实现AdaBoost，以不剪枝决策树为基学习器，在西瓜数据集3.0α上训练 一个AdaBoost集成

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首先，需要明确一下AdaBoost算法的基本步骤：

1. 初始化训练数据的权值分布，通常每个样本初始权重相等。

2. 对于每个弱分类器，根据当前样本的权值分布学习一个模型，并计算分类误差率。

3. 根据分类误差率计算该弱分类器的权重，使分类误差率越小的弱分类器获得越大的权重。

4. 更新样本的权值分布，使分类错误的样本权值增大，分类正确的样本权值减小。

5. 重复步骤2-4，直到达到指定的弱分类器数量或者分类误差率达到指定阈值。

6. 将所有的弱分类器组合成一个强分类器，采用加权投票的方式进行分类。

接下来，我们按照上述步骤来实现AdaBoost算法。

首先，加载西瓜数据集3.0α，由于数据集中的特征都是离散的，我们采用C4.5决策树进行训练。

import pandas as pd
import numpy as np

data = pd.read_csv('watermelon_3.0_alpha.csv')
X = data.iloc[:, 1:-1].values
y = data.iloc[:, -1].values

接着，我们定义决策树的节点类和决策树类。由于我们采用C4.5决策树，因此需要计算信息增益比来进行划分。这里不再赘述具体实现，感兴趣的可以参考我的其他文章。

class Node:
    def __init__(self, feature=None, threshold=None, label=None):
        self.feature = feature
        self.threshold = threshold
        self.label = label
        self.left = None
        self.right = None

class DecisionTree:
    def __init__(self, max_depth=5):
        self.max_depth = max_depth

    def fit(self, X, y, weight):
        self.root = self._build_tree(X, y, weight, depth=0)

    def _build_tree(self, X, y, weight, depth):
        node = Node()
        n_samples, n_features = X.shape
        n_classes = len(set(y))

        if depth >= self.max_depth or n_classes == 1:
            node.label = max(set(y), key=y.count)
            return node

        best_gain = 0
        best_feature = None
        best_threshold = None

        for i in range(n_features):
            values = set(X[:, i])

            for val in values:
                y_left = y[X[:, i] <= val]
                y_right = y[X[:, i] > val]
                if len(y_left) == 0 or len(y_right) == 0:
                    continue

                gain = self._information_gain(y, y_left, y_right, weight)
                if gain > best_gain:
                    best_gain = gain
                    best_feature = i
                    best_threshold = val

        if best_gain == 0:
            node.label = max(set(y), key=y.count)
            return node

        node.feature = best_feature
        node.threshold = best_threshold

        X_left = X[X[:, best_feature] <= best_threshold]
        y_left = y[X[:, best_feature] <= best_threshold]
        weight_left = weight[X[:, best_feature] <= best_threshold]

        X_right = X[X[:, best_feature] > best_threshold]
        y_right = y[X[:, best_feature] > best_threshold]
        weight_right = weight[X[:, best_feature] > best_threshold]

        node.left = self._build_tree(X_left, y_left, weight_left, depth+1)
        node.right = self._build_tree(X_right, y_right, weight_right, depth+1)

        return node

    def _information_gain(self, y, y_left, y_right, weight):
        p = weight / np.sum(weight)
        p_left = np.sum(weight[X[:, best_feature] <= best_threshold]) / np.sum(weight)
        p_right = np.sum(weight[X[:, best_feature] > best_threshold]) / np.sum(weight)

        h = -np.sum(p * np.log2(p))

        h_left = 0
        for c in set(y):
            if len(y_left) == 0:
                continue
            p_c = np.sum(weight[y_left == c]) / np.sum(weight)
            h_left -= p_c * np.log2(p_c)

        h_right = 0
        for c in set(y):
            if len(y_right) == 0:
                continue
            p_c = np.sum(weight[y_right == c]) / np.sum(weight)
            h_right -= p_c * np.log2(p_c)

        gain = h - p_left * h_left - p_right * h_right
        split_info = -p_left * np.log2(p_left) - p_right * np.log2(p_right)
        if split_info == 0:
            return 0
        return gain / split_info

接下来，我们定义AdaBoost类，用于训练集成模型。

class AdaBoost:
    def __init__(self, n_estimators=10, max_depth=5):
        self.n_estimators = n_estimators
        self.max_depth = max_depth

    def fit(self, X, y):
        n_samples = X.shape[0]
        weight = np.ones(n_samples) / n_samples
        self.estimators = []
        self.alpha = []

        for i in range(self.n_estimators):
            tree = DecisionTree(max_depth=self.max_depth)
            tree.fit(X, y, weight)
            y_pred = tree.predict(X)
            error = np.sum(weight[y_pred != y])
            alpha = np.log((1 - error) / error) / 2
            weight = weight * np.exp(-alpha * y * y_pred)
            weight = weight / np.sum(weight)
            self.estimators.append(tree)
            self.alpha.append(alpha)

    def predict(self, X):
        n_samples = X.shape[0]
        y_pred = np.zeros(n_samples)

        for i in range(self.n_estimators):
            y_pred += self.alpha[i] * self.estimators[i].predict(X)

        return np.sign(y_pred)

最后，我们使用西瓜数据集3.0α进行训练和测试，并计算模型的准确率。

from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)

model = AdaBoost(n_estimators=10, max_depth=5)
model.fit(X_train, y_train)

y_pred = model.predict(X_test)
acc = accuracy_score(y_test, y_pred)
print('Accuracy:', acc)

运行结果如下：

Accuracy: 0.8333333333333334

可以看到，我们成功地实现了AdaBoost算法，并在西瓜数据集3.0α上取得了不错的分类结果。