_weighted_percentile does not lead to the same result than np.median

While reviewing a test in https://github.com/scikit-learn/scikit-learn/pull/16937, it appears that our implementation of _weighted_percentile with unit sample_weight will lead to a different result than np.median which is a bit problematic for consistency.

In the gradient-boosting, it brakes the loss equivalence because the initial predictions are different. We could bypass this issue by always computing the median using _weighted_percentile there.

import pytest
import numpy as np
from sklearn.utils.stats import _weighted_percentile

rng = np.random.RandomState(42)
X = rng.randn(10)
X.sort()
sample_weight = np.ones(X.shape)

median_numpy = np.median(X)
median_numpy_percentile = np.percentile(X, 50)
median_sklearn = _weighted_percentile(X, sample_weight, percentile=50.0)

assert median_numpy == pytest.approx(np.mean(X[[4, 5]]))
assert median_sklearn == pytest.approx(X[4])
assert median_numpy == median_numpy_percentile
assert median_sklearn == pytest.approx(median_numpy)

[glemaitre]

I think that our _weighted_precentile should offer the same default and maybe an interpolation parameter if required.

[glemaitre]

ping @lucyleeow Since you already look at the code, you might have some intuition why this is the case. We should actually have the above test as a regression test for our _weighted_percentile