Let's say that you want to build a model that predicts two possible outcomes with a probability for each. To be clear, i'm not talking about a problem where the target variable is binary and you want to model p(x=1) vs p(x=0). I mean the target variable can take on any value, but has a bimodal distribution. Rather than predict some value in the middle, I want to return both likely values along with the relative probability of one vs the other. How would you go about doing this?
As an extension to the problem, what if you want to build a model that returns two different regressions or sub-models (instead of just two different values) and a probability that a given input falls along one of the regressions relative to the other.
As a final clarification, I'm not talking about building some sort of decision tree where you apply one set of rules for one subset of the population and a different set of rules for another subset. I want to model two possible outcomes for all points in a population.