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Joint Selective State Space Model and Detrending for Robust Time Series Anomaly Detection

Junqi Chen, Xu Tan, Sylwan Rahardja, Jiawei Yang, Susanto Rahardja

TL;DR

The paper tackles two core challenges in time series anomaly detection: capturing long-range dependencies and generalizing to non-stationary data. It introduces a detector based on the Selective State Space Model (S6) and a multi-stage detrending pipeline, combining HP-based trend removal with DMamba blocks to produce reliable anomaly scores. Across NASA, SMD, and SWaT datasets, the approach outperforms 12 strong baselines, achieving about a 6.2% relative gain in average F1-AF and demonstrating robustness to non-stationary trends. The work lays a foundation for more advanced S6-based TSAD detectors that can operate effectively in real-world, non-stationary environments.

Abstract

Deep learning-based sequence models are extensively employed in Time Series Anomaly Detection (TSAD) tasks due to their effective sequential modeling capabilities. However, the ability of TSAD is limited by two key challenges: (i) the ability to model long-range dependency and (ii) the generalization issue in the presence of non-stationary data. To tackle these challenges, an anomaly detector that leverages the selective state space model known for its proficiency in capturing long-term dependencies across various domains is proposed. Additionally, a multi-stage detrending mechanism is introduced to mitigate the prominent trend component in non-stationary data to address the generalization issue. Extensive experiments conducted on realworld public datasets demonstrate that the proposed methods surpass all 12 compared baseline methods.

Joint Selective State Space Model and Detrending for Robust Time Series Anomaly Detection

TL;DR

The paper tackles two core challenges in time series anomaly detection: capturing long-range dependencies and generalizing to non-stationary data. It introduces a detector based on the Selective State Space Model (S6) and a multi-stage detrending pipeline, combining HP-based trend removal with DMamba blocks to produce reliable anomaly scores. Across NASA, SMD, and SWaT datasets, the approach outperforms 12 strong baselines, achieving about a 6.2% relative gain in average F1-AF and demonstrating robustness to non-stationary trends. The work lays a foundation for more advanced S6-based TSAD detectors that can operate effectively in real-world, non-stationary environments.

Abstract

Deep learning-based sequence models are extensively employed in Time Series Anomaly Detection (TSAD) tasks due to their effective sequential modeling capabilities. However, the ability of TSAD is limited by two key challenges: (i) the ability to model long-range dependency and (ii) the generalization issue in the presence of non-stationary data. To tackle these challenges, an anomaly detector that leverages the selective state space model known for its proficiency in capturing long-term dependencies across various domains is proposed. Additionally, a multi-stage detrending mechanism is introduced to mitigate the prominent trend component in non-stationary data to address the generalization issue. Extensive experiments conducted on realworld public datasets demonstrate that the proposed methods surpass all 12 compared baseline methods.
Paper Structure (17 sections, 8 equations, 4 figures, 3 tables, 1 algorithm)

This paper contains 17 sections, 8 equations, 4 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Problem Statement
  5. S6 Model
  6. Time Series Detrending
  7. Method
  8. HP Trend Filter
  9. DMamba Blocks
  10. Final Reconstructed Output
  11. Experiments
  12. Setup
  13. Datasets
  14. Baselines
  15. Implementation details
  16. ...and 2 more sections

Figures (4)

  • Figure 1: Illustration of different sequence models gathering context information, where $k$ denotes the kernel size, $t$ denotes the time-step, $\bm{x}_{1:t-1}$ represents the context information, $\bm{x}_t$ and $\bm{y}_t$ represent the input and output in current time-step, respectively. (a) TCN's context was constrained by the kernel size $k$. (b) SA in the Transformer could capture long-term context but lacked information compression. (c-d) RNN and SSM could compress context information by a finite state.
  • Figure 2: The structure of the proposed method includes a HP trend filter, multiple DMamba blocks, and an output module.
  • Figure 3: The structure of Mamba block.
  • Figure 4: A visualization from the SWaT dataset, which contains non-stationary data. The first row shows the input signal and extracted trend. The second row displays anomaly scores from various detectors. Baseline methods were influenced by trends, leading to false alarms, while our proposed method generated reliable scores by incorporating detrending mechanisms.