DecisionTreeRegressor 的 Predict_proba 的等效项

scikit-learn 的DecisionTreeClassifier支持通过以下方式预测每个类别的概率predict_proba()功能。这不存在于DecisionTreeRegressor:

AttributeError：“DecisionTreeRegressor”对象没有属性“predict_proba”

我的理解是，决策树分类器和回归器之间的基本机制非常相似，主要区别在于回归器的预测是作为潜在叶子的平均值来计算的。所以我希望能够提取每个值的概率。

是否有另一种方法来模拟这个，例如通过处理树结构 https://scikit-learn.org/stable/auto_examples/tree/plot_unveil_tree_structure.html#sphx-glr-auto-examples-tree-plot-unveil-tree-structure-py? The code https://github.com/scikit-learn/scikit-learn/blob/55bf5d9/sklearn/tree/tree.py#L804 for DecisionTreeClassifier's predict_proba不能直接转让。

该函数改编自以下代码赫尔潘德尔的回答 https://stackoverflow.com/a/53592809/1840471提供每个结果的概率：

from sklearn.tree import DecisionTreeRegressor
import pandas as pd

def decision_tree_regressor_predict_proba(X_train, y_train, X_test, **kwargs):
    """Trains DecisionTreeRegressor model and predicts probabilities of each y.

    Args:
        X_train: Training features.
        y_train: Training labels.
        X_test: New data to predict on.
        **kwargs: Other arguments passed to DecisionTreeRegressor.

    Returns:
        DataFrame with columns for record_id (row of X_test), y 
        (predicted value), and prob (of that y value).
        The sum of prob equals 1 for each record_id.
    """
    # Train model.
    m = DecisionTreeRegressor(**kwargs).fit(X_train, y_train)
    # Get y values corresponding to each node.
    node_ys = pd.DataFrame({'node_id': m.apply(X_train), 'y': y_train})
    # Calculate probability as 1 / number of y values per node.
    node_ys['prob'] = 1 / node_ys.groupby(node_ys.node_id).transform('count')
    # Aggregate per node-y, in case of multiple training records with the same y.
    node_ys_dedup = node_ys.groupby(['node_id', 'y']).prob.sum().to_frame()\
        .reset_index()
    # Extract predicted leaf node for each new observation.
    leaf = pd.DataFrame(m.decision_path(X_test).toarray()).apply(
        lambda x:x.to_numpy().nonzero()[0].max(), axis=1).to_frame(
            name='node_id')
    leaf['record_id'] = leaf.index
    # Merge with y values and drop node_id.
    return leaf.merge(node_ys_dedup, on='node_id').drop(
        'node_id', axis=1).sort_values(['record_id', 'y'])

示例（参见这个笔记本 https://colab.research.google.com/drive/1O475-dUdJNtwg8osS8FfpVH_QeMRwf9g?usp=sharing):

from sklearn.datasets import load_boston
from sklearn.model_selection import train_test_split
X, y = load_boston(True)
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)
# Works better with min_samples_leaf > 1.
res = decision_tree_regressor_predict_proba(X_train, y_train, X_test,
                                            random_state=0, min_samples_leaf=5)
res[res.record_id == 2]
#      record_id       y        prob
#   25         2    20.6    0.166667
#   26         2    22.3    0.166667
#   27         2    22.7    0.166667
#   28         2    23.8    0.333333
#   29         2    25.0    0.166667