def _gauss_log_pi(self, mu, log_sig):
sigma = tf.exp(log_sig)
normal = Normal(mu, sigma)
z = normal.sample()
actions = self._squash_actions(z)
gauss_log_prob = normal.log_prob(z)
log_pi = gauss_log_prob - self._squash_correction(z)
return log_pi[:, None], actions
def gen_one_step(self, z, u):
p_mean, p_var = self.p_transition(z, u)
p = MultivariateNormalDiag(p_mean, tf.sqrt(p_var))
z_step = p.sample()
return z_step
def one_step(self, a, x):
z = a[0]
u, enc = x
q_mean, q_var = self.q_transition(z, enc, u)
p_mean, p_var = self.p_transition(z, u)
q = MultivariateNormalDiag(q_mean, tf.sqrt(q_var))
p = MultivariateNormalDiag(p_mean, tf.sqrt(p_var))
z_step = q.sample()
kl = kl_divergence(q, p)
return z_step, kl
class MMDEvaluator:
def __init__(self,
z_dim,
repeats_count: int = 3,
samples_limit: int = 2000):
self.__z_dim = z_dim
self.__repeats_count = repeats_count
self.__samples_limit = samples_limit
def build(self):
self.__tensor_z_encoded = tf.placeholder(shape=np.append([None],
self.__z_dim),
dtype=tf.float32)
self.__distr = MultivariateNormalDiag(loc=tf.zeros(self.__z_dim),
scale_diag=tf.ones(self.__z_dim))
self.__tensor_z_sampled = self.__distr.sample(
tf.shape(self.__tensor_z_encoded)[0])
self.__tensor_mmd_penalty = mmd_penalty(self.__tensor_z_encoded,
self.__tensor_z_sampled)
def __compute_wae_distance(self, session, latent):
mmd_penalty_sum = 0
feed_dict = {
self.__tensor_z_encoded: latent,
}
for _ in range(self.__repeats_count):
mmd_penalty_sum += session.run(self.__tensor_mmd_penalty,
feed_dict)
avg_mmd_penalty = mmd_penalty_sum / self.__repeats_count
return avg_mmd_penalty
def evaluate(self, session, z):
print('Computing MMD')
if z.shape[0] > self.__samples_limit:
index = np.random.choice(z.shape[0],
self.__samples_limit,
replace=False)
wae_distance = self.__compute_wae_distance(session, z[index])
else:
wae_distance = self.__compute_wae_distance(session, z)
return [('wae_distance', wae_distance)]
def gmm_log_pi(self, log_weights, mu, log_std):
sigma = tf.exp(log_std)
normal = Normal(mu, sigma)
# sample from GMM
sample_w = tf.stop_gradient(
tf.multinomial(logits=log_weights, num_samples=1))
sample_z = tf.stop_gradient(normal.sample())
mask = tf.one_hot(sample_w[:, 0], depth=self._actor.K)
z = tf.reduce_sum(sample_z * mask[:, :, None], axis=1)
action = self.squash_action(z)
# calculate log policy
gauss_log_pi = normal.log_prob(z[:, None, :])
log_pi = tf.reduce_logsumexp(gauss_log_pi + log_weights, axis=-1)
log_pi -= tf.reduce_logsumexp(log_weights, axis=-1)
log_pi -= self.get_squash_correction(z)
log_pi *= self._temp
return log_pi[:, None], action
class Network(object):
def __init__(self, state_dim, act_dim):
self.input = tfl.input_data([None, state_dim])
self.variables_v = tf.trainable_variables()
net = self.input
for h in [64, 64]:
net = tfl.fully_connected(net, h, activation='tanh')
net = tfl.fully_connected(net, 1, activation='linear')
self.vpred = tf.squeeze(net, axis=[1])
self.variables_v = tf.trainable_variables()[len(self.variables_v):]
self.variables_p = tf.trainable_variables()
net = self.input
for h in [64, 64]:
net = tfl.fully_connected(net, h, activation='tanh')
mean = tfl.fully_connected(net, act_dim, activation='linear')
logstd = tf.Variable(
initial_value=np.zeros(act_dim).astype(np.float32))
self.variables_p = tf.trainable_variables()[len(self.variables_p):]
self.mvn = MultivariateNormalDiag(mean, tf.exp(logstd))
self.sample = self.mvn.sample()
def one_step_IAF(self, a, x):
z = a[0]
#log_q = a[1]
u, enc = x
input_h = tf.concat([z, enc, u], 1) #input should have enc(x), u and previous z
h = self.q_henc(input_h) #h encoding for iaf
q_mean, q_var = self.q_transition(z, enc, u)
p_mean, p_var = self.p_transition(z, u)
q = MultivariateNormalDiag(q_mean, tf.sqrt(q_var))
p = MultivariateNormalDiag(p_mean, tf.sqrt(p_var))
z_step = q.sample()
log_q = q.log_prob(z_step) #before performing the iaf step
z_step_iaf, q_var = self.q_transition_IAF(z_step, h)
log_q = log_q - tf.reduce_sum(tf.log(q_var + 1e-5), axis=1) #after performing the iaf step
log_p = p.log_prob(z_step_iaf) #TODO: check if this is correct? Should we be getting the probability of z_step or z_step_iaf?
return z_step_iaf, log_q, log_p
class Layer(object):
def __init__(self,
layer_index,
kern,
output_dim,
n_inducing,
X,
n_sample=100,
fixed_mean=True):
eps_dim = int(n_inducing * output_dim)
self.layer_index = layer_index
self.kernel = kern
self.input_dim = kern.input_dim
self.output_dim = output_dim
self.eps_dim = eps_dim
self.n_sample = n_sample
self.n_inducing = n_inducing
self.fixed_mean = fixed_mean # bool, Defatl = True for all layers before the last layer.
print("========= Layer {} summary =========".format(layer_index))
print("::::: LAYOUT")
print("----- [Input dimension] : ", self.input_dim)
print("----- [Output dimension] : ", self.output_dim)
"""
The prior distribution is set to be i.i.d Gaussian distributions.
"""
"""================== Initialization of the inducing point =================="""
with tf.variable_scope('theta'): # scope [theta]
self.Z = tf.Variable(kmeans2(X, self.n_inducing,
minit='points')[0],
dtype=tf.float64,
name='Z')
"""================== Initialization of the GAN and noise sampler =================="""
self.gan = GAN(self.n_inducing, self.output_dim, self.input_dim,
self.layer_index)
_prior_mean = 0.0
_prior_var = 1.0
self.prior_mean = [_prior_mean] * int(n_inducing * output_dim)
self.prior_var = [_prior_var] * int(n_inducing * output_dim)
self.mu, self.scale = [0.] * eps_dim, [1.0] * eps_dim
# In the paper we use a single global eps while in this implementation we disentangle them.
self.eps_sampler = MultiNormal(self.mu, self.scale)
print("----- [Prior mean] : ", _prior_mean)
print("----- [Prior var] : ", _prior_var)
"""================== Initialization of the skip layer connection =================="""
if self.input_dim == self.output_dim:
self.W_skiplayer = np.eye(self.input_dim)
elif self.input_dim < self.output_dim:
self.W_skiplayer = np.concatenate([
np.eye(self.input_dim),
np.zeros((self.input_dim, self.output_dim - self.input_dim))
],
axis=1)
else:
_, _, V = np.linalg.svd(X, full_matrices=False)
self.W_skiplayer = V[:self.output_dim, :].T
""" return the mean & cov in X given inducing points&values"""
def gan_base_conditional(self,
Kmn,
Kmm,
Knn,
f,
full_cov=False,
q_sqrt=None,
white=False):
if full_cov != False:
print("ERROR! full_cov NOT IMPLEMENTED!")
num_func = f.shape[2] # R
Lm = tf.cholesky(Kmm)
# Compute the projection matrix A
A = tf.matrix_triangular_solve(Lm, Kmn, lower=True)
# Compute the covariance due to the conditioning
fvar = Knn - tf.reduce_sum(tf.square(A), 0)
fvar = tf.tile(fvar[None, :], [num_func, 1]) # R x N
# Another backsubstitution in the unwhitened case
if not white:
A = tf.matrix_triangular_solve(tf.transpose(Lm), A, lower=False)
fmean = tf.einsum("zx,nzo->nxo", A, f)
if q_sqrt is not None:
if q_sqrt.get_shape().ndims == 2:
LTA = A * tf.expand_dims(tf.transpose(q_sqrt), 2) # R x M x N
elif q_sqrt.get_shape().ndims == 3:
L = q_sqrt
A_tiled = tf.tile(tf.expand_dims(A, 0),
tf.stack([num_func, 1, 1]))
LTA = tf.matmul(L, A_tiled, transpose_a=True) # R x M x N
else: # pragma: no cover
raise ValueError("Bad dimension for q_sqrt: %s" %
str(q_sqrt.get_shape().ndims))
fvar = fvar + tf.reduce_sum(tf.square(LTA), 1) # R x N
fvar = tf.transpose(fvar)
return fmean, fvar # n_sample x N x R, N x R
def gan_conditional(self, X):
"""
Given f, representing the GP at the points X, produce the mean and
(co-)variance of the GP at the points Xnew.
Additionally, there may be Gaussian uncertainty about f as represented by
q_sqrt. In this case `f` represents the mean of the distribution and
q_sqrt the square-root of the covariance.
:: [params] :: white
Additionally, the GP may have been centered (whitened) so that
p(v) = N(0, I)
f = L v
thus
p(f) = N(0, LL^T) = N(0, K).
In this case `f` represents the values taken by v.
The method can either return the diagonals of the covariance matrix for
each output (default) or the full covariance matrix (full_cov=True).
Let R = output_dim, N = N_x, M = n_inducing;
We assume R independent GPs, represented by the columns of f (and the
first dimension of q_sqrt).
:param Xnew: data matrix, size N x D. Evaluate the GP at these new points
:param X: data points, size M x D.
:param kern: GPflow kernel.
:param f: data matrix, M x R, representing the function values at X,
for K functions.
:param q_sqrt: matrix of standard-deviations or Cholesky matrices,
size M x R or R x M x M.
:param white: boolean of whether to use the whitened representation as
described above.
:return:
- mean: N x R
- variance: N x R (full_cov = False), R x N x N (full_cov = True)
"""
self.eps = tf.reshape(
self.eps_sampler.sample(self.n_sample), # n_sample * self.eps_dim
[self.n_sample, self.n_inducing, self.output_dim])
self.Z_repeat = tf.cast(
tf.tile(tf.reshape(self.Z, [1, self.n_inducing, self.input_dim]),
[self.n_sample, 1, 1]), tf.float32)
self.eps_with_z = tf.concat([self.eps, self.Z_repeat], axis=2)
self.post = tf.cast(self.gan.generator(self.eps_with_z),
tf.float64) # n_sample * n_inducing * output_dim
Kxz = self.kernel.K(X, self.Z)
Kzx = self.kernel.K(self.Z, X)
Kzz = self.kernel.K(
self.Z) + tf.eye(self.n_inducing, dtype=tf.float64) * 1e-7
self.Kzz = Kzz
self.determinant = tf.matrix_determinant(Kzz)
Kxx = self.kernel.Kdiag(X) # Just the diagonal part.
mu, _var1 = self.gan_base_conditional(Kzx,
Kzz,
Kxx,
self.post,
full_cov=False,
q_sqrt=None,
white=True)
mean = tf.reduce_mean(mu, axis=0) # n_X * output_dim
_var2 = tf.einsum("nxi,nxi->xi", mu, mu) / self.n_sample
_var3 = -tf.einsum("xi,xi->xi", mean, mean)
var = _var1 + _var2 + _var3 # Use momentum matching for mixtures of Gaussians to estimate posterior variance.
return mean, var
def prior_sampler(self, prior_batch_size):
self.prob_prior = MultiNormal(self.prior_mean, self.prior_var)
samples = tf.reshape(
self.prob_prior.sample(prior_batch_size),
[prior_batch_size, self.n_inducing, self.output_dim])
return samples
def network(self, inputs, pi_raw_action, q_action, phase, num_samples):
# TODO: Remove alpha (not using multimodal)
# shared net
shared_net = tf.contrib.layers.fully_connected(
inputs,
self.shared_layer_dim,
activation_fn=None,
weights_initializer=tf.contrib.layers.variance_scaling_initializer(
factor=1.0, mode="FAN_IN", uniform=True),
weights_regularizer=tf.contrib.layers.l2_regularizer(0.01),
biases_initializer=tf.contrib.layers.variance_scaling_initializer(
factor=1.0, mode="FAN_IN", uniform=True))
shared_net = self.apply_norm(shared_net,
activation_fn=tf.nn.relu,
phase=phase,
layer_num=1)
# action branch
pi_net = tf.contrib.layers.fully_connected(
shared_net,
self.actor_layer_dim,
activation_fn=None,
weights_initializer=tf.contrib.layers.variance_scaling_initializer(
factor=1.0, mode="FAN_IN", uniform=True),
weights_regularizer=None,
biases_initializer=tf.contrib.layers.variance_scaling_initializer(
factor=1.0, mode="FAN_IN", uniform=True))
pi_net = self.apply_norm(pi_net,
activation_fn=tf.nn.relu,
phase=phase,
layer_num=2)
# no activation
pi_mu = tf.contrib.layers.fully_connected(
pi_net,
self.num_modal * self.action_dim,
activation_fn=None,
weights_initializer=tf.contrib.layers.variance_scaling_initializer(
factor=1.0, mode="FAN_IN", uniform=True),
# weights_initializer=tf.random_uniform_initializer(-3e-3, 3e-3),
weights_regularizer=None,
# tf.contrib.layers.l2_regularizer(0.001),
biases_initializer=tf.contrib.layers.variance_scaling_initializer(
factor=1.0, mode="FAN_IN", uniform=True))
# biases_initializer=tf.random_uniform_initializer(-3e-3, 3e-3))
pi_logstd = tf.contrib.layers.fully_connected(
pi_net,
self.num_modal * self.action_dim,
activation_fn=tf.tanh,
weights_initializer=tf.random_uniform_initializer(0, 1),
weights_regularizer=None,
# tf.contrib.layers.l2_regularizer(0.001),
biases_initializer=tf.random_uniform_initializer(-3e-3, 3e-3))
pi_alpha = tf.contrib.layers.fully_connected(
pi_net,
self.num_modal,
activation_fn=tf.tanh,
weights_initializer=tf.random_uniform_initializer(-3e-3, 3e-3),
weights_regularizer=None,
# tf.contrib.layers.l2_regularizer(0.001),
biases_initializer=tf.random_uniform_initializer(-3e-3, 3e-3))
# reshape output
assert (self.num_modal == 1)
# pi_mu = tf.reshape(pi_mu, [-1, self.num_modal, self.action_dim])
# pi_logstd = tf.reshape(pi_logstd, [-1, self.num_modal, self.action_dim])
# pi_alpha = tf.reshape(pi_alpha, [-1, self.num_modal, 1])
pi_mu = tf.reshape(pi_mu, [-1, self.action_dim])
pi_logstd = tf.reshape(pi_logstd, [-1, self.action_dim])
pi_alpha = tf.reshape(pi_alpha, [-1, 1])
# exponentiate logstd
# pi_std = tf.exp(tf.scalar_mul(self.sigma_scale, pi_logstd))
pi_std = tf.exp(self.LOG_STD_MIN + 0.5 *
(self.LOG_STD_MAX - self.LOG_STD_MIN) *
(pi_logstd + 1))
# construct MultivariateNormalDiag dist.
mvn = MultivariateNormalDiag(loc=pi_mu, scale_diag=pi_std)
if self.actor_update == "reparam":
# pi = mu + tf.random_normal(tf.shape(mu)) * std
# logp_pi = self.gaussian_likelihood(pi, mu, log_std)
# pi_mu: (batch_size, action_dim)
# (batch_size x num_samples, action_dim)
# If updating multiple samples
stacked_pi_mu = tf.expand_dims(pi_mu, 1)
stacked_pi_mu = tf.tile(stacked_pi_mu, [1, num_samples, 1])
stacked_pi_mu = tf.reshape(
stacked_pi_mu,
(-1,
self.action_dim)) # (batch_size * num_samples, action_dim)
stacked_pi_std = tf.expand_dims(pi_std, 1)
stacked_pi_std = tf.tile(stacked_pi_std, [1, num_samples, 1])
stacked_pi_std = tf.reshape(
stacked_pi_std,
(-1,
self.action_dim)) # (batch_size * num_samples, action_dim)
noise = tf.random_normal(tf.shape(stacked_pi_mu))
# (batch_size * num_samples, action_dim)
pi_raw_samples = stacked_pi_mu + noise * stacked_pi_std
pi_raw_samples_logprob = self.gaussian_loglikelihood(
pi_raw_samples, stacked_pi_mu, stacked_pi_std)
pi_raw_samples = tf.reshape(pi_raw_samples,
(-1, num_samples, self.action_dim))
pi_raw_samples_logprob = tf.reshape(
pi_raw_samples_logprob, (-1, num_samples, self.action_dim))
else:
pi_raw_samples_og = mvn.sample(num_samples)
# dim: (batch_size, num_samples, action_dim)
pi_raw_samples = tf.transpose(pi_raw_samples_og, [1, 0, 2])
# get raw logprob
pi_raw_samples_logprob_og = mvn.log_prob(pi_raw_samples_og)
pi_raw_samples_logprob = tf.transpose(pi_raw_samples_logprob_og,
[1, 0, 2])
# apply tanh
pi_mu = tf.tanh(pi_mu)
pi_samples = tf.tanh(pi_raw_samples)
pi_samples_logprob = pi_raw_samples_logprob - tf.reduce_sum(tf.log(
self.clip_but_pass_gradient(1 - pi_samples**2, l=0, u=1) + 1e-6),
axis=-1)
pi_mu = tf.multiply(pi_mu, self.action_max)
pi_samples = tf.multiply(pi_samples, self.action_max)
# compute logprob for input action
pi_raw_actions_logprob = mvn.log_prob(pi_raw_action)
pi_action = tf.tanh(pi_raw_action)
pi_actions_logprob = pi_raw_actions_logprob - tf.reduce_sum(tf.log(
self.clip_but_pass_gradient(1 - pi_action**2, l=0, u=1) + 1e-6),
axis=-1)
# TODO: Remove alpha
# compute softmax prob. of alpha
max_alpha = tf.reduce_max(pi_alpha, axis=1, keepdims=True)
pi_alpha = tf.subtract(pi_alpha, max_alpha)
pi_alpha = tf.exp(pi_alpha)
normalize_alpha = tf.reciprocal(
tf.reduce_sum(pi_alpha, axis=1, keepdims=True))
pi_alpha = tf.multiply(normalize_alpha, pi_alpha)
# Q branch
with tf.variable_scope('qf'):
q_actions_prediction = self.q_network(shared_net, q_action, phase)
with tf.variable_scope('qf', reuse=True):
# if len(tf.shape(pi_samples)) == 3:
pi_samples_reshaped = tf.reshape(
pi_samples, (self.batch_size * num_samples, self.action_dim))
# else:
# assert(len(tf.shape(pi_samples)) == 2)
# pi_samples_reshaped = pi_samples
q_samples_prediction = self.q_network(shared_net,
pi_samples_reshaped, phase)
# print(pi_raw_action, pi_action)
# print(pi_raw_actions_logprob, pi_raw_actions_logprob)
# print(pi_action, pi_actions_logprob)
return pi_alpha, pi_mu, pi_std, pi_raw_samples, pi_samples, pi_samples_logprob, pi_actions_logprob, q_samples_prediction, q_actions_prediction
class Network:
def inference_value(self, observation_space):
"""
Creates a neural-network value function approximator
Args:
observation_space: observation space of the environment
Returns:
Nothing, the network is usable only after calling this method
"""
self.variables = tf.trainable_variables()
self.input_pl = tf.placeholder(tf.float32, [None, observation_space],
name='Input_PL')
#2 hidden layer with 100 neurons each
net = tf.layers.dense(
self.input_pl,
100,
activation=tf.nn.tanh,
kernel_initializer=tf.random_normal_initializer(stddev=.1))
net = tf.layers.dense(
net,
100,
activation=tf.nn.tanh,
kernel_initializer=tf.random_normal_initializer(stddev=.1))
net = tf.layers.dense(
net,
1,
kernel_initializer=tf.random_normal_initializer(stddev=.01))
self.predict = tf.squeeze(net, axis=[1])
self.variables = tf.trainable_variables()[len(self.variables):]
def inference_policy(self, observation_space, action_space):
"""
Creates a neural-network policy approximator
Args:
observation_space: observation space of the environment
action_space: action space of the environment
Returns:
Nothing, the network is usable only after calling this method
"""
self.variables = tf.trainable_variables()
self.input_pl = tf.placeholder(tf.float32, [None, observation_space],
name='Input_PL')
#2 hidden layers with 100 neurons each
net = tf.layers.dense(
self.input_pl,
100,
activation=tf.nn.tanh,
kernel_initializer=tf.random_normal_initializer(stddev=.1))
net = tf.layers.dense(
net,
100,
activation=tf.nn.tanh,
kernel_initializer=tf.random_normal_initializer(stddev=.1))
mean = tf.layers.dense(
net,
action_space,
kernel_initializer=tf.random_normal_initializer(stddev=.01))
self.std = tf.Variable(np.ones(action_space).astype(np.float32))
self.mvn = MultivariateNormalDiag(mean, self.std)
self.sample = self.mvn.sample()
self.variables = tf.trainable_variables()[len(self.variables):]
def copy_to(self, target_network):
"""
Operations to copy from self to target
Args:
target_network: network to be copied into
Returns:
copy_ops: tf-operations (have to be run inside a tf.Session)
"""
v1 = self.variables
v2 = target_network.variables
copy_ops = [v2[i].assign(v1[i]) for i in range(len(v1))]
return copy_ops
class Layer(object):
""" has skip layer connection;
define self.U to be the non-trainable variables (self.M, self.outputs)"""
def __init__(self, layer_index, kern, output_dim, n_inducing, X,
fixed_mean=True,n_sample=100, eps_dim=32):
print("=== Layer {} summary ===".format(layer_index))
print("--- Input dimension: ",kern.input_dim)
print("--- Output dimension: ",output_dim)
eps_dim=int(n_inducing*output_dim)
self.layer_index = layer_index
self.kernel = kern
self.input_dim, self.output_dim, self.eps_dim = kern.input_dim, output_dim, eps_dim
self.n_sample = n_sample
self.n_inducing = n_inducing
self.fixed_mean = fixed_mean # bool
self.prior_mean = [0.0] * int(n_inducing*output_dim)
self.prior_var = [1.0] * int(n_inducing*output_dim)
self.mu, self.scale = [0.] * eps_dim, [1.0] * eps_dim
self.eps_sampler = MultiNormal(self.mu, self.scale)
###################################################################################
with tf.variable_scope('theta'):
self.Z = tf.Variable(kmeans2(X, self.n_inducing, minit='points')[0], dtype=tf.float64, name='Z')
###################################################################################
self.gan = GAN(self.n_inducing, self.output_dim, self.layer_index, self.input_dim)
###################################################################################
if self.input_dim == self.output_dim:
self.W_skiplayer = np.eye(self.input_dim)
elif self.input_dim < self.output_dim:
self.W_skiplayer = np.concatenate([np.eye(self.input_dim),
np.zeros((self.input_dim, self.output_dim - self.input_dim))], axis=1)
else:
_, _, V = np.linalg.svd(X, full_matrices=False)
self.W_skiplayer = V[:self.output_dim, :].T
###################################################################################
""" 1. trainable=False because this is the prior, and it is not a variable to be learn from SGD;
2. exist because ??? """
self.U = tf.Variable(np.zeros((self.n_inducing, self.output_dim)), dtype=tf.float64, trainable=False, name='U')
""" return the mean & cov in X given inducing points&values"""
def gan_base_conditional(self, Kmn, Kmm, Knn, f,
full_cov=False, q_sqrt=None, white=False):
if full_cov!=False:
print("BUG! full_cov NOT IMPLEMENTED!")
# compute kernel stuff
num_func = f.shape[2] # R
Lm = tf.cholesky(Kmm)
# Compute the projection matrix A
A = tf.matrix_triangular_solve(Lm, Kmn, lower=True)
# compute the covariance due to the conditioning
fvar = Knn - tf.reduce_sum(tf.square(A), 0)
fvar = tf.tile(fvar[None, :], [num_func, 1]) # R x N
# another backsubstitution in the unwhitened case
if not white:
A = tf.matrix_triangular_solve(tf.transpose(Lm), A, lower=False)
fmean = tf.einsum("zx,nzo->nxo",A,f)
if q_sqrt is not None:
if q_sqrt.get_shape().ndims == 2:
LTA = A * tf.expand_dims(tf.transpose(q_sqrt), 2) # R x M x N
elif q_sqrt.get_shape().ndims == 3:
L = q_sqrt
A_tiled = tf.tile(tf.expand_dims(A, 0), tf.stack([num_func, 1, 1]))
LTA = tf.matmul(L, A_tiled, transpose_a=True) # R x M x N
else: # pragma: no cover
raise ValueError("Bad dimension for q_sqrt: %s" %
str(q_sqrt.get_shape().ndims))
fvar = fvar + tf.reduce_sum(tf.square(LTA), 1) # R x N
fvar = tf.transpose(fvar) # N x R
return fmean, fvar # n_sample x N x R, N x R
"""# return the mean and cov in Xnew
# this discribe the distribution of p( f in Xnew | X, f )"""
def gan_conditional(self, X):
"""
Given f, representing the GP at the points X, produce the mean and
(co-)variance of the GP at the points Xnew.
Additionally, there may be Gaussian uncertainty about f as represented by
q_sqrt. In this case `f` represents the mean of the distribution and
q_sqrt the square-root of the covariance.
:: [params] :: white
Additionally, the GP may have been centered (whitened) so that
p(v) = N(0, I)
f = L v
thus
p(f) = N(0, LL^T) = N(0, K).
In this case `f` represents the values taken by v.
The method can either return the diagonals of the covariance matrix for
each output (default) or the full covariance matrix (full_cov=True).
We assume R independent GPs, represented by the columns of f (and the
first dimension of q_sqrt).
:param Xnew: data matrix, size N x D. Evaluate the GP at these new points
:param X: data points, size M x D.
:param kern: GPflow kernel.
:param f: data matrix, M x R, representing the function values at X,
for K functions.
:param q_sqrt: matrix of standard-deviations or Cholesky matrices,
size M x R or R x M x M.
:param white: boolean of whether to use the whitened representation as
described above.
:return:
- mean: N x R
- variance: N x R (full_cov = False), R x N x N (full_cov = True)
"""
self.eps = tf.reshape(self.eps_sampler.sample(self.n_sample), # n_sample * self.eps_dim
[self.n_sample, self.n_inducing, self.output_dim])
self.Z_repeat = tf.cast(tf.tile(tf.reshape(self.Z,
[1, self.n_inducing, self.input_dim]),
[self.n_sample, 1, 1]),
tf.float32)
self.eps_with_z = tf.concat([self.eps,self.Z_repeat], axis = 2)
self.post = tf.cast(self.gan.generator(self.eps_with_z,reuse = True), tf.float64) # self.n_sample * n_Z * self.output_dim
Kxz = self.kernel.K(X, self.Z) # n_X * n_Z
Kzx = self.kernel.K(self.Z, X)
Kzz = self.kernel.K(self.Z) + tf.eye(self.n_inducing, dtype=tf.float64) * 1e-7
self.Kzz = Kzz
self.determinant = tf.matrix_determinant(Kzz)
Kxx = self.kernel.Kdiag(X)
mu , _var1 = self.gan_base_conditional(Kzx, Kzz, Kxx, self.post, full_cov=False, q_sqrt=None, white=True)
mean = tf.reduce_mean(mu, axis=0) # n_X * self.output_dim
_var2 = tf.einsum("nxi,nyi->ixy",mu,mu)/self.n_sample
_var3 = - tf.einsum("xi,yi->ixy",mean,mean)
var = _var1 + tf.transpose( tf.linalg.diag_part(_var2) + tf.linalg.diag_part(_var3) )
return mean,var
""" log density of prior"""
def prior_sampler(self, prior_batch_size):
self.prob_prior = MultiNormal(self.prior_mean, self.prior_var)
samples = tf.reshape(self.prob_prior.sample(prior_batch_size), [prior_batch_size, self.n_inducing, self.output_dim])
return samples
def prior(self):
return -tf.reduce_sum(tf.square(self.U)) / 2.0 * 1.0
