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

TL;DR

COGNOS targets a fundamental flaw in reconstruction-based TSAD: the residuals from $L_{MSE}$ training are often non-Gaussian and autocorrelated, leading to noisy anomaly scores. It introduces Gaussian-White Noise Regularization to shape residuals toward Gaussian white noise and pairs this with a Kalman Smoothing post-processor that is statistically optimal under those residual properties. The framework is model-agnostic and shows substantial, consistent improvements (e.g., average F-score uplift of $57.9\%$ across $12$ backbones and multiple real-world datasets). This approach directly regularizes output statistics rather than latent representations, yielding robust, stable anomaly signals with broad practical impact for TSAD systems. The work suggests a new direction for anomaly detection research focused on final residual statistics and optimal post-processing, with potential extensions to multivariate and video anomaly detection.

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.

Figures (16)

• Figure 1: Limitations of standard MSE-based training for anomaly detection, illustrated using a Transformer on the SWaT dataset. (a) The resulting anomaly score is highly noisy, creating a poor signal-to-noise ratio where true anomalous deviations are masked. (b) The Q-Q plot reveals that reconstruction residuals are strongly non-Gaussian, indicating poorly modeled underlying noise. (c) The autocorrelation plot shows significant temporal correlation remaining in the residuals, suggesting the model failed to capture all predictable patterns.
• Figure 2: COGNOS Overview: Backbones are trained with Gaussian white noise regularization, and residuals are then post-processed using a Kalman smoother to generate stable anomaly scores.
• Figure 3: Qualitative comparison of anomaly scores on the SWaT and PSM datasets using a Transformer backbone. The vanilla MSE baseline produces noisy scores, whereas COGNOS yields stable scores with a clear separation between normal and anomalous periods.
• Figure 4: Visual analysis of reconstruction residuals for the FiLM backbone on the PSM dataset. Top row: Residuals from the vanilla method show strong autocorrelation (ACF) and non-Gaussianity (Q-Q plot). Bottom row: COGNOS successfully regularizes the residuals, suppressing autocorrelation and enforcing a distribution much closer to Gaussian white noise.
• Figure 5: The impact of the Bias-Variance Tradeoff $\lambda$ on four backbones across the MSL and SWaT datasets.