I built a gbm model (using caret package) in order to predict the probability of someone buy or not a car. However as this kind of model act as a black box my issue is to replicate the "profile" of the group who has higher probability to buy. There is any way to discover the values of the predictors that generate high prob?
I'd suggest starting with "partial dependence" plots which essentially show the effect of each feature (or set of features) with all other effects averaged out. A gbm can capture complex multivariate feature interactions so this won't tell the whole story but it is a good place to start.
Assuming you used the gbm package via carret the gbm.plot function can be used to make such plots.
Assuming you're using R, the function is
relative.influence(..). But you don't need it because
summary(mod) would give you the same thing.