With #29705, we have a simple way to freeze estimators, which means there is no need for cv="prefit". This also opens the door for #8350 to make Pipeline and FeatureUnion follow our conventions. This issue is to discuss the API implications of introducing FrozenEstimator. Here are the two I had in mind:

cv="prefit"

For the cv case, users pass a frozen estimator directly into cv:

rf = RandomForestClassifer()
rf.fit(X_train, y_train)
frozen_rf = FrozenEstimator(rf)

calibration = CalibratedClassifierCV(frozen_rf)
calibration.fit(X_calib, y_calib)

Making this change will simplify our codebase with cv="prefit"

compose.Pipeline

We introduce a new compose.Pipeline which follows our conventions with clone. (The current pipeline.Pipeline does not clone.)

from sklearn.compose import Pipeline

prep = ColumnTransformer(...)
prep.fit(X_train, y_train)
frozen_prep = FrozenEstimator(prep)

pipe = Pipeline([frozen_prep, LogisticRegression()])

pipe.fit(X_another, y_another)

In both cases, I like prefer the semantics of FrozenEstimator.