多元线性回归（梯度下降法）

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import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# 读取数据

data = np.loadtxt('Delivery.csv',delimiter=',')
print(data)


# 构造特征x，目标y
# 特征
x_data = data[:,0:-1]
y_data = data[:,-1]

# 初始化学习率    （步长）
learning_rate = 0.0001
# 初始化 截距
theta0 = 0
# 初始化 系数
theta1 = 0
theta2 = 0

# 初始化最大迭代次数
n_iterables = 100

def compute_mse(theta0,theta1,theta2,x_data,y_data):
    '''
    计算代价函数
    '''
    total_error = 0
    for i in range(len(x_data)):
        # 计算损失  （真实值-预测值）**2
        total_error += (y_data[i]-(theta0 + theta1*x_data[i,0]+theta2*x_data[i,1]))**2

    mse_ = total_error/len(x_data)/2

    return mse_

def gradient_descent(x_data,y_data,theta0,theta1,theta2,learning_rate,n_iterables):
    '''
    梯度下降法
    '''
    m = len(x_data)
    # 循环
    for i in range(n_iterables):
        # 初始化theta0，theta1，theta2偏导数
        theta0_grad = 0
        theta1_grad = 0
        theta2_grad = 0

        # 计算偏导的总和再平均
        # 遍历m次
        for j in range(m):
            theta0_grad += (1/m)*((theta1*x_data[j,0]+theta2*x_data[j,1]+theta0)-y_data[j])
            theta1_grad += (1/m)*((theta1*x_data[j,0]+theta2*x_data[j,1]+theta0)-y_data[j])*x_data[j,0]
            theta2_grad += (1/m)*((theta1*x_data[j,0]+theta2*x_data[j,1]+theta0)-y_data[j])*x_data[j,1]
        # 更新theta
        theta0 = theta0 - (learning_rate*theta0_grad)
        theta1 = theta1 - (learning_rate*theta1_grad)
        theta2 = theta2 - (learning_rate*theta2_grad)

        return theta0,theta1,theta2

# 可视化分布
fig = plt.figure()
ax = Axes3D(fig)
ax.scatter(x_data[:,0],x_data[:,1],y_data)
plt.show()

print(f"开始：截距theta0={theta0},theta1={theta1},theta2={theta2},损失={compute_mse(theta0,theta1,theta2,x_data,y_data)}")
print("开始跑起来了~")
theta0,theta1,theta2 = gradient_descent(x_data,y_data,theta0,theta1,theta2,learning_rate,n_iterables)
print(f"迭代{n_iterables}次后：截距theta0={theta0},theta1={theta1},theta2={theta2},损失={compute_mse(theta0,theta1,theta2,x_data,y_data)}")


# 绘制预期平面
x_0 = x_data[:,0]
x_1 = x_data[:,1]

# 生成网格矩阵
x_0,x_1 = np.meshgrid(x_0,x_1)

# y
y_hat = theta0 + theta1*x_0 +theta2*x_1

ax.plot_surface(x_0,x_1,y_hat)

# 设置标签
ax.set_xlabel('Miles')
ax.set_ylabel('nums')
ax.set_zlabel('Time')

plt.show()