python使用梯度下降算法实现一个多线性回归

古城微笑少年丶 2023-01-03 11:29 62阅读 0赞

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python使用梯度下降算法实现一个多线性回归，供大家参考，具体内容如下

**图示：**

![Image 1][]

import pandas as pd
    import matplotlib.pylab as plt
    import numpy as np
    # Read data from csv
    pga = pd.read_csv("D:\python3\data\Test.csv")
    # Normalize the data 归一化值 (x - mean) / (std)
    pga.AT = (pga.AT - pga.AT.mean()) / pga.AT.std()
    pga.V = (pga.V - pga.V.mean()) / pga.V.std()
    pga.AP = (pga.AP - pga.AP.mean()) / pga.AP.std()
    pga.RH = (pga.RH - pga.RH.mean()) / pga.RH.std()
    pga.PE = (pga.PE - pga.PE.mean()) / pga.PE.std()

def cost(theta0, theta1, theta2, theta3, theta4, x1, x2, x3, x4, y):

# Initialize cost #

J = 0

# The number of observations #

m = len(x1)

# Loop through each observation #

# 通过每次观察进行循环 #

for i in range(m):

# Compute the hypothesis #

# 计算假设 #

h=theta0+x1\[i\]\*theta1+x2\[i\]\*theta2+x3\[i\]\*theta3+x4\[i\]\*theta4

# Add to cost #

J += (h - y\[i\])\*\*2

# Average and normalize cost #

J /= (2\*m)  
return J

# The cost for theta0=0 and theta1=1 #

def partial\_cost\_theta4(theta0,theta1,theta2,theta3,theta4,x1,x2,x3,x4,y):  
h = theta0 + x1 \* theta1 + x2 \* theta2 + x3 \* theta3 + x4 \* theta4  
diff = (h - y) \* x4  
partial = diff.sum() / (x2.shape\[0\])  
return partial

def partial\_cost\_theta3(theta0,theta1,theta2,theta3,theta4,x1,x2,x3,x4,y):  
h = theta0 + x1 \* theta1 + x2 \* theta2 + x3 \* theta3 + x4 \* theta4  
diff = (h - y) \* x3  
partial = diff.sum() / (x2.shape\[0\])  
return partial

def partial\_cost\_theta2(theta0,theta1,theta2,theta3,theta4,x1,x2,x3,x4,y):  
h = theta0 + x1 \* theta1 + x2 \* theta2 + x3 \* theta3 + x4 \* theta4  
diff = (h - y) \* x2  
partial = diff.sum() / (x2.shape\[0\])  
return partial

def partial\_cost\_theta1(theta0,theta1,theta2,theta3,theta4,x1,x2,x3,x4,y):  
h = theta0 + x1 \* theta1 + x2 \* theta2 + x3 \* theta3 + x4 \* theta4  
diff = (h - y) \* x1  
partial = diff.sum() / (x2.shape\[0\])  
return partial

# 对theta0 进行求导 #

# Partial derivative of cost in terms of theta0 #

def partial\_cost\_theta0(theta0, theta1, theta2, theta3, theta4, x1, x2, x3, x4, y):  
h = theta0 + x1 \* theta1 + x2 \* theta2 + x3 \* theta3 + x4 \* theta4  
diff = (h - y)  
partial = diff.sum() / (x2.shape\[0\])  
return partial

def gradient\_descent(x1,x2,x3,x4,y, alpha=0.1, theta0=0, theta1=0,theta2=0,theta3=0,theta4=0):  
max\_epochs = 1000 \# Maximum number of iterations 最大迭代次数  
counter = 0 \# Intialize a counter 当前第几次  
c = cost(theta0, theta1, theta2, theta3, theta4, x1, x2, x3, x4, y) \#\# Initial cost 当前代价函数  
costs = \[c\] \# Lets store each update 每次损失值都记录下来

# Set a convergence threshold to find where the cost function in minimized #

# When the difference between the previous cost and current cost #

# is less than this value we will say the parameters converged #

# 设置一个收敛的阈值 (两次迭代目标函数值相差没有相差多少,就可以停止了) #

convergence\_thres = 0.000001  
cprev = c + 10  
theta0s = \[theta0\]  
theta1s = \[theta1\]  
theta2s = \[theta2\]  
theta3s = \[theta3\]  
theta4s = \[theta4\]

# When the costs converge or we hit a large number of iterations will we stop updating #

# 两次间隔迭代目标函数值相差没有相差多少(说明可以停止了) #

while (np.abs(cprev - c) > convergence\_thres) and (counter < max\_epochs):  
cprev = c

# Alpha times the partial deriviative is our updated #

# 先求导, 导数相当于步长 #

update0 = alpha \* partial\_cost\_theta0(theta0, theta1, theta2, theta3, theta4, x1, x2, x3, x4, y)  
update1 = alpha \* partial\_cost\_theta1(theta0, theta1, theta2, theta3, theta4, x1, x2, x3, x4, y)  
update2 = alpha \* partial\_cost\_theta2(theta0, theta1, theta2, theta3, theta4, x1, x2, x3, x4, y)  
update3 = alpha \* partial\_cost\_theta3(theta0, theta1, theta2, theta3, theta4, x1, x2, x3, x4, y)  
update4 = alpha \* partial\_cost\_theta4(theta0, theta1, theta2, theta3, theta4, x1, x2, x3, x4, y)

# Update theta0 and theta1 at the same time #

# We want to compute the slopes at the same set of hypothesised parameters #

# so we update after finding the partial derivatives #

# \-= 梯度下降，+=梯度上升 #

theta0 -= update0  
theta1 -= update1  
theta2 -= update2  
theta3 -= update3  
theta4 -= update4

# Store thetas #

theta0s.append(theta0)  
theta1s.append(theta1)  
theta2s.append(theta2)  
theta3s.append(theta3)  
theta4s.append(theta4)

# Compute the new cost #

# 当前迭代之后，参数发生更新 #

c = cost(theta0, theta1, theta2, theta3, theta4, x1, x2, x3, x4, y)

# Store updates，可以进行保存当前代价值 #

# 将当前的theta0, theta1, costs值都返回去 #

\#return \{‘theta0’: theta0, ‘theta1’: theta1, ‘theta2’: theta2, ‘theta3’: theta3, ‘theta4’: theta4, “costs”: costs\}  
return \{‘costs’:costs\}

print(“costs =”, gradient\_descent(pga.AT, pga.V,pga.AP,pga.RH,pga.PE)\[‘costs’\])  
descend = gradient\_descent(pga.AT, pga.V,pga.AP,pga.RH,pga.PE, alpha=.01)  
plt.scatter(range(len(descend\[“costs”\])), descend\[“costs”\])  
plt.show()

损失函数随迭代次数变换图：

![Image 1][]

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