cart回归树代码

下面是一个简单的 CART 回归树的 Python 代码实现：

import numpy as np

class CartRegressionTree:
    def __init__(self, max_depth=2, min_samples_split=2):
        self.max_depth = max_depth
        self.min_samples_split = min_samples_split
        self.tree = None
    
    def split(self, X, y):
        best_feature_index, best_threshold, best_loss = None, None, np.inf
        for feature_index in range(X.shape[1]):
            feature_values = X[:, feature_index]
            for threshold in feature_values:
                left_indices = feature_values <= threshold
                right_indices = feature_values > threshold
                if len(y[left_indices]) >= self.min_samples_split and len(y[right_indices]) >= self.min_samples_split:
                    left_loss = np.mean((y[left_indices] - np.mean(y[left_indices])) ** 2)
                    right_loss = np.mean((y[right_indices] - np.mean(y[right_indices])) ** 2)
                    loss = left_loss + right_loss
                    if loss < best_loss:
                        best_feature_index = feature_index
                        best_threshold = threshold
                        best_loss = loss
        return best_feature_index, best_threshold

    def build_tree(self, X, y, depth):
        if depth == self.max_depth or len(y) < self.min_samples_split:
            return np.mean(y)
        feature_index, threshold = self.split(X, y)
        if feature_index is None:
            return np.mean(y)
        left_indices = X[:, feature_index] <= threshold
        right_indices = X[:, feature_index] > threshold
        left_subtree = self.build_tree(X[left_indices], y[left_indices], depth+1)
        right_subtree = self.build_tree(X[right_indices], y[right_indices], depth+1)
        return (feature_index, threshold, left_subtree, right_subtree)

    def fit(self, X, y):
        self.tree = self.build_tree(X, y, 0)
    
    def predict(self, X):
        if self.tree is None:
            raise Exception("Tree has not been trained yet!")
        predictions = []
        for sample in X:
            node = self.tree
            while isinstance(node, tuple):
                if sample[node[0]] <= node[1]:
                    node = node[2]
                else:
                    node = node[3]
            predictions.append(node)
        return np.array(predictions)

其中，`max_depth` 表示树的最大深度，`min_samples_split` 表示每个节点最少需要多少个样本才能继续分裂。`split` 函数用于在当前节点上找到最佳的分裂特征和阈值，`build_tree` 函数递归地构建树，`predict` 函数用于对新数据进行预测。