To write a program to implement the the Logistic Regression Using Gradient Descent.
- Hardware โ PCs
- Anaconda โ Python 3.7 Installation / Jupyter notebook
- Import the packages required.
- Read the dataset.
- Define X and Y array.
- Define a function for costFunction,cost and gradient.
- Define a function to plot the decision boundary and predict the Regression value.
Program to implement the the Logistic Regression Using Gradient Descent.
Developed by: Y SHAVEDHA
RegisterNumber: 212221230095
import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize
data = np.loadtxt("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()
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()
plotDecisionBoundary(res.x,X,y)
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)
Thus the program to implement the the Logistic Regression Using Gradient Descent is written and verified using python programming.