【机器学习】作业Exam2

多变量线性回归

同理。
注意，这里我使用归一化处理，所以预测出来的结果都是在小数点，要预测结果的话反过来乘过去就行了。

import pandas as pd
import matplotlib.pyplot as plt

# 计算损失
def compute_loss(x1, x2, y, w1, w2, b):
    m = x1.shape[0]
    loss = 0.
    for i in range(m):
        loss += (w1 * x1[i] + w2 * x2[i] + b - y[i]) ** 2
    return loss / (2 * m)

# 梯度下降
def gradient_descent(x1, x2, y, w1, w2, b, eta, iterations):
    m = x1.shape[0]
    loss_history = []
    for _ in range(iterations):
        sum_w1 = 0.
        sum_w2 = 0.
        sum_b = 0.
        for i in range(m):
            error = w1 * x1[i] + w2 * x2[i] + b - y[i]
            sum_w1 += error * x1[i]
            sum_w2 += error * x2[i]
            sum_b += error
        w1 -= eta * sum_w1 / m
        w2 -= eta * sum_w2 / m
        b -= eta * sum_b / m
        loss_history.append(compute_loss(x1, x2, y, w1, w2, b))
    return w1, w2, b, loss_history


def predict(x1, x2, w1, w2, b):
    return w1 * x1 + w2 * x2 + b


if __name__ == '__main__':
    # 读取数据
    data = pd.read_csv(r'D:\BaiduNetdiskDownload\data_sets\ex1data2.txt', names=["x1", "x2", "y"])

    # 保存均值和标准差以备标准化和反标准化
    mean_x1 = data['x1'].mean()
    mean_x2 = data['x2'].mean()
    mean_y = data['y'].mean()
    std_x1 = data['x1'].std()
    std_x2 = data['x2'].std()
    std_y = data['y'].std()

    # 标准化数据
    data['x1'] = (data['x1'] - mean_x1) / std_x1
    data['x2'] = (data['x2'] - mean_x2) / std_x2
    data['y'] = (data['y'] - mean_y) / std_y

    x1 = data['x1']
    x2 = data['x2']
    y = data['y']

    # 训练模型
    w1, w2, b, loss_history = gradient_descent(x1, x2, y, 0, 0, 0, 0.01, 1000)
    print(f'Trained model parameters: w1 = {w1}, w2 = {w2}, b = {b}')

    # 绘制损失曲线
    epochs = range(len(loss_history))
    plt.plot(epochs, loss_history, color='red', label='loss')
    plt.xlabel('Epoch')
    plt.ylabel('Loss')
    plt.title('Loss Curve')
    plt.legend()
    plt.grid(True)
    plt.show()

    # 预测房价
    new_data = pd.DataFrame({'x1': [2104,1600,1416], 'x2': [3,3,2]})
    new_data['x1'] = (new_data['x1'] - mean_x1) / std_x1
    new_data['x2'] = (new_data['x2'] - mean_x2) / std_x2

    predicted_price_standardized = predict(new_data['x1'], new_data['x2'], w1, w2, b)

    # 反标准化预测结果
    predicted_price = predicted_price_standardized * std_y + mean_y
    print(f'Predicted price: {predicted_price}')

一些图表

损失：

参数(归一化之后)：

w1 = 0.8785036522230538, w2 = -0.046916657038053915, b = -1.1073884126473927e-16