ML/Logistic_Regression(SD).py at master · aditya-67/ML · GitHub

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def Sigmoid(z):
	G_of_Z = float(1.0 / float((1.0 + math.exp(-1.0*z))))
	return G_of_Z

def Hypothesis(theta, x):
	z = 0
	for i in xrange(len(theta)):
		z += x[i]*theta[i]
	return Sigmoid(z)

def Cost_Function(X,Y,theta,m):
	sumOfErrors = 0
	for i in xrange(m):
		xi = X[i]
		hi = Hypothesis(theta,xi)
		if Y[i] == 1:
			error = Y[i] * math.log(hi)
		elif Y[i] == 0:
			error = (1-Y[i]) * math.log(1-hi)
		sumOfErrors += error
	const = -1/m
	J = const * sumOfErrors
	print 'cost is ', J
	return J

def Cost_Function_Derivative(X,Y,theta,j,m,alpha):
	sumErrors = 0
	for i in xrange(m):
		xi = X[i]
		xij = xi[j]
		hi = Hypothesis(theta,X[i])
		error = (hi - Y[i])*xij
		sumErrors += error
	m = len(Y)
	constant = float(alpha)/float(m)
	J = constant * sumErrors
	return J

def Gradient_Descent(X,Y,theta,m,alpha):
	new_theta = []
	constant = alpha/m
	for j in xrange(len(theta)):
		CFDerivative = Cost_Function_Derivative(X,Y,theta,j,m,alpha)
		new_theta_value = theta[j] - CFDerivative
		new_theta.append(new_theta_value)
	return new_theta

def Logistic_Regression(X,Y,alpha,theta,num_iters):
	m = len(Y)
	for x in xrange(num_iters):
		new_theta = Gradient_Descent(X,Y,theta,m,alpha)
		theta = new_theta
		if x % 100 == 0:
			#here the cost function is used to present the final hypothesis of the model in the same form for each gradient-step iteration
			Cost_Function(X,Y,theta,m)
			print 'theta ', theta
			print 'cost is ', Cost_Function(X,Y,theta,m)