无法在梯度下降算法中更新 python 中的数组

Question

In this code I have produced a dataset using gaussian distribution and then I have tried to apply stochastic gradient descent In each iteration, I am updating the theta array. But, it is not getting updated. It remains zero after every iteration. Gradient is non zero. But still, theta is not updated

Help me please

import numpy as np # linear algebra
import pandas as pd 
# data processing, CSV file I/O (e.g. pd.read_csv)
import math
import random
import matplotlib.pyplot as plt

#generating random samples

theta=np.array([3,1,2])

    

X=[]
E=[]
Y=[]
a1=3
v1=4
a2=-1
v2=4
v3=2


for i in range (0,1000000):
    x1=(1/math.sqrt(2*3.14*v1))* math.exp(-(random.random()-a1)**2/(2*v1))
    x2=(1/math.sqrt(2*3.14*v2))* math.exp(-(random.random()-a2)**2/(2*v2))
    X.append([x1,x2])
    e=(1/math.sqrt(2*3.14*v3))* math.exp(-(random.random())**2/(2*v3))
    y=theta[0]+theta[1]*x1+theta[2]*x2 + e
    Y.append(y)
    E.append(e)


#Now Applying Stochastic Gradient
##Batch_Size = 1
r=1
learning_rate=0.001
theta=np.array([0,0,0])


theta = theta.reshape(3,1)

X= pd.DataFrame(X,columns=['X1','X2'])
Y=pd.DataFrame(Y,columns=['Y'])
Y.head()

from sklearn.model_selection import train_test_split

X_train,X_test,y_train,y_test=train_test_split(X,Y,test_size=40,random_state=50)

X_train['X0']=np.ones(len(X_train))
y_train.head()

def gradient_descent(x,y,theta,lr):
    m=len(y)
    prediction=(x.dot(theta)).to_numpy()
    gradient = prediction-y.to_numpy()
    current_cost= (1/2*m)*np.sum(np.square(prediction-y.to_numpy()) )
       
    return gradient,current_cost

n_iterations=1000
import random
theta_history=[]
cost_history=[]
for i in range(0,n_iterations):
    
    xi=X_train.sample(r)
    yi=y_train.sample(r)
    
    
    m=len(xi)
    gradient,current_cost= gradient_descent(xi,yi,theta,learning_rate)
    theta[0]= theta[0]-learning_rate* 
    ((1/m)*np.sum(np.multiply(gradient,xi['X1'].to_numpy().reshape(m,1))))  
    theta[1]= theta[1]-learning_rate* 
    ((1/m)*np.sum(np.multiply(gradient,xi['X2'].to_numpy().reshape(m,1))))
    theta[2]= theta[2]-learning_rate* 
    ((1/m)*np.sum(np.multiply(gradient,xi['X0'].to_numpy().reshape(m,1))))
    print("theta=",theta)
    
    theta_history.append(theta)
    cost_history.append(current_cost)
    
    
    
    if prev_index>=len(X_train):
        break  

Answer 1

You reassigned theta on line 34 to empty values: theta=np.array([0,0,0])