# Is it possible to train probabilistic model to return several distributions?

I have nonlinear data of function y(x), which is let's say parabolic. At some points of x there are several y's (look at the picture).

Is it possible to train a probabilistic model to return several distributions (when needed) i.e. several means and variances. For example: when I feed a (x=a) to the model -> it returns 2 red distributions (2 means and 2 variances), and when I feed b (x=b) to the model -> it returns 1 blue distribution.

Thanks.

• Interesting question! Can you flip x,y so that you have a proper function x(y). Commented Aug 26, 2019 at 17:40
• For reference the function your trying to describe is a one to many function as in one x value gives many y values (if my a-level maths serves me correctly). It technically isn't a function as functions can't be one to many. Commented Aug 27, 2019 at 10:41

The conditional distribution of $$Y$$ when $$X=a$$ is bimodal. The mean is in the middle, and reporting it as such is correct (the mean of $$1,2,3,91,92,93$$ is indeed $$47$$).