ENH add support for array API to various metric

[virchan]

Reference Issues/PRs

Towards #29678, #26024

What does this implement/fix? Explain your changes.

This PR updates the following functions in sklearn.metrics:

1. MAE mean_absolute_error
2. MAPE mean_absolute_percentage_error
3. MSE mean_squared_error
4. RMSE root_mean_squared_error
5. MSLE mean_squared_log_error
6. RMSLE root_mean_squared_log_error

Specifically:

1. The functions MSLE and RMSLE now check whether y_true and y_pred are within the correct domain for the function $y = \log(1 + x)$, rather than $y = \log(x)$, as was previously implemented, addressing issue root_mean_squared_log_error & mean_squared_log_error: ValueError should be raised only if y_true or y_pred contain a value below -1, not below 0 #29678.
2. The functions RMSE, MSLE, and RMSLE are now compatible with the Array API and have been added to the relevant tests, partially addressing issue Make more of the "tools" of scikit-learn Array API compatible #26024.
3. The functions MAE, MAPE, MSE, and RMSE now explicitly check if a scalar is returned when multioutput=uniform_average.

Any other comments?

1. This is the same as the PR Updating root_mean_squared_log_error & mean_squared_log_error #29686, which was closed due to re-branching.
2. The description has been updated to reflect the recent changes.

[OmarManzoor]

Other than the comment I added, this looks good.

[adrinjalali]

I'd like to see what @ogrisel thinks here.

[ogrisel]

LGTM besides the following nitpicky suggestion. I will commit it and if CI goes through, it will auto-merge.

[virchan]

Thank you for your time!

[ogrisel]

I realized I merged with running the CUDA CI first... Let's be hopeful...

[ogrisel]

At least the tests pass with pytorch on MPS device, I tried locally.

[ogrisel]

All is fine with CUDA apparently: https://github.com/scikit-learn/scikit-learn/actions/runs/11076066477/job/30778541141