Logistic Regression

LogisticRegression.py

def sigmoid(X):
    return 1 / (1 + (e ** (-1*X)))
    

def gradient(theta, x, y):
    grad = np.zeros(theta.shape).flatten()
    m = y.size
    h = sigmoid(x.dot(theta))
    for jth in range(x.shape[1]):
        xjth = x[:, jth]
        gradjth = (1./m) * ((h - y) * xjth).sum()
        grad[jth] = gradjth
    return grad


def costFunction(theta, x, y):
    J = 0
    m = y.size
    h = sigmoid(x.dot(theta))
    J = (1./m) * (-y.dot(log(h)) - (1 - y).dot(log(1 - h)))
    return J

''' Optimize the theta using Newton (TNC) algorithm '''
Result = op.minimize(fun=costFunction, x0=theta, args=(x, y), method='TNC', jac=gradient)
opt_theta = Result.x