I would like to implement various AI-estimators for quantile estimation for a regression problem. It would be necessary to have non-crossing quantiles, that is larger quantiles would correspond to higher prediction values.
My objective is to have a multidimensional prediction vector as an output in the estimation, each dimension corresponding to a specific quantile. Maybe I would have to define a custom loss function, as well, for that purpose. I would like to try different methods such as deeplearning or gradient boosting or random forests.
Anyone having an idea how to build such AI-estimators? My preferred library choice would be scikit-learn.
Can someone give me an idea how to do this?