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

加载数据集

data = load_breast_cancer() X = data.data y = data.target

将数据集分为训练集和测试集

train_X = X[:400] train_y = y[:400] test_X = X[400:] test_y = y[400:]

定义类别特定的属性值加权朴素贝叶斯类

class NaiveBayes: def init(self, alpha=1.0): self.alpha = alpha

def fit(self, X, y):
    self.classes = np.unique(y)
    self.n_classes = len(self.classes)
    self.n_features = X.shape[1]
    self.mean = np.zeros((self.n_classes, self.n_features))
    self.var = np.zeros((self.n_classes, self.n_features))
    self.prior = np.zeros(self.n_classes)
    
    for i, c in enumerate(self.classes):
        X_c = X[y == c]
        self.mean[i] = X_c.mean(axis=0)
        self.var[i] = X_c.var(axis=0)
        self.prior[i] = X_c.shape[0] / X.shape[0]

def predict(self, X):
    joint_prob = np.zeros((X.shape[0], self.n_classes))
    for i, c in enumerate(self.classes):
        joint_prob[:, i] = np.log(self.prior[i]) + \
            np.sum(np.log(self.pdf(X, self.mean[i], self.var[i], self.alpha)), axis=1)
    return self.classes[np.argmax(joint_prob, axis=1)]

def pdf(self, X, mean, var, alpha):
    eps = 1e-6
    return np.exp(-(X - mean)**2 / (2 * (var + eps))) / np.sqrt(2 * np.pi * (var + eps)) * alpha

def get_params(self):
    return np.hstack((self.mean.ravel(), self.var.ravel(), self.prior.ravel()))

def set_params(self, params):
    mean_start = 0
    mean_end = self.n_classes * self.n_features
    var_start = mean_end
    var_end = mean_end + self.n_classes * self.n_features
    prior_start = var_end
    prior_end = prior_start + self.n_classes
    self.mean = np.reshape(params[mean_start:mean_end], (self.n_classes, self.n_features))
    self.var = np.reshape(params[var_start:var_end], (self.n_classes, self.n_features))
    self.prior = np.reshape(params[prior_start:prior_end], self.n_classes)

定义损失函数

def loss_func(weights, model, X, y): model.set_params(weights) y_pred = model.predict(X) cll = -np.sum(np.log(model.prior[y]) + np.sum(np.log(model.pdf(X, model.mean[y], model.var[y], model.alpha)), axis=1)) mse = ((y - y_pred)**2).mean() return model.alpha * cll + (1 - model.alpha) * mse

初始化模型

nb = NaiveBayes()

最小化损失函数，得到最优权重矩阵

res = minimize(loss_func, nb.get_params(), args=(nb, train_X, train_y), method='L-BFGS-B') nb.set_params(res.x)

在测试集上进行预测

y_pred = nb.predict(test_X) accuracy = (y_pred == test_y).mean() print('Accuracy:', accuracy