Add sample_weight support to StandardScaler (and friends?)

[amueller]

Via #15583:
it would be nice to have sample_weight support in StandardScaler. I don't see how to do that for sparse data right now, though (without touching the Cython code).

[jnothman]

Touching the cython code doesn't look that hard, but it would require deciding if we want to duplicate the functions to handle the weighted case, or whether we can reuse the exisiting code paths (risking loss in both efficiency and precision).

[NicolasHug]

In #14696 we duplicate. I think it's worth it as long as the function is simple enough?

[lorentzenchr]

This would also help a "sparse" solution of #3702.

[amueller]

Actually, I'm using a numpy/scipy based helper in my PR and I think this should be fine as long as we don't need inplace?

[panpiort8]

I can take that issue

[panpiort8]

Computing weighted mean and variance (for non-sparse matrix) in partial_fit requires applying _incremental_mean_and_var twice or developing new (to my knowledge) method similar to _incremental_mean_and_var, but with sample_weight (like here). I believe latter option is far better and should be dealt with another issue. What do you think, guys?

[jnothman]

I'm okay with the latter proposal, but I'd need to see a pull request to be confident

[amueller]

I think we should just use a non-cython variant as I did here:
https://github.com/scikit-learn/scikit-learn/pull/15583/files#diff-ce89de6ba5554a75729d37eca95fc24dR835

[panpiort8]

I think we should just use a non-cython variant as I did here:
https://github.com/scikit-learn/scikit-learn/pull/15583/files#diff-ce89de6ba5554a75729d37eca95fc24dR835

But we want StandardScaler to compute stats in incremental (batch) manner, which is, I believe, quite different.

[lorentzenchr]

#18510 and #18682 added sample_weight to StandardScaler for dense and sparse input.