From global to local MDI variable importances for random forests and when they are Shapley values Supplementary materials

A.1 Proof of Theorem 1 Theorem 1. (MDI are Shapley values) F or all feature X The other way around is trivial. A.4 Proof of Theorem 4 Theorem 4. If a variable is locally irrelevant at x with respect to Y , then Imp The proof stems from the definition of the local irrelevance.