# Anomaly Attribution of Multivariate Time Series using Counterfactual Reasoning

arXiv: https://arxiv.org/abs/2109.06562 · HTML: https://mlsanity.com/paper/2109.06562/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 13 references that are in the map.
- First posted on arXiv 14 Sep 2021.

## Builds on (most cited first, 4 of 4)

- [A review on outlier/anomaly detection in time series data](https://mlsanity.com/paper/2002.04236/) (2020)
- [Detecting Regions of Maximal Divergence for Spatio-Temporal Anomaly Detection](https://mlsanity.com/paper/1804.07091/) (2018)
- [TSInsight: A local-global attribution framework for interpretability in time-series data](https://mlsanity.com/paper/2004.02958/) (2020)
- [Time Series Data Cleaning: From Anomaly Detection to Anomaly Repairing (Technical Report)](https://mlsanity.com/paper/2003.12396/) (2020)

## Built on by (most cited first, 3 of 3)

- [DCFO: Density-Based Counterfactuals for Outliers -- Additional Material](https://mlsanity.com/paper/2512.10659/) (2025)
- [Transformer-based Multivariate Time Series Anomaly Localization](https://mlsanity.com/paper/2501.08628/) (2025)
- [Advancing climate model interpretability: Feature attribution for Arctic melt anomalies](https://mlsanity.com/paper/2502.07741/) (2025)

## Abstract (arXiv)

There are numerous methods for detecting anomalies in time series, but that is only the first step to understanding them. We strive to exceed this by explaining those anomalies. Thus we develop a novel attribution scheme for multivariate time series relying on counterfactual reasoning. We aim to answer the counterfactual question of would the anomalous event have occurred if the subset of the involved variables had been more similarly distributed to the data outside of the anomalous interval. Specifically, we detect anomalous intervals using the Maximally Divergent Interval (MDI) algorithm, replace a subset of variables with their in-distribution values within the detected interval and observe if the interval has become less anomalous, by re-scoring it with MDI. We evaluate our method on multivariate temporal and spatio-temporal data and confirm the accuracy of our anomaly attribution of multiple well-understood extreme climate events such as heatwaves and hurricanes.