What question did this study set out to answer?

This study aims to develop a model-agnostic metric for detecting influential outliers using SHAP values and residuals.

July 9, 2026Stat0 citationsOpen Access

Model‐Agnostic Influential Outlier Metric

CJColin JonesCarleton University DCDavid A. CampbellIndiana University – Purdue University Indianapolis

Key Points

This study aims to develop a model-agnostic metric for detecting influential outliers using SHAP values and residuals.
Defined influence using transformed SHAP values and residuals via normalizing flows.
Illustrated the IOM across multiple models including linear models, neural networks, and tree-based methods.
Demonstrated effective detection of influential outliers across various modeling approaches.
Highlighted both advantages and limitations of the influential outlier metric in different contexts.

Abstract

ABSTRACT The influential outlier metric (IOM) provides model‐agnostic influential outlier detection. We define influence of an observation using a combination of SHapley Additive exPlanation (SHAP) values and the residual. Both are transformed using normalizing flows, changing their respective measures to Gaussian distributions. The transformed SHAP values and residuals define the IOM as a product of two independent random variables, allowing critical values for a given significance level . We illustrate the advantages and limitations of this approach in several models including the linear model, neural networks, the random forest and gradient‐boosted trees.

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