Describe the workflow you want to enable

As we are waiting for a reviewer to review #22754 , @thomasjpfan suggested we just move forward with our goals of creating a package of more exotic tree splits. E.g. https://arxiv.org/abs/1909.11799. While we wait for reviewers, the suggestion is to make a package within scikit-learn-contrib.

Although we would like for #22754 to be eventually merged into scikit-learn, we understand reviewer backlog is an issue. To move forward while reviews occur, we would need to subclass existing scikit-learn code. Ideally, we would like to introduce minor refactoring changes that would make this task significantly easier.

We would like to subclass directly from scikit-learn without requiring us to keep an up-to-date fork of scikit-learn with all the bug fixes and maintenance that the dev team here does. We can limit this if we modularize the Python/Cython functions inside the sklearn/tree module.

Describe your proposed solution

I am proposing two refactoring modifications that have no impact on the performance of the current tree estimators in scikit-learn.

1. Refactor the BaseDecisionTree Python class to have the following functions that can be overridden in a subclass:

• _set_tree_class: sets the Tree Cython class that the Python API uses
• _set_splitter: sets the Splitter Cython class that the Python API uses

For example, this makes the subclassing of BaseDecisionTree cleaner:

2. Refactor the Tree Cython class to have the following functions:

• _set_node_values: transfers split node values to the storage node
• _compute_feature_value: uses the storage node and the input data to compute the feature value to split on

For example, see

3. Refactor the TreeBuilder Cython class to pass around a Split pointer, rather than the struct itself

This will enable someone to use C-level functions to pass around another struct with a similar structure as Split.

For example, see

Describe alternatives you've considered, if relevant

Alternatives would require maintaining a copy of the sklearn/tree module and keep it up-to-date w/ sklearn changes. If this was just one Cython file, I would say it is possible, but the necessary ingredients span some of the underlying private API, making this a very time-consuming task. Introducing modularity into the private API that does not impact existing performance, therefore seems to be the best path forward?

Moreover, by introducing these refactoring changes, #22754 has a smaller diff and lower-cost to review.

Additional context

#22754 demonstrates that there is no performance regression, or issues w/ existing DecisionTree, or RandomForest when introducing these changes.