Laplace noising versus simulated out of sample methods (cross frames)

Nina Zumel recently mentioned the use of Laplace noise in "count codes" by Misha Bilenko (see here and here) as a known method to break the overfit bias that comes from using the same data to design impact codes and fit a next level model. It is a fascinating method inspired by differential privacy methods, that Nina and I respect but don't actually use in production. Please read on for my discussion of some of the limitations of the technique, and how we solve the problem for impact coding (also called "effects codes"), and a worked example in R.We define a nested model as any model where the results of a sub-model are used as inputs for a later model. Common examples include variable preparation, ensemble methods, super-learning, and stacking. Nested models are very common in machine learning.