EXP 5 Implementation-of-Logistic-Regression-Using-Gradient-Descent

AIM:

To write a program to implement the the Logistic Regression Using Gradient Descent.

Equipments Required:

Hardware – PCs
Anaconda – Python 3.7 Installation / Jupyter notebook

Algorithm

1.Use the standard libraries in python for finding linear regression.

2.Set variables for assigning dataset values.

3.Import linear regression from sklearn.

4.Predict the values of array.

5.Calculate the accuracy, confusion and classification report b importing the required modules from sklearn.

6.Obtain the graph.

Program:

Program to implement the the Logistic Regression Using Gradient Descent.

Developed by: SASIRAJKUMAR T J
RegisterNumber: 212222230137

import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize
data=np.loadtxt("/content/ex2data1.txt",delimiter=',')
X=data[:, [0, 1]]
y=data[:, 2]
X[:5]
y[:5]
plt.figure()
plt.scatter(X[y == 1][:, 0], X[y ==1][:, 1], label="Admitted")
plt.scatter(X[y == 0][:, 0], X[y ==0][:, 1], label=" Not Admitted")
plt.xlabel("Exam 1 score")
plt.ylabel("Exam 2 score")
plt.legend()
plt.show()
def sigmoid(z):
  return 1 / (1 + np.exp(-z))
plt.plot()
X_plot = np.linspace(-10,10,100)
plt.plot(X_plot, sigmoid(X_plot))
plt.show()
def costFunction(theta,X,y):
  h=sigmoid(np.dot(X,theta))
  j=-(np.dot(y,np.log(h))+np.dot(1-y,np.log(1-h)))/X.shape[0]
  grad=np.dot(x.T,h-y)/x.shape[0]
  return j,grad
X_train=np.hstack((np.ones((X.shape[0],1)),X))
theta=np.array([0,0,0])
j,grad=costFunction(theta,X_train,y)
print(j)
print(grad)
x_train=np.hstack((np.ones((X.shape[0],1)),X))
theta=np.array([-24,0.2,0.2])
j,grad=costFunction(theta,X_train,y)
print(j)
print(grad)
def cost(theta,X,y):
  h=sigmoid(np.dot(X,theta))
  j=-(np.dot(y,np.log(h))+np.dot(1-y,np.log(1-h)))/X.shape[0]
  return j
def gradient(theta,X,y):
  h=sigmoid(np.dot(X,theta))
  grad=np.dot(X.T,h-y)/X.shape[0]
  return grad
X_train=np.hstack((np.ones((X.shape[0],1)),X))
theta=np.array([0,0,0])
res=optimize.minimize(fun=cost,x0=theta,args=(X_train,y),method='Newton-CG',jac=gradient)
print(res.fun)
print(res.x)
def plotDecisionBoundary(theta,X,y):
  x_min,x_max=X[:,0].min()-1,X[:,0].max()+1
  y_min,y_max=X[:,1].min()-1,X[:,1].max()+1
  xx,yy=np.meshgrid(np.arange(x_min,x_max,0.1),np.arange(y_min,y_max,0.1))
  X_plot=np.c_[xx.ravel(),yy.ravel()]
  X_plot=np.hstack((np.ones((X_plot.shape[0],1)),X_plot))
  y_plot=np.dot(X_plot,theta).reshape(xx.shape)
  plt.figure()
  plt.scatter(X[y == 1][:, 0], X[y ==1][:, 1], label="Admitted")
  plt.scatter(X[y == 0][:, 0], X[y ==0][:, 1], label=" Not Admitted")
  plt.contour(xx,yy,y_plot,levels=[0])
  plt.xlabel("Exam 1 score")
  plt.ylabel("Exam 2 score")
  plt.legend()
  plt.show()
prob=sigmoid(np.dot(np.array([1,45,85]),res.x))
print(prob)
def predict(theta, X):
  X_train=np.hstack((np.ones((X.shape[0],1)),X))
  prob=sigmoid(np.dot(X_train,theta))
  return (prob >= 0.5).astype(int)
np.mean(predict(res.x,X)==y)