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