I am training a random forest model with ~100 features (call them
Then I add a new feature
X101 = A * X100, where
A is a positive constant.
X101 is perfectly collinear with
X100 and in principle adds no new information. However, training/testing the model with this new set of "independent" variables results in an apparent improvement in the model predictions, in the sense that the new model has a small but significant increase in AUC.
Under what circumstances could this happen?