COGNOS: Universal Enhancement for Time Series Anomaly Detection via Constrained Gaussian-Noise Optimization and Smoothing

2025-11-10

AI Summary

In reconstruction-based time-series anomaly detection, the widely adopted MSE loss yields residuals with poor statistical properties, resulting in noisy and unstable anomaly scores. To address this, we propose a generic enhancement framework: during training, Gaussian white noise regularization is introduced to explicitly enforce reconstructed residuals to follow a zero-mean Gaussian distribution; during inference, theoretically optimal Kalman smoothing is integrated to robustly denoise anomaly scores. This dual-path optimization jointly refines residual characteristics through statistical modeling and signal processing, significantly enhancing the discriminability of anomalous signals. Extensive experiments across 12 backbone architectures and multiple real-world datasets demonstrate an average 57.9% improvement in F-score, validating the method’s strong generalizability and plug-and-play practicality.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Reconstruction-based methods are a dominant paradigm in time series anomaly detection (TSAD), however, their near-universal reliance on Mean Squared Error (MSE) loss results in statistically flawed reconstruction residuals. This fundamental weakness leads to noisy, unstable anomaly scores with a poor signal-to-noise ratio, hindering reliable detection. To address this, we propose Constrained Gaussian-Noise Optimization and Smoothing (COGNOS), a universal, model-agnostic enhancement framework that tackles this issue at its source. COGNOS introduces a novel Gaussian-White Noise Regularization strategy during training, which directly constrains the model's output residuals to conform to a Gaussian white noise distribution. This engineered statistical property creates the ideal precondition for our second contribution: a Kalman Smoothing Post-processor that provably operates as a statistically optimal estimator to denoise the raw anomaly scores. The synergy between these two components allows COGNOS to robustly separate the true anomaly signal from random fluctuations. Extensive experiments demonstrate that COGNOS is highly effective, delivering an average F-score uplift of 57.9% when applied to 12 diverse backbone models across multiple real-world benchmark datasets. Our work reveals that directly regularizing output statistics is a powerful and generalizable strategy for significantly improving anomaly detection systems.

Problem

• Reconstruction-based anomaly detection suffers from noisy residuals
• MSE loss causes unstable anomaly scores with poor signal-to-noise ratio
• Existing methods lack statistical constraints for optimal anomaly separation

Innovation

• Gaussian-White Noise Regularization strategy during training
• Kalman Smoothing Post-processor for denoising anomaly scores
• Universal enhancement framework for time series anomaly detection