QuantileRegressor has been implemented in #9978
However, it was reported to have an issue with large array of data where linear programming solvers require to form huge matrices for the optimization problem.

A potential solution is to have an online solver using partial_fit. However, it is not clear which solvers would be best to solve this issue.

Has proposed by @agramfort #9978 (comment), we should benchmark the different available solvers before making an implementation choice.

Pinging @RPyElec @avidale @agramfort @lorentzenchr @GaelVaroquaux that were involved in the discussion in the former pull-request.

Tasks:

• Add support for sparse X (relatively easy). ENH support sparse data input for QuantileRegressor #21086
• Propose an algorithm for a partial_fit method, test and benchmark it (difficult task). FEA add pinball loss to SGDRegressor #22043
• Survey alternative solvers from the literature.