def nn_predict(params, inputs):
for W, b in params:
outputs = np.dot(inputs, W) + b # [N,D]
#inputs = rbf(outputs)
inputs = sigmoid(outputs)
#inputs = relu(outputs)
return outputs # [N, dim_last]
def print_perf(params, iter, gradient):
if iter % 30 == 0:
save_images(sigmoid(params),
'results/4/thetas.png',
vmin=0.0,
vmax=1.0)
print(batched_loss(params, iter))
def print_perf(params, iter, gradient):
if iter % 30 == 0:
#save_images(sigmoid(params), 'q4plot.png')
fig = plt.figure(1)
fig.clf()
ax = fig.add_subplot(111)
plot_images(sigmoid(params), ax)
print(batched_loss(params, iter))
def neglogprob(params, data):
# Implement this as the solution for 4c!
params = sigmoid(params)
result = np.exp(
np.dot(data,
np.log(params).T) + np.dot(1 - data,
np.log(1 - params).T))
result = np.mean(result, axis=1)
result = np.log(result)
return -np.mean(result)
def print_perf(params, iter, gradient):
if iter % 30 == 0:
save_images(sigmoid(params), 'q4plot.png')
print(batched_loss(params, iter))
def generate_from_prior(gen_params, num_samples, noise_dim, rs):
latents = rs.randn(num_samples, noise_dim)
return sigmoid(neural_net_predict(gen_params, latents))
def generate_from_prior(gen_params, num_samples, noise_dim, rs):
latents = rs.randn(num_samples, noise_dim)
return sigmoid(neural_net_predict(gen_params, latents))
results = []
for c in range(theta.shape[0]):
cur_theta = theta[c, 0:half_image.shape[0]]
results.append(
np.prod(cur_theta**half_image * (1 - cur_theta)**(1 - half_image)))
return np.array(results)
# The optimizers provided by autograd can optimize lists, tuples, or dicts of parameters.
# You may use these optimizers for Q4, but implement your own gradient descent optimizer for Q3!
optimized_params = adam(objective_grad,
init_params,
step_size=0.2,
num_iters=10000,
callback=print_perf)
num_images = 20
result = np.zeros((20, 784))
images_from_train = train_images[0:20, :]
result[:, 0:392] = images_from_train[:, 0:392]
for im in range(num_images):
top_probs = top_prob_list(sigmoid(optimized_params),
images_from_train[im, 0:392])
top_prob_sum = np.sum(top_probs)
for i in range(392, 784):
numerator = 0.0
for c in range(K):
numerator += sigmoid(optimized_params[c, i]) * top_probs[c]
result[im, i] = numerator / top_prob_sum
save_images(result, "q4d.jpg")
def print_perf(params, iter, gradient):
if iter % 30 == 0:
save_images(sigmoid(params),
'results/4/thetas.png',
vmin=0.0,
vmax=1.0)
print(batched_loss(params, iter))
# The optimizers provided by autograd can optimize lists, tuples, or dicts of parameters.
# You may use these optimizers for Q4, but implement your own gradient descent optimizer for Q3!
optimized_params = adam(objective_grad,
theta,
step_size=0.2,
num_iters=10000,
callback=print_perf)
theta = sigmoid(optimized_params)
np.save('results/4/theta.npy', theta)
def xi_given_xtop(xtop):
p_top_c = np.ndarray(shape=(K))
for c in range(K):
p_top_c[c] = np.exp(
np.log(theta[c, :392]**xtop *
(1 - theta[c, :392])**(1 - xtop)).sum())
p = (theta[:, 392:] * p_top_c.reshape(
(-1, 1))).sum(axis=0) / p_top_c.sum(axis=0)
return p
samples = train_images[:20]
p_bottom = np.ndarray(shape=(20, 392))
for i in range(20):
x_top_temp = np.full(theta_top_temp.shape, x_top_temp)
first = theta_top_temp**x_top_temp * (1 - theta_top_temp)**(1 -
x_top_temp)
first = np.prod(first, axis=1)
first = np.full(theta_bottom_temp.T.shape, first).T
x_bottom_temp = np.full(theta_bottom_temp.shape, x_bottom_temp)
second = theta_bottom_temp
second = np.sum(first * second, axis=0)
first = np.sum(first, axis=0)
result[i, int(theta.shape[1] / 2):] = second / first
result[i, :int(theta.shape[1] / 2)] = x[:int(theta.shape[1] / 2)]
return result
if __name__ == '__main__':
N_data, train_images, train_labels, test_images, test_labels = load_mnist()
optimized_params = adam(objective_grad,
init_params,
step_size=0.2,
num_iters=10000,
callback=print_perf)
optimized_params = sigmoid(optimized_params)
save_images(optimized_params, '4_c.jpg')
picked_images = train_images[
np.random.permutation(train_images.shape[0])[:20], :]
images = plot_bottom_half(picked_images, optimized_params)
save_images(images, '4_d.jpg')
