import numpy as np

# 生成随机数据
np.random.seed(0)
X = np.random.rand(100, 1)
y = 4 + 3 * X + np.random.randn(100, 1)

# 初始化模型参数
theta = np.random.randn(2, 1)

# 定义损失函数
def mse_loss(X, y, theta):
    m = len(X)
    y_hat = X.dot(theta)
    loss = np.sum((y_hat - y) ** 2) / (2 * m)
    return loss

# 使用梯度下降法优化
def gradient_descent(X, y, theta, learning_rate, iterations):
    m = len(X)
    for i in range(iterations):
        y_hat = X.dot(theta)
        gradient = X.T.dot(y_hat - y) / m
        theta -= learning_rate * gradient
    return theta

# 训练模型
X_b = np.c_[np.ones((100, 1)), X]
theta_best = gradient_descent(X_b, y, theta, learning_rate=0.1, iterations=1000)

# 输出模型参数和损失值
print("模型参数：", theta_best)
print("均方误差：", mse_loss(X_b, y, theta_best))

import numpy as np

# 生成随机数据
np.random.seed(0)
X = np.random.rand(100, 2)
y = np.random.randint(0, 2, size=(100, 1))

# 添加偏置项
X_b = np.c_[np.ones((100, 1)), X]

# 初始化模型参数
theta = np.random.randn(3, 1)

# 定义sigmoid函数
def sigmoid(z):
    return 1 / (1 + np.exp(-z))

# 定义交叉熵损失函数
def cross_entropy_loss(X, y, theta):
    m = len(X)
    z = X.dot(theta)
    y_hat = sigmoid(z)
    loss = -np.sum(y * np.log(y_hat) + (1 - y) * np.log(1 - y_hat)) / m
    return loss

# 使用梯度下降法优化
def gradient_descent(X, y, theta, learning_rate, iterations):
    m = len(X)
    for i in range(iterations):
        z = X.dot(theta)
        y_hat = sigmoid(z)
        gradient = X.T.dot(y_hat - y) / m
        theta -= learning_rate * gradient
    return theta

# 训练模型
theta_best = gradient_descent(X_b, y, theta, learning_rate=0.1, iterations=1000)

# 输出模型参数和损失值
print("模型参数：", theta_best)
print("交叉熵损失：", cross_entropy_loss(X_b, y, theta_best))

import numpy as np
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from sklearn.svm import LinearSVC
from sklearn.metrics import hinge_loss

# 生成随机数据
X, y = make_classification(n_samples=100, n_features=2, n_informative=2, n_redundant=0, random_state=0)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0)

# 训练模型
clf = LinearSVC(loss='hinge', random_state=0)
clf.fit(X_train, y_train)

# 预测结果
y_pred_train = clf.predict(X_train)
y_pred_test = clf.predict(X_test)

# 计算损失值
loss_train = hinge_loss(y_train, y_pred_train)
loss_test = hinge_loss(y_test, y_pred_test)

# 输出损失值
print("训练集Hinge损失：", loss_train)
print("测试集Hinge损失：", loss_test)