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.
That data can be modeled as a statistical process, where the distributions and parameters change as a function of x. This is in contrast to modeling it as a typical statistical distribution which assumes the same distribution and parameters throughout a range.
The &quot;a&quot; range could be modeled as a bimodal distribution and the &quot;b&quot; range could be modeled as a unimodal distribution.