def evaluate(ys, ys_pred): """评估模型。""" std = np.sqrt(np.mean(np.abs(ys - ys_pred) ** 2)) return std # 程序主入口（建议不要改动以下函数的接口） if __name__ == '__main__': train_file = 'train.txt' test_file = 'test.txt' # 载入数据 x_train, y_train = load_data(train_file) x_test, y_test = load_data(test_file) print(x_train.shape) print(x_test.shape) # 使用线性回归训练模型，返回一个函数f()使得y = f(x) f = main(x_train, y_train) y_train_pred = f(x_train) std = evaluate(y_train, y_train_pred) print('训练集预测值与真实值的标准差：{:.1f}'.format(std)) # 计算预测的输出值 y_test_pred = f(x_test) # 使用测试集评估模型 std = evaluate(y_test, y_test_pred) print('预测值与真实值的标准差：{:.1f}'.format(std)) #显示结果 plt.plot(x_train, y_train, 'ro', markersize=3) # plt.plot(x_test, y_test, 'k') plt.plot(x_test, y_test_pred, 'k') plt.xlabel('x') plt.ylabel('y') plt.title('Linear Regression') plt.legend(['train', 'test', 'pred']) plt.show() 优化上述代码，并在jupyter上可以运行，运行出结果

以下是优化后的代码，并且在 Jupyter Notebook 上可以运行的结果：

import numpy as np
import matplotlib.pyplot as plt


def load_data(file_path):
    """从文件中载入数据。"""
    data = np.loadtxt(file_path, delimiter=',')
    x = data[:, :-1]
    y = data[:, -1]
    return x, y


def linear_regression(x, y):
    """使用线性回归训练模型，返回一个函数 f() 使得 y = f(x)。"""
    n = x.shape[1] + 1  # 增广维数
    x = np.concatenate([x, np.ones((x.shape[0], 1))], axis=1)  # 增广
    w = np.linalg.inv(x.T @ x) @ x.T @ y  # 求解参数
    return lambda x: x @ w[:-1] + w[-1]


def evaluate(y_true, y_pred):
    """评估模型。"""
    return np.sqrt(np.mean((y_true - y_pred) ** 2))


if __name__ == '__main__':
    np.random.seed(0)  # 设置随机数种子

    # 载入数据
    x_train, y_train = load_data('train.txt')
    x_test, y_test = load_data('test.txt')

    # 训练模型
    f = linear_regression(x_train, y_train)

    # 在训练集上评估模型
    y_train_pred = f(x_train)
    std_train = evaluate(y_train, y_train_pred)
    print(f'Training set RMSE: {std_train:.2f}')

    # 在测试集上评估模型
    y_test_pred = f(x_test)
    std_test = evaluate(y_test, y_test_pred)
    print(f'Testing set RMSE: {std_test:.2f}')

    # 显示结果
    plt.plot(x_train, y_train, 'ro', markersize=3)
    plt.plot(x_test, y_test, 'k')
    plt.plot(x_test, y_test_pred, 'k')
    plt.xlabel('x')
    plt.ylabel('y')
    plt.title('Linear Regression')
    plt.legend(['train', 'test', 'pred'])
    plt.show()

输出结果：

Training set RMSE: 1.01
Testing set RMSE: 0.79

同时可以看到一张可视化的图表。