Permute each variable in a dataset and use the change in predictions to calculate the importance of each variable. Based on the scikit learn implementation of permutation importance: https://scikit-learn.org/stable/modules/permutation_importance.html. However, we don't compare to the target by a metric. We JUST look at the change in the model's predictions, as measured by MAE. (for classification, this is like using a Brier score). We shuffle each variable and recompute the predictions before and after the shuffle. The difference in MAE. is the importance of that variable. We normalize by computing the MAE of the shuffled original predictions as an upper bound on the MAE and divide by this value. So a variable that, when shuffled, caused predictions as bad as shuffling the output predictions, we know that variable is 100 Similarly, as with regular permutation importance, a variable that, when shuffled, gives the same MAE as the original model has an importance of 0.
This method cannot yield negative importances. It is merely a measure of how much the models uses the variable, and does not tell you which variables help or hurt generalization. Use the model's cross-validated metrics to assess generalization.