Breiman 1984 feature importance of a variable $j$ for a regression tree $T$ is:
Sklearn regression tree feature importance can be get as follows:
Where $\hat{l}_t^2$ is MSE improvement after splitting a such node $t$ and $v_t$ is the variable used to split that node. The summation means how much the variable $j$ decreased the impurity of some tree $T$. Is this equivalent (if normalized) to sklearn Feature importance ? Breiman hasn't used "Gini importance" to describe feature importance like sklearn has done, Would the expression "gini importance" be just a way to name it on normalized case?
