def plot_logreg(data, degree, theta, E_list):
"""
Plot the results for the logistic regression exercice
:param data:
:param degree:
:param theta:
:param Jtrain:
:param Jtest:
:return:
"""
# Plot the list of errors
if len(E_list) > 0:
fig, ax = plt.subplots(1)
ax.plot(E_list, linewidth=2)
ax.set_xlabel('Iteration number')
ax.set_ylabel('Error')
ax.set_title('Error monitoring')
# Plot the solution on with training and testing set
K = 100
x_min = -1
x_max = 1
[xx1, xx2] = np.meshgrid(np.linspace(x_min, x_max, K),
np.linspace(x_min, x_max, K))
XX = poly_2D_design_matrix(xx1.reshape(K**2, 1), xx2.reshape(K**2, 1),
degree)
hh = sig(XX.dot(theta)).reshape(K, K)
fig, ax = plt.subplots(1, 2)
for k, st in zip([0, 1], ['train', 'test']):
x1 = data['x1_' + st]
x2 = data['x2_' + st]
y = data['y_' + st]
XX = poly_2D_design_matrix(x1, x2, degree)
J = logreg.cost(theta, XX, y)
ax[k].pcolor(xx1, xx2, hh, cmap='cool')
pos, neg = y, np.logical_not(y)
ax[k].scatter(x1[pos], x2[pos], marker='o', color='black', s=20)
ax[k].scatter(x1[neg], x2[neg], marker='x', color='white', s=40)
ax[k].contour(xx1, xx2, hh, levels=[.5], linewidths=[3])
ax[k].set_xlabel('x1')
if k == 0:
ax[k].set_ylabel('x2')
ax[k].set_title('{} set J: {:.3f}'.format(st, J))
# cbar = plt.colorbar()
# cbar.ax.set_ylabel('h(x)')
ax[k].set_xlim([x_min, x_max])
ax[k].set_ylim([x_min, x_max])
def f(theta): return lr.cost(theta, X_train, data['y_train'])
def df(theta): return lr.grad(theta, X_train, data['y_train'])
def f(theta):
return lr.cost(theta, X_train, data['y_train'])
def cost_cb(th):
costs.append(logreg.cost(th,Xfm,y,lda))
# skip gradient descent or fminunc
#newths = scopt.optimize.fmin(logreg.cost,th,args=(X,y,0))
lda = 0
epsilon = 0.0001
niter = 10000
alphas = (0.1,0.5,1,2)
pltnum = (221,222,223,224)
alpha_costs = {}
for alpha in alphas:
costs = []
newths = th
prev_cost = float("inf")
for i in range(niter):
new_cost = logreg.cost(newths,X,y,lda)
if prev_cost -new_cost <= epsilon:
break
costs.append(new_cost)
prev_cost = new_cost
newths = logreg.bgd(newths,X,y,alpha,lda)
costs = np.array(costs)
alpha_costs[alpha] = costs
numpts = 64
x_min, x_max = x1.min(), x1.max()
y_min, y_max = x2.min(), x2.max()
hx = (x_max -x_min)/numpts
hy = (y_max -y_min)/numpts
input('\nProgram paused. Press enter to continue.')
# =================== Part 2: Cost and Gradient descent ===================
(m, n) = X.shape
# Append column of ones to X
ones = np.ones((m, n + 1))
ones[:, 1:] = X
X = ones
# Initialize fitting parameters
initial_theta = np.zeros(n + 1)
# Compute and display initial cost and gradient
(J, grad) = cost(initial_theta, X, y)
print('Cost at initial theta (zeros): %f' % J)
print('Expected cost (approx): 0.693')
print('Gradient at initial theta (zeros): ')
print(grad)
print('Expected gradients (approx):\n -0.1000\n -12.0092\n -11.2628')
# Compute and display cost and gradient with non-zero theta
test_theta = np.array([-24, 0.2, 0.2])
(J, grad) = cost(test_theta, X, y)
print('\nCost at test theta: %f' % J)
print('Expected cost (approx): 0.218')
print('Gradient at test theta: ')
print(grad)
# skip gradient descent or fminunc
#newths = scopt.optimize.fmin(logreg.cost,th,args=(X,y,0))
lda = 0
epsilon = 0.0001
niter = 10000
alphas = (0.1, 0.5, 1, 2)
pltnum = (221, 222, 223, 224)
alpha_costs = {}
for alpha in alphas:
costs = []
newths = th
prev_cost = float("inf")
for i in range(niter):
new_cost = logreg.cost(newths, X, y, lda)
if prev_cost - new_cost <= epsilon:
break
costs.append(new_cost)
prev_cost = new_cost
newths = logreg.bgd(newths, X, y, alpha, lda)
costs = np.array(costs)
alpha_costs[alpha] = costs
numpts = 64
x_min, x_max = x1.min(), x1.max()
y_min, y_max = x2.min(), x2.max()
hx = (x_max - x_min) / numpts
hy = (y_max - y_min) / numpts
def cost_cb(th):
costs.append(logreg.cost(th, Xfm, y, lda))