def _test_linear_regression(self, default, dtype):
def build_toy_dataset(N, w, noise_std=0.1):
D = len(w)
x = np.random.randn(N, D)
y = np.dot(x, w) + np.random.normal(0, noise_std, size=N)
return x, y
with self.test_session() as sess:
N = 40 # number of data points
D = 10 # number of features
w_true = np.random.randn(D)
X_train, y_train = build_toy_dataset(N, w_true)
X_test, y_test = build_toy_dataset(N, w_true)
X = tf.placeholder(dtype, [N, D])
w = Normal(loc=tf.zeros(D, dtype=dtype),
scale=tf.ones(D, dtype=dtype))
b = Normal(loc=tf.zeros(1, dtype=dtype),
scale=tf.ones(1, dtype=dtype))
y = Normal(loc=ed.dot(X, w) + b,
scale=0.1 * tf.ones(N, dtype=dtype))
n_samples = 2000
if not default:
qw = Empirical(
tf.Variable(tf.zeros([n_samples, D], dtype=dtype)))
qb = Empirical(
tf.Variable(tf.zeros([n_samples, 1], dtype=dtype)))
inference = ed.HMC({
w: qw,
b: qb
},
data={
X: X_train,
y: y_train
})
else:
inference = ed.HMC([w, b], data={X: X_train, y: y_train})
qw = inference.latent_vars[w]
qb = inference.latent_vars[b]
inference.run(step_size=0.01)
self.assertAllClose(qw.mean().eval(), w_true, rtol=5e-1, atol=5e-1)
self.assertAllClose(qb.mean().eval(), [0.0], rtol=5e-1, atol=5e-1)
old_t, old_n_accept = sess.run([inference.t, inference.n_accept])
if not default:
self.assertEqual(old_t, n_samples)
else:
self.assertEqual(old_t, 1e4)
self.assertGreater(old_n_accept, 0.1)
sess.run(inference.reset)
new_t, new_n_accept = sess.run([inference.t, inference.n_accept])
self.assertEqual(new_t, 0)
self.assertEqual(new_n_accept, 0)
def main(_):
ed.set_seed(42)
# MODEL
z = MultivariateNormalTriL(
loc=tf.ones(2),
scale_tril=tf.cholesky(tf.constant([[1.0, 0.8], [0.8, 1.0]])))
# INFERENCE
qz = Empirical(params=tf.get_variable("qz/params", [1000, 2]))
inference = ed.HMC({z: qz})
inference.run()
# CRITICISM
sess = ed.get_session()
mean, stddev = sess.run([qz.mean(), qz.stddev()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior stddev:")
print(stddev)
fig, ax = plt.subplots()
trace = sess.run(qz.params)
ax.scatter(trace[:, 0], trace[:, 1], marker=".")
mvn_plot_contours(z, ax=ax)
plt.show()
def main(_):
# data
J = 8
data_y = np.array([28, 8, -3, 7, -1, 1, 18, 12])
data_sigma = np.array([15, 10, 16, 11, 9, 11, 10, 18])
# model definition
mu = Normal(0., 10.)
logtau = Normal(5., 1.)
theta_prime = Normal(tf.zeros(J), tf.ones(J))
sigma = tf.placeholder(tf.float32, J)
y = Normal(mu + tf.exp(logtau) * theta_prime, sigma * tf.ones([J]))
data = {y: data_y, sigma: data_sigma}
# ed.KLqp inference
with tf.variable_scope('q_logtau'):
q_logtau = Normal(tf.get_variable('loc', []),
tf.nn.softplus(tf.get_variable('scale', [])))
with tf.variable_scope('q_mu'):
q_mu = Normal(tf.get_variable('loc', []),
tf.nn.softplus(tf.get_variable('scale', [])))
with tf.variable_scope('q_theta_prime'):
q_theta_prime = Normal(tf.get_variable('loc', [J]),
tf.nn.softplus(tf.get_variable('scale', [J])))
inference = ed.KLqp({logtau: q_logtau, mu: q_mu,
theta_prime: q_theta_prime}, data=data)
inference.run(n_samples=15, n_iter=60000)
print("==== ed.KLqp inference ====")
print("E[mu] = %f" % (q_mu.mean().eval()))
print("E[logtau] = %f" % (q_logtau.mean().eval()))
print("E[theta_prime]=")
print((q_theta_prime.mean().eval()))
print("==== end ed.KLqp inference ====")
print("")
print("")
# HMC inference
S = 400000
burn = S // 2
hq_logtau = Empirical(tf.get_variable('hq_logtau', [S]))
hq_mu = Empirical(tf.get_variable('hq_mu', [S]))
hq_theta_prime = Empirical(tf.get_variable('hq_thetaprime', [S, J]))
inference = ed.HMC({logtau: hq_logtau, mu: hq_mu,
theta_prime: hq_theta_prime}, data=data)
inference.run()
print("==== ed.HMC inference ====")
print("E[mu] = %f" % (hq_mu.params.eval()[burn:].mean()))
print("E[logtau] = %f" % (hq_logtau.params.eval()[burn:].mean()))
print("E[theta_prime]=")
print(hq_theta_prime.params.eval()[burn:, ].mean(0))
print("==== end ed.HMC inference ====")
print("")
print("")
def test_hmc_default(self):
with self.test_session() as sess:
x = TransformedDistribution(
distribution=Normal(1.0, 1.0),
bijector=tf.contrib.distributions.bijectors.Softplus())
x.support = 'nonnegative'
inference = ed.HMC([x])
inference.initialize(auto_transform=True, step_size=0.8)
tf.global_variables_initializer().run()
for _ in range(inference.n_iter):
info_dict = inference.update()
inference.print_progress(info_dict)
# Check approximation on constrained space has same moments as
# target distribution.
n_samples = 10000
x_unconstrained = inference.transformations[x]
qx = inference.latent_vars[x_unconstrained]
qx_constrained = Empirical(
x_unconstrained.bijector.inverse(qx.params))
x_mean, x_var = tf.nn.moments(x.sample(n_samples), 0)
qx_mean, qx_var = tf.nn.moments(qx_constrained.params[500:], 0)
stats = sess.run([x_mean, qx_mean, x_var, qx_var])
self.assertAllClose(stats[0], stats[1], rtol=1e-1, atol=1e-1)
self.assertAllClose(stats[2], stats[3], rtol=1e-1, atol=1e-1)
def test_hmc(self):
with self.test_session():
N, D, W_1, W_2, W_3, b_1, b_2, X, y, X_train, y_train = self._test(
)
T = 1 # number of MCMC samples
qW_1 = Empirical(params=tf.Variable(tf.random_normal([T, D, 20])))
qW_2 = Empirical(params=tf.Variable(tf.random_normal([T, 20, 15])))
qW_3 = Empirical(params=tf.Variable(tf.random_normal([T, 15, 1])))
qb_1 = Empirical(params=tf.Variable(tf.random_normal([T, 20])))
qb_2 = Empirical(params=tf.Variable(tf.random_normal([T, 15])))
inference = ed.HMC(
{
W_1: qW_1,
b_1: qb_1,
W_2: qW_2,
b_2: qb_2,
W_3: qW_3
},
data={
y: y_train,
X: X_train
})
inference.run()
def ed_graph_2(disc=1):
# Priors
if str(sys.argv[4]) == 'laplace':
W_0 = Laplace(loc=tf.zeros([D, n_hidden]), scale=(std**2/D)*tf.ones([D, n_hidden]))
W_1 = Laplace(loc=tf.zeros([n_hidden, K]), scale=(std**2/n_hidden)*tf.ones([n_hidden, K]))
b_0 = Laplace(loc=tf.zeros(n_hidden), scale=(std**2/D)*tf.ones(n_hidden))
b_1 = Laplace(loc=tf.zeros(K), scale=(std**2/n_hidden)*tf.ones(K))
if str(sys.argv[4]) == 'normal':
W_0 = Normal(loc=tf.zeros([D, n_hidden]), scale=std*D**(-.5)*tf.ones([D, n_hidden]))
W_1 = Normal(loc=tf.zeros([n_hidden, K]), scale=std*n_hidden**(-.5)*tf.ones([n_hidden, K]))
b_0 = Normal(loc=tf.zeros(n_hidden), scale=std*D**(-.5)*tf.ones(n_hidden))
b_1 = Normal(loc=tf.zeros(K), scale=std*n_hidden**(-.5)*tf.ones(K))
if str(sys.argv[4]) == 'T':
W_0 = StudentT(df=df*tf.ones([D, n_hidden]), loc=tf.zeros([D, n_hidden]), scale=std**2/D*tf.ones([D, n_hidden]))
W_1 = StudentT(df=df*tf.ones([n_hidden, K]), loc=tf.zeros([n_hidden, K]), scale=std**2/n_hidden*tf.ones([n_hidden, K]))
b_0 = StudentT(df=df*tf.ones([n_hidden]), loc=tf.zeros(n_hidden), scale=std**2/D*tf.ones(n_hidden))
b_1 = StudentT(df=df*tf.ones([K]), loc=tf.zeros(K), scale=std**2/n_hidden*tf.ones(K))
x = tf.placeholder(tf.float32, [None, None])
y = Categorical(logits=nn(x, W_0, b_0, W_1, b_1))
# We use a placeholder for the labels in anticipation of the traning data.
y_ph = tf.placeholder(tf.int32, [None])
# Use a placeholder for the pre-trained posteriors
w0 = tf.placeholder(tf.float32, [n_samp, D, n_hidden])
w1 = tf.placeholder(tf.float32, [n_samp, n_hidden, K])
b0 = tf.placeholder(tf.float32, [n_samp, n_hidden])
b1 = tf.placeholder(tf.float32, [n_samp, K])
# Empirical distribution
qW_0 = Empirical(params=tf.Variable(w0))
qW_1 = Empirical(params=tf.Variable(w1))
qb_0 = Empirical(params=tf.Variable(b0))
qb_1 = Empirical(params=tf.Variable(b1))
if str(sys.argv[3]) == 'hmc':
inference = ed.HMC({W_0: qW_0, b_0: qb_0, W_1: qW_1, b_1: qb_1}, data={y: y_ph})
if str(sys.argv[3]) == 'sghmc':
inference = ed.SGHMC({W_0: qW_0, b_0: qb_0, W_1: qW_1, b_1: qb_1}, data={y: y_ph})
# Initialse the inference variables
if str(sys.argv[3]) == 'hmc':
inference.initialize(step_size = disc*leap_size, n_steps = step_no, n_print=100)
if str(sys.argv[3]) == 'sghmc':
inference.initialize(step_size = disc*leap_size, friction=disc**2*0.1, n_print=100)
return ((x, y), y_ph, W_0, b_0, W_1, b_1, qW_0, qb_0, qW_1, qb_1, inference,
w0, w1, b0, b1)
def _test_normal_normal(self, default, dtype):
with self.test_session() as sess:
x_data = np.array([0.0] * 50, dtype=np.float32)
mu = Normal(loc=tf.constant(0.0, dtype=dtype),
scale=tf.constant(1.0, dtype=dtype))
x = Normal(loc=mu,
scale=tf.constant(1.0, dtype=dtype),
sample_shape=50)
n_samples = 2000
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
if not default:
qmu = Empirical(
params=tf.Variable(tf.ones(n_samples, dtype=dtype)))
inference = ed.HMC({mu: qmu}, data={x: x_data})
else:
inference = ed.HMC([mu], data={x: x_data})
qmu = inference.latent_vars[mu]
inference.run()
self.assertAllClose(qmu.mean().eval(), 0, rtol=1e-1, atol=1e-1)
self.assertAllClose(qmu.stddev().eval(),
np.sqrt(1 / 51),
rtol=1e-1,
atol=1e-1)
old_t, old_n_accept = sess.run([inference.t, inference.n_accept])
if not default:
self.assertEqual(old_t, n_samples)
else:
self.assertEqual(old_t, 1e4)
self.assertGreater(old_n_accept, 0.1)
sess.run(inference.reset)
new_t, new_n_accept = sess.run([inference.t, inference.n_accept])
self.assertEqual(new_t, 0)
self.assertEqual(new_n_accept, 0)
def test_normalnormal_run(self):
with self.test_session() as sess:
x_data = np.array([0.0] * 50, dtype=np.float32)
mu = Normal(loc=0.0, scale=1.0)
x = Normal(loc=tf.ones(50) * mu, scale=1.0)
qmu = Empirical(params=tf.Variable(tf.ones(2000)))
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
inference = ed.HMC({mu: qmu}, data={x: x_data})
inference.run()
self.assertAllClose(qmu.mean().eval(), 0, rtol=1e-2, atol=1e-2)
self.assertAllClose(qmu.stddev().eval(), np.sqrt(1 / 51),
rtol=1e-2, atol=1e-2)
def test_indexedslices(self):
"""Test that gradients accumulate when tf.gradients doesn't return
tf.Tensor (IndexedSlices)."""
with self.test_session() as sess:
N = 10 # number of data points
K = 2 # number of clusters
T = 1 # number of MCMC samples
x_data = np.zeros(N, dtype=np.float32)
mu = Normal(0.0, 1.0, sample_shape=K)
c = Categorical(logits=tf.zeros(N))
x = Normal(tf.gather(mu, c), tf.ones(N))
qmu = Empirical(params=tf.Variable(tf.ones([T, K])))
qc = Empirical(params=tf.Variable(tf.ones([T, N])))
inference = ed.HMC({mu: qmu}, data={x: x_data})
inference.initialize()
def main(_):
# DATA
trait_true = np.random.normal(size=[FLAGS.nsubj, 1])
thresh_true = np.random.normal(size=[1, FLAGS.nitem])
X_data = np.random.binomial(1, expit(trait_true - thresh_true))
# MODEL
trait = Normal(loc=0.0, scale=1.0, sample_shape=[FLAGS.nsubj, 1])
thresh = Normal(loc=0.0, scale=1.0, sample_shape=[1, FLAGS.nitem])
X = Bernoulli(logits=trait - thresh)
# INFERENCE
q_trait = Empirical(params=tf.get_variable("q_trait/params",
[FLAGS.T, FLAGS.nsubj, 1]))
q_thresh = Empirical(params=tf.get_variable("q_thresh/params",
[FLAGS.T, 1, FLAGS.nitem]))
inference = ed.HMC({trait: q_trait, thresh: q_thresh}, data={X: X_data})
inference.run(step_size=0.1)
# Alternatively, use variational inference.
# q_trait = Normal(
# loc=tf.get_variable("q_trait/loc", [FLAGS.nsubj, 1]),
# scale=tf.nn.softplus(
# tf.get_variable("q_trait/scale", [FLAGS.nsubj, 1])))
# q_thresh = Normal(
# loc=tf.get_variable("q_thresh/loc", [1, FLAGS.nitem]),
# scale=tf.nn.softplus(
# tf.get_variable("q_thresh/scale", [1, FLAGS.nitem])))
# inference = ed.KLqp({trait: q_trait, thresh: q_thresh}, data={X: X_data})
# inference.run(n_iter=2500, n_samples=10)
# CRITICISM
# Check that the inferred posterior mean captures the true traits.
plt.scatter(trait_true, q_trait.mean().eval())
plt.show()
print("MSE between true traits and inferred posterior mean:")
print(np.mean(np.square(trait_true - q_trait.mean().eval())))
def run(self, data, method="klqp", **kwargs):
if method == "klqp":
print(">> Initializing ... ", end="")
inference = ed.KLqp(self.unwind_latent_vars(), data=data)
inference.initialize(**kwargs)
print("ok")
# RUNNING THE INFERENCE
sess = ed.get_session()
init = tf.global_variables_initializer()
init.run()
losses = []
for _ in tqdm(range(inference.n_iter)):
info_dict = inference.update()
losses.append(info_dict['loss'])
plt.figure(figsize=(7, 3))
plt.title("Loss")
plt.semilogy(losses)
plt.show()
elif method == "hmc":
print(">> Initializing ... ", end="")
inference = ed.HMC(self.unwind_latent_vars(), data=data)
inference.initialize(**kwargs)
print("ok")
# RUNNING THE INFERENCE
sess = ed.get_session()
init = tf.global_variables_initializer()
init.run()
acceptance_rates = []
for _ in tqdm(range(inference.n_iter)):
info_dict = inference.update()
acceptance_rates.append(info_dict['accept_rate'])
plt.figure(figsize=(7, 3))
plt.title("Acceptance Rate")
plt.semilogy(acceptance_rates)
plt.show()
def main(_):
ed.set_seed(42)
# DATA
x_data = np.array([0.0] * 50)
# MODEL: Normal-Normal with known variance
mu = Normal(loc=0.0, scale=1.0)
x = Normal(loc=mu, scale=1.0, sample_shape=50)
# INFERENCE
qmu = Empirical(params=tf.get_variable("qmu/params", [1000],
initializer=tf.zeros_initializer()))
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
inference = ed.HMC({mu: qmu}, data={x: x_data})
inference.run()
# CRITICISM
sess = ed.get_session()
mean, stddev = sess.run([qmu.mean(), qmu.stddev()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior stddev:")
print(stddev)
# Check convergence with visual diagnostics.
samples = sess.run(qmu.params)
# Plot histogram.
plt.hist(samples, bins='auto')
plt.show()
# Trace plot.
plt.plot(samples)
plt.show()
# tf.select = tf.where
ed.set_seed(42)
# MODEL
#tf_x = tf.Variable(x.T, trainable=False)
tf_x = tf.Variable(x.T, trainable=False, dtype=tf.float32)
# Standard normal prior on coefficients
#beta = ed.models.Normal(mu=tf.zeros(D), sigma=tf.ones(D))
beta = ed.models.Normal(loc=tf.zeros(D), scale=tf.ones(D))
logit_pred = tf.squeeze(tf.matmul(tf.expand_dims(beta, 0), tf_x))
#ed_y = ed.models.BernoulliWithSigmoidP(p=logit_pred)
ed_y = ed.models.Bernoulli(logits=logit_pred)
# INFERENCE
qbeta = ed.models.Empirical(params=tf.Variable(tf.zeros([n_iterations, D])))
#inference = ed.HMC({beta:qbeta}, data={ed_y:y})
inference = ed.HMC({beta: qbeta}, data={ed_y: y.astype(int)})
t0 = time.time()
inference.run(step_size=step_size, n_steps=n_steps)
ed_time = time.time() - t0
print 'Edward took %.3f seconds' % ed_time
sess = ed.get_session()
ed_samples = sess.run(qbeta.params)
#plot(ed_samples[:, 0])
def train(self, X_train, y_train, X_val, is_print=True):
''' set up BNN and run HMC inference '''
def neural_network(X):
# set up the BNN structure using tf
if self.activation_fn == 'relu':
h = tf.maximum(tf.matmul(X, W_0) + b_0, 0) # relu
elif self.activation_fn == 'Lrelu':
a = 0.2
h = tf.maximum(
tf.matmul(X, W_0) + b_0,
a * (tf.matmul(X, W_0) + b_0)) # leakly relu
elif self.activation_fn == 'erf':
h = tf.erf(tf.matmul(X, W_0) + b_0)
elif self.activation_fn == 'tanh':
h = tf.tanh(tf.matmul(X, W_0) + b_0)
# h = tf.tanh(1.23*tf.matmul(X, W_0) + b_0) # add 1.23 for close to GP erf
elif self.activation_fn == 'sigmoid':
h = tf.sigmoid(tf.matmul(X, W_0) + b_0)
elif self.activation_fn == 'softplus':
self.c = 2. # if this is bigger -> relu behaviour, but less 'soft'
h = tf.divide(
tf.log(
tf.exp(tf.multiply(tf.matmul(X, W_0) + b_0, c)) + 1),
c)
elif self.activation_fn == 'rbf':
self.beta_2 = 1 / (2 * self.g_var)
h = tf.exp(-self.beta_2 * tf.square(X - W_0))
h = tf.matmul(h, W_1) #+ b_1
return tf.reshape(h, [-1])
def neural_network_deep(X):
# set up the BNN structure using tf
if self.activation_fn == 'relu':
h1 = tf.maximum(tf.matmul(X, W_0) + b_0, 0) # relu
h = tf.maximum(tf.matmul(h1, W_1) + b_1, 0) # relu
elif self.activation_fn == 'Lrelu':
a = 0.2
h1 = tf.maximum(
tf.matmul(X, W_0) + b_0,
a * (tf.matmul(X, W_0) + b_0)) # leakly relu
h = tf.maximum(
tf.matmul(h1, W_1) + b_1,
a * (tf.matmul(h1, W_1) + b_1)) # leakly relu
elif self.activation_fn == 'erf':
h1 = tf.erf(tf.matmul(X, W_0) + b_0)
h = tf.erf(tf.matmul(h1, W_1) + b_1)
else:
raise Exception('tp: activation not implemented')
h = tf.matmul(h, W_2) #+ b_2
return tf.reshape(h, [-1])
if self.activation_fn == 'relu' or self.activation_fn == 'softplus' or self.activation_fn == 'Lrelu':
init_stddev_0_w = np.sqrt(self.w_0_var) # /d_in
init_stddev_0_b = np.sqrt(self.b_0_var) # /d_in
init_stddev_1_w = 1.0 / np.sqrt(
self.hidden_size) #*np.sqrt(10) # 2nd layer init. dist
elif self.activation_fn == 'tanh' or self.activation_fn == 'erf':
init_stddev_0_w = np.sqrt(
self.w_0_var) # 1st layer init. dist for weights
init_stddev_0_b = np.sqrt(self.b_0_var) # for bias
init_stddev_1_w = 1.0 / np.sqrt(
self.hidden_size) # 2nd layer init. dist
elif self.activation_fn == 'rbf':
init_stddev_0_w = np.sqrt(self.u_var) # centres = sig_u
init_stddev_0_b = np.sqrt(self.g_var) # fixed /beta
init_stddev_1_w = 1.0 / np.sqrt(
self.hidden_size) # 2nd layer init. dist
n = X_train.shape[0]
X_dim = X_train.shape[1]
y_dim = 1 #y_train.shape[1]
with tf.name_scope("model"):
W_0 = Normal(loc=tf.zeros([X_dim, self.hidden_size]),
scale=init_stddev_0_w *
tf.ones([X_dim, self.hidden_size]),
name="W_0")
if self.deep_NN == False:
W_1 = Normal(loc=tf.zeros([self.hidden_size, y_dim]),
scale=init_stddev_1_w *
tf.ones([self.hidden_size, y_dim]),
name="W_1")
b_0 = Normal(loc=tf.zeros(self.hidden_size),
scale=init_stddev_0_b * tf.ones(self.hidden_size),
name="b_0")
b_1 = Normal(loc=tf.zeros(1), scale=tf.ones(1), name="b_1")
else:
W_1 = Normal(
loc=tf.zeros([self.hidden_size, self.hidden_size]),
scale=init_stddev_1_w * tf.ones([self.hidden_size, y_dim]),
name="W_1")
b_0 = Normal(loc=tf.zeros(self.hidden_size),
scale=init_stddev_0_b * tf.ones(self.hidden_size),
name="b_0")
W_2 = Normal(loc=tf.zeros([self.hidden_size, y_dim]),
scale=init_stddev_1_w *
tf.ones([self.hidden_size, y_dim]),
name="W_2")
b_1 = Normal(loc=tf.zeros(self.hidden_size),
scale=init_stddev_1_w * tf.ones(self.hidden_size),
name="b_1")
b_2 = Normal(loc=tf.zeros(1), scale=tf.ones(1), name="b_2")
X = tf.placeholder(tf.float32, [n, X_dim], name="X")
if self.deep_NN == False:
y = Normal(loc=neural_network(X),
scale=np.sqrt(self.data_noise) * tf.ones(n),
name="y")
else:
y = Normal(loc=neural_network_deep(X),
scale=np.sqrt(self.data_noise) * tf.ones(n),
name="y")
# inference
if self.deep_NN == False:
qW_0 = Empirical(
tf.Variable(tf.zeros([self.n_samples, X_dim,
self.hidden_size])))
qW_1 = Empirical(
tf.Variable(tf.zeros([self.n_samples, self.hidden_size,
y_dim])))
qb_0 = Empirical(
tf.Variable(tf.zeros([self.n_samples, self.hidden_size])))
qb_1 = Empirical(tf.Variable(tf.zeros([self.n_samples, y_dim])))
else:
qW_0 = Empirical(
tf.Variable(tf.zeros([self.n_samples, X_dim,
self.hidden_size])))
qW_1 = Empirical(
tf.Variable(
tf.zeros(
[self.n_samples, self.hidden_size, self.hidden_size])))
qW_2 = Empirical(
tf.Variable(tf.zeros([self.n_samples, self.hidden_size,
y_dim])))
qb_0 = Empirical(
tf.Variable(tf.zeros([self.n_samples, self.hidden_size])))
qb_1 = Empirical(
tf.Variable(tf.zeros([self.n_samples, self.hidden_size])))
qb_2 = Empirical(tf.Variable(tf.zeros([self.n_samples, y_dim])))
# get some priors
### !!! TODO, turn this into a proper function
# X_pred = X_val.astype(np.float32).reshape((X_val.shape[0], 1))
# self.y_priors = tf.stack([nn_predict(X_pred, W_0.sample(), W_1.sample(),b_0.sample(), b_1.sample())
# for _ in range(10)])
# Neal 2012
# Too large a stepsize will result in a very low acceptance rate for states
# proposed by simulating trajectories. Too small a stepsize will either waste
# computation time, by the same factor as the stepsize is too small, or (worse)
# will lead to slow exploration by a random walk,
# https://stats.stackexchange.com/questions/304942/how-to-set-step-size-in-hamiltonian-monte-carlo
# If ϵ is too large, then there will be large discretisation error and low acceptance, if ϵ
# is too small then more expensive leapfrog steps will be required to move large distances.
# Ideally we want the largest possible value of ϵ
# that gives reasonable acceptance probability. Unfortunately this may vary for different values of the target variable.
# A simple heuristic to set this may be to do a preliminary run with fixed L,
# gradually increasing ϵ until the acceptance probability is at an appropriate level.
# Setting the trajectory length by trial and error therefore seems necessary.
# For a problem thought to be fairly difficult, a trajectory with L = 100 might be a
# suitable starting point. If preliminary runs (with a suitable ε; see above) show that HMC
# reaches a nearly independent point after only one iteration, a smaller value of L might be
# tried next. (Unless these “preliminary” runs are actually sufficient, in which case there is
# of course no need to do more runs.) If instead there is high autocorrelation in the run
# with L = 100, runs with L = 1000 might be tried next
# It may also be advisable to randomly sample ϵ
# and L form suitable ranges to avoid the possibility of having paths that are close to periodic as this would slow mixing.
if self.deep_NN == False:
inference = ed.HMC({
W_0: qW_0,
b_0: qb_0,
W_1: qW_1,
b_1: qb_1
},
data={
X: X_train,
y: y_train.ravel()
})
else:
inference = ed.HMC(
{
W_0: qW_0,
b_0: qb_0,
W_1: qW_1,
b_1: qb_1,
W_2: qW_2,
b_2: qb_2
},
data={
X: X_train,
y: y_train.ravel()
})
inference.run(step_size=self.step_size,
n_steps=self.n_steps) # logdir='log'
# drop first chunk of burn in samples
if self.deep_NN == False:
self.qW_0_keep = qW_0.params[self.burn_in:].eval()
self.qW_1_keep = qW_1.params[self.burn_in:].eval()
self.qb_0_keep = qb_0.params[self.burn_in:].eval()
self.qb_1_keep = qb_1.params[self.burn_in:].eval()
else:
self.qW_0_keep = qW_0.params[self.burn_in:].eval()
self.qW_1_keep = qW_1.params[self.burn_in:].eval()
self.qb_0_keep = qb_0.params[self.burn_in:].eval()
self.qW_2_keep = qW_2.params[self.burn_in:].eval()
self.qb_1_keep = qb_1.params[self.burn_in:].eval()
self.qb_2_keep = qb_2.params[self.burn_in:].eval()
return
def ed_graph_init():
# Graph for prior distributions
if str(sys.argv[4]) == 'laplace':
W_0 = Laplace(loc=tf.zeros([D, n_hidden]),
scale=tf.ones([D, n_hidden]))
W_1 = Laplace(loc=tf.zeros([n_hidden, K]),
scale=(std**2 / n_hidden) * tf.ones([n_hidden, K]))
b_0 = Laplace(loc=tf.zeros(n_hidden), scale=tf.ones(n_hidden))
b_1 = Laplace(loc=tf.zeros(K), scale=(std**2 / n_hidden) * tf.ones(K))
if str(sys.argv[4]) == 'normal':
W_0 = Normal(loc=tf.zeros([D, n_hidden]), scale=tf.ones([D, n_hidden]))
W_1 = Normal(loc=tf.zeros([n_hidden, K]),
scale=std * n_hidden**(-.5) * tf.ones([n_hidden, K]))
b_0 = Normal(loc=tf.zeros(n_hidden), scale=tf.ones(n_hidden))
b_1 = Normal(loc=tf.zeros(K), scale=std * n_hidden**(-.5) * tf.ones(K))
if str(sys.argv[4]) == 'T':
W_0 = StudentT(df=df * tf.ones([D, n_hidden]),
loc=tf.zeros([D, n_hidden]),
scale=tf.ones([D, n_hidden]))
W_1 = StudentT(df=df * tf.ones([n_hidden, K]),
loc=tf.zeros([n_hidden, K]),
scale=std**2 / n_hidden * tf.ones([n_hidden, K]))
b_0 = StudentT(df=df * tf.ones([n_hidden]),
loc=tf.zeros(n_hidden),
scale=tf.ones(n_hidden))
b_1 = StudentT(df=df * tf.ones([K]),
loc=tf.zeros(K),
scale=std**2 / n_hidden * tf.ones(K))
# Inputs
x = tf.placeholder(tf.float32, [None, D])
# Regression likelihood
y = Normal(loc=nn(x, W_0, b_0, W_1, b_1),
scale=std_out * tf.ones([tf.shape(x)[0]]))
# We use a placeholder for the labels in anticipation of the traning data.
y_ph = tf.placeholder(tf.float32, [None])
# Graph for posterior distribution
if str(sys.argv[4]) == 'normal':
qW_0 = Empirical(
params=tf.Variable(tf.random_normal([n_samp, D, n_hidden])))
qW_1 = Empirical(params=tf.Variable(
tf.random_normal([n_samp, n_hidden, K],
stddev=std * (n_hidden**-.5))))
qb_0 = Empirical(
params=tf.Variable(tf.random_normal([n_samp, n_hidden])))
qb_1 = Empirical(params=tf.Variable(
tf.random_normal([n_samp, K], stddev=std * (n_hidden**-.5))))
if str(sys.argv[4]) == 'laplace' or str(sys.argv[4]) == 'T':
# Use a placeholder otherwise cannot assign a tensor > 2GB
w0 = tf.placeholder(tf.float32, [n_samp, D, n_hidden])
w1 = tf.placeholder(tf.float32, [n_samp, n_hidden, K])
b0 = tf.placeholder(tf.float32, [n_samp, n_hidden])
b1 = tf.placeholder(tf.float32, [n_samp, K])
# Empirical distribution
qW_0 = Empirical(params=tf.Variable(w0))
qW_1 = Empirical(params=tf.Variable(w1))
qb_0 = Empirical(params=tf.Variable(b0))
qb_1 = Empirical(params=tf.Variable(b1))
# Build inference graph
if str(sys.argv[3]) == 'hmc':
inference = ed.HMC({
W_0: qW_0,
b_0: qb_0,
W_1: qW_1,
b_1: qb_1
},
data={y: y_ph})
if str(sys.argv[3]) == 'sghmc':
inference = ed.SGHMC({
W_0: qW_0,
b_0: qb_0,
W_1: qW_1,
b_1: qb_1
},
data={y: y_ph})
# Initialse the inference variables
if str(sys.argv[3]) == 'hmc':
inference.initialize(step_size=leap_size, n_steps=step_no, n_print=100)
if str(sys.argv[3]) == 'sghmc':
inference.initialize(step_size=leap_size, friction=0.4, n_print=100)
if str(sys.argv[4]) == 'laplace' or str(sys.argv[4]) == 'T':
return ((x, y), y_ph, W_0, b_0, W_1, b_1, qW_0, qb_0, qW_1, qb_1,
inference, w0, w1, b0, b1)
else:
return (x,
y), y_ph, W_0, b_0, W_1, b_1, qW_0, qb_0, qW_1, qb_1, inference
from edward.models import Bernoulli, Normal, Empirical
from scipy.special import expit
# DATA
nsubj = 200
nitem = 25
trait_true = np.random.normal(size=[nsubj, 1])
thresh_true = np.random.normal(size=[1, nitem])
X_data = np.random.binomial(1, expit(trait_true - thresh_true))
# MODEL
trait = Normal(mu=tf.zeros([nsubj, 1]), sigma=tf.ones([nsubj, 1]))
thresh = Normal(mu=tf.zeros([1, nitem]), sigma=tf.ones([1, nitem]))
X = Bernoulli(logits=tf.sub(trait, thresh))
# INFERENCE
T = 5000 # number of posterior samples
q_trait = Empirical(params=tf.Variable(tf.zeros([T, nsubj, 1])))
q_thresh = Empirical(params=tf.Variable(tf.zeros([T, 1, nitem])))
inference = ed.HMC({trait: q_trait, thresh: q_thresh}, data={X: X_data})
inference.run(step_size=0.1)
# CRITICISM
# Check that the inferred posterior mean captures the true traits.
plt.scatter(trait_true, q_trait.mean().eval())
plt.show()
print("MSE between true traits and inferred posterior mean:")
print(np.mean(np.square(trait_true - q_trait.mean().eval())))
"""Correlated normal posterior. Inference with Hamiltonian Monte Carlo.
"""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import edward as ed
import tensorflow as tf
from edward.models import Empirical, MultivariateNormalFull
ed.set_seed(42)
# MODEL
z = MultivariateNormalFull(mu=tf.ones(2),
sigma=tf.constant([[1.0, 0.8], [0.8, 1.0]]))
# INFERENCE
qz = Empirical(params=tf.Variable(tf.random_normal([1000, 2])))
inference = ed.HMC({z: qz})
inference.run()
# CRITICISM
sess = ed.get_session()
mean, std = sess.run([qz.mean(), qz.std()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior std:")
print(std)
from edward.models import Empirical, Normal
ed.set_seed(42)
# DATA
x_data = np.array([0.0] * 50)
# MODEL: Normal-Normal with known variance
mu = Normal(mu=0.0, sigma=1.0)
x = Normal(mu=tf.ones(50) * mu, sigma=1.0)
# INFERENCE
qmu = Empirical(params=tf.Variable(tf.zeros(1000)))
# analytic solution: N(mu=0.0, sigma=\sqrt{1/51}=0.140)
inference = ed.HMC({mu: qmu}, data={x: x_data})
inference.run()
# CRITICISM
sess = ed.get_session()
mean, std = sess.run([qmu.mean(), qmu.std()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior std:")
print(std)
# Check convergence with visual diagnostics.
samples = sess.run(qmu.params)
# Plot histogram.
plt.hist(samples, bins='auto')
#data = tf.constant("C", shape=(N,)) #???
#data = tf.constant(0, shape=(N,))
#data = tf.constant(20, shape=(N,))
data = np.ones((N,))*17
##Infer:
T=10000
qtheta = Empirical(params=tf.Variable(0.5+tf.zeros([T]))) #Why need tf.Variable here?
tf.summary.scalar('qtheta', qtheta)
#proposal_theta = Beta(concentration1=1.0, concentration0=1.0, sample_shape=(1,))
# proposal_theta = Normal(loc=theta,scale=0.5)
# inference = ed.MetropolisHastings({theta: qtheta}, {theta: proposal_theta}, {formulas: data})
sess = ed.get_session()
inference = ed.HMC({theta: qtheta}, {formulas: data})
inference.initialize()
tf.global_variables_initializer().run()
for _ in range(inference.n_iter):
info_dict = inference.update()
inference.print_progress(info_dict)
inference.finalize()
train_writer = tf.summary.FileWriter('/tmp/tensorflow/',sess.graph)
# qtheta = Beta(tf.Variable(1.0), tf.Variable(1.0)) #Why need tf.Variable here?
# inference = ed.KLqp({theta: qtheta}, {formulas: data})
w0 = tf.Variable(p0)
w1 = tf.Variable(p1)
b0 = tf.Variable(pp0)
b1 = tf.Variable(pp1)
# Empirical distribution
qW_0 = Empirical(params=w0)
qW_1 = Empirical(params=w1)
qb_0 = Empirical(params=b0)
qb_1 = Empirical(params=b1)
if str(sys.argv[2]) == 'hmc':
inference = ed.HMC({
W_0: qW_0,
b_0: qb_0,
W_1: qW_1,
b_1: qb_1
},
data={y: y_ph})
if str(sys.argv[2]) == 'sghmc':
inference = ed.SGHMC({
W_0: qW_0,
b_0: qb_0,
W_1: qW_1,
b_1: qb_1
},
data={y: y_ph})
# Initialse the infernce variables
if str(sys.argv[2]) == 'hmc':
inference.initialize(step_size=leap_size, n_steps=step_no, n_print=100)
def main(_):
ed.set_seed(42)
# DATA
X_train, y_train = build_toy_dataset(FLAGS.N)
# MODEL
X = tf.placeholder(tf.float32, [FLAGS.N, FLAGS.D])
w = Normal(loc=tf.zeros(FLAGS.D), scale=3.0 * tf.ones(FLAGS.D))
b = Normal(loc=tf.zeros([]), scale=3.0 * tf.ones([]))
y = Bernoulli(logits=ed.dot(X, w) + b)
# INFERENCE
qw = Empirical(params=tf.get_variable("qw/params", [FLAGS.T, FLAGS.D]))
qb = Empirical(params=tf.get_variable("qb/params", [FLAGS.T]))
inference = ed.HMC({w: qw, b: qb}, data={X: X_train, y: y_train})
inference.initialize(n_print=10, step_size=0.6)
# Alternatively, use variational inference.
# qw_loc = tf.get_variable("qw_loc", [FLAGS.D])
# qw_scale = tf.nn.softplus(tf.get_variable("qw_scale", [FLAGS.D]))
# qb_loc = tf.get_variable("qb_loc", []) + 10.0
# qb_scale = tf.nn.softplus(tf.get_variable("qb_scale", []))
# qw = Normal(loc=qw_loc, scale=qw_scale)
# qb = Normal(loc=qb_loc, scale=qb_scale)
# inference = ed.KLqp({w: qw, b: qb}, data={X: X_train, y: y_train})
# inference.initialize(n_print=10, n_iter=600)
tf.global_variables_initializer().run()
# Set up figure.
fig = plt.figure(figsize=(8, 8), facecolor='white')
ax = fig.add_subplot(111, frameon=False)
plt.ion()
plt.show(block=False)
# Build samples from inferred posterior.
n_samples = 50
inputs = np.linspace(-5, 3, num=400, dtype=np.float32).reshape((400, 1))
probs = tf.stack([
tf.sigmoid(ed.dot(inputs, qw.sample()) + qb.sample())
for _ in range(n_samples)
])
for t in range(inference.n_iter):
info_dict = inference.update()
inference.print_progress(info_dict)
if t % inference.n_print == 0:
outputs = probs.eval()
# Plot data and functions
plt.cla()
ax.plot(X_train[:], y_train, 'bx')
for s in range(n_samples):
ax.plot(inputs[:], outputs[s], alpha=0.2)
ax.set_xlim([-5, 3])
ax.set_ylim([-0.5, 1.5])
plt.draw()
plt.pause(1.0 / 60.0)
def ed_graph_2(disc=1):
# Priors
if str(sys.argv[4]) == 'laplace':
W_0 = Laplace(loc=tf.zeros([D, n_hidden]),
scale=(std**2 / D) * tf.ones([D, n_hidden]))
W_1 = Laplace(loc=tf.zeros([n_hidden, n_hidden]),
scale=(std**2 / n_hidden) *
tf.ones([n_hidden, n_hidden]))
W_2 = Laplace(loc=tf.zeros([n_hidden, K]),
scale=(std**2 / n_hidden) * tf.ones([n_hidden, K]))
b_0 = Laplace(loc=tf.zeros(n_hidden),
scale=(std**2 / D) * tf.ones(n_hidden))
b_1 = Laplace(loc=tf.zeros(n_hidden),
scale=(std**2 / n_hidden) * tf.ones(n_hidden))
b_2 = Laplace(loc=tf.zeros(K), scale=(std**2 / n_hidden) * tf.ones(K))
if str(sys.argv[4]) == 'normal':
W_0 = Normal(loc=tf.zeros([D, n_hidden]),
scale=std * D**-.5 * tf.ones([D, n_hidden]))
W_1 = Normal(loc=tf.zeros([n_hidden, K]),
scale=std * n_hidden**-.5 * tf.ones([n_hidden, K]))
W_2 = Normal(loc=tf.zeros([n_hidden, K]),
scale=std * n_hidden**-.5 * tf.ones([n_hidden, K]))
b_0 = Normal(loc=tf.zeros(n_hidden),
scale=std * D**-.5 * tf.ones(n_hidden))
b_1 = Normal(loc=tf.zeros(n_hidden),
scale=10 * n_hidden**(-.5) * tf.ones(n_hidden))
b_2 = Normal(loc=tf.zeros(K), scale=10 * n_hidden**(-.5) * tf.ones(K))
if str(sys.argv[4]) == 'T':
W_0 = StudentT(df=df * tf.ones([D, n_hidden]),
loc=tf.zeros([D, n_hidden]),
scale=(std**2 / D) * tf.ones([D, n_hidden]))
W_1 = StudentT(df=df * tf.ones([n_hidden, n_hidden]),
loc=tf.zeros([n_hidden, n_hidden]),
scale=(std**2 / n_hidden) *
tf.ones([n_hidden, n_hidden]))
W_2 = StudentT(df=df * tf.ones([n_hidden, K]),
loc=tf.zeros([n_hidden, K]),
scale=(std**2 / n_hidden) * tf.ones([n_hidden, K]))
b_0 = StudentT(df=df * tf.ones([n_hidden]),
loc=tf.zeros(n_hidden),
scale=(std**2 / D) * tf.ones(n_hidden))
b_1 = StudentT(df=df * tf.ones([n_hidden]),
loc=tf.zeros(n_hidden),
scale=(std**2 / n_hidden) * tf.ones(n_hidden))
b_2 = StudentT(df=df * tf.ones([K]),
loc=tf.zeros(K),
scale=(std**2 / n_hidden) * tf.ones(K))
x = tf.placeholder(tf.float32, [None, None])
y = Categorical(logits=nn(x, W_0, b_0, W_1, b_1, W_2, b_2))
# We use a placeholder for the labels in anticipation of the traning data.
y_ph = tf.placeholder(tf.int32, [N])
# Use a placeholder for the pre-trained posteriors
p0 = tf.placeholder(tf.float32, [n_samp, D, n_hidden])
p1 = tf.placeholder(tf.float32, [n_samp, n_hidden, n_hidden])
p2 = tf.placeholder(tf.float32, [n_samp, n_hidden, K])
pp0 = tf.placeholder(tf.float32, [n_samp, n_hidden])
pp1 = tf.placeholder(tf.float32, [n_samp, n_hidden])
pp2 = tf.placeholder(tf.float32, [n_samp, K])
w0 = tf.Variable(p0)
w1 = tf.Variable(p1)
w2 = tf.Variable(p2)
b0 = tf.Variable(pp0)
b1 = tf.Variable(pp1)
b2 = tf.Variable(pp2)
# Empirical distribution
qW_0 = Empirical(params=w0)
qW_1 = Empirical(params=w1)
qW_2 = Empirical(params=w2)
qb_0 = Empirical(params=b0)
qb_1 = Empirical(params=b1)
qb_2 = Empirical(params=b2)
if str(sys.argv[3]) == 'hmc':
inference = ed.HMC(
{
W_0: qW_0,
b_0: qb_0,
W_1: qW_1,
b_1: qb_1,
W_2: qW_2,
b_2: qb_2
},
data={y: y_ph})
if str(sys.argv[3]) == 'sghmc':
inference = ed.SGHMC(
{
W_0: qW_0,
b_0: qb_0,
W_1: qW_1,
b_1: qb_1,
W_2: qW_2,
b_2: qb_2
},
data={y: y_ph})
# Initialse the inference variables
if str(sys.argv[3]) == 'hmc':
inference.initialize(step_size=leap_size,
n_steps=step_no,
n_print=100,
scale={y: float(mnist.train.num_examples) / N})
if str(sys.argv[3]) == 'sghmc':
inference.initialize(step_size=leap_size,
friction=0.4,
n_print=100,
scale={y: float(mnist.train.num_examples) / N})
return ((x, y), y_ph, W_0, b_0, W_1, b_1, W_2, b_2, qW_0, qb_0, qW_1, qb_1,
qW_2, qb_2, inference, p0, p1, p2, pp0, pp1, pp2, w0, w1, w2, b0,
b1, b2)
# for i in range(10):
# print(x.eval())
##Observations:
#data=tf.ones(10, dtype=tf.int32) #NOT WORKING!
data = [1, 1, 1, 1, 1, 1, 1, 1, 0, 1]
##Infer:
#Variational
#qtheta = Beta(tf.Variable(1.0), tf.Variable(1.0)) #Why need tf.Variable here?
# inference = ed.KLqp({theta: qtheta}, {x: data})
# inference.run(n_samples=5, n_iter=1000)
#MonteCarlo
T = 10000
qtheta = Empirical(
params=tf.Variable(0.5 + tf.zeros([T, 1]))
) #Beta(tf.Variable(1.0), tf.Variable(1.0)) #Why need tf.Variable here?
#proposal_theta = Beta(concentration1=1.0, concentration0=1.0, sample_shape=(1,))
#proposal_theta = Normal(loc=theta,scale=0.5)
#inference = ed.MetropolisHastings({theta: qtheta}, {theta: proposal_theta}, {x: data})
inference = ed.HMC({theta: qtheta}, {x: data})
inference.run()
##Results:
qtheta_samples = qtheta.sample(1000).eval()
print(qtheta_samples.mean())
plt.hist(qtheta_samples)
plt.show()
def train(self,
filename,
total_batches=10,
discrete_batch_iters=1000,
continus_batch_iters=10000):
sess = tf.Session()
restorer = tf.train.import_meta_graph(filename, clear_devices=True)
print("<meta graph imported>")
[
tf.add_to_collection(
'd_pi_q',
Empirical(tf.Variable(tf.zeros(tf.shape(var))),
name='Empirical_d_pi_q_' +
str.split(str.split(var.name, '/')[0], '_')[-2]))
for var in tf.get_collection('d_pi')
]
for var in tf.get_collection('c_w'):
idx = str.split(str.split(var.name, '/')[0], '_')[-2]
tf.add_to_collection(
'c_w_q',
Empirical(tf.Variable(tf.zeros(tf.shape(var))),
name='Empirical_c_w_q_' + idx))
print(var.get_shape().as_list())
tf.add_to_collection(
'c_b_q',
Empirical(tf.Variable(tf.zeros(
var.get_shape().as_list()[:-1])),
name='Empirical_c_b_q_' + idx))
tf.add_to_collection(
'c_sigma_q',
Empirical(tf.Variable(tf.zeros([1])),
name='Empirical_c_sigma_q_' + idx))
print("<variables collected>")
variable_map = dict(
zip(
tf.get_collection('d') + tf.get_collection('c'),
self.design_matrix[:,
tuple(np.arange(self.num_discrete_variables)
)].flatten('F').tolist() +
self.design_matrix[:, self.continus_variable_idxs].flatten(
'F').tolist()))
discrete_prior_map = dict(
zip(tf.get_collection('d_pi'), tf.get_collection('d_pi_q')))
continus_prior_map = dict(
zip(
tf.get_collection('c_w') + tf.get_collection('c_b') +
tf.get_collection('c_sigma'),
tf.get_collection('c_w_q') + tf.get_collection('c_b_q') +
tf.get_collection('c_sigma_q')))
print("<running inference>")
inference_d = ed.Gibbs(discrete_prior_map,
data=dict(variable_map.items() +
continus_prior_map.items()))
inference_c = ed.HMC(continus_prior_map,
data=dict(variable_map.items() +
discrete_prior_map.items()))
inference_d.initialize(n_iter=discrete_batch_iters)
inference_c.initialize(n_iter=continus_batch_iters)
sess.run(tf.global_variables_initializer())
for _ in range(total_batches):
for _ in range(inference_d.n_iter):
info_dict = inference_d.update()
inference_d.print_progress(info_dict)
inference_d.n_iter += discrete_batch_iters
inference_d.n_print = int(discrete_batch_iters / 10)
inference_d.progbar = Progbar(inference_d.n_iter)
for _ in range(inference_c.n_iter):
info_dict = inference_c.update()
inference_c.print_progress(info_dict)
inference_c.n_iter += continus_batch_iters
inference_c.n_print = int(continus_batch_iters / 10)
inference_c.progbar = Progbar(inference_c.n_iter)
inference_d.finalize()
inference_c.finalize()
filename = ''.join(str.split(filename, '.')[:-1],
'.') + '_trained_model'
saver = tf.train.Saver()
saver.save(sess, filename)
tf.train.export_meta_graph(
filename + '.meta',
as_text=True,
collection_list=['d_pi', 'd', 'c_w', 'c_b', 'c_sigma', 'c'])
N = 40 # number of data points
D = 1 # number of features
X_train, y_train = build_toy_dataset(N)
X = tf.placeholder(tf.float32, [N, D])
w = Normal(loc=tf.zeros(D), scale=1.0 * tf.ones(D))
b = Normal(loc=tf.zeros([]), scale=1.0 * tf.ones([]))
y = Bernoulli(logits=ed.dot(X, w) + b)
# inference
T = 5000
qw = Empirical(params=tf.Variable(tf.random_normal([T, D])))
qb = Empirical(params=tf.Variable(tf.random_normal([T])))
inference = ed.HMC({w: qw, b: qb}, data={X: X_train, y: y_train})
inference.initialize(n_print=10, step_size=0.6)
tf.global_variables_initializer().run()
# criticism & set up figure
fig = plt.figure(figsize=(8, 8), facecolor='white')
ax = fig.add_subplot(111, frameon=False)
plt.ion()
plt.show(block=False)
n_samples = 50
inputs = np.linspace(-5, 3, num=400, dtype=np.float32).reshape((400, 1))
probs = tf.stack([
tf.sigmoid(ed.dot(inputs, qw.sample()) + qb.sample())
for _ in range(n_samples)
def test_monte_carlo(self):
tf.InteractiveSession()
ed.set_seed(42)
# DATA
X_train = np.zeros([500, 100])
y_train = np.zeros(500)
N = X_train.shape[0] # data points
D = X_train.shape[1] # feature
T = 1 # number of MCMC samples
# MODEL
W_1 = Normal(mu=tf.zeros([D, 20]), sigma=tf.ones([D, 20]) * 100)
W_2 = Normal(mu=tf.zeros([20, 15]), sigma=tf.ones([20, 15]) * 100)
W_3 = Normal(mu=tf.zeros([15, 1]), sigma=tf.ones([15, 1]) * 100)
b_1 = Normal(mu=tf.zeros(20), sigma=tf.ones(20) * 100)
b_2 = Normal(mu=tf.zeros(15), sigma=tf.ones(15) * 100)
x_ph = tf.placeholder(tf.float32, [N, D])
y = Bernoulli(logits=four_layer_nn(x_ph, W_1, W_2, W_3, b_1, b_2))
# INFERENCE
qW_1 = Empirical(params=tf.Variable(tf.random_normal([T, D, 20])))
qW_2 = Empirical(params=tf.Variable(tf.random_normal([T, 20, 15])))
qW_3 = Empirical(params=tf.Variable(tf.random_normal([T, 15, 1])))
qb_1 = Empirical(params=tf.Variable(tf.random_normal([T, 20])))
qb_2 = Empirical(params=tf.Variable(tf.random_normal([T, 15])))
# note ideally these would be separate test methods; there's an
# issue with the tensorflow graph when re-running the above
# unfortunately
inference = ed.HMC(
{
W_1: qW_1,
b_1: qb_1,
W_2: qW_2,
b_2: qb_2,
W_3: qW_3
},
data={
y: y_train,
x_ph: X_train
})
inference.run()
inference = ed.SGLD(
{
W_1: qW_1,
b_1: qb_1,
W_2: qW_2,
b_2: qb_2,
W_3: qW_3
},
data={
y: y_train,
x_ph: X_train
})
inference.run()
inference = ed.MetropolisHastings(
{
W_1: qW_1,
b_1: qb_1,
W_2: qW_2,
b_2: qb_2,
W_3: qW_3
}, {
W_1: W_1,
b_1: b_1,
W_2: W_2,
b_2: b_2,
W_3: W_3
},
data={
y: y_train,
x_ph: X_train
})
inference.run()
import numpy as np
import tensorflow as tf
from edward.models import Bernoulli, Empirical, Normal
from scipy.special import expit
ed.set_seed(123)
N = 5810 # number of data points
D = 54 # number of features
# DATA
w_true = np.random.randn(D)
X_data = np.random.randn(N, D)
p = expit(np.dot(X_data, w_true))
y_data = np.array([np.random.binomial(1, i) for i in p])
# MODEL
X = tf.Variable(X_data.astype(np.float32), trainable=False)
w = Normal(mu=tf.zeros(D), sigma=tf.ones(D))
y = Bernoulli(logits=ed.dot(X, w))
# INFERENCE
T = 5000
qw = Empirical(params=tf.Variable(tf.zeros([T, D])))
inference = ed.HMC({w: qw}, data={y: y_data})
inference.run(step_size=0.05)
# CRITICISM
print("Mean squared error in true values to inferred posterior mean:")
print(tf.reduce_mean(tf.square(w_true - qw.mean())).eval())
def main(_):
outdir = setup_outdir()
ed.set_seed(FLAGS.seed)
((Xtrain, ytrain), (Xtest, ytest)) = blr_utils.get_data()
N, D = Xtrain.shape
N_test, D_test = Xtest.shape
print("Xtrain")
print(Xtrain)
print(Xtrain.shape)
if 'synthetic' in FLAGS.exp:
w = Normal(loc=tf.zeros(D), scale=1.0 * tf.ones(D))
X = tf.placeholder(tf.float32, [N, D])
y = Bernoulli(logits=ed.dot(X, w))
#n_posterior_samples = 100000
n_posterior_samples = 10
qw_empirical = Empirical(
params=tf.get_variable("qw/params", [n_posterior_samples, D]))
inference = ed.HMC({w: qw_empirical}, data={X: Xtrain, y: ytrain})
inference.initialize(n_print=10, step_size=0.6)
tf.global_variables_initializer().run()
inference.run()
empirical_samples = qw_empirical.sample(50).eval()
#fig, ax = plt.subplots()
#ax.scatter(posterior_samples[:,0], posterior_samples[:,1])
#plt.show()
weights, q_components = [], []
ll_trains, ll_tests, bin_ac_trains, bin_ac_tests, elbos, rocs, gaps = [], [], [], [], [], [], []
total_time, times = 0., []
for iter in range(0, FLAGS.n_fw_iter):
print("iter %d" % iter)
g = tf.Graph()
with g.as_default():
sess = tf.InteractiveSession()
with sess.as_default():
tf.set_random_seed(FLAGS.seed)
# MODEL
w = Normal(loc=tf.zeros(D), scale=1.0 * tf.ones(D))
X = tf.placeholder(tf.float32, [N, D])
y = Bernoulli(logits=ed.dot(X, w))
X_test = tf.placeholder(tf.float32, [N_test, D_test])
y_test = Bernoulli(logits=ed.dot(X_test, w))
qw = construct_base_dist([D], iter, 'qw')
inference_time_start = time.time()
inference = relbo.KLqp({w: qw},
fw_iterates=get_fw_iterates(
weights, w, q_components),
data={
X: Xtrain,
y: ytrain
},
fw_iter=iter)
tf.global_variables_initializer().run()
inference.run(n_iter=FLAGS.LMO_iter)
inference_time_end = time.time()
total_time += float(inference_time_end - inference_time_start)
joint = Joint(Xtrain, ytrain, sess)
if iter > 0:
qtw_prev = build_mixture(weights, q_components)
gap = compute_duality_gap(joint, qtw_prev, qw)
gaps.append(gap)
np.savetxt(os.path.join(outdir, "gaps.csv"),
gaps,
delimiter=',')
print("duality gap", gap)
# update weights
gamma = 2. / (iter + 2.)
weights = [(1. - gamma) * w for w in weights]
weights.append(gamma)
# update components
q_components = update_iterate(q_components, qw)
if len(q_components) > 1 and FLAGS.fw_variant == 'fc':
print("running fully corrective")
# overwrite the weights
weights = fully_corrective(
build_mixture(weights, q_components), joint)
if True:
# remove inactivate iterates
weights = list(weights)
for i in reversed(range(len(weights))):
if weights[i] == 0:
del weights[i]
del q_components[i]
weights = np.array(
weights
) # TODO type acrobatics to make elements deletable
elif len(q_components
) > 1 and FLAGS.fw_variant == 'line_search':
print("running line search")
weights = line_search(
build_mixture(weights[:-1], q_components[:-1]), qw,
joint)
qtw_new = build_mixture(weights, q_components)
if False:
for i, comp in enumerate(qtw_new.components):
print("component", i, "\tmean",
comp.mean().eval(), "\tstddev",
comp.stddev().eval())
train_lls = [
sess.run(y.log_prob(ytrain),
feed_dict={
X: Xtrain,
w: qtw_new.sample().eval()
}) for _ in range(50)
]
train_lls = np.mean(train_lls, axis=0)
ll_trains.append((np.mean(train_lls), np.std(train_lls)))
test_lls = [
sess.run(y_test.log_prob(ytest),
feed_dict={
X_test: Xtest,
w: qtw_new.sample().eval()
}) for _ in range(50)
]
test_lls = np.mean(test_lls, axis=0)
ll_tests.append((np.mean(test_lls), np.std(test_lls)))
logits = np.mean([
np.dot(Xtest,
qtw_new.sample().eval()) for _ in range(50)
],
axis=0)
ypred = tf.sigmoid(logits).eval()
roc_score = roc_auc_score(ytest, ypred)
rocs.append(roc_score)
print('roc_score', roc_score)
print('ytrain', np.mean(train_lls), np.std(train_lls))
print('ytest', np.mean(test_lls), np.std(test_lls))
order = np.argsort(ytest)
plt.scatter(range(len(ypred)), ypred[order], c=ytest[order])
plt.savefig(os.path.join(outdir, 'ypred%d.pdf' % iter))
plt.close()
np.savetxt(os.path.join(outdir, "train_lls.csv"),
ll_trains,
delimiter=',')
np.savetxt(os.path.join(outdir, "test_lls.csv"),
ll_tests,
delimiter=',')
np.savetxt(os.path.join(outdir, "rocs.csv"),
rocs,
delimiter=',')
x_post = ed.copy(y, {w: qtw_new})
x_post_t = ed.copy(y_test, {w: qtw_new})
print(
'log lik train',
ed.evaluate('log_likelihood',
data={
x_post: ytrain,
X: Xtrain
}))
print(
'log lik test',
ed.evaluate('log_likelihood',
data={
x_post_t: ytest,
X_test: Xtest
}))
#ll_train = ed.evaluate('log_likelihood', data={x_post: ytrain, X:Xtrain})
#ll_test = ed.evaluate('log_likelihood', data={x_post_t: ytest, X_test:Xtest})
bin_ac_train = ed.evaluate('binary_accuracy',
data={
x_post: ytrain,
X: Xtrain
})
bin_ac_test = ed.evaluate('binary_accuracy',
data={
x_post_t: ytest,
X_test: Xtest
})
print('binary accuracy train', bin_ac_train)
print('binary accuracy test', bin_ac_test)
#latest_elbo = elbo(qtw_new, joint, w)
#foo = ed.KLqp({w: qtw_new}, data={X: Xtrain, y: ytrain})
#op = myloss(foo)
#print("myloss", sess.run(op[0], feed_dict={X: Xtrain, y: ytrain}), sess.run(op[1], feed_dict={X: Xtrain, y: ytrain}))
#append_and_save(ll_trains, ll_train, "loglik_train.csv", np.savetxt)
#append_and_save(ll_tests, ll_train, "loglik_test.csv", np.savetxt) #append_and_save(bin_ac_trains, bin_ac_train, "bin_acc_train.csv", np.savetxt) #append_and_save(bin_ac_tests, bin_ac_test, "bin_acc_test.csv", np.savetxt)
##append_and_save(elbos, latest_elbo, "elbo.csv", np.savetxt)
#print('log-likelihood train ', ll_train)
#print('log-likelihood test ', ll_test)
#print('binary_accuracy train ', bin_ac_train)
#print('binary_accuracy test ', bin_ac_test)
#print('elbo', latest_elbo)
times.append(total_time)
np.savetxt(os.path.join(setup_outdir(), 'times.csv'), times)
tf.reset_default_graph()
)
# Inference arguments
latent_vars = {mu: q_mu, inv_softplus_sigma: q_inv_softplus_sigma}
data = {y: y_train}
# Inference
inference = ed.KLqp(latent_vars, data)
inference.run(n_samples=5, n_iter=2500)
print(q_mu.mean().eval())
print(q_inv_softplus_sigma.mean().eval())
# Empirical Model with Sampler
# Posterior distribution families
q_mu = Empirical(params=tf.Variable(tf.random_normal([2000])))
q_inv_softplus_sigma = Empirical(params=tf.Variable(tf.random_normal([2000])))
# Inference arguments
latent_vars = {mu: q_mu, inv_softplus_sigma: q_inv_softplus_sigma}
data = {y: y_train}
# Inference
inference = ed.HMC(latent_vars, data)
inference.run(step_size=0.003, n_steps=5)
print(tf.reduce_mean(q_mu.params[1000:]).eval())
print(
tf.nn.softplus(tf.reduce_mean(q_inv_softplus_sigma.params[1000:])).eval())
os.makedirs(IMG_DIR)
# DATA
mnist = input_data.read_data_sets(DATA_DIR, one_hot=True)
x_train, _ = mnist.train.next_batch(N)
# MODEL
z = Normal(mu=tf.zeros([N, d]), sigma=tf.ones([N, d]))
logits = generative_network(z)
x = Bernoulli(logits=logits)
# INFERENCE
T = int(100 * 1000)
qz = Empirical(params=tf.Variable(tf.random_normal([T, N, d])))
inference_e = ed.HMC({z: qz}, data={x: x_train})
inference_e.initialize()
inference_m = ed.MAP(data={x: x_train, z: tf.gather(qz.params, inference_e.t)})
optimizer = tf.train.AdamOptimizer(0.01, epsilon=1.0)
inference_m.initialize(optimizer=optimizer)
init = tf.global_variables_initializer()
init.run()
n_iter_per_epoch = 100
n_epoch = T // n_iter_per_epoch
for epoch in range(n_epoch):
avg_loss = 0.0
widgets = ["epoch #%d|" % epoch, Percentage(), Bar(), ETA()]