简单线性回归（梯度下降法） python实现

import numpy as np
import matplotlib.pyplot as plt

points = np.genfromtxt("data.csv",delimiter=",")
#points
#提取points中的两列数据，分别作为x,y
x=points[:,0];
y=points[:,1];

#用plt画出散点图
plt.scatter(x,y)
plt.show()

# 损失函数是系数的函数，另外还要传入数据的x,y
def compute_cost(w,b,points):
    total_cost=0
    M =len(points)
    for i in range(M):
        x=points[i,0]
        y=points[i,1]
        total_cost += (y-w*x-b)**2
    return total_cost/M #一除都是浮点 两个除号是地板除，整型。 如 3 // 4

alpha = 0.0000001
initial_w = 0
initial_b = 0
num_iter =20

def grad_desc(points,initial_w,initial_b,alpha,num_iter):
    w = initial_w
    b = initial_b
    # 定义一个list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):
        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)
    #对每个点代入公式求和
    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_b +=  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

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)

print("cost_list:",cost_list)
print("cost is:",cost)
plt.plot(cost_list)

plt.scatter(x,y)

pred_y= w*x+b

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