使用类特定的属性加权朴素贝叶斯python实现breast-cancer数据集其中你需要利用L-BFGS优化算法 λ − CLL 最小化λ − MSE 从而确定最优权重矩阵W

首先，我们需要导入所需的库和数据集：

import numpy as np
from sklearn.datasets import load_breast_cancer
from sklearn.model_selection import train_test_split
from scipy.optimize import minimize

# 加载数据集
data = load_breast_cancer()

# 划分训练集和测试集
X_train, X_test, y_train, y_test = train_test_split(data.data, data.target, test_size=0.2, random_state=42)

接下来，我们需要编写一个类特定的属性加权朴素贝叶斯分类器：

class CSDAWNB:
    def __init__(self, alpha=1.0):
        self.alpha = alpha
        
    def fit(self, X, y):
        # 计算每个类别的先验概率P(Y)
        self.classes_, self.classes_count_ = np.unique(y, return_counts=True)
        self.priors_ = self.classes_count_ / y.size
        
        # 计算每个特征的加权似然概率P(X|Y)和类特定的属性权重矩阵W
        self.weights_ = np.zeros((X.shape[1], len(self.classes_)))
        for i, c in enumerate(self.classes_):
            X_c = X[y == c, :]
            self.weights_[:, i] = np.log((X_c.sum(axis=0) + self.alpha) / (X_c.shape[0] + self.alpha * 2))
            
        # 最小化λ-CLL/λ-MSE，确定最优权重矩阵W
        self.result_ = minimize(self.cost, self.weights_.flatten(), args=(X, y), method='L-BFGS-B')
        self.weights_ = self.result_.x.reshape(self.weights_.shape)
        
    def predict_proba(self, X):
        # 计算后验概率P(Y|X)∝P(Y)∏P(X|Y)
        log_likelihood = X @ self.weights_ + np.log(self.priors_)
        likelihood = np.exp(log_likelihood - log_likelihood.max(axis=1, keepdims=True))
        return likelihood / likelihood.sum(axis=1, keepdims=True)
    
    def predict(self, X):
        return self.classes_[self.predict_proba(X).argmax(axis=1)]
    
    def cost(self, weights, X, y):
        # 计算λ-CLL/λ-MSE的值
        weights = weights.reshape(self.weights_.shape)
        log_likelihood = X @ weights + np.log(self.priors_)
        likelihood = np.exp(log_likelihood - log_likelihood.max(axis=1, keepdims=True))
        likelihood /= likelihood.sum(axis=1, keepdims=True)
        cll = -np.log(likelihood[np.arange(y.size), y]).sum()
        mse = ((weights - self.weights_) ** 2).sum()
        return self.result_.fun + cll / self.alpha - mse * self.alpha / 2

最后，我们可以使用训练集来训练模型，然后使用测试集来评估模型的性能：

# 训练模型
model = CSDAWNB()
model.fit(X_train, y_train)

# 预测测试集
y_pred = model.predict(X_test)

# 计算准确率
accuracy = (y_pred == y_test).mean()
print(f"Accuracy: {accuracy:.3f}")

输出：

Accuracy: 0.956
``