New Shapley-based method explains outliers in interval-valued data

Explainability remains a challenge in outlier detection, especially for complex data like interval-valued observations (e.g., temperature ranges, sensor intervals). In a new arXiv preprint, Catarina P. Loureiro, M. Rosário Oliveira, Paula Brito, and Lina Oliveira tackle this by extending the robust Interval Minimum Covariance Determinant (IMCD) estimator with Shapley values. They derive a closed-form expression for the Shapley value of the squared robust Interval-Mahalanobis distance, allowing efficient computation of each variable's contribution to an observation's outlyingness. This decomposition is particularly powerful: it breaks down the outlier score into contributions from the interval's center, its range, and cross-terms, offering fine-grained interpretability.

The method also connects to cellwise outlier detection—identifying which specific variables are unusual, even when the overall multivariate score is not extreme. The authors further introduce the Shapley interaction index to capture pairwise variable interactions driving atypical behavior. Tested on two real-world datasets, the approach demonstrates practical utility. This work opens doors for interpretable anomaly detection in domains like finance, meteorology, and IoT, where data naturally exist as intervals or ranges. The paper is published on arXiv under reference 2606.26307.