Apologies if this has been brought up before. I did have a quick check of https://github.com/scikit-learn/scikit-learn/issues?q=is%3Aissue+sort%3Aupdated-desc+mean+error+is%3Aclosed+label%3Amodule%3Ametrics

Describe the workflow you want to enable

I am interested in the sign of the error and if possible I would rather do it in scikit-learn than numpy.

mean_absolute_error(y_true, y_pred, absolute=False) to return np.average(y_pred - y_true)
mean_absolute_error(y_true, y_pred) returns same as before

Describe your proposed solution

Adding the absolute=False will update https://github.com/scikit-learn/scikit-learn/blob/fd237278e/sklearn/metrics/_regression.py#L122L190 to be

                           absolute=True, sample_weight=None,
                           multioutput='uniform_average'):
...
    Parameters
    ----------
    absolute: bool
        Return MAE or ME.
...
    if absolute:
        output_errors = np.average(np.abs(y_pred - y_true),
                                   weights=sample_weight, axis=0)
    else:
        output_errors = np.average(y_pred - y_true,
                                   weights=sample_weight, axis=0)

Describe alternatives you've considered, if relevant

Not sure if a new metric is needed i.e. mean_error.

I believe this approach of a new argument was applied to mean_squared_error (squared=True). See #12895

Additional context

If this is of interest I'll be happy to work on this during the scipy sprint.