptive Confidence Segments (MACS). Both leverage statistical online learning and segmentation principles for local, contextually sensitive adaptation, maintaining guarantees on false alarm rates even under evolving distributions. Our experiments across Wafer Manufacturing benchmark datasets show significant F1-score improvement compared to traditional percentile and rolling quantile approaches. This work demonstrates that robust, statistically principled adaptive thresholds enable reliable, interpretable, and timely detection of diverse real-world anomalies.

Problem

• Adapt anomaly detection to nonstationary time series environments
• Overcome limitations of static thresholds with dynamic adaptation
• Maintain false alarm guarantees under evolving data distributions

Innovation

• Segmented Confidence Sequences for local adaptation
• Multi-Scale Adaptive Confidence Segments framework
• Statistical online learning with segmentation principles