Question

def gradient_descent(feature_matrix, label, learning_rate = 0.05, epoch = 1000):
"""
Implement gradient descent algorithm for regression.
  
Args:
feature_matrix - A numpy matrix describing the given data, with ones added as the first column. Each row
represents a single data point.
  
label - The correct value of response variable, corresponding to feature_matrix.
  
learning_rate - the learning rate with default value 0.5
  
epoch - the number of iterations with default value 1000

Returns: A numpy array for the final value of theta
"""
n = len(label)
theta = np.zeros(feature_matrix.shape[1]) # initialize theta to be zero vector
for i in range(epoch):
# your code below
# compute (average) gradient below

# update theta below
  
# compute the value of cost function
# It is not necessary to comput cost here. But it is common to use cost
# in the termination condition of the loop

  
# your code above
# test
# print(i, theta, cost)
  
return theta
raise NotImplementedError

= 0.05, epoch = 1000): def gradient_descent (feature_matrix, label, learning_rate Implement gradient descent algorithm for regression. Args: feature_matrix - A numpy matrix describing the given data, with ones added as the first column. Each row represents a single data point. Label The correct value of response variable, corresponding to feature_matrix. Learning_rate - the Learning rate with default value 0.5 epoch the number of iterations with default value 1000 Returns: A numpy array for the final value of theta BF BF AF n = len(label) theta = np.zeros(feature_matrix.shape[1]) # initialize theta to be zero vector for i in range(epoch): # your code below # compute (average) gradient below # update theta below # compute the value of cost function # It is not necessary to comput cost here. But it is common to use cost # in the termination condition of the loop # your code above # test # print(i, theta, cost) return theta raise Not ImplementedError

Answer 1

import numpy as np

x=np.array([2104,1600,2400,1416,3000,1985,1534])          #feature matrix

mean=x.mean()

std=x.std()

x=(x-mean)/std

x=np.c_[np.ones(np.size(x)),x]                          #adding 1 in the first column

y=np.array([400,330,369,232,540,300,315])

alpha=0.01                                              #learning rate

m=len(y)

theta=np.random.rand(2)

def Grad_dec(x,y,m,alpha,theta):

    for i in range(1000):

        p=np.dot(x,theta)

        error=p-y

        cost=sum(error**2)/(2*m)

        

        theta=theta-(alpha/m)*np.dot(x.T,error)

    return cost,theta

cost,theta=Grad_dec(x,y,m,alpha,theta)

print(theta)

test_data=int(input('Enter test value:'))

test_data=(test_data-mean)/std

test_data=np.array([1,test_data])

print(round(np.dot(test_data.T,theta),4))

File Edit Selection View Go Run Terminal Help .p4.py - HTML1 - Visual Studio Code х EXPLORER e amir5.py e p1.py p4.py sales.txt <> tut8.html <> tut9.html V OPEN EDITORS 2 UNSAVED • amir5.py C:\Users\... e p1.py #feature matrix 3 . p4.py sales.txt 5 <> tut8.html <> tut9.html 6 #adding 1 in the first column 7 #learning rate V HTML1 a.exe 9 a.java C a1.c А p4.py ... 1 import numpy as np 2 x=np.array([2104,1600,2400,1416,3000,1985,1534]) mean=x.mean() 4 std=x.std() x=(x-mean)/std X=np.c_[np.ones(np.size(x)),x] y=np.array([400,330,369,232,540,300,315]) 8 alpha=0.01 m=len(y) 10 theta=np.random.rand(2) 11 def Grad_dec(x,y,m, alpha, theta): 12 for i in range (1000): p=np.dot(x, theta) 14 error=p-y cost=sum(error**2)/(2*m) 16 17 theta=theta-(alpha/m) *np.dot(x.T,error) 18 return cost, theta cost, theta=Grad_dec(x,y,m, alpha, theta) 20 print(theta) 21 test_data=int(input('Enter test value:')) 22 test_data=(test_data-mean/std test_data=np.array([1, test_data]) print(round(np.dot(test_data.T, theta),4)) a1.exe 13 15 e p1.py e p2.py p3.py è p4.py sales.txt 19 # tut2.css <> tut2.html <> tut3.html <> tut4.html 23 24 V OUTLINE v Grad_dec [@] alpha [@] cost PROBLEMS OUTPUT DEBUG CONSOLE TERMINAL 1: bash [@] error [@] i AMIR KHAN@Amir-khan MINGW64 ~/Desktop/HTML/HTML1 $ python p4.py [355.1275577 81.55329702] Enter test value:45 47.3385 [@] m [@] p [e] theta AMIR KHAN@Amir-khan MINGW64 ~/Desktop/HTML/HTML1 [e] theta Talv > TIMELINE > MAVEN Python 3.7.4 32-bit ⓇOAO Ln 24, Col 42 Spaces: 4 UTF-8 CRLF Python Go Live 21:05 29-07-2020 O Type here to search TT e 11 O Il D ENG 2