def costFunctionReg(theta, X, y, lambd):
m = np.size(y)
grad = np.zeros(np.size(theta))
g1 = sigmoid(np.dot(X, theta))
grad1 = 1 / m * np.dot(X.T, g1 - y)
J1 = -1 / m * sum(
np.multiply(y, np.log(g1)) + np.multiply(1 - y, np.log(1 - g1)))
J = J1 + lambd / (2 * m) * (sum(np.power(theta, 2)) - theta[0]**2)
grad[0] = grad1[0]
for i in range(1, np.size(theta)):
grad[i] = grad1[i] + lambd / m * theta[i]
return J, grad
def predict(theta, X, y):
m = np.shape(X)[0]
p = np.zeros((m, 1))
z = np.dot(X, theta)
Y = sigmoid(z)
for i in range(m):
if Y[i] >= 0.5:
p[i] = 1
else:
p[i] = 0
s = np.zeros(m)
for i in range(m):
if p[i] == y[i]:
s[i] = 1
return s
def classify(nnParams, Input_layer_size, First_hidden_layer_size,
Second_hidden_layer_size, num_labels, X):
W2 = np.reshape(nnParams[0],
(First_hidden_layer_size, Input_layer_size + 1),
order='F').T
W3 = np.reshape(nnParams[1],
(Second_hidden_layer_size, First_hidden_layer_size + 1),
order='F').T
W4 = np.reshape(nnParams[2], (num_labels, Second_hidden_layer_size + 1),
order='F').T
# Number of samples
m = np.size(X, axis=0)
# Feed Forward
X = np.concatenate((np.ones((m, 1)), X), axis=1)
O1 = sigmoid(W2.T @ X.T)
O1 = np.concatenate((np.ones((np.size(O1.T, axis=0), 1)), O1.T), axis=1)
O2 = sigmoid(W3.T @ O1.T)
O2 = np.concatenate((np.ones((np.size(O2.T, axis=0), 1)), O2.T), axis=1)
h = sigmoid(W4.T @ O2.T).T
testClass = np.argmax(h, axis=1) + 1
return (testClass)
'''
%% ============== Part 4: Predict and Accuracies ==============
% After learning the parameters, you'll like to use it to predict the outcomes
% on unseen data. In this part, you will use the logistic regression model
% to predict the probability that a student with score 45 on exam 1 and
% score 85 on exam 2 will be admitted.
%
% Furthermore, you will compute the training and test set accuracies of
% our model.
%
% Your task is to complete the code in predict.m
% Predict probability for a student with score 45 on exam 1
% and score 85 on exam 2
'''
prob = sigmoid(np.array([1,45,85]).dot(theta))
print('For a student with scores 45 and 85, we predict an admission probability of ', prob)
# Compute accuracy on our training set
p = predict(theta, X)
p = p.reshape((-1,1))
#p_y = np.hstack((p,y))
#print(p_y)
print('Train Accuracy: ', np.mean((p == y) * 100.))
def predict(theta, X):
return 0.5 <= sigmoid(X.dot(theta))
plotDecisionBoundary(theta, X, y)
plt.show()
'''
%% ============== Part 4: Predict and Accuracies ==============
% After learning the parameters, you'll like to use it to predict the outcomes
% on unseen data. In this part, you will use the logistic regression model
% to predict the probability that a student with score 45 on exam 1 and
% score 85 on exam 2 will be admitted.
%
% Furthermore, you will compute the training and test set accuracies of
% our model.
%
% Your task is to complete the code in predict.m
% Predict probability for a student with score 45 on exam 1
% and score 85 on exam 2
'''
prob = sigmoid(np.array([1, 45, 85]).dot(theta))
print(
'For a student with scores 45 and 85, we predict an admission probability of ',
prob)
# Compute accuracy on our training set
p = predict(theta, X)
p = p.reshape((-1, 1))
#p_y = np.hstack((p,y))
#print(p_y)
print('Train Accuracy: ', np.mean((p == y) * 100.))
# Run fmin_bfgs to obtain the optimal theta
#theta, cost, *unused = opt.fmin_bfgs(f=cost_func, fprime=grad_func, x0=initial_theta,
# maxiter=400, full_output=True, disp=False)
result = opt.minimize(fun=cost_func,
x0=initial_theta,
method='BFGS',
jac=grad_func,
options={'disp': True})
# Print theta to screen
print('Cost at theta found by fminunc:', result.fun)
#print('Expected cost (approx): 0.203\n');
theta = np.reshape(result.x, (n + 1, 1))
print(theta)
print(' -25.161\n 0.206\n 0.201\n')
# Plot Boundary
plt.figure(1)
plotDecisionBoundary(theta, X, y)
#============== Part 4: Predict and Accuracies ==============
temp = [1, 45, 85]
prob = sigmoid(np.dot(temp, theta))
print('we predict an admission probability of ', prob)
#0.775 +/- 0.002
# Compute accuracy on our training set
s = predict(theta, X, y)
result = np.mean(s) * 100
print('Train Accuracy:', result)