Regularization of the Cost Function in Python

regularize_cost_function.py

# import numpy library
import numpy as np

# Create a test dataset
Z= np.random.rand(2,1)
y= np.random.rand(2,1)

# define sigmoid function

def sigmoid(x, derivative=False):
    sigm = 1. / (1. + np.exp(-x))
    if derivative:
        return sigm * (1. - sigm)
    return sigm
    
# define cost function 

def cost_func(init_theta,Z,y):
    m=len(Z)
    cost=sum(-1*(y*(np.log(sigmoid(np.dot(Z,init_theta))))+(1-y)*(np.log(1-(sigmoid(np.dot(Z,init_theta)))))))*(1/m)
    return cost
    
# initialize variables

init_theta=np.zeros((Z.shape[1],1))
cost=cost_func(init_theta,Z,y)

# check the output
print(cost)

# regularize the cost function

def cost_func_reg(init_theta,Z,y,lambbda):
    m=len(Z)
    cost=sum((y*(np.log(sigmoid(np.dot(Z,init_theta))))+(1-y)*(np.log(1-(sigmoid(np.dot(Z,init_theta)))))))*(-1/m)+((lambbda/(2*m))*sum(theta**2))
    return cost
    
# check the output
cost_func_reg(init_theta,Z,y,(np.random.rand(2,1)))