I have been playing around with post processing the results of the random forest for regression machine learning algorithm in order to try and do better than the default mean of all trees prediction. Chapter 16 of Elements of statistical learning talks about how and why this can be done using regularised regression (in that case elastic net).
On the other hand, I routinely re-calibrate the results of random forests using a logistic model, since I often see the kind of bias discussed in this question, and find that a simple linear logistic regression model tends to account for it. I have found that the calibration needs to be done on the ensemble prediction, attempting to calibrate individual trees doesn't work nearly as well.
I am unsure then of how to proceed when you want to do both of these things. If you do the elastic net regression first, you are finding the optimal weighted mean/subset of the forest ensemble for the biased prediction. I see no reason to be sure that this will be the optimal combination for a re-calibrated prediction. I don't see how the elastic net analysis could be run simultaneously with re-calibration, as the calibration is non-linear.
The non-linear problem of mutuality optimising the calibration parameters as well as weights and sub-set selection is doable is principle, but seem almost intractable computationally for large data sets.
Can anyone suggest an efficient path for achieving both of these aims in an optimised way?