Hi,
I am trying to figure out theta 0 and theta 1 for the ML linear regression challenge : Hardwork Pays Off.
I have tried the following code and a lot of combinations of theta 0 and theta 1. However, when I plot the error function, it is observed that initially the error is zero and then it jumps to infinity. please help.
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from mpl_toolkits.mplot3d import axes3d
# Setting data
dfx = pd.read_csv('.../Training Data/Linear_X_Train.csv')
dfy = pd.read_csv('.../Training Data/Linear_Y_Train.csv')
x = dfx.values
y = dfy.values
x = x.reshape((-1,))
y = y.reshape((-1,))
plt.scatter(x,y)
X = (x-x.mean())/x.std()
Y = y
print (X.shape[0])
plt.scatter(X,Y)
plt.show()
plt.hist(X, 10)
plt.show()
plt.hist(Y,10)
plt.show()
def hypothesis(x,theta):
return theta[0] + theta[1]*x
def error(X,Y,theta):
m = X.shape[0]
error = 0
for i in range(m):
hx = hypothesis(X[i],theta)
error += (hx-Y[i])**2
return error
def gradient(X,Y,theta):
grad = np.zeros((2,))
m = X.shape[0]
for i in range(m):
hx = hypothesis(X[i],theta)
grad[0] += (hx-Y[i])
grad[1] += (hx-Y[i])*X[i]
return grad
#Algorithm
def gradientDescent(X,Y,learning_rate=0.1):
theta = np.array([1.0,0.0])
#theta = theta.astype('float64')
print (type(theta))
itr = 0
max_itr = 100
error_list = []
theta_list = []
while(itr<=max_itr):
grad = gradient(X,Y,theta)
e = error(X,Y,theta)
#print (e)
error_list.append(e)
theta_list.append((theta[0],theta[1]))
theta[0] = theta[0] - learning_rate*grad[0]
theta[1] = theta[1] - learning_rate*grad[1]
itr += 1
return theta,error_list,theta_list
# In[128]:
final_theta, error_list,theta_list = gradientDescent(X,Y)
plt.plot(theta_list)
plt.show()
plt.plot(error_list)
plt.show()
print (final_theta)
Kindly help