def check_e_step():
"""Check the E-step updates by making sure they maximize the variational
objective with respect to the responsibilities. Note that this does not
fully check your solution to Part 2, since it only applies to fully observed
images."""
np.random.seed(0)
NUM_IMAGES = 100
X = util.read_mnist_images(mixture.TRAIN_IMAGES_FILE)
X = X[:NUM_IMAGES, :]
model = mixture.train_from_labels(show=False)
# reduce the number of observations so that the posterior is less peaked
X = X[:, ::50]
model.params.theta = model.params.theta[:, ::50]
R = model.compute_posterior(X)
opt = variational_objective(model, X, R, model.params.pi, model.params.theta)
if not np.allclose(R.sum(1), 1.):
print 'Uh-oh. Rows of R do not seem to sum to 1.'
else:
ok = True
for i in range(20):
new_R = perturb_R(R)
new_obj = variational_objective(model, X, new_R, model.params.pi, model.params.theta)
if new_obj > opt:
ok = False
if ok:
print 'The E-step seems OK.'
else:
print 'Something seems to be wrong with the E-step.'
ok = True
for i in range(20):
new_R = perturb_R(R)
new_obj = variational_objective(model, X, new_R, model.params.pi,
model.params.theta)
if new_obj > opt:
ok = False
if ok:
print('The E-step seems OK.')
else:
print('Something seems to be wrong with the E-step.')
if __name__ == '__main__':
check_e_step()
check_m_step()
print("Part 1 values:")
mixture.print_part_1_values()
print("Part 2 values:")
mixture.print_part_2_values() # uses train_from_labels
print("Training with labels()")
model = mixture.train_from_labels()
print("log_probs_by_digit_class")
mixture.print_log_probs_by_digit_class(model)
print("Training with em()")
mixture.train_with_em()
pylab.show()