[FEATURE] (Linear) Quantile Regression

Heya!

At some point, I implemented the LADRegression, which basically minimized sum |y_i - model(X_i)|. This also has the effect that the model over- and underestimates 50% of the time. As in the ImbalancedRegression, we can also penalize over- and underestimations differently, with some parameter quantile. This would have the effect that the model overestimates a share of quantile samples and underestimates in 1-quantile of the cases.

This one would be useful for having some kind of nice confidence intervals around predictions by training a model with quantile=0.05 and another one with quantile=0.95, for example.

I implemented it here. It’s basically a more general LADregression.

How about we put this into scikit-lego and make the LADRegression just a Quantileregression(quantile=0.5)? Or remove it completely.

Best Robert

[MBrouns]

I’d say quantile regression is super useful! indeed AFAIK, scikit-garden is focused on tree-based models so having it in this project makes sense.

I’m okay with having both LADRegression and QuantileRegression around for a while, although we should probably either rewrite LADRegression to use the QuantileRegression, or deprecate the former

[koaning]

Grand. @Garve feel free to get started on a PR then. I think the example you show here will work swell for the docs too 👍

It’d be preferable to have a PR where the LADRegression uses the QuantileRegression under the hood. Feel free to let me know if there’s a good reason to delay that though.