def test_hmc_custom(self):
with self.test_session() as sess:
x = TransformedDistribution(
distribution=Normal(1.0, 1.0),
bijector=tf.contrib.distributions.bijectors.Softplus())
x.support = 'nonnegative'
qx = Empirical(tf.Variable(tf.random_normal([1000])))
inference = ed.HMC({x: qx})
inference.initialize(auto_transform=True, step_size=0.8)
tf.global_variables_initializer().run()
for _ in range(inference.n_iter):
info_dict = inference.update()
# Check approximation on constrained space has same moments as
# target distribution.
n_samples = 10000
x_unconstrained = inference.transformations[x]
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_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_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 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_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.Gibbs({mu: qmu}, data={x: x_data})
else:
inference = ed.Gibbs([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_metropolis_hastings(self):
N, D, W_1, W_2, W_3, b_1, b_2, x_ph, 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.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()
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 test_normalnormal_float32(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=mu, scale=1.0, sample_shape=50)
n_samples = 2000
qmu = Empirical(params=tf.Variable(tf.ones(n_samples)))
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
inference = ed.MetropolisHastings({mu: qmu}, {mu: mu},
data={x: x_data})
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])
self.assertEqual(old_t, n_samples)
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)
# DATA
x_data = np.array([0, 1, 0, 0, 0, 0, 0, 0, 0, 1])
# MODEL
p = Beta(1.0, 1.0)
x = Bernoulli(probs=p, sample_shape=10)
# INFERENCE
qp = Empirical(params=tf.get_variable(
"qp/params", [1000], initializer=tf.constant_initializer(0.5)))
proposal_p = Beta(3.0, 9.0)
inference = ed.MetropolisHastings({p: qp}, {p: proposal_p}, data={x: x_data})
inference.run()
# CRITICISM
# exact posterior has mean 0.25 and std 0.12
sess = ed.get_session()
mean, stddev = sess.run([qp.mean(), qp.stddev()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior stddev:")
print(stddev)
x_post = ed.copy(x, {p: qp})
tx_rep, tx = ed.ppc(
lambda xs, zs: tf.reduce_mean(tf.cast(xs[x_post], tf.float32)),
data={x_post: x_data})
ed.ppc_stat_hist_plot(
tx[0], tx_rep, stat_name=r'$T \equiv$mean', bins=10)
plt.show()
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)
n_samples = 2000
qmu = Empirical(params=tf.Variable(tf.ones(n_samples)))
proposal_mu = Normal(loc=0.0, scale=1.0)
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
inference = ed.MetropolisHastings({mu: qmu},
{mu: proposal_mu},
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-1, atol=1e-1)
old_t, old_n_accept = sess.run([inference.t, inference.n_accept])
self.assertEqual(old_t, n_samples)
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 collapsed_gibbs(self, wordIds, S, T):
K = self.K
V = self.V
D = self.D
N = self.N
latent_vars = {}
training_data = {}
qbeta = Empirical(tf.Variable(tf.zeros([S, K, V]) + 0.01))
latent_vars[self.beta] = qbeta
qtheta = [None] * D
qz = [None] * D
for d in range(D):
qtheta[d] = Empirical(tf.Variable(tf.zeros([S, K]) + 0.1))
latent_vars[self.theta[d]] = qtheta[d]
qz[d] = Empirical(tf.Variable(tf.zeros([S, N[d]], dtype=tf.int32)))
latent_vars[self.z[d]] = qz[d]
training_data[self.w[d]] = wordIds[d]
self.latent_vars = latent_vars
proposal_vars = {}
proposal_vars[self.beta] = ed.complete_conditional(self.beta)
cond_set = set(self.w + self.z)
for d in range(D):
proposal_vars[self.theta[d]] = \
ed.complete_conditional(self.theta[d])
proposal_vars[self.z[d]] = \
ed.complete_conditional(self.z[d], cond_set)
self.inference = ed.Gibbs(latent_vars, proposal_vars, training_data)
print("collapsed gibbs setup finished")
self.inference.initialize(n_iter=T, n_print=1)
print("initialize finished")
self.__run_inference__(T)
self.qbeta_sample = qbeta.eval()
def main(_):
ed.set_seed(42)
# DATA
x_data = build_toy_dataset(FLAGS.N)
# MODEL
pi = Dirichlet(concentration=tf.ones(FLAGS.K))
mu = Normal(0.0, 1.0, sample_shape=[FLAGS.K, FLAGS.D])
sigma = InverseGamma(concentration=1.0, rate=1.0,
sample_shape=[FLAGS.K, FLAGS.D])
c = Categorical(logits=tf.log(pi) - tf.log(1.0 - pi), sample_shape=FLAGS.N)
x = Normal(loc=tf.gather(mu, c), scale=tf.gather(sigma, c))
# INFERENCE
qpi = Empirical(params=tf.get_variable(
"qpi/params",
[FLAGS.T, FLAGS.K],
initializer=tf.constant_initializer(1.0 / FLAGS.K)))
qmu = Empirical(params=tf.get_variable("qmu/params",
[FLAGS.T, FLAGS.K, FLAGS.D],
initializer=tf.zeros_initializer()))
qsigma = Empirical(params=tf.get_variable("qsigma/params",
[FLAGS.T, FLAGS.K, FLAGS.D],
initializer=tf.ones_initializer()))
qc = Empirical(params=tf.get_variable("qc/params",
[FLAGS.T, FLAGS.N],
initializer=tf.zeros_initializer(),
dtype=tf.int32))
gpi = Dirichlet(concentration=tf.constant([1.4, 1.6]))
gmu = Normal(loc=tf.constant([[1.0, 1.0], [-1.0, -1.0]]),
scale=tf.constant([[0.5, 0.5], [0.5, 0.5]]))
gsigma = InverseGamma(concentration=tf.constant([[1.1, 1.1], [1.1, 1.1]]),
rate=tf.constant([[1.0, 1.0], [1.0, 1.0]]))
gc = Categorical(logits=tf.zeros([FLAGS.N, FLAGS.K]))
inference = ed.MetropolisHastings(
latent_vars={pi: qpi, mu: qmu, sigma: qsigma, c: qc},
proposal_vars={pi: gpi, mu: gmu, sigma: gsigma, c: gc},
data={x: x_data})
inference.initialize()
sess = ed.get_session()
tf.global_variables_initializer().run()
for _ in range(inference.n_iter):
info_dict = inference.update()
inference.print_progress(info_dict)
t = info_dict['t']
if t == 1 or t % inference.n_print == 0:
qpi_mean, qmu_mean = sess.run([qpi.mean(), qmu.mean()])
print("")
print("Inferred membership probabilities:")
print(qpi_mean)
print("Inferred cluster means:")
print(qmu_mean)
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))
proposal_w = Normal(loc=w, scale=0.5 * tf.ones(D, dtype=dtype))
proposal_b = Normal(loc=b, scale=0.5 * tf.ones(1, 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.ReplicaExchangeMC(
{w: qw, b: qb}, {w: proposal_w, b: proposal_b},
data={X: X_train, y: y_train})
else:
inference = ed.ReplicaExchangeMC(
[w, b], {w: proposal_w, b: proposal_b},
data={X: X_train, y: y_train})
qw = inference.latent_vars[w]
qb = inference.latent_vars[b]
inference.run()
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 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_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_normalnormal_run(self):
with self.test_session() as sess:
x_data = np.array([0.0] * 50, dtype=np.float32)
mu = Normal(mu=0.0, sigma=1.0)
x = Normal(mu=tf.ones(50) * mu, sigma=1.0)
qmu = Empirical(params=tf.Variable(tf.ones(5000)))
# analytic solution: N(mu=0.0, sigma=\sqrt{1/51}=0.140)
inference = ed.SGLD({mu: qmu}, data={x: x_data})
inference.run(step_size=0.2)
self.assertAllClose(qmu.mean().eval(), 0, rtol=1e-2, atol=1e-2)
self.assertAllClose(qmu.std().eval(), np.sqrt(1 / 51),
rtol=5e-2, atol=5e-2)
def __init__(self, latent_vars=None, data=None):
"""Create an inference algorithm.
Args:
latent_vars: list or dict, optional.
Collection of random variables (of type `RandomVariable` or
`tf.Tensor`) to perform inference on. If list, each random
variable will be approximated using a `Empirical` random
variable that is defined internally (with unconstrained
support). If dictionary, each value in the dictionary must be a
`Empirical` random variable.
data: dict, optional.
Data dictionary which binds observed variables (of type
`RandomVariable` or `tf.Tensor`) to their realizations (of
type `tf.Tensor`). It can also bind placeholders (of type
`tf.Tensor`) used in the model to their realizations.
"""
if isinstance(latent_vars, list):
with tf.variable_scope(None, default_name="posterior"):
latent_vars = {z: Empirical(params=tf.Variable(tf.zeros(
[1e4] + z.batch_shape.concatenate(z.event_shape).as_list())))
for z in latent_vars}
elif isinstance(latent_vars, dict):
for qz in six.itervalues(latent_vars):
if not isinstance(qz, Empirical):
raise TypeError("Posterior approximation must consist of only "
"Empirical random variables.")
elif len(qz.sample_shape) != 0:
raise ValueError("Empirical posterior approximations must have "
"a scalar sample shape.")
super(MonteCarlo, self).__init__(latent_vars, data)
def __init__(self, latent_vars, proposal_vars, data=None,
inverse_temperatures=np.logspace(0, -2, 5), exchange_freq=0.1):
"""Create an inference algorithm.
Args:
proposal_vars: dict of RandomVariable to RandomVariable.
Collection of random variables to perform inference on; each is
binded to a proposal distribution $g(z' \mid z)$.
inverse_temperatures: list of inverse temperature.
exchange_freq: frequency of exchanging replica.
"""
check_latent_vars(proposal_vars)
self.proposal_vars = proposal_vars
self.n_replica = len(inverse_temperatures)
if inverse_temperatures[0] != 1:
raise ValueError("inverse_temperatures[0] must be 1.")
self.inverse_temperatures = [tf.convert_to_tensor(inverse_temperature,
dtype=list(latent_vars.values())[0].dtype)
for inverse_temperature in
inverse_temperatures]
# Make replica.
self.replica_vars = []
for inverse_temperature in self.inverse_temperatures:
self.replica_vars.append({z: Empirical(params=tf.Variable(tf.zeros(
qz.params.shape, dtype=latent_vars[z].dtype))) for z, qz in
six.iteritems(latent_vars)})
self.exchange_freq = exchange_freq
super(ReplicaExchangeMC, self).__init__(latent_vars, data)
def test_data_tensor(self):
with self.test_session() as sess:
x_data = tf.zeros(50)
mu = Normal(0.0, 1.0)
x = Normal(mu, 1.0, sample_shape=50)
qmu = Empirical(tf.Variable(tf.ones(1000)))
# analytic solution: N(mu=0.0, sigma=\sqrt{1/51}=0.140)
inference = ed.Gibbs({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 init_posterior(self, positive=True, empirical=True, n_samples=1000):
if empirical:
if positive:
self.posterior = Empirical(params=tf.nn.softplus(
tf.Variable(tf.random_normal([n_samples]))))
else:
self.posterior = Empirical(
params=tf.Variable(tf.random_normal([
n_samples,
])))
else:
if positive:
self.posterior = Normal(
loc=tf.Variable(tf.random_normal([1])),
scale=tf.nn.softplus(tf.Variable(tf.random_normal([1]))))
def test_normalnormal_float32(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=mu, scale=1.0, sample_shape=50)
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_beta_bernoulli(self):
with self.test_session() as sess:
x_data = np.array([0, 1, 0, 0, 0, 0, 0, 0, 0, 1])
p = Beta(1.0, 1.0)
x = Bernoulli(probs=p, sample_shape=10)
qp = Empirical(tf.Variable(tf.zeros(1000)))
inference = ed.Gibbs({p: qp}, data={x: x_data})
inference.run()
true_posterior = Beta(3.0, 9.0)
val_est, val_true = sess.run([qp.mean(), true_posterior.mean()])
self.assertAllClose(val_est, val_true, rtol=1e-2, atol=1e-2)
val_est, val_true = sess.run([qp.variance(), true_posterior.variance()])
self.assertAllClose(val_est, val_true, rtol=1e-2, atol=1e-2)
def __init__(self, latent_vars=None, empirical_vars=None, **kwargs):
"""__init__
Parameters
----------
latent_vars : list / dict, optional
Latent variables of the probabilistic model to approximate with diagonal Gaussians. If dict,
the variables given are used for approximation.
empirical_vars: dict, optional
Variables used for SGLD sampling which build the model parameter of the evaluated model for sampling.
Compared to normal SGLD sampling we don't save multiple samples but only the last state to save memory.
"""
if isinstance(latent_vars, list):
with tf.variable_scope("posterior"):
latent_vars = {
rv:
Normal(mu=tf.Variable(tf.zeros(rv.get_batch_shape())),
sigma=tf.Variable(tf.zeros(rv.get_batch_shape())))
for rv in latent_vars
}
elif isinstance(latent_vars, dict):
for qz in six.itervalues(latent_vars):
if not (isinstance(qz, Normal)
or isinstance(qz, NormalWithSoftplusSigma)):
raise TypeError(
"Posterior approximation must consist of only "
"Normal random variables.")
if isinstance(empirical_vars, dict):
for ez in six.itervalues(empirical_vars):
if not (isinstance(ez, tf.Variable)):
raise TypeError("Empirical vals must be tf.Variables.")
empirical_vals = empirical_vars
else:
with tf.variable_scope("empirical"):
empirical_vals = {
rv: tf.Variable(
tf.random_normal(rv.get_batch_shape().as_list(),
stddev=0.1))
for rv, _ in six.iteritems(latent_vars)
}
with tf.variable_scope("empirical"):
empiricals = {
rv: Empirical(params=tf.expand_dims(k, 0))
for rv, k in six.iteritems(empirical_vals)
}
# Build variables needed for online calculation of mean and variance
with tf.variable_scope("deltas"):
deltas = {
rv: tf.Variable(tf.zeros(rv.get_batch_shape().as_list()))
for rv, _ in six.iteritems(latent_vars)
}
self.empirical_vals = empirical_vals
self.approximations = latent_vars
self.deltas = deltas
self.update_iters = tf.Variable(tf.constant(1, tf.int32))
super(VariationalGaussAdam, self).__init__(latent_vars=empiricals,
**kwargs)
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(_):
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", [2000, 2]))
inference = ed.SGLD({z: qz})
inference.run(step_size=5.0)
# 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)
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", [2000, 2]))
inference = ed.SGLD({z: qz})
inference.run(step_size=5.0)
# 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)
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 __init__(self, num_data, num_cluster, vector_dim, num_mcmc_sample):
self.K = num_cluster
self.D = vector_dim
self.N = num_data
self.pi = Dirichlet(tf.ones(self.K))
self.mu = Normal(tf.zeros(self.D),
tf.ones(self.D),
sample_shape=self.K)
self.sigmasq = InverseGamma(tf.ones(self.D),
tf.ones(self.D),
sample_shape=self.K)
self.x = ParamMixture(self.pi, {
'loc': self.mu,
'scale_diag': tf.sqrt(self.sigmasq)
},
MultivariateNormalDiag,
sample_shape=self.N)
self.z = self.x.cat
self.T = num_mcmc_sample # number of MCMC samples
self.qpi = Empirical(tf.Variable(tf.ones([self.T, self.K]) / self.K))
self.qmu = Empirical(tf.Variable(tf.zeros([self.T, self.K, self.D])))
self.qsigmasq = Empirical(
tf.Variable(tf.ones([self.T, self.K, self.D])))
self.qz = Empirical(
tf.Variable(tf.zeros([self.T, self.N], dtype=tf.int32)))
def test_normalnormal_float32(self):
with self.test_session() as sess:
x_data = np.array([0.0] * 50, dtype=np.float32)
mu = Normal(loc=tf.constant(0.0, dtype=tf.float64),
scale=tf.constant(1.0, dtype=tf.float64))
x = Normal(loc=mu,
scale=tf.constant(1.0, dtype=tf.float64),
sample_shape=50)
n_samples = 2000
qmu = Empirical(params=tf.Variable(tf.ones(n_samples, dtype=tf.float64)))
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
inference = ed.MetropolisHastings({mu: qmu},
{mu: mu},
data={x: x_data})
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)
def gibbs(self, wordIds, S, T):
K = self.K
V = self.V
D = self.D
N = self.N
latent_vars = {}
training_data = {}
qbeta = Empirical(tf.Variable(tf.zeros([S, K, V]) + 0.01))
latent_vars[self.beta] = qbeta
qtheta = [None] * D
qz = [None] * D
for d in range(D):
qtheta[d] = Empirical(tf.Variable(tf.zeros([S, K]) + 0.1))
latent_vars[self.theta[d]] = qtheta[d]
qz[d] = Empirical(tf.Variable(tf.zeros([S, N[d]], dtype=tf.int32)))
latent_vars[self.z[d]] = qz[d]
training_data[self.w[d]] = wordIds[d]
self.latent_vars = latent_vars
self.inference = ed.Gibbs(latent_vars, data=training_data)
print("gibbs setup finished")
self.inference.initialize(n_iter=T, n_print=1)
self.__run_inference__(T)
self.qbeta_sample = qbeta.eval()
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()
def main(_):
# Data generation (known mean)
xn_data = np.random.normal(FLAGS.loc, FLAGS.scale, FLAGS.N)
print("scale: {}".format(FLAGS.scale))
# Prior definition
alpha = 0.5
beta = 0.7
# Posterior inference
# Probabilistic model
ig = InverseGamma(alpha, beta)
xn = Normal(FLAGS.loc, tf.sqrt(ig), sample_shape=FLAGS.N)
# Inference
qig = Empirical(params=tf.get_variable(
"qig/params", [1000], initializer=tf.constant_initializer(0.5)))
proposal_ig = InverseGamma(2.0, 2.0)
inference = ed.MetropolisHastings({ig: qig},
{ig: proposal_ig}, data={xn: xn_data})
inference.run()
sess = ed.get_session()
print("Inferred scale: {}".format(sess.run(tf.sqrt(qig.mean()))))
def main(_):
# Data generation (known mean)
xn_data = np.random.normal(FLAGS.loc, FLAGS.scale, FLAGS.N)
print("scale: {}".format(FLAGS.scale))
# Prior definition
alpha = 0.5
beta = 0.7
# Posterior inference
# Probabilistic model
ig = InverseGamma(alpha, beta)
xn = Normal(FLAGS.loc, tf.sqrt(ig), sample_shape=FLAGS.N)
# Inference
qig = Empirical(params=tf.get_variable(
"qig/params", [1000], initializer=tf.constant_initializer(0.5)))
proposal_ig = InverseGamma(2.0, 2.0)
inference = ed.MetropolisHastings({ig: qig}, {ig: proposal_ig},
data={xn: xn_data})
inference.run()
sess = ed.get_session()
print("Inferred scale: {}".format(sess.run(tf.sqrt(qig.mean()))))
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.SGLD({
w: qw,
b: qb
},
data={
X: X_train,
y: y_train
})
else:
inference = ed.SGLD([w, b], data={X: X_train, y: y_train})
qw = inference.latent_vars[w]
qb = inference.latent_vars[b]
inference.run(step_size=0.001)
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)
class Emp:
"""A very simple wrapper around the Empirical class of Edward. Once
the model is built with some samples, one can then draw aditional
samples from it through the evaluate method
"""
def __init__(self, model_id):
self.model_id = model_id
def build(self,Y):
self.var = Empirical(Y)
return self
def getVar(self):
return self.var
def evaluate(self, num_samples):
return self.var.sample([num_samples]).eval(session=ed.get_session())
"""
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([2000, 2])))
inference = ed.SGLD({z: qz})
inference.run(step_size=5.0)
# 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 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(loc=tf.zeros([nsubj, 1]), scale=tf.ones([nsubj, 1]))
thresh = Normal(loc=tf.zeros([1, nitem]), scale=tf.ones([1, nitem]))
X = Bernoulli(logits=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())))
import numpy as np
import tensorflow as tf
from edward.models import Empirical, Normal
ed.set_seed(42)
# DATA
x_data = np.array([0.0] * 50, dtype=np.float32)
# 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])))
proposal_mu = Normal(mu=0.0, sigma=tf.sqrt(1.0 / 51.0))
# analytic solution: N(mu=0.0, sigma=\sqrt{1/51}=0.140)
inference = ed.MetropolisHastings({mu: qmu}, {mu: proposal_mu},
data={x: x_data})
inference.run()
# CRITICISM
# Check convergence with visual diagnostics.
sess = ed.get_session()
mean, std = sess.run([qmu.mean(), qmu.std()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior std:")
def _test(self, params, n): x = Empirical(params=params) val_est = x.sample(n).shape.as_list() val_true = n + tf.convert_to_tensor(params).shape.as_list()[1:] self.assertEqual(val_est, val_true)
import numpy as np
import tensorflow as tf
from edward.models import Bernoulli, Beta, Empirical
ed.set_seed(42)
# DATA
x_data = np.array([0, 1, 0, 0, 0, 0, 0, 0, 0, 1])
# MODEL
p = Beta(1.0, 1.0)
x = Bernoulli(tf.ones(10) * p)
# INFERENCE
qp = Empirical(params=tf.Variable(tf.zeros([1000]) + 0.5))
proposal_p = Beta(3.0, 9.0)
inference = ed.MetropolisHastings({p: qp}, {p: proposal_p}, data={x: x_data})
inference.run()
# CRITICISM
# exact posterior has mean 0.25 and std 0.12
sess = ed.get_session()
mean, stddev = sess.run([qp.mean(), qp.stddev()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior stddev:")
print(stddev)
def main(_):
ed.set_seed(42)
# DATA
X_train, y_train = build_toy_dataset(FLAGS.N)
X_test, y_test = build_toy_dataset(FLAGS.N)
# MODEL
X = tf.placeholder(tf.float32, [FLAGS.N, FLAGS.D])
w = Normal(loc=tf.zeros(FLAGS.D), scale=tf.ones(FLAGS.D))
b = Normal(loc=tf.zeros(1), scale=tf.ones(1))
y = Normal(loc=ed.dot(X, w) + b, scale=tf.ones(FLAGS.N))
# INFERENCE
qw = Empirical(params=tf.get_variable("qw/params", [FLAGS.T, FLAGS.D]))
qb = Empirical(params=tf.get_variable("qb/params", [FLAGS.T, 1]))
inference = ed.SGHMC({w: qw, b: qb}, data={X: X_train, y: y_train})
inference.run(step_size=1e-3)
# CRITICISM
# Plot posterior samples.
sns.jointplot(qb.params.eval()[FLAGS.nburn:FLAGS.T:FLAGS.stride],
qw.params.eval()[FLAGS.nburn:FLAGS.T:FLAGS.stride])
plt.show()
# Posterior predictive checks.
y_post = ed.copy(y, {w: qw, b: qb})
# This is equivalent to
# y_post = Normal(loc=ed.dot(X, qw) + qb, scale=tf.ones(FLAGS.N))
print("Mean squared error on test data:")
print(ed.evaluate('mean_squared_error', data={X: X_test, y_post: y_test}))
print("Displaying prior predictive samples.")
n_prior_samples = 10
w_prior = w.sample(n_prior_samples).eval()
b_prior = b.sample(n_prior_samples).eval()
plt.scatter(X_train, y_train)
inputs = np.linspace(-1, 10, num=400)
for ns in range(n_prior_samples):
output = inputs * w_prior[ns] + b_prior[ns]
plt.plot(inputs, output)
plt.show()
print("Displaying posterior predictive samples.")
n_posterior_samples = 10
w_post = qw.sample(n_posterior_samples).eval()
b_post = qb.sample(n_posterior_samples).eval()
plt.scatter(X_train, y_train)
inputs = np.linspace(-1, 10, num=400)
for ns in range(n_posterior_samples):
output = inputs * w_post[ns] + b_post[ns]
plt.plot(inputs, output)
plt.show()
# DATA
X_train, y_train = build_toy_dataset(N)
X_test, y_test = build_toy_dataset(N)
# MODEL
X = tf.placeholder(tf.float32, [N, D])
w = Normal(loc=tf.zeros(D), scale=tf.ones(D))
b = Normal(loc=tf.zeros(1), scale=tf.ones(1))
y = Normal(loc=ed.dot(X, w) + b, scale=tf.ones(N))
# INFERENCE
T = 5000 # Number of samples.
nburn = 100 # Number of burn-in samples.
stride = 10 # Frequency with which to plot samples.
qw = Empirical(params=tf.Variable(tf.random_normal([T, D])))
qb = Empirical(params=tf.Variable(tf.random_normal([T, 1])))
inference = ed.SGHMC({w: qw, b: qb}, data={X: X_train, y: y_train})
inference.run(step_size=1e-3)
# CRITICISM
# Plot posterior samples.
sns.jointplot(qb.params.eval()[nburn:T:stride],
qw.params.eval()[nburn:T:stride])
plt.show()
# Posterior predictive checks.
y_post = ed.copy(y, {w: qw, b: qb})
"""
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, MultivariateNormalTriL
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.Variable(tf.random_normal([2000, 2])))
inference = ed.SGLD({z: qz})
inference.run(step_size=5.0)
# 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)
import numpy as np
import tensorflow as tf
from edward.models import Bernoulli, Beta, Empirical
ed.set_seed(42)
# DATA
x_data = np.array([0, 1, 0, 0, 0, 0, 0, 0, 0, 1])
# MODEL
p = Beta(a=1.0, b=1.0)
x = Bernoulli(p=tf.ones(10) * p)
# INFERENCE
qp = Empirical(params=tf.Variable(tf.zeros([1000]) + 0.5))
proposal_p = Beta(a=3.0, b=9.0)
data = {x: x_data}
inference = ed.MetropolisHastings({p: qp}, {p: proposal_p}, data)
inference.run()
# CRITICISM
# exact posterior has mean 0.25 and std 0.12
sess = ed.get_session()
mean, std = sess.run([qp.mean(), qp.std()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior std:")
print(std)
"""
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([2000, 2])))
inference = ed.SGLD({z: qz})
inference.run(step_size=5.0)
# 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)
def _test(params, n): x = Empirical(params=params) val_est = get_dims(x.sample(n)) val_true = n + get_dims(params)[1:] assert val_est == val_true
import numpy as np
import tensorflow as tf
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(loc=0.0, scale=1.0)
x = Normal(loc=tf.ones(50) * mu, scale=1.0)
# INFERENCE
qmu = Empirical(params=tf.Variable(tf.zeros([1000])))
proposal_mu = Normal(loc=0.0, scale=tf.sqrt(1.0 / 51.0))
# analytic solution: N(loc=0.0, scale=\sqrt{1/51}=0.140)
inference = ed.MetropolisHastings({mu: qmu}, {mu: proposal_mu},
data={x: x_data})
inference.run()
# CRITICISM
# Check convergence with visual diagnostics.
sess = ed.get_session()
mean, stddev = sess.run([qmu.mean(), qmu.stddev()])
print("Inferred posterior mean:")
print(mean)
print("Inferred posterior stddev:")
N = 40 # number of data points
D = 1 # number of features
# DATA
X_train, y_train = build_toy_dataset(N)
# MODEL
X = tf.placeholder(tf.float32, [N, D])
w = Normal(loc=tf.zeros(D), scale=3.0 * tf.ones(D))
b = Normal(loc=tf.zeros([]), scale=3.0 * tf.ones([]))
y = Bernoulli(logits=ed.dot(X, w) + b)
# INFERENCE
T = 5000 # number of samples
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()
# 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
import tensorflow as tf
from edward.models import InverseGamma, Normal, Empirical
N = 1000
# Data generation (known mean)
loc = 7.0
scale = 0.7
xn_data = np.random.normal(loc, scale, N)
print('sigma={}'.format(sigma))
# Prior definition
alpha = tf.Variable(0.5, trainable=False)
beta = tf.Variable(0.7, trainable=False)
# Posterior inference
# Probabilistic model
ig = InverseGamma(alpha, beta)
xn = Normal(loc, tf.ones([N]) * tf.sqrt(ig))
# Inference
qig = Empirical(params=tf.Variable(tf.zeros(1000) + 0.5))
proposal_ig = InverseGamma(2.0, 2.0)
inference = ed.MetropolisHastings({ig: qig},
{ig: proposal_ig}, data={xn: xn_data})
inference.run()
sess = ed.get_session()
print('Inferred sigma={}'.format(sess.run(tf.sqrt(qig.mean()))))