One of the methods to address a classification predictive analysis on an imbalanced set consist on undersample the majority class (others approaches consist on: undersample the majority class, synthesize new minority classes...).
So assume hereafter we use any of those solutions and then we train an algorithm with the new generated data set. Will this trained algorithm be useful to predict further data from this system which is in general imbalanced?
Or to make it more concrete, is it possible in general to train a model with a balanced training set so that we can effectively predict an imbalanced prediction set? Or both should be generarly either balanced or imbalanced?