Some questions regarding the expected behaviour:

1. When using a pipeline, do we expect values to reflect the data scale after or before preprocessing. Values before preprocessing will require support of inverse_transform which will be challenging for some transformer (e.g., ColumnTransformer, PolynomialFeature, etc.);
2. In the case of data augmentation within a pipeline (e.g., PolynomialFeature), one would be interested to know the interaction of an augmented feature.

If a pipeline is passed, we should be quantifying in terms of its input features... If the user wants otherwise they should slice it.

After couple of iterations this morning is what I thought as well. This will make thing so difficult otherwise. get_feature_names will be handy in case a user need to slice it.

Feel free to ping when you need reviews! (I'll look at #14035)

I think this is good to be reviewed @thomasjpfan @NicolasHug

I will probably add an example to illustrate to we can use the ColumnTransformer

We would need to merge #15354 before then.

I dropped the support and put a meaningful error message depending of the type of X

Same remark for https://scikit-learn.org/dev/auto_examples/plot_partial_dependence_visualization_api.html

I updated the examples. However, be aware that we still have to specify features and features_names. I only updated partial_dependence and not plot_partial_dependence. So the next upcoming PR is to make plot_partial_dependence infer the features_names for dataframe such that one has only to give a list of features names.

@NicolasHug Can we merge this one.

@thomasjpfan as well :P

Thanks @glemaitre !