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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?

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