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We show that regression predictions from linear and tree-based models can berepresented as linear combinations of target instances in the training data.This also holds for models constructed as ensembles of trees, including RandomForests and Gradient Boosting Machines. The weights used in these linearcombinations are measures of instance importance, complementing existingmeasures of feature importance, such as SHAP and LIME. We refer to thesemeasures as AXIL weights (Additive eXplanations with Instance Loadings). SinceAXIL weights are additive across instances, they offer both local and globalexplanations. Our work contributes to the broader effort to make machinelearning predictions more interpretable and explainable.

Instance-based Explanations for Gradient Boosting Machine Predictions with AXIL Weights