def one_vs_all(X, y, num_labels, lmd):
# Some useful variables
(m, n) = X.shape
# You need to return the following variables correctly
all_theta = np.zeros((num_labels, n + 1))
# Add ones to the X data 2D-array
X = np.c_[np.ones(m), X]
for i in range(num_labels):
print('Optimizing for handwritten number {}...'.format(i))
# ===================== Your Code Here =====================
# Instructions : You should complete the following code to train num_labels
# logistic regression classifiers with regularization
# parameter lambda
#
#
# Hint: you can use y == c to obtain a vector of True(1)'s and False(0)'s that tell you
# whether the ground truth is true/false for this class
#
# Note: For this assignment, we recommend using opt.fmin_cg to optimize the cost
# function. It is okay to use a for-loop (for c in range(num_labels) to
# loop over the different classes
#
iclass = i if i else 10
y_i = np.array([1 if x == iclass else 0 for x in y])
cost_func = lambda t : lCF.lr_cost_function(t, X, y_i, lmd)[0]
grad_func = lambda t: lCF.lr_cost_function(t, X, y_i, lmd)[1]
theta = opt.fmin_cg(f=cost_func, x0=all_theta[i].T, maxiter=100, fprime=grad_func, disp=True)
all_theta[i] = theta
# ============================================================
print('Done')
return all_theta
# ===================== Part 2-a: Vectorize Logistic Regression =====================
# In this part of the exercise, you will reuse your logistic regression
# code from the last exercise. Your task here is to make sure that your
# regularized logistic regression implementation is vectorized. After
# that, you will implement one-vs-all classification for the handwritten
# digit dataset
#
# Test case for lrCostFunction
print('Testing lrCostFunction()')
theta_t = np.array([-2, -1, 1, 2])
X_t = np.c_[np.ones(5), np.arange(1, 16).reshape((3, 5)).T/10]
y_t = np.array([1, 0, 1, 0, 1])
lmda_t = 3
cost, grad = lCF.lr_cost_function(theta_t, X_t, y_t, lmda_t)
np.set_printoptions(formatter={'float': '{: 0.6f}'.format})
print('Cost: {:0.7f}'.format(cost))
print('Expected cost: 2.534819')
print('Gradients:\n{}'.format(grad))
print('Expected gradients:\n[ 0.146561 -0.548558 0.724722 1.398003]')
input('Program paused. Press ENTER to continue')
# ===================== Part 2-b: One-vs-All Training =====================
print('Training One-vs-All Logistic Regression ...')
lmd = 0.1
def grad_func(t):
return lCF.lr_cost_function(t, X, y_i, lmd)[1]
def cost_func(t):
return lCF.lr_cost_function(t, X, y_i, lmd)[0]
def grad_func(t): return lr_cost_function(X,y,t,lmd)[1]
def cost_func(t): return lr_cost_function(X,y,t,lmd)[0]
# Randomly select 100 data points to display
shuffle_100_X = np.arange(0, m, 1, dtype=int)
np.random.shuffle(shuffle_100_X)
sel = X[shuffle_100_X[0:100], :]
display_data(sel)
print('Program paused. Press enter to continue.\n')
# pause_func()
# ============ Part 2a: Vectorize Logistic Regression ============
# Test case for lrCostFunction
print('\nTesting lrCostFunction() with regularization')
theta_t = np.array([[-2], [-1], [1], [2]])
X_t = np.append(np.ones((5, 1)), np.arange(1, 16).reshape(5, 3, order='F') / 10, axis=1)
y_t = np.array([[1], [0], [1], [0], [1]])
lambda_t = 3
J, grad = lr_cost_function(theta_t, X_t, y_t, lambda_t)
print('\nCost: \n', J, '\nExpected cost: 2.534819\n')
print('Gradients:\n', grad, '\nExpected gradients:\n', ' 0.146561\n -0.548558\n 0.724722\n 1.398003\n')
print('Program paused. Press enter to continue.\n')
# pause_func()
# ============ Part 2b: One-vs-All Training ============
print('\nTraining One-vs-All Logistic Regression...\n')
ova_lambda = 0.1
all_theta = one_vs_all(X, y, num_labels, ova_lambda)
print('Program paused. Press enter to continue.\n')
# pause_func()
# ================ Part 3: Predict for One-Vs-All ================
pred = predict_one_vs_all(all_theta, X) + 1
print('\nTraining Set Accuracy: \n', np.mean((pred == y) * 100))