Question

def stochastic_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
# generate a random integer between 0 and n
  
# compute gradient at this randomly selected feature vector below
  
# update theta below

# compute average squared error or empirical risk or 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

def stochastic_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 BF BF BF n = len(label) theta = np.zeros(feature_matrix.shape[1]) # initialize theta to be zero vector for i in range(epoch): # your code below # generate a random integer between 0 and n # compute gradient at this randomly selected feature vector below # update theta below # compute average squared error or empirical risk or 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

feature_matrix=np.array([310,270,350,251,410,308,263])     

mean=feature_matrix.mean()

std=feature_matrix.std()

feature_matrix=(feature_matrix-mean)/std

feature_matrix=np.c_[np.ones(np.size(feature_matrix)),feature_matrix]                         

label=np.array([50,43,46,33,44,40,41])

learning_rate=0.01                                            

m=len(label)

theta=np.random.rand(2)

def Grad_dec(feature_matrix,label,m,learning_rate,theta):

    for i in range(1000):

        p=np.dot(feature_matrix,theta)

        error=p-label

        cost=sum(error**2)/(2*m)

        

        theta=theta-(learning_rate/m)*np.dot(feature_matrix.T,error)

    return cost,theta

cost,theta=Grad_dec(feature_matrix,label,m,learning_rate,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 p1.py p4.py х sales.txt <> tut8.html <> tut9.html V OPEN EDITORS 1 UNSAVED e p4.py • amir5.py C:\Users\... 1 2 e p1.py 3 p4.py sales.txt 4. 5 <> tut8.html <> tut9.html 6 7 8 V HTML1 a.exe import numpy as np feature_matrix=np.array([310,270,350,251,410,308,263]) mean=feature_matrix.mean() std=feature_matrix.std() feature_matrix=(feature_matrix-mean)/std feature_matrix=np.c_[np.ones(np.size(feature_matrix)),feature_matrix] label=np.array([50,43,46,33,44,40,41]) learning_rate=0.01 m=len(label) theta=np.random.rand(2) def Grad_dec(feature_matrix,label,m, learning_rate, theta): for i in range(1000): p=np.dot(feature_matrix, theta) error=p-label cost=sum(error**2)/(2*m) 9 10 a.java 11 C a1.c 12 А a1.exe 13 14 15 e p1.py e p2.py p3.py è p4.py 16 17 18 19 sales.txt # tut2.css 20 theta=theta-(learning_rate/m)*np.dot(feature_matrix.T, error) return cost, theta cost, theta=Grad_dec(feature_matrix,label,m, learning_rate, 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)) <> tut2.html <> tut3.html <> tut4.html 21 22 23 24 V OUTLINE v Grad_dec PROBLEMS [@] cost OUTPUT DEBUG CONSOLE TERMINAL 1: bash + 0 [@] error [@] feature_matrix [@] i [@] label AMIR KHAN@Amir-khan MINGW64 /Desktop/HTML/HTML1 $ python p4.py [42.42675515 2.49018378] Enter test value:32 29.1534 [@] learning_rate [@] m AMIR KHAN@Amir-khan MINGW64 ~/Desktop/HTML/HTML1 $ I ral thota > TIMELINE > MAVEN Python 3.7.4 32-bit ⓇOAO Ln 21, Col 42 Spaces: 4 UTF-8 CRLF Python Go Live 50 00:12 30-07-2020 O Type here to search TT O e 11 Il C ENG