写一个sklearn调用决策树模块2.自编程实现ID3,CART算法 对贷款申请样本数据表进行预测分类

回答：

1. 使用sklearn调用决策树模块的代码：

from sklearn import datasets
from sklearn.tree import DecisionTreeClassifier
from sklearn.model_selection import train_test_split

# 加载样本数据集
iris = datasets.load_iris()
X = iris.data
y = iris.target

# 分割数据集
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)

# 建立决策树分类器
clf = DecisionTreeClassifier()
clf.fit(X_train, y_train)

# 预测测试集结果
y_pred = clf.predict(X_test)
print("预测结果:", y_pred)

2. 自编程实现ID3,CART算法对贷款申请样本数据表进行预测分类，可以参考以下代码：

import pandas as pd
import numpy as np
import math

# 数据集
dataset = pd.DataFrame({
    'income': ['high', 'high', 'medium', 'low', 'low', 'low', 'medium', 'high', 'medium', 'low'],
    'age': ['young', 'young', 'young', 'middle_aged', 'senior', 'senior', 'middle_aged', 'middle_aged', 'senior', 'senior'],
    'student': ['no', 'no', 'no', 'no', 'yes', 'yes', 'yes', 'no', 'yes', 'yes'],
    'credit_rating': ['fair', 'excellent', 'fair', 'fair', 'fair', 'excellent', 'excellent', 'fair', 'fair', 'fair'],
    'class': ['no', 'no', 'yes', 'yes', 'yes', 'no', 'yes', 'no', 'yes', 'yes']
})

# 计算信息熵
def calc_entropy(data):
    n = data.shape[0]
    label_count = data.iloc[:, -1].value_counts()
    p = label_count / n
    entropy = (-p * np.log2(p)).sum()
    return entropy

# 计算条件熵
def calc_conditional_entropy(data, feature):
    n = data.shape[0]
    H_D_A = 0
    feature_values = set(data[feature])
    for feature_value in feature_values:
        sub_data = data[data[feature] == feature_value]
        H_D_A += sub_data.shape[0]/n * calc_entropy(sub_data)
    return H_D_A

# 计算信息增益
def calc_info_gain(data, feature):
    return calc_entropy(data) - calc_conditional_entropy(data, feature)

# 计算信息增益比
def calc_info_gain_ratio(data, feature):
    info_gain = calc_info_gain(data, feature)
    return info_gain / calc_entropy(data)

# 决策树节点
class TreeNode:
    def __init__(self, name: str = None, feature: str = None, value=None, is_leaf=False):
        self.name = name  # 节点名称
        self.feature = feature  # 特征名称
        self.value = value  # 特征取值
        self.children = []  # 孩子
        self.is_leaf = is_leaf  # 是否是叶子结点


# ID3算法
def ID3(data, epsilon=0.1):
    features = set(data.columns) - set(['class'])
    max_info_gain = 0
    best_feature = None
    for feature in features:
        cur_info_gain = calc_info_gain(data, feature)
        if cur_info_gain > max_info_gain:
            max_info_gain = cur_info_gain
            best_feature = feature
    if best_feature is None:
        return TreeNode(name='leaf', value=data.iloc[0, -1], is_leaf=True)

    node = TreeNode(name='node', feature=best_feature)

    feature_values = set(data[best_feature])
    for feature_value in feature_values:
        sub_data = data[data[best_feature] == feature_value]
        sub_tree = ID3(sub_data, epsilon)
        sub_tree.value = feature_value
        node.children.append(sub_tree)

    return node

# CART算法
def CART(data, epsilon=0.1):
    features = set(data.columns) - set(['class'])
    max_info_gain_ratio = 0
    best_feature = None
    for feature in features:
        cur_info_gain_ratio = calc_info_gain_ratio(data, feature)
        if cur_info_gain_ratio > max_info_gain_ratio:
            max_info_gain_ratio = cur_info_gain_ratio
            best_feature = feature

    if best_feature is None:
        return TreeNode(name='leaf', value=data.iloc[0, -1], is_leaf=True)

    node = TreeNode(name='node', feature=best_feature)

    left_data = data[data[best_feature] == data.iloc[0][best_feature]]
    right_data = data[data[best_feature] != data.iloc[0][best_feature]]

    node.children.append(CART(left_data, epsilon))
    node.children.append(CART(right_data, epsilon))

    return node

# 预测
def predict(tree: TreeNode, sample):
    while not tree.is_leaf:
        feature_value = sample[tree.feature]
        for child_node in tree.children:
            if child_node.value == feature_value:
                tree = child_node
                break
    return tree.value

# 构建决策树
tree_id3 = ID3(dataset)

tree_cart = CART(dataset)

# 预测样本数据
sample_data = pd.DataFrame({
    'income': ['medium'],
    'age': ['young'],
    'student': ['no'],
    'credit_rating': ['fair']
})

print("ID3预测结果:", predict(tree_id3, sample_data))
print("CART预测结果:", predict(tree_cart, sample_data))

注：以上代码仅作为提供参考的示例代码，仅仅支持对已知数据集进行预测，需要根据实际情况进行修改和优化。