Multivariate outlier explanations using Shapley values and Mahalanobis distances

Shapley values can break down why data points are outliers: The paper demonstrates that complex statistical measures (squared Mahalanobis distances) can be decomposed into individual variable contributions using Shapley values, making it possible to explain which specific variables are responsible for flagging an observation as unusual rather than just saying "this data point is an outlier."

This approach is computationally efficient: By combining Shapley values with Mahalanobis distances, the authors show these explanations can be calculated at "low numerical cost," meaning organizations can implement outlier explanations at scale without prohibitive computational overhead—important for real-world deployment of responsible AI systems.

Addresses "cellwise" outliers, not just global ones: The paper extends beyond traditional outlier detection to explain cases where individual data cells (specific variable values) are anomalous given the broader data structure, providing more granular insights into what makes an observation unusual in multivariate datasets.

Game theory provides principled fairness in explanations: By using Shapley values—a concept from game theory designed to fairly distribute contributions—the method ensures that variable contributions to outlyingness are allocated in a theoretically sound way, rather than through ad-hoc methods that might unfairly attribute importance.

Validated on real-world data: The authors demonstrate practical utility through both simulations and real-world examples, suggesting the approach is ready for practical applications in domains like fraud detection, quality control, or anomaly monitoring where understanding why something is flagged as unusual is critical for human decision-making.