def main():
print 'Loading data...'
X, y = load_data('ex2data2.txt')
print 'First 10 examples from dataset:'
print '\t\tX\t\t y'
for i in range(10):
print ' {0}\t{1}'.format(X[i], y[i])
print 'Plotting data...'
plot_data(X, y)
print 'Normalizing features...'
X, mu, sigma = feature_normalize(X)
print 'Adding polynomial features...'
X = map_feature(X[:, 0], X[:, 1])
initial_theta = np.zeros((X.shape[1], 1))
lambda_ = 1
print 'Computing cost...'
cost, grad = cost_function_reg(initial_theta, X, y, lambda_)
print 'Optimizing using gradient descent...'
alpha = 0.05
num_iters = 1000
theta = np.zeros((X.shape[1], 1))
theta, J_history = gradient_descent_multi_reg(
X, y, theta, alpha, num_iters, lambda_)
plt.plot(range(1, len(J_history) + 1), J_history, '-b')
plt.xlabel('Number of iterations')
plt.ylabel('Cost J')
plt.show()
print 'Theta computed from gradient descent:'
print theta
chip_data = np.array([[-0.5, 0.7]])
chip_data = (chip_data - mu) / sigma
chip_data = np.insert(chip_data, 0, 1, axis=1)
chip_data = map_feature(chip_data[:, 0], chip_data[:, 1])
prob = sigmoid(chip_data.dot(theta))
print 'For a microchip with test of -0.5 and 0.7, we predict an acceptance of {0}%'.format(prob[0, 0] * 100)
print 'Computing accuracy:\n'
p = predict(theta, X)
accuracy = np.mean(y == p)
print 'Train Accuracy: {0}%'.format(accuracy * 100)
def cost_function_reg(theta, X, y, lambda_):
h = sigmoid(X.dot(theta))
log_h = np.log(h)
one_minus_h = 1 - h
log_one_minus_h = np.log(one_minus_h)
vectorized_cost = -y * log_h - (1 - y) * log_one_minus_h
m = len(y)
J = np.sum(vectorized_cost) / m
theta[0] = 0
regularization = lambda_ / (2 * m) * sum(theta ** 2)
J = J + regularization
error = h - y
grad = X.T.dot(error)
grad = grad / m
grad = grad + (lambda_ * theta) / m
return J, grad
lda_costs[lda] = costs
# newths = np.zeros(Xfm.shape[1])
# prev_cost = float("inf")
# costs = []
# for j in range(niter):
# new_cost = logreg.cost(newths,Xfm,y,lda)
# if prev_cost -new_cost <= epsilon:
# break
# costs.append(new_cost)
# prev_cost = new_cost
# newths = logreg.bgd(newths,Xfm,y,alpha,lda)
# lda_costs[lda] = costs
ymg = map(lambda x: 1 if logreg.sigmoid(x) >= 0.5 else 0, np.dot(Xmg,np.matrix(newths).T)) # logreg
# ymg = map(lambda x: 1 if logreg.sigmoid(x) >= 0.5 else 0, Xmg*np.matrix(newths).T) # logreg
ymg = np.array(ymg).reshape(xx.shape)
plt.subplot(pltnum[i])
plt.title("lambda = " +str(lda))
plt.xlabel("x_1")
plt.ylabel("x_2")
plt.pcolormesh(xx, yy, ymg, cmap=plt.cm.Paired)
plt.scatter(x1,x2,c=y,cmap=mpl.cm.get_cmap("Greens"))
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
# find largest x and y range
def plot_costs():
plt.clf()
res = minimize(cost, initial_theta, (X, y), method='BFGS', jac=True)
theta = res.x
J = res.fun
# Print theta to screen
print('Cost at theta found by fminunc: %f' % J)
print('Expected cost (approx): 0.203')
print('theta: ')
print(theta)
print('Expected theta (approx):')
print(' -25.161\n 0.206\n 0.201')
# Plot Boundary
plot_decision_boundary(theta, X, y)
input('\nProgram paused. Press enter to continue.')
# ============== Part 4: Predict and Accuracies ==============
prob = sigmoid(np.array([1, 45, 85]).dot(theta))
print(
'For a student with scores 45 and 85, we predict an admission probability of %f'
% prob)
print('Expected value: 0.775 +/- 0.002\n')
# Compute accuracy on our training set
p = predict(theta, X)
print('Train Accuracy: %f' % (np.mean(p == y) * 100))
print('Expected accuracy (approx): 89.0')
def eval_probs(X, Theta) : (m, n) = X.shape probs = np.array([[logreg.sigmoid(np.dot(X[i, :], Theta.transpose()))] \ for i in range(m)]) return probs
lda_costs[lda] = costs
# newths = np.zeros(Xfm.shape[1])
# prev_cost = float("inf")
# costs = []
# for j in range(niter):
# new_cost = logreg.cost(newths,Xfm,y,lda)
# if prev_cost -new_cost <= epsilon:
# break
# costs.append(new_cost)
# prev_cost = new_cost
# newths = logreg.bgd(newths,Xfm,y,alpha,lda)
# lda_costs[lda] = costs
ymg = map(lambda x: 1 if logreg.sigmoid(x) >= 0.5 else 0,
np.dot(Xmg,
np.matrix(newths).T)) # logreg
# ymg = map(lambda x: 1 if logreg.sigmoid(x) >= 0.5 else 0, Xmg*np.matrix(newths).T) # logreg
ymg = np.array(ymg).reshape(xx.shape)
plt.subplot(pltnum[i])
plt.title("lambda = " + str(lda))
plt.xlabel("x_1")
plt.ylabel("x_2")
plt.pcolormesh(xx, yy, ymg, cmap=plt.cm.Paired)
plt.scatter(x1, x2, c=y, cmap=mpl.cm.get_cmap("Greens"))
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())