# CoCAI: Copula-based Conformal Anomaly Identification for Multivariate Time-Series

arXiv: https://arxiv.org/abs/2507.17796 · HTML: https://mlsanity.com/paper/2507.17796/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 42 references that are in the map.
- First posted on arXiv 23 Jul 2025.

## Builds on (most cited first, 11 of 11)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [Conformal Prediction for STL Runtime Verification](https://mlsanity.com/paper/2211.01539/) (2022)
- [Dive into Time-Series Anomaly Detection: A Decade Review](https://mlsanity.com/paper/2412.20512/) (2024)
- [Robust Conformal Prediction for STL Runtime Verification under Distribution Shift](https://mlsanity.com/paper/2311.09482/) (2023)
- [Conformal Quantitative Predictive Monitoring of STL Requirements for Stochastic Processes](https://mlsanity.com/paper/2211.02375/) (2022)
- [Robust Anomaly Detection for Time-series Data](https://mlsanity.com/paper/2202.02721/) (2022)
- [Learning-Based Approaches to Predictive Monitoring with Conformal Statistical Guarantees](https://mlsanity.com/paper/2312.01959/) (2023)
- [Diffusion-based Time Series Forecasting for Sewerage Systems](https://mlsanity.com/paper/2506.08577/) (2025)

## Built on by (most cited first, 1 of 1)

- [Localized Anomaly Detection via Differentiable D-vine Copulas](https://mlsanity.com/paper/2607.25020/) (2026)

## Abstract (arXiv)

We propose a novel framework that harnesses the power of generative artificial intelligence and copula-based modeling to address two critical challenges in multivariate time-series analysis: delivering accurate predictions and enabling robust anomaly detection. Our method, Copula-based Conformal Anomaly Identification for Multivariate Time-Series (CoCAI), leverages a diffusion-based model to capture complex dependencies within the data, enabling high quality forecasting. The model's outputs are further calibrated using a conformal prediction technique, yielding predictive regions which are statistically valid, i.e., cover the true target values with a desired confidence level. Starting from these calibrated forecasts, robust outlier detection is performed by combining dimensionality reduction techniques with copula-based modeling, providing a statistically grounded anomaly score. CoCAI benefits from an offline calibration phase that allows for minimal overhead during deployment and delivers actionable results rooted in established theoretical foundations. Empirical tests conducted on real operational data derived from water distribution and sewerage systems confirm CoCAI's effectiveness in accurately forecasting target sequences of data and in identifying anomalous segments within them.