机器学习模型与算法 ----- 多元线性回归

 

 

 

 

 

 

 

 

 

python代码实现：

import numpy as np
import matplotlib.pyplot as plt

points = np.genfromtxt('data.csv',delimiter=',')

# points

x = points[:, 0]
y = points[:, 1]

plt.scatter(x, y)#散点图
plt.show()

 

 # 定义损失函数

def compute_cost(w, b, points):
    total_cost = 0
    M = len(points)
    
    #逐点计算平方损失误差，然后求平均数
    for i in range(M):
        x = points[i, 0]
        y = points[i, 1]
        total_cost += (y - w * x -b) ** 2
        
    return total_cost/M

# 定义模型的超参数

alpha = 0.0001
initial_w = 0
initial_b = 0
num_iter = 10

 

# 定义核心梯度下降函数

def grad_desc(points, initial_w, initial_b, alpha, num_iter):
    w = initial_w
    b = initial_b
    
    # 定义一个列表，保存所有的损失函数值，用来显示下降过程
    
    cost_list = []
    
    for i in range(num_iter): # 设置迭代 实现下降
        cost_list.append(compute_cost(w, b, points))
        w, b = step_grad_desc(w, b, alpha, points) 
    
    return [w, b, cost_list]

def step_grad_desc( current_w, current_b, alpha, points):
    sum_grad_w = 0
    sum_grad_b = 0
    M = len(points)
    
    #对每个点带入公式求和
    for i in range(M):
        x = points[i, 0]
        y = points[i, 1] 
        sum_grad_w += ( current_w * x + current_b - y) * x
        sum_grad_w += current_w * x + current_b - y

# 用公式求当前梯度
    grad_w = 2/M * sum_grad_w
    grad_b = 2/M * sum_grad_b

 

 

# 梯度下降，更新当前的w和b
    updated_w = current_w - alpha * grad_w
    updated_b = current_b - alpha * grad_b
    
    return updated_w, updated_b

 # 调用运行梯度下降算法计算最优的w和b

w, b, cost_list = grad_desc(points, initial_w, initial_b, alpha, num_iter)

print("w is: ", w)
print("b is: ", b)

cost = compute_cost(w, b, points)# 损失

print("cost is: ", cost)


plt.plot(cost_list)
plt.show()

 

 

# 画出拟合曲线

plt.scatter(x, y)

pred_y = w * x + b

plt.plot(x, pred_y, c='r')
plt.show()