VUS: Effective and Efficient Accuracy Measures for Time-Series Anomaly Detection

TL;DR

This paper evaluates existing and proposes new accuracy measures for time-series anomaly detection, emphasizing threshold-independent metrics like AUC-ROC, AUC-PR, and introducing VUS for more robust and efficient evaluation.

Contribution

It systematically analyzes evaluation measures for time-series AD, extends AUC measures for range anomalies, and introduces VUS, a novel threshold-independent measure with optimized implementations.

Findings

AUC-ROC and AUC-PR are more robust for time-series AD evaluation.

VUS provides a threshold-independent, parameter-free assessment of anomaly detection quality.

The proposed measures outperform traditional metrics in robustness and efficiency.

Abstract

Anomaly detection (AD) is a fundamental task for time-series analytics with important implications for the downstream performance of many applications. In contrast to other domains where AD mainly focuses on point-based anomalies (i.e., outliers in standalone observations), AD for time series is also concerned with range-based anomalies (i.e., outliers spanning multiple observations). Nevertheless, it is common to use traditional point-based information retrieval measures, such as Precision, Recall, and F-score, to assess the quality of methods by thresholding the anomaly score to mark each point as an anomaly or not. However, mapping discrete labels into continuous data introduces unavoidable shortcomings, complicating the evaluation of range-based anomalies. Notably, the choice of evaluation measure may significantly bias the experimental outcome. Despite over six decades of attention, there has never been a large-scale systematic quantitative and qualitative analysis of time-series AD evaluation measures. This paper extensively evaluates quality measures for time-series AD to assess their robustness under noise, misalignments, and different anomaly cardinality ratios. Our results indicate that measures producing quality values independently of a threshold (i.e., AUC-ROC and AUC-PR) are more suitable for time-series AD. Motivated by this observation, we first extend the AUC-based measures to account for range-based anomalies. Then, we introduce a new family of parameter-free and threshold-independent measures, Volume Under the Surface (VUS), to evaluate methods while varying parameters. We also introduce two optimized implementations for VUS that reduce significantly the execution time of the initial implementation. Our findings demonstrate that our four measures are significantly more robust in assessing the quality of time-series AD methods.