def klqp(self, docs, S, T, wordVec):
K = self.K
D = self.D
nu = self.nu
self.latent_vars = latent_vars = {}
training_data = {}
qmu = Normal(loc=tf.Variable(tf.random_normal([K, nu])),
scale=tf.nn.softplus(tf.Variable(tf.zeros([K, nu]))))
latent_vars[self.mu] = qmu
qpsi0 = tf.Variable(tf.eye(nu, batch_shape=[K]))
Ltril = tf.linalg.LinearOperatorLowerTriangular(
ds.matrix_diag_transform(qpsi0,
transform=tf.nn.softplus)).to_dense()
qsigma = WishartCholesky(df=tf.ones([K]) * nu,
scale=Ltril,
cholesky_input_output_matrices=True)
latent_vars[self.sigma] = qsigma
for d in range(D):
training_data[self.w[d]] = docs[d]
self.qmu = qmu
# self.qsigma_inv = qsigma_inv = tf.matrix_inverse(qsigma)
self.qw = MultivariateNormalTriL(loc=qmu, scale_tril=qsigma)
V = len(wordVec)
logprobs = [None] * V
for i in range(V):
logprobs[i] = self.qw.log_prob(wordVec[i])
self.qbeta = tf.convert_to_tensor(logprobs)
self.inference = ed.KLqp(latent_vars, data=training_data)
self.inference.initialize(n_iter=T, n_print=10, n_samples=S)
self.__run_inference__(T)
def main(_):
ed.set_seed(42)
# DATA
x_data = build_toy_dataset(FLAGS.N, FLAGS.V)
# MODEL
x_ph = tf.placeholder(tf.float32, [FLAGS.N, FLAGS.V])
# Form (N, V, V) covariance, one matrix per data point.
K = tf.stack([
rbf(tf.reshape(xn, [FLAGS.V, 1])) + tf.diag([1e-6, 1e-6])
for xn in tf.unstack(x_ph)
])
f = MultivariateNormalTriL(loc=tf.zeros([FLAGS.N, FLAGS.V]),
scale_tril=tf.cholesky(K))
x = Poisson(rate=tf.exp(f))
# INFERENCE
qf = Normal(loc=tf.get_variable("qf/loc", [FLAGS.N, FLAGS.V]),
scale=tf.nn.softplus(
tf.get_variable("qf/scale", [FLAGS.N, FLAGS.V])))
inference = ed.KLqp({f: qf}, data={x: x_data, x_ph: x_data})
inference.run(n_iter=5000)
def gaussian_process_classification_example():
ed.set_seed(42)
data, metadata = crabs('~/data')
X_train = data[:100, 3:]
y_train = data[:100, 1]
N = X_train.shape[0] # Number of data points.
D = X_train.shape[1] # Number of features.
print('Number of data points: {}'.format(N))
print('Number of features: {}'.format(D))
#--------------------
# Model.
X = tf.placeholder(tf.float32, [N, D])
f = MultivariateNormalTriL(loc=tf.zeros(N), scale_tril=tf.cholesky(rbf(X)))
y = Bernoulli(logits=f)
#--------------------
# Inference.
# Perform variational inference.
qf = Normal(loc=tf.get_variable('qf/loc', [N]),
scale=tf.nn.softplus(tf.get_variable('qf/scale', [N])))
inference = ed.KLqp({f: qf}, data={X: X_train, y: y_train})
inference.run(n_iter=5000)
def __init__(self, latent_vars, data=None):
"""Create an inference algorithm.
Args:
latent_vars: list of RandomVariable or
dict of RandomVariable to RandomVariable.
Collection of random variables to perform inference on. If list,
each random variable will be implictly optimized using a
`MultivariateNormalTriL` random variable that is defined
internally (with unconstrained support). If dictionary, each
random variable must be a `MultivariateNormalDiag`,
`MultivariateNormalTriL`, or `Normal` random variable.
"""
if isinstance(latent_vars, list):
with tf.variable_scope(None, default_name="posterior"):
latent_vars = {rv: MultivariateNormalTriL(
loc=tf.Variable(tf.random_normal(rv.batch_shape)),
scale_tril=tf.Variable(tf.random_normal(
rv.batch_shape.concatenate(rv.batch_shape[-1]))))
for rv in latent_vars}
elif isinstance(latent_vars, dict):
for qz in six.itervalues(latent_vars):
if not isinstance(
qz, (MultivariateNormalDiag, MultivariateNormalTriL, Normal)):
raise TypeError("Posterior approximation must consist of only "
"MultivariateNormalDiag, MultivariateTriL, or "
"Normal random variables.")
# call grandparent's method; avoid parent (MAP)
super(MAP, self).__init__(latent_vars, data)
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_multivariate_normal_tril(self):
with self.test_session() as sess:
N, D, w_true, X_train, y_train, X, w, b, y = self._setup()
# INFERENCE. Initialize scales at identity to verify if we
# learned an approximately zero determinant.
qw = MultivariateNormalTriL(
loc=tf.Variable(tf.random_normal([D])),
scale_tril=tf.Variable(tf.diag(tf.ones(D))))
qb = MultivariateNormalTriL(
loc=tf.Variable(tf.random_normal([1])),
scale_tril=tf.Variable(tf.diag(tf.ones(1))))
inference = ed.Laplace({w: qw, b: qb}, data={X: X_train, y: y_train})
inference.run(n_iter=100)
self._test(sess, qw, qb, w_true)
def construct_model():
nku = len(Ku)
nkv = len(Kv)
obs = tf.placeholder(tf.float32, R_.shape)
Ug = TransformedDistribution(distribution=Normal(tf.zeros([nku]), tf.ones([nku])),
bijector=tf.contrib.distributions.bijectors.Exp())
Vg = TransformedDistribution(distribution=Normal(tf.zeros([nkv]), tf.ones([nkv])),
bijector=tf.contrib.distributions.bijectors.Exp())
Ua = TransformedDistribution(distribution=Normal(tf.zeros([1]), tf.ones([1])),
bijector=tf.contrib.distributions.bijectors.Exp())
Va = TransformedDistribution(distribution=Normal(tf.zeros([1]), tf.ones([1])),
bijector=tf.contrib.distributions.bijectors.Exp())
cKu = tf.cholesky(Ku + tf.eye(I) / Ua) # TODO: rank 1 chol update
cKv = tf.cholesky(Kv + tf.eye(J) / Va)
Uw1 = MultivariateNormalTriL(tf.zeros([L, I]),
tf.reduce_sum(cKu / tf.reshape(tf.sqrt(Ug), [nku, 1, 1]), axis=0))
Vw1 = MultivariateNormalTriL(tf.zeros([L, J]),
tf.reduce_sum(cKv / tf.reshape(tf.sqrt(Vg), [nkv, 1, 1]), axis=0))
logits = nn(Uw1, Vw1)
R = AugmentedBernoulli(logits=logits, c=c, obs=obs, value=tf.cast(logits > 0, tf.int32))
qUg = TransformedDistribution(distribution=NormalWithSoftplusScale(tf.Variable(tf.zeros([nku])),
tf.Variable(tf.ones([nku]))),
bijector=tf.contrib.distributions.bijectors.Exp())
qVg = TransformedDistribution(distribution=NormalWithSoftplusScale(tf.Variable(tf.zeros([nkv])),
tf.Variable(tf.ones([nkv]))),
bijector=tf.contrib.distributions.bijectors.Exp())
qUa = TransformedDistribution(distribution=NormalWithSoftplusScale(tf.Variable(tf.zeros([1])),
tf.Variable(tf.ones([1]))),
bijector=tf.contrib.distributions.bijectors.Exp())
qVa = TransformedDistribution(distribution=NormalWithSoftplusScale(tf.Variable(tf.zeros([1])),
tf.Variable(tf.ones([1]))),
bijector=tf.contrib.distributions.bijectors.Exp())
qUw1 = MultivariateNormalTriL(tf.Variable(tf.zeros([L, I])), tf.Variable(tf.eye(I)))
qVw1 = MultivariateNormalTriL(tf.Variable(tf.zeros([L, J])), tf.Variable(tf.eye(J)))
return obs, Ug, Vg, Ua, Va, cKu, cKv, Uw1, Vw1, R, qUg, qVg, qUa, qVa, qUw1, qVw1
def __init__(self, latent_vars, data=None):
"""
Parameters
----------
latent_vars : list of RandomVariable or
dict of RandomVariable to RandomVariable
Collection of random variables to perform inference on. If list,
each random variable will be implictly optimized using a
``MultivariateNormalTriL`` random variable that is defined
internally (with unconstrained support). If dictionary, each
random variable must be a ``MultivariateNormalDiag``,
``MultivariateNormalTriL``, or ``Normal`` random variable.
Notes
-----
If ``MultivariateNormalDiag`` or ``Normal`` random variables are
specified as approximations, then the Laplace approximation will
only produce the diagonal. This does not capture correlation among
the variables but it does not require a potentially expensive
matrix inversion.
Examples
--------
>>> X = tf.placeholder(tf.float32, [N, D])
>>> w = Normal(loc=tf.zeros(D), scale=tf.ones(D))
>>> y = Normal(loc=ed.dot(X, w), scale=tf.ones(N))
>>>
>>> qw = MultivariateNormalTriL(
>>> loc=tf.Variable(tf.random_normal([D])),
>>> scale_tril=tf.Variable(tf.random_normal([D, D])))
>>>
>>> inference = ed.Laplace({w: qw}, data={X: X_train, y: y_train})
"""
if isinstance(latent_vars, list):
with tf.variable_scope("posterior"):
latent_vars = {rv: MultivariateNormalTriL(
loc=tf.Variable(tf.random_normal(rv.batch_shape)),
scale_tril=tf.Variable(tf.random_normal(
rv.batch_shape.concatenate(rv.batch_shape[-1]))))
for rv in latent_vars}
elif isinstance(latent_vars, dict):
for qz in six.itervalues(latent_vars):
if not isinstance(
qz, (MultivariateNormalDiag, MultivariateNormalTriL, Normal)):
raise TypeError("Posterior approximation must consist of only "
"MultivariateNormalDiag, MultivariateTriL, or "
"Normal random variables.")
# call grandparent's method; avoid parent (MAP)
super(MAP, self).__init__(latent_vars, data)
def __init__(self, latent_vars, data=None):
"""Create an inference algorithm.
Args:
latent_vars: list of RandomVariable or
dict of RandomVariable to RandomVariable.
Collection of random variables to perform inference on. If list,
each random variable will be implictly optimized using a
`MultivariateNormalTriL` random variable that is defined
internally with unconstrained support and is initialized using
standard normal draws. If dictionary, each random
variable must be a `MultivariateNormalDiag`,
`MultivariateNormalTriL`, or `Normal` random variable.
"""
if isinstance(latent_vars, list):
with tf.variable_scope(None, default_name="posterior"):
latent_vars_dict = {}
for z in latent_vars:
# Define location to have constrained support and
# unconstrained free parameters.
batch_event_shape = z.batch_shape.concatenate(
z.event_shape)
loc = tf.Variable(tf.random_normal(batch_event_shape))
if hasattr(z, 'support'):
z_transform = transform(z)
if hasattr(z_transform, 'bijector'):
loc = z_transform.bijector.inverse(loc)
scale_tril = tf.Variable(
tf.random_normal(
batch_event_shape.concatenate(
batch_event_shape[-1])))
qz = MultivariateNormalTriL(loc=loc, scale_tril=scale_tril)
latent_vars_dict[z] = qz
latent_vars = latent_vars_dict
del latent_vars_dict
elif isinstance(latent_vars, dict):
for qz in six.itervalues(latent_vars):
if not isinstance(
qz,
(MultivariateNormalDiag, MultivariateNormalTriL, Normal)):
raise TypeError(
"Posterior approximation must consist of only "
"MultivariateNormalDiag, MultivariateTriL, or "
"Normal random variables.")
# call grandparent's method; avoid parent (MAP)
super(MAP, self).__init__(latent_vars, data)
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 __init__(self, K, D, N, nu, use_param=False):
self.K = K # number of topics
self.D = D # number of documents
self.N = N # number of words of each document
self.nu = nu
self.alpha = alpha = tf.zeros([K]) + 0.1
mu0 = tf.constant([0.0] * nu)
sigma0 = tf.eye(nu)
self.sigma = sigma = WishartCholesky(
df=nu,
scale=sigma0,
cholesky_input_output_matrices=True,
sample_shape=K)
# sigma_inv = tf.matrix_inverse(sigma)
self.mu = mu = Normal(mu0, tf.ones(nu), sample_shape=K)
self.theta = theta = [None] * D
self.z = z = [None] * D
self.w = w = [None] * D
for d in range(D):
theta[d] = Dirichlet(alpha)
if use_param:
w[d] = ParamMixture(mixing_weights=theta[d],
component_params={
'loc': mu,
'scale_tril': sigma
},
component_dist=MultivariateNormalTriL,
sample_shape=N[d])
z[d] = w[d].cat
else:
z[d] = Categorical(probs=theta[d], sample_shape=N[d])
components = [
MultivariateNormalTriL(loc=tf.gather(mu, k),
scale_tril=tf.gather(sigma, k),
sample_shape=N[d]) for k in range(K)
]
w[d] = Mixture(cat=z[d],
components=components,
sample_shape=N[d])
def define_prior(N, D, sigma_noise, sigma_signal, lengthscale):
"""
Define a Gaussian process prior.
Parameters
----------
N : int
The number of observations.
D : int
The number of input dimensions.
sigma_noise : float
The noise variance.
sigma_signal : float
The signal variance.
lengthscale : float or array-like
The lengthscale parameter. Can either be a scalar or vector of size D
where D is the number of dimensions of the input space.
Returns
-------
X : tf.placeholder, shape (N, D)
A placeholder for the input data.
K : tf.Tensor, shape (N, N)
The covariance matrix.
f : edward.RandomVariable, shape (N,)
The Gaussian process prior.
"""
# define model
X = tf.placeholder(tf.float32, [N, D])
K = (rbf(X, variance=sigma_signal, lengthscale=lengthscale) +
np.eye(N) * sigma_noise)
f = MultivariateNormalTriL(loc=tf.zeros(N), scale_tril=tf.cholesky(K))
# check dimensions
assert X.shape == (N, D)
assert K.shape == (N, N)
assert f.shape == (N, )
return X, K, f
def _initialize_output_model(self):
with self.sess.as_default():
with self.sess.graph.as_default():
if self.output_scale is None:
output_scale = self.decoder_scale
else:
output_scale = self.output_scale
if self.mv:
self.out = MultivariateNormalTriL(
loc=tf.layers.Flatten()(self.decoder),
scale_tril= output_scale
)
else:
self.out = Normal(
loc=self.decoder,
scale = output_scale
)
if self.normalize_data and self.constrain_output:
self.out = TransformedDistribution(
self.out,
bijector=tf.contrib.distributions.bijectors.Sigmoid()
)
import numpy as np
import edward as ed
import tensorflow as tf
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from edward.models import Normal, MultivariateNormalTriL, Empirical
ed.set_seed(42)
T = 5000 # number of sampling
D = 3 # dimension
cov = [[ 1.36, 0.62, 0.93],
[ 0.80, 1.19, 0.43],
[ 0.57, 0.73, 1.06]]
# model
z = MultivariateNormalTriL(loc=tf.ones(D),
scale_tril=tf.cholesky(cov))
# inference
qz = MultivariateNormalTriL(loc=tf.Variable(tf.zeros(D)),
scale_tril=tf.nn.softplus(tf.Variable(tf.zeros((D, D)))))
inference = ed.KLqp({z:qz})
# qz = Empirical(tf.Variable(tf.random_normal([T,D])))
# inference = ed.HMC({z:qz})
inference.run()
# criticism
sess = ed.get_session()
mean, stddev = sess.run([qz.mean(), qz.stddev()])
print("Inferred posterior mean: ", mean)
period_pre = tf.Variable(np.log(np.exp(7.0 * len_init) - 1), dtype=tf.float32)
period_len_pre = tf.Variable(1.0)
period_var_pre = tf.Variable(np.log(np.exp(0.5) - 1), dtype=tf.float32) #
period = tf.nn.softplus(period_pre)
period_length = tf.nn.softplus(period_len_pre)
Kuu = kernelfx(xu, xu)
fu_loc = tf.zeros((p, m))
fu_scale = tf.cast(tf.cholesky(Kuu + offset * tf.eye(m, dtype=tf.float64),
name='fu_scale'),
dtype=tf.float32)
u = MultivariateNormalTriL(loc=fu_loc, scale_tril=fu_scale, name='pu')
x = Normal(loc=tf.zeros((M, Q)), scale=1.0)
Kfu = kernelfx(x, xu)
Kff = kernelfx(x, x)
Kuuinv = tf.matrix_inverse(Kuu + offset * tf.eye(m, dtype=tf.float64))
KfuKuuinv = tf.matmul(Kfu, Kuuinv)
KffKuuinvU = [
tf.reshape(
tf.matmul(KfuKuuinv,
tf.expand_dims(tf.cast(u[i], dtype=tf.float64), axis=1)),
[-1]) for i in range(0, p)
]
def val_loocv(X_input,
y_input,
param_in,
sigma_sq_in,
max_VI_iter,
qf_in,
mean_prior=0):
f_pred_all = np.zeros(X_input.shape[0])
loo = LeaveOneOut()
temp_sess = tf.Session()
N = int(X_input.shape[0])
D = int(X_input.shape[1])
for train_index, test_index in loo.split(X_input):
X_star_input = X_input[test_index, :].reshape(1, -1)
X_other_input = X_input[train_index, :]
y_other_input = y_input[train_index].reshape(-1, 1)
k_star = rbf_fun(X_other_input,
X_star_input,
lengthscale=param_in[0],
variance=param_in[1])[0]
k_star_1 = matern_fun(X_other_input,
X_star_input,
lengthscale_in=param_in[2],
gamma_in=param_in[3])[0]
k_star_2 = rat_quadratic_fun(X_other_input,
X_star_input,
magnitude=param_in[4],
lengthscale=param_in[5],
diffuseness=param_in[6])[0]
k_star_all = tf.add(tf.add(k_star, k_star_1), k_star_2)
x_only_part = rbf_fun(X_other_input,
lengthscale=param_in[0],
variance=param_in[1])[0]
x_only_part = tf.add(
x_only_part,
matern_fun(X_other_input,
lengthscale_in=param_in[2],
gamma_in=param_in[3])[0])
x_only_part = tf.add(
x_only_part,
rat_quadratic_fun(X_other_input,
magnitude=param_in[4],
lengthscale=param_in[5],
diffuseness=param_in[6])[0])
x_only_part = tf.add(
x_only_part, tf.multiply(sigma_sq_in,
tf.eye(int(X_input.shape[0]))))
x_only_part_inv = tf.linalg.inv(x_only_part)
# Inference from Edward Part
X = tf.placeholder(tf.float32, [N - 1, D])
f = MultivariateNormalTriL(loc=tf.zeros(N - 1),
scale_tril=tf.cholesky(x_only_part))
y = Poisson(rate=tf.nn.softplus(f))
w_mat = tf.matmul(x_only_part_inv, k_star_all)
y_other_input = tf.reshape(y_other_input, [-1])
y_other_input = tf.cast(y_other_input, dtype=tf.float32)
inference_vi = ed.KLqp({f: qf_in},
data={
X: X_other_input,
y: y_other_input
})
inference_vi.run(n_iter=max_VI_iter)
y_post = ed.copy(y, {f: qf_in})
m_mat = y_post.eval()
f_star_each = mean_prior + \
tf.matmul(tf.transpose(w_mat),
(tf.reshape(y_other_input, [-1, 1]) - m_mat))
f_pred_all[test_index] = temp_sess.run(f_star_each)
sum_sq_err = np.sum(np.square(y_input - f_pred_all))
return f_pred_all, sum_sq_err
# it seems like the test and training data need to have the same N
X_test, y_test = X_test[:-1, :], y_test[:-1]
# unfortunately not sure how to make the linear kernel work at this moment
N, P = X_train.shape
X_tf = tf.placeholder(tf.float32, [N, P])
# latent stochastic function
# ok so here in the loc position is where we can get (x *element-wise* b)
b = Bernoulli(varbvs_prior, dtype=np.float32) # prior from varbvs
gp_mu = tf.reduce_mean(tf.multiply(X_tf, tf.reshape(tf.tile(b, [N]), [N, P])),
1) # mean for prior over GP
f = MultivariateNormalTriL(
loc=gp_mu,
scale_tril=tf.cholesky(
rbf(X_tf)) # uses rbf kernel for covariance of GP for now
)
qf = Normal(loc=tf.get_variable("qf/loc", [N]),
scale=tf.nn.softplus(tf.get_variable("qf/scale", [N])))
# respose
y_tf = Bernoulli(logits=f)
# inference
infer = ed.KLqp({f: qf}, data={X_tf: X_train, y_tf: y_train})
infer.run(n_samples=3, n_iter=5000)
# criticism
y_post = ed.copy(y_tf, {f: qf})
Langevin dynamics.
"""
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)
for n in range(N):
f_n = multivariate_normal.rvs(cov=K, size=1)
for v in range(V):
x[n, v] = poisson.rvs(mu=np.exp(f_n[v]), size=1)
return x
ed.set_seed(42)
N = 308 # number of NBA players
V = 2 # number of shot locations
# DATA
x_data = build_toy_dataset(N, V)
# MODEL
x_ph = tf.placeholder(tf.float32, [N, V]) # inputs to Gaussian Process
# Form (N, V, V) covariance, one matrix per data point.
K = tf.stack([rbf(tf.reshape(xn, [V, 1])) + tf.diag([1e-6, 1e-6])
for xn in tf.unstack(x_ph)])
f = MultivariateNormalTriL(loc=tf.zeros([N, V]), scale_tril=tf.cholesky(K))
x = Poisson(rate=tf.exp(f))
# INFERENCE
qf = Normal(loc=tf.Variable(tf.random_normal([N, V])),
scale=tf.nn.softplus(tf.Variable(tf.random_normal([N, V]))))
inference = ed.KLqp({f: qf}, data={x: x_data, x_ph: x_data})
inference.run(n_iter=5000)
num_classes=5,
num_per_class=30,
rate=0.4)
N = data.shape[0]
D = 2 # number of features
K = 2 # number of latent dimensions
H1 = 2
H2 = 2
# Model: deep/shallow GP (generative model)
X = Normal(loc=tf.zeros([N, K]), scale=tf.ones([N, K]))
Kernal = rbf(X) + tf.eye(N) * 1e-6
cholesky = tf.tile(tf.reshape(tf.cholesky(Kernal), [1, N, N]), [H1, 1, 1])
h1 = MultivariateNormalTriL(loc=tf.zeros([H1, N]), scale_tril=cholesky)
Kernal1 = rbf(tf.transpose(h1)) + tf.eye(N) * 1e-6
cholesky1 = tf.tile(tf.reshape(tf.cholesky(Kernal1), [1, N, N]), [H2, 1, 1])
h2 = MultivariateNormalTriL(loc=tf.zeros([H2, N]), scale_tril=cholesky1)
Kernal2 = rbf(tf.transpose(h2)) + tf.eye(N) * 1e-6
cholesky2 = tf.tile(tf.reshape(tf.cholesky(Kernal2), [1, N, N]), [D, 1, 1])
Y = MultivariateNormalTriL(loc=tf.zeros([D, N]), scale_tril=cholesky2)
# Inference (recongnition model)
qX = Normal(loc=tf.Variable(tf.random_normal([N, K])),
scale=tf.nn.softplus(tf.Variable(tf.random_normal([N, K]))))
inference = ed.KLqp({X: qX}, data={Y: data.transpose()})
inference.run(n_iter=1000)
xn_data = np.random.multivariate_normal(mu, sigma, N)
plt.scatter(xn_data[:, 0], xn_data[:, 1], cmap=cm.gist_rainbow, s=5)
plt.show()
print('mu={}'.format(mu))
print('sigma={}'.format(sigma))
# Prior definition
v_prior = tf.constant(3., dtype=tf.float64)
W_prior = tf.constant(generate_random_positive_matrix(D), dtype=tf.float64)
m_prior = tf.constant(np.array([0.5, 0.5]), dtype=tf.float64)
k_prior = tf.constant(0.6, dtype=tf.float64)
# Posterior inference
# Probabilistic model
sigma = WishartCholesky(df=v_prior, scale=W_prior)
mu = MultivariateNormalTriL(m_prior, k_prior * sigma)
xn = MultivariateNormalTriL(tf.reshape(tf.tile(mu, [N]), [N, D]),
tf.reshape(tf.tile(sigma, [N, 1]), [N, 2, 2]))
# Variational model
# Variational model
qmu = MultivariateNormalTriL(
tf.Variable(tf.random_normal([D], dtype=tf.float64)),
tf.nn.softplus(tf.Variable(tf.random_normal([D, D], dtype=tf.float64))))
L = tf.Variable(tf.random_normal([D, D], dtype=tf.float64))
qsigma = WishartCholesky(
tf.nn.softplus(
tf.Variable(tf.random_normal([], dtype=tf.float64)) + D + 1),
LinearOperatorTriL(L).to_dense())
# Inference
from edward.models import Bernoulli, MultivariateNormalTriL, Normal
from edward.util import rbf
ys = df['index'].values
xs = df[['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']].values
N = xs.shape[0]
D = xs.shape[1]
print("Number of data points: {}".format(N))
print("Number of features: {}".format(D))
# In[4]:
X = tf.placeholder(tf.float32, [N, D])
f = MultivariateNormalTriL(loc=tf.zeros(N), scale_tril=tf.cholesky(rbf(X)))
y = Bernoulli(logits=f)
# In[ ]:
qf = Normal(loc=tf.get_variable("qf/loc", [N]),
scale=tf.nn.softplus(tf.get_variable("qf/scale", [N])))
# In[ ]:
inference = ed.KLqp({f: qf}, data={X: xs, y: ys})
inference.run(n_iter=5000)
from edward.models import Normal, Exponential
import tensorflow as tf
# 都是RandomVariable衍生出来
# 一元分布
Normal(loc=tf.constant(0.0), scale=tf.constant(1.0))
Normal(loc=tf.zeros(5), scale=tf.ones(5))
Exponential(rate=tf.ones([2, 3]))
# 多元分布
from edward.models import Dirichlet, MultivariateNormalTriL
K = 3
Dirichlet(concentration=tf.constant([0.1] * K)) # K为Dirichlet分布
MultivariateNormalTriL(loc=tf.zeros([5, K]),
scale_tril=tf.ones([5, K, K])) # loc的最后一位表示维数
MultivariateNormalTriL(loc=tf.zeros([2, 5, K]),
scale_tril=tf.ones([2, 5, K, K]))
# 每个RandomVariable有方法log_prob()，mean()，sample()，且与计算图上的一个张量对应
# 可以支持诸多运算
from edward.models import Normal
x = Normal(loc=tf.zeros(10), scale=tf.ones(10))
y = tf.constant(5.0)
x + y, x - y, x * y, x / y
tf.tanh(x * y)
tf.gather(x, 2)
print(x[2])
# 有向图模型
from edward.models import Bernoulli, Beta