variable importance in boosted regression tree

I have trouble understanding how relative influence of a variable is calculated in a boosted regression tree. I am reading from the following paper by Friedman and Meulman.

Multiple additive regression trees with application in epidemiology http://onlinelibrary.wiley.com/doi/10.1002/sim.1501/pdf

"The relative contribution of any one explanatory variable ($x_j$) is based on how often it is selected to split individual trees, weighted by the squared improvement to the model ($I_j^2$) resulting from the sum of these trees (i.e. from $m = 1$ to $M$ the total number of trees):

$$\hat I_j^2 = \frac{1}{M} \sum_{m=1}^M I_j^2(Tm)$$

where $I_j^2$ is the relative influence of input variable $j$ for individual tree $Tm$

I do not understand how the term $I_j^2$ (which is the squared improvement of the model) is calculated for each tree. Can anyone please explain me this.

• which text are you talking about? Aug 31, 2016 at 14:48
• Possible duplicate: stats.stackexchange.com/questions/162162/… Aug 31, 2016 at 15:02
• Thanks. I was looking for an explanation which is opposite to what is given in the link you provided. I am looking for a simpler explanation (something like back of the envelope calculation) whereas the link gave a bit code-like explanation which goes above head. Sorry :( Aug 31, 2016 at 15:47
• No problem, fair enough. I'll try to add an answer like that later in the day. Aug 31, 2016 at 16:47