def calc_grad(theta, X, y, lambda_):
m = len(y)
h = ex2.sigmoid(X.dot(theta))
error = h - y
r = lambda_ / m * theta
r[0] = 0
grad = X.T.dot(error) / m + r
return grad
def cost_reg(theta, x, y, lambda_):
"Compute cost for logistic regression with regularization"
m = len(x)
theta = np.matrix(theta)
x = np.matrix(x)
y = np.matrix(y)
h = sigmoid(x * theta.T)
log_l = np.multiply(-y, np.log(h)) - np.multiply(1 - y, np.log(1 - h))
reg = (lambda_ / 2 * m) * np.power(theta[:, 1:theta.shape[1]], 2).sum()
return log_l.sum() / m + reg
def cost_function_reg(theta, X, y, Lambda):
"""Compute cost and gradient for logistic regression with regularization
compute the cost of using theta as the parameter for regularized logistic regression
and the gradient of the cost w.r.t. to the parameters.
"""
# Initialize some useful values
m, n = X.shape
theta = theta.reshape(n, 1)
h = sigmoid(X.dot(theta))
J = np.sum(-y*np.log(h)-(1-y)*np.log(1-h))/m + Lambda*np.sum(theta[1:]**2)/m/2
grad = X.T.dot(h-y)/m
grad[1:] = grad[1:] + Lambda*theta[1:]/m
return J, grad.ravel()
def gradient_reg(theta, x, y, lambda_):
"Compute gradient for logistic regression with regularization"
m = len(x)
theta = np.matrix(theta)
x = np.matrix(x)
y = np.matrix(y)
parameters = int(theta.ravel().shape[1])
grad = np.zeros(parameters)
h = sigmoid(x * theta.T)
error = h - y
for i in range(parameters):
g = (error.T * x[:, i]) / m
grad[i] = g if (i == 0) else g + ((lambda_ / m) * theta[:, i])
return grad
def calc_J(theta, X, y, lambda_):
m = len(y)
h = ex2.sigmoid(X.dot(theta))
t = -y * np.log(h) - (1 - y) * np.log(1 - h)
J = sum(t) / m + lambda_ / (2 * m) * sum(theta[1:-1]**2)
return J[0]