Strong Linear Baselines Strike Back: Closed-Form Linear Models as Gaussian Process Conditional Density Estimators for TSAD

TL;DR

This paper demonstrates that simple linear autoregressive models with closed-form solutions can match or outperform complex deep neural networks in time series anomaly detection, offering a more efficient alternative.

Contribution

It introduces a closed-form linear model for TSAD that captures various anomaly types and achieves superior accuracy with less computational cost.

Findings

Linear models match or outperform deep detectors.

Proposed approach is computationally efficient.

Linear models effectively capture diverse anomalies.

Abstract

Research in time series anomaly detection (TSAD) has largely focused on developing increasingly sophisticated, hard-to-train, and expensive-to-infer neural architectures. We revisit this paradigm and show that a simple linear autoregressive anomaly score with the closed-form solution provided by ordinary least squares (OLS) regression consistently matches or outperforms state-of-the-art deep detectors. From a theoretical perspective, we show that linear models capture a broad class of anomaly types, estimating a finite-history Gaussian process conditional density. From a practical side, across extensive univariate and multivariate benchmarks, the proposed approach achieves superior accuracy while requiring orders of magnitude fewer computational resources. Thus, future research should consistently include strong linear baselines and, more importantly, develop new benchmarks with richer temporal structures pinpointing the advantages of deep learning models.