@amueller If this needs a contributor, I'd like to tackle it. I'm confused though why this is different than what is being proposed in #6217.

@mrecachinas I need to look more deeply into that but it doesn't seem to touch _weighted_percentile

Another way for this feature is if numpy/numpy#9211 gets merged.
@MechCoder @mrecachinas Are there use cases within scikit-learn?

@lorentzenchr I just found this old issue.
Basically, I think that we are going to solve the issue in #17377
It has some effect in the GBDT and I think that we will be limited regarding the implementation with assumption that we do about the sample_weight.

Actually, this is a non-issue:

import numpy as np
np.quantile(y, 0.5, method="inverted_cdf")  # 0

results in 0. And that is totally correct. In fact, each value in [0, 1] minimizes the mean absolute error:

from sklearn.metrics import mean_absolute_error

mean_absolute_error(y, [0, 0])  #  0.5
mean_absolute_error(y, [1, 1])  #  0.5

Also, each value $q_{0.5} \in [0, 1]$ fulfills the classical nonexceedance criterion $P(q_\alpha < Y) \leq \alpha$ and $P(Y \leq Y)\geq \alpha$ for $\alpha=0.5$.