def _test(alpha, beta, n):
rv = InverseGamma(alpha=alpha, beta=beta)
rv_sample = rv.sample(n)
x = rv_sample.eval()
x_tf = tf.constant(x, dtype=tf.float32)
alpha = alpha.eval()
beta = beta.eval()
assert np.allclose(
rv.log_prob(x_tf).eval(), stats.invgamma.logpdf(x, alpha, scale=beta))
def _test(alpha, beta, n):
rv = InverseGamma(alpha=alpha, beta=beta)
rv_sample = rv.sample(n)
x = rv_sample.eval()
x_tf = tf.constant(x, dtype=tf.float32)
alpha = alpha.eval()
beta = beta.eval()
assert np.allclose(rv.log_prob(x_tf).eval(),
stats.invgamma.logpdf(x, alpha, scale=beta))
init = tf.initialize_all_variables()
init.run()
for _ in range(inference.n_iter):
info_dict = inference.update()
inference.print_progress(info_dict)
t = info_dict['t']
if t % inference.n_print == 0:
print("Inferred cluster means:")
print(sess.run(qmu.value()))
# Average per-cluster and per-data point likelihood over many posterior samples.
log_liks = []
for _ in range(100):
mu_sample = qmu.sample()
sigma_sample = qsigma.sample()
# Take per-cluster and per-data point likelihood.
log_lik = []
for k in range(K):
x_post = Normal(mu=tf.ones([N, 1]) * tf.gather(mu_sample, k),
sigma=tf.ones([N, 1]) * tf.gather(sigma_sample, k))
log_lik.append(tf.reduce_sum(x_post.log_prob(x_train), 1))
log_lik = tf.pack(log_lik) # has shape (K, N)
log_liks.append(log_lik)
log_liks = tf.reduce_mean(log_liks, 0)
# Choose the cluster with the highest likelihood for each data point.
clusters = tf.argmax(log_liks, 0).eval()
plt.scatter(x_train[:, 0], x_train[:, 1], c=clusters, cmap=cm.bwr)
def _test(alpha, beta, n): x = InverseGamma(alpha=alpha, beta=beta) val_est = get_dims(x.sample(n)) val_true = n + get_dims(alpha) assert val_est == val_true
sess = ed.get_session()
init = tf.global_variables_initializer()
init.run()
for _ in range(inference.n_iter):
info_dict = inference.update()
inference.print_progress(info_dict)
t = info_dict['t']
if t % inference.n_print == 0:
print("Inferred cluster means:")
print(sess.run(qmu.mean()))
# Calculate likelihood for each data point and cluster assignment,
# averaged over many posterior samples. ``x_post`` has shape (N, 100, K, D).
mu_sample = qmu.sample(100)
sigma_sample = qsigma.sample(100)
x_post = Normal(mu=tf.ones([N, 1, 1, 1]) * mu_sample,
sigma=tf.ones([N, 1, 1, 1]) * sigma_sample)
x_broadcasted = tf.tile(tf.reshape(x_train, [N, 1, 1, D]), [1, 100, K, 1])
# Sum over latent dimension, then average over posterior samples.
# ``log_liks`` ends up with shape (N, K).
log_liks = x_post.log_prob(x_broadcasted)
log_liks = tf.reduce_sum(log_liks, 3)
log_liks = tf.reduce_mean(log_liks, 1)
# Choose the cluster with the highest likelihood for each data point.
clusters = tf.argmax(log_liks, 1).eval()
plt.scatter(x_train[:, 0], x_train[:, 1], c=clusters, cmap=cm.bwr)
plt.axis([-3, 3, -3, 3])
plt.title("Predicted cluster assignments")
qmu_sigma = tf.nn.softplus(tf.Variable(tf.random_normal([K * D])))
qsigma_alpha = tf.nn.softplus(tf.Variable(tf.random_normal([K * D])))
qsigma_beta = tf.nn.softplus(tf.Variable(tf.random_normal([K * D])))
qpi = Dirichlet(alpha=qpi_alpha)
qmu = Normal(mu=qmu_mu, sigma=qmu_sigma)
qsigma = InverseGamma(alpha=qsigma_alpha, beta=qsigma_beta)
data = {'x': x_train}
inference = ed.KLqp({'pi': qpi, 'mu': qmu, 'sigma': qsigma}, data, model)
inference.run(n_iter=2500, n_samples=10, n_minibatch=20)
# Average per-cluster and per-data point likelihood over many posterior samples.
log_liks = []
for s in range(100):
zrep = {
'pi': qpi.sample(()),
'mu': qmu.sample(()),
'sigma': qsigma.sample(())
}
log_liks += [model.predict(data, zrep)]
log_liks = tf.reduce_mean(log_liks, 0)
# Choose the cluster with the highest likelihood for each data point.
clusters = tf.argmax(log_liks, 0).eval()
plt.scatter(x_train[:, 0], x_train[:, 1], c=clusters, cmap=cm.bwr)
plt.axis([-3, 3, -3, 3])
plt.title("Predicted cluster assignments")
plt.show()
qpi_alpha = tf.nn.softplus(tf.Variable(tf.random_normal([K])))
qmu_mu = tf.Variable(tf.random_normal([K * D]))
qmu_sigma = tf.nn.softplus(tf.Variable(tf.random_normal([K * D])))
qsigma_alpha = tf.nn.softplus(tf.Variable(tf.random_normal([K * D])))
qsigma_beta = tf.nn.softplus(tf.Variable(tf.random_normal([K * D])))
qpi = Dirichlet(alpha=qpi_alpha)
qmu = Normal(mu=qmu_mu, sigma=qmu_sigma)
qsigma = InverseGamma(alpha=qsigma_alpha, beta=qsigma_beta)
data = {'x': x_train}
inference = ed.KLqp({'pi': qpi, 'mu': qmu, 'sigma': qsigma}, data, model)
inference.run(n_iter=2500, n_samples=10, n_minibatch=20)
# Average per-cluster and per-data point likelihood over many posterior samples.
log_liks = []
for s in range(100):
zrep = {'pi': qpi.sample(()),
'mu': qmu.sample(()),
'sigma': qsigma.sample(())}
log_liks += [model.predict(data, zrep)]
log_liks = tf.reduce_mean(log_liks, 0)
# Choose the cluster with the highest likelihood for each data point.
clusters = tf.argmax(log_liks, 0).eval()
plt.scatter(x_train[:, 0], x_train[:, 1], c=clusters, cmap=cm.bwr)
plt.axis([-3, 3, -3, 3])
plt.title("Predicted cluster assignments")
plt.show()
