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

arXiv: https://arxiv.org/abs/2502.13318 · HTML: https://mlsanity.com/paper/2502.13318/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 53 references that are in the map.
- First posted on arXiv 18 Feb 2025.

## Builds on (most cited first, 7 of 7)

- [A review on outlier/anomaly detection in time series data](https://mlsanity.com/paper/2002.04236/) (2020)
- [Precision and Recall for Time Series](https://mlsanity.com/paper/1803.03639/) (2018)
- [Navigating the Metric Maze: A Taxonomy of Evaluation Metrics for Anomaly Detection in Time Series](https://mlsanity.com/paper/2303.01272/) (2023)
- [Band-limited Training and Inference for Convolutional Neural Networks](https://mlsanity.com/paper/1911.09287/) (2019)
- [Series2Graph: Graph-based Subsequence Anomaly Detection for Time Series](https://mlsanity.com/paper/2207.12208/) (2022)
- [Matrix Profile Goes MAD: Variable-Length Motif And Discord Discovery in Data Series](https://mlsanity.com/paper/2008.13447/) (2020)
- [Ensemble Grammar Induction For Detecting Anomalies in Time Series](https://mlsanity.com/paper/2001.11102/) (2020)

## Built on by (most cited first, 13 of 13)

- [PaAno: Patch-Based Representation Learning for Time-Series Anomaly Detection](https://mlsanity.com/paper/2602.01359/) (2026)
- [MLLM4TS: Leveraging Vision and Multimodal Language Models for General Time-Series Analysis](https://mlsanity.com/paper/2510.07513/) (2025)
- [Surprised by Attention: Predictable Query Dynamics for Time Series Anomaly Detection](https://mlsanity.com/paper/2603.12916/) (2026)
- [Disjoint or Overlapping? Inference Windowing for Reconstruction-Based Time Series Anomaly Detection](https://mlsanity.com/paper/2606.09874/) (2026)
- [A Comparative Study of Adaptation Strategies for Time Series Foundation Models in Anomaly Detection](https://mlsanity.com/paper/2601.00446/) (2026)
- [Strong Linear Baselines Strike Back: Closed-Form Linear Models as Gaussian Process Conditional Density Estimators for TSAD](https://mlsanity.com/paper/2602.00672/) (2026)
- [IMPACT: Influence Modeling for Open-Set Time Series Anomaly Detection](https://mlsanity.com/paper/2603.29183/) (2026)
- [Bridging Classification and Reconstruction: Cooperative Time Series Anomaly Detection](https://mlsanity.com/paper/2605.26193/) (2026)
- [CAAD: Causality-Aware Multivariate Time Series Anomaly Detection via Multi-Scale Alignment and Structural Causal Consistency](https://mlsanity.com/paper/2607.08555/) (2026)
- [What Streaming Anomaly Detection Finds (and Misses) in Industrial Time Series](https://mlsanity.com/paper/2609.39232/) (2026)
- [Detect, Explain, Interpret: An End-to-End Benchmark for Time Series Anomaly Detection, Explainability and Interpretability](https://mlsanity.com/paper/2610.01168/) (2026)
- [Correlation-Aware Reconstruction for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2610.15250/) (2026)
- [Retrieval Over Training: Similarity search-based Model Selection for Time Series Anomaly Detection](https://mlsanity.com/paper/2610.20243/) (2026)

## Abstract (arXiv)

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.