Currently we have a long list of exclusions (sklearn.utils.testing.{DONT_TEST,OTHER,META_ESTIMATORS}) from our common tests. We would like every estimator to undergo some amount of common testing. This is a concern of #6715, and one potential solution is #6599, which would allow us to annotate each estimator with its traits from which each test's applicability can be determined.

However:

• some estimators (such as Pipeline, GridSearchCV) cannot be constructed without explicit parameters.
• some estimators' behaviour differs substantially between some parameter choices such that each should be checked by common tests (see also [WIP] Test determinism of estimators #7270 (comment)).

To allow more estimators to be tested upon discovery, we need a way to specify the parameter sets that it may be constructed with for basic API testing.