# Multivariate Time Series Anomaly Detection by Capturing Coarse-Grained Intra- and Inter-Variate Dependencies

arXiv: https://arxiv.org/abs/2501.16364 · HTML: https://mlsanity.com/paper/2501.16364/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 36 references that are in the map.
- First posted on arXiv 22 Jan 2025.

## Builds on (most cited first, 14 of 14)

- [Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding](https://mlsanity.com/paper/1802.04431/) (2018)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [Unsupervised Anomaly Detection via Variational Auto-Encoder for Seasonal KPIs in Web Applications](https://mlsanity.com/paper/1802.03903/) (2018)
- [A Multimodal Anomaly Detector for Robot-Assisted Feeding Using an LSTM-based Variational Autoencoder](https://mlsanity.com/paper/1711.00614/) (2017)
- [Multivariate Time-series Anomaly Detection via Graph Attention Network](https://mlsanity.com/paper/2009.02040/) (2020)
- [Time-Series Anomaly Detection Service at Microsoft](https://mlsanity.com/paper/1906.03821/) (2019)
- [DCdetector: Dual Attention Contrastive Representation Learning for Time Series Anomaly Detection](https://mlsanity.com/paper/2306.10347/) (2023)
- [Local Evaluation of Time Series Anomaly Detection Algorithms](https://mlsanity.com/paper/2206.13167/) (2022)
- [RobustTAD: Robust Time Series Anomaly Detection via Decomposition and Convolutional Neural Networks](https://mlsanity.com/paper/2002.09545/) (2020)
- [TFAD: A Decomposition Time Series Anomaly Detection Architecture with Time-Frequency Analysis](https://mlsanity.com/paper/2210.09693/) (2022)
- [Deep Learning-Based Anomaly Detection in Cyber-Physical Systems: Progress and Opportunities](https://mlsanity.com/paper/2003.13213/) (2020)
- [Detecting Multivariate Time Series Anomalies with Zero Known Label](https://mlsanity.com/paper/2208.02108/) (2022)
- [Adaptive Performance Anomaly Detection for Online Service Systems via Pattern Sketching](https://mlsanity.com/paper/2201.02944/) (2022)
- [Practical Anomaly Detection over Multivariate Monitoring Metrics for Online Services](https://mlsanity.com/paper/2308.09937/) (2023)

## Built on by (most cited first, 8 of 8)

- [CrossAD: Time Series Anomaly Detection with Cross-scale Associations and Cross-window Modeling](https://mlsanity.com/paper/2510.12489/) (2025)
- [STAR: Boosting Time Series Foundation Models for Anomaly Detection through State-aware Adapter](https://mlsanity.com/paper/2510.16014/) (2025)
- [We Need a More Robust Classifier: Dual Causal Learning Empowers Domain-Incremental Time Series Classification](https://mlsanity.com/paper/2601.10312/) (2026)
- [SEDformer: Event-Synchronous Spiking Transformers for Irregular Telemetry Time Series Forecasting](https://mlsanity.com/paper/2602.02230/) (2026)
- [LEFT: Learnable Fusion of Tri-view Tokens for Unsupervised Time Series Anomaly Detection](https://mlsanity.com/paper/2602.08638/) (2026)
- [VAN-AD: Visual Masked Autoencoder with Normalizing Flow For Time Series Anomaly Detection](https://mlsanity.com/paper/2603.26842/) (2026)
- [Multivariate Time Series Anomaly Detection via Dual-Branch Reconstruction and Autoregressive Flow-based Residual Density Estimation](https://mlsanity.com/paper/2604.08582/) (2026)
- [MORA: Modeling Observed Changes for Drift-Robust Time-Series Anomaly Detection](https://mlsanity.com/paper/2610.09473/) (2026)

## Abstract (arXiv)

Multivariate time series anomaly detection is essential for failure management in web application operations, as it directly influences the effectiveness and timeliness of implementing remedial or preventive measures. This task is often framed as a semi-supervised learning problem, where only normal data are available for model training, primarily due to the labor-intensive nature of data labeling and the scarcity of anomalous data. Existing semi-supervised methods often detect anomalies by capturing intra-variate temporal dependencies and/or inter-variate relationships to learn normal patterns, flagging timestamps that deviate from these patterns as anomalies. However, these approaches often fail to capture salient intra-variate temporal and inter-variate dependencies in time series due to their focus on excessively fine granularity, leading to suboptimal performance. In this study, we introduce MtsCID, a novel semi-supervised multivariate time series anomaly detection method. MtsCID employs a dual network architecture: one network operates on the attention maps of multi-scale intra-variate patches for coarse-grained temporal dependency learning, while the other works on variates to capture coarse-grained inter-variate relationships through convolution and interaction with sinusoidal prototypes. This design enhances the ability to capture the patterns from both intra-variate temporal dependencies and inter-variate relationships, resulting in improved performance. Extensive experiments across seven widely used datasets demonstrate that MtsCID achieves performance comparable or superior to state-of-the-art benchmark methods.