Include init_score on the Python Booster class

[JoshuaC3]

Summary

Add init_score_values as a parameter on the Python Booster class. Currently, it is only available on the Dataset class.

Motivation

Currently, it is a little tricky to find init_score after a model is trained. While it can be set, and therefore known, when boost_from_average it isn't. When saving a model, the easy access to this presumably gets lost. Therefore, it would be useful to have it as an attribute on the model.

It then allows us to access it via the sklearn API.

Description

See here for further details and initial motivation.

[JoshuaC3]

Possibly something like,

    for dataset_name, eval_name, score, _ in evaluation_result_list:
        booster.best_score[dataset_name][eval_name] = score

    booster.init_score_value = trainset.get_init_score()

    if not keep_training_booster:
        booster.model_from_string(booster.model_to_string(), False).free_dataset()

here.

[StrikerRUS]

Closed in favor of being in #2302. We decided to keep all feature requests in one place.

Welcome to contribute this feature! Please re-open this issue (or post a comment if you are not a topic starter) if you are actively working on implementing this feature.