def elbo_h_gaussian_x_bernoulli(d,
z,
mean_q,
log_var_q,
mean_prior,
log_var_prior,
p_out,
x,
mask,
settings,
temperature_KL=1.0,
test=False):
if not test:
mask_sum = T.sum(mask, axis=1)
# We some over output_dim and we take the mean over batch_size and sequence_length
log_p_x_given_h = log_bernoulli(
x=x, p=p_out,
eps=settings.tolerance_softmax) * mask.dimshuffle(
0, 1, 'x')
log_p_x_given_h = log_p_x_given_h.sum(axis=(1, 2)) / mask_sum
log_p_x_given_h_tot = log_p_x_given_h.mean()
kl_divergence = kl_normal2_normal2(mean_q, log_var_q,
mean_prior, log_var_prior)
# kl_divergence has size (batch_size, sequence_length, output_dim)
kl_divergence_tmp = kl_divergence * mask.dimshuffle(0, 1, 'x')
kl_divergence_tmp = kl_divergence_tmp.sum(axis=(1,
2)) / mask_sum
kl_divergence_tot = T.mean(kl_divergence_tmp)
lower_bound = log_p_x_given_h_tot - temperature_KL * kl_divergence_tot
return lower_bound
else:
mask_sum = T.sum(mask, axis=1)
log_p_x_given_h = log_bernoulli(
x=x, p=p_out,
eps=settings.tolerance_softmax) * mask.dimshuffle(
0, 1, 'x')
log_p_x_given_h_tot = log_p_x_given_h.sum(axis=(1,
2)) / mask_sum
kl_divergence = kl_normal2_normal2(mean_q, log_var_q,
mean_prior, log_var_prior)
# kl_divergence has size (batch_size, sequence_length, output_dim)
kl_divergence_seq = T.reshape(
kl_divergence,
(settings.batch_size, -1, settings.latent_size_z))
kl_divergence_seq = kl_divergence_seq * mask.dimshuffle(
0, 1, 'x')
kl_divergence_tot = kl_divergence_seq.sum(axis=(1,
2)) / mask_sum
lower_bound = log_p_x_given_h_tot - temperature_KL * kl_divergence_tot
return lower_bound
def log_likelihood(z, z_mu, z_log_var, x_mu, x, analytic_kl_term):
if analytic_kl_term:
kl_term = kl_normal2_stdnormal(z_mu, z_log_var).sum(axis = 1)
log_px_given_z = log_bernoulli(x, x_mu, eps = 1e-6).sum(axis = 1)
LL = T.mean(-kl_term + log_px_given_z)
else:
log_qz_given_x = log_normal2(z, z_mu, z_log_var).sum(axis = 1)
log_pz = log_stdnormal(z).sum(axis = 1)
log_px_given_z = log_bernoulli(x, x_mu, eps = 1e-6).sum(axis = 1)
LL = T.mean(log_pz + log_px_given_z - log_qz_given_x)
return LL
def latent_gaussian_x_bernoulli(z, z_mu, psi_u_list, z_log_var, x_mu, x, eq_samples, iw_samples, epsilon=1e-6):
"""
Latent z : gaussian with standard normal prior
decoder output : bernoulli
When the output is bernoulli then the output from the decoder
should be sigmoid. The sizes of the inputs are
z: (batch_size*Eq_samples*ivae_samples*nsamples, num_latent)
z_mu: (batch_size, num_latent)
z_log_var: (batch_size, num_latent)
x_mu: (batch_size*Eq_samples*ivae_samples*nsamples, num_latent)
x: (batch_size, num_features)
Reference: Burda et. al. 2015 "Importance Weighted Autoencoders"
"""
# reshape the variables so batch_size, eq_samples and iw_samples are separate dimensions
z = z.reshape((-1, eq_samples, iw_samples, latent_size))
x_mu = x_mu.reshape((-1, eq_samples, iw_samples, num_features))
# dimshuffle x since we need to broadcast it when calculationg the binary
# cross-entropy
x = x.dimshuffle(0,'x','x',1) # x: (batch_size, eq_samples, iw_samples, num_latent)
for i in range(len(psi_u_list)):
psi_u_list[i] = psi_u_list[i].reshape((-1, eq_samples, iw_samples))
#calculate LL components, note that we sum over the feature/num_unit dimension
z_mu = z_mu.dimshuffle(0,'x','x',1) # mean: (batch_size, num_latent)
z_log_var = z_log_var.dimshuffle(0,'x','x',1) # logvar: (batch_size, num_latent)
log_qz_given_x = log_normal2(z, z_mu, z_log_var).sum(axis=3)
log_pz = log_stdnormal(z).sum(axis=3)
log_px_given_z = log_bernoulli(x, T.clip(x_mu,epsilon,1-epsilon)).sum(axis=3)
#normalizing flow loss
sum_log_psiu = 0
for psi_u in psi_u_list:
sum_log_psiu += T.log(T.abs_(1+psi_u))
#all log_*** should have dimension (batch_size, eq_samples, iw_samples)
# Calculate the LL using log-sum-exp to avoid underflow
a = log_pz + log_px_given_z - log_qz_given_x + sum_log_psiu # size: (batch_size, eq_samples, iw_samples)
a_max = T.max(a, axis=2, keepdims=True) # size: (batch_size, eq_samples, 1)
# LL is calculated using Eq (8) in burda et al.
# Working from inside out of the calculation below:
# T.exp(a-a_max): (bathc_size, Eq_samples, iw_samples)
# -> subtract a_max to avoid overflow. a_max is specific for each set of
# importance samples and is broadcoasted over the last dimension.
#
# T.log( T.mean(T.exp(a-a_max), axis=2): (batch_size, Eq_samples)
# -> This is the log of the sum over the importance weighted samples
#
# Lastly we add T.mean(a_max) to correct for the log-sum-exp trick
LL = T.mean(a_max) + T.mean( T.log( T.mean(T.exp(a-a_max), axis=2)))
return LL, T.mean(log_qz_given_x), T.mean(log_pz), T.mean(log_px_given_z)
def latent_gaussian_x_bernoulli(z, z_mu, z_log_var, x, x_mu, analytic_kl_term):
"""
Latent z : gaussian with standard normal prior
decoder output : bernoulli
When the output is bernoulli then the output from the decoder
should be sigmoid.
"""
if analytic_kl_term:
kl_term = kl_normal2_stdnormal(z_mu, z_log_var).sum(axis=1)
log_px_given_z = log_bernoulli(x, x_mu).sum(axis=1)
LL = T.mean(-kl_term + log_px_given_z)
else:
log_qz_given_x = log_normal2(z, z_mu, z_log_var).sum(axis=1)
log_pz = log_stdnormal(z).sum(axis=1)
log_px_given_z = log_bernoulli(x, x_mu).sum(axis=1)
LL = T.mean(log_pz + log_px_given_z - log_qz_given_x)
return LL
def lower_bound(z, z_mu, x_mu, x, eq_samples, iw_samples, epsilon=1e-6):
from theano.gradient import disconnected_grad as dg
# reshape the variables so batch_size, eq_samples and iw_samples are
# separate dimensions
z = z.reshape((-1, eq_samples, iw_samples, latent_size))
x_mu = x_mu.reshape((-1, eq_samples, iw_samples, num_features))
# prepare x, z for broadcasting
# size: (batch_size, eq_samples, iw_samples, num_features)
x = x.dimshuffle(0, 'x', 'x', 1)
# size: (batch_size, eq_samples, iw_samples, num_latent)
z_mu = z_mu.dimshuffle(0, 'x', 'x', 1)
log_qz_given_x = log_bernoulli(z, z_mu, eps=epsilon).sum(axis=3)
z_prior = T.ones_like(z)*np.float32(0.5)
log_pz = log_bernoulli(z, z_prior).sum(axis=3)
log_px_given_z = log_bernoulli(x, x_mu, eps=epsilon).sum(axis=3)
# Calculate the LL using log-sum-exp to avoid underflow
log_pxz = log_pz + log_px_given_z
# L is (bs, mc) See definition of L in appendix eq. 14
L = log_sum_exp(log_pxz - log_qz_given_x, axis=2) + \
T.log(1.0/T.cast(iw_samples, 'float32'))
grads_model = T.grad(-L.mean(), p_params)
# L_corr should correspond to equation 10 in the paper
L_corr = L.dimshuffle(0, 1, 'x') - get_vimco_baseline(
log_pxz - log_qz_given_x)
g_lb_inference = T.mean(T.sum(dg(L_corr) * log_qz_given_x) + L)
grads_inference = T.grad(-g_lb_inference, q_params)
grads = grads_model + grads_inference
LL = log_mean_exp(log_pz + log_px_given_z - log_qz_given_x, axis=2)
return (LL,
T.mean(log_qz_given_x), T.mean(log_pz), T.mean(log_px_given_z),
grads)
def latent_gaussian_x_bernoulli(z, z_mu, z_log_var, x_mu, x, eq_samples, iw_samples, epsilon=1e-6):
"""
Latent z : gaussian with standard normal prior
decoder output : bernoulli
When the output is bernoulli then the output from the decoder
should be sigmoid. The sizes of the inputs are
z: (batch_size*eq_samples*iw_samples, num_latent)
z_mu: (batch_size, num_latent)
z_log_var: (batch_size, num_latent)
x_mu: (batch_size*eq_samples*iw_samples, num_features)
x: (batch_size, num_features)
Reference: Burda et al. 2015 "Importance Weighted Autoencoders"
"""
# reshape the variables so batch_size, eq_samples and iw_samples are separate dimensions
z = z.reshape((-1, eq_samples, iw_samples, latent_size))
x_mu = x_mu.reshape((-1, eq_samples, iw_samples, num_features))
# dimshuffle x, z_mu and z_log_var since we need to broadcast them when calculating the pdfs
x = x.dimshuffle(0, 'x', 'x', 1) # size: (batch_size, eq_samples, iw_samples, num_features)
z_mu = z_mu.dimshuffle(0, 'x', 'x', 1) # size: (batch_size, eq_samples, iw_samples, num_latent)
z_log_var = z_log_var.dimshuffle(0, 'x', 'x', 1) # size: (batch_size, eq_samples, iw_samples, num_latent)
# calculate LL components, note that the log_xyz() functions return log prob. for indepenedent components separately
# so we sum over feature/latent dimensions for multivariate pdfs
log_qz_given_x = log_normal2(z, z_mu, z_log_var).sum(axis=3)
log_pz = log_stdnormal(z).sum(axis=3)
log_px_given_z = log_bernoulli(x, x_mu, eps=epsilon).sum(axis=3)
#all log_*** should have dimension (batch_size, eq_samples, iw_samples)
# Calculate the LL using log-sum-exp to avoid underflow
a = log_pz + log_px_given_z - log_qz_given_x # size: (batch_size, eq_samples, iw_samples)
a_max = T.max(a, axis=2, keepdims=True) # size: (batch_size, eq_samples, 1)
# LL is calculated using Eq (8) in Burda et al.
# Working from inside out of the calculation below:
# T.exp(a-a_max): (batch_size, eq_samples, iw_samples)
# -> subtract a_max to avoid overflow. a_max is specific for each set of
# importance samples and is broadcasted over the last dimension.
#
# T.log( T.mean(T.exp(a-a_max), axis=2) ): (batch_size, eq_samples)
# -> This is the log of the sum over the importance weighted samples
#
# The outer T.mean() computes the mean over eq_samples and batch_size
#
# Lastly we add T.mean(a_max) to correct for the log-sum-exp trick
LL = T.mean(a_max) + T.mean( T.log( T.mean(T.exp(a-a_max), axis=2) ) )
return LL, T.mean(log_qz_given_x), T.mean(log_pz), T.mean(log_px_given_z)
def latent_gaussian_x_bernoulli(z, z_mu, z_log_var, x_mu, x, eq_samples, iw_samples, epsilon=1e-6):
"""
Latent z : gaussian with standard normal prior
decoder output : bernoulli
When the output is bernoulli then the output from the decoder
should be sigmoid. The sizes of the inputs are
z: (batch_size*eq_samples*iw_samples, num_latent)
z_mu: (batch_size, num_latent)
z_log_var: (batch_size, num_latent)
x_mu: (batch_size*eq_samples*iw_samples, num_features)
x: (batch_size, num_features)
Reference: Burda et al. 2015 "Importance Weighted Autoencoders"
"""
# reshape the variables so batch_size, eq_samples and iw_samples are separate dimensions
z = z.reshape((-1, eq_samples, iw_samples, latent_size))
x_mu = x_mu.reshape((-1, eq_samples, iw_samples, num_features))
# dimshuffle x, z_mu and z_log_var since we need to broadcast them when calculating the pdfs
x = x.dimshuffle(0, 'x', 'x', 1) # size: (batch_size, eq_samples, iw_samples, num_features)
z_mu = z_mu.dimshuffle(0, 'x', 'x', 1) # size: (batch_size, eq_samples, iw_samples, num_latent)
z_log_var = z_log_var.dimshuffle(0, 'x', 'x', 1) # size: (batch_size, eq_samples, iw_samples, num_latent)
# calculate LL components, note that the log_xyz() functions return log prob. for indepenedent components separately
# so we sum over feature/latent dimensions for multivariate pdfs
log_qz_given_x = log_normal2(z, z_mu, z_log_var).sum(axis=3)
log_pz = log_stdnormal(z).sum(axis=3)
log_px_given_z = log_bernoulli(x, T.clip(x_mu, epsilon, 1 - epsilon)).sum(axis=3)
#all log_*** should have dimension (batch_size, eq_samples, iw_samples)
# Calculate the LL using log-sum-exp to avoid underflow
a = log_pz + log_px_given_z - log_qz_given_x # size: (batch_size, eq_samples, iw_samples)
a_max = T.max(a, axis=2, keepdims=True) # size: (batch_size, eq_samples, 1)
# LL is calculated using Eq (8) in Burda et al.
# Working from inside out of the calculation below:
# T.exp(a-a_max): (batch_size, eq_samples, iw_samples)
# -> subtract a_max to avoid overflow. a_max is specific for each set of
# importance samples and is broadcasted over the last dimension.
#
# T.log( T.mean(T.exp(a-a_max), axis=2) ): (batch_size, eq_samples)
# -> This is the log of the sum over the importance weighted samples
#
# The outer T.mean() computes the mean over eq_samples and batch_size
#
# Lastly we add T.mean(a_max) to correct for the log-sum-exp trick
LL = T.mean(a_max) + T.mean( T.log( T.mean(T.exp(a-a_max), axis=2) ) )
return LL, T.mean(log_qz_given_x), T.mean(log_pz), T.mean(log_px_given_z)
def lower_bound(z, z_mu, x_mu, x, eq_samples, iw_samples, epsilon=1e-6):
from theano.gradient import disconnected_grad as dg
# reshape the variables so batch_size, eq_samples and iw_samples are
# separate dimensions
z = z.reshape((-1, eq_samples, iw_samples, latent_size))
x_mu = x_mu.reshape((-1, eq_samples, iw_samples, num_features))
# prepare x, z for broadcasting
# size: (batch_size, eq_samples, iw_samples, num_features)
x = x.dimshuffle(0, 'x', 'x', 1)
# size: (batch_size, eq_samples, iw_samples, num_latent)
z_mu = z_mu.dimshuffle(0, 'x', 'x', 1)
log_qz_given_x = log_bernoulli(z, z_mu, eps=epsilon).sum(axis=3)
z_prior = T.ones_like(z) * np.float32(0.5)
log_pz = log_bernoulli(z, z_prior).sum(axis=3)
log_px_given_z = log_bernoulli(x, x_mu, eps=epsilon).sum(axis=3)
# Calculate the LL using log-sum-exp to avoid underflow
log_pxz = log_pz + log_px_given_z
# L is (bs, mc) See definition of L in appendix eq. 14
L = log_sum_exp(log_pxz - log_qz_given_x, axis=2) + \
T.log(1.0/T.cast(iw_samples, 'float32'))
grads_model = T.grad(-L.mean(), p_params)
# L_corr should correspond to equation 10 in the paper
L_corr = L.dimshuffle(0, 1,
'x') - get_vimco_baseline(log_pxz - log_qz_given_x)
g_lb_inference = T.mean(T.sum(dg(L_corr) * log_qz_given_x) + L)
grads_inference = T.grad(-g_lb_inference, q_params)
grads = grads_model + grads_inference
LL = log_mean_exp(log_pz + log_px_given_z - log_qz_given_x, axis=2)
return (LL, T.mean(log_qz_given_x), T.mean(log_pz), T.mean(log_px_given_z),
grads)
def latent_gaussian_x_bernoulli(z, z_mu, z_log_var, x_mu, x, analytic_kl_term):
"""
Latent z : gaussian with standard normal prior
decoder output : bernoulli
When the output is bernoulli then the output from the decoder
should be sigmoid. The sizes of the inputs are
z: (batch_size, num_latent)
z_mu: (batch_size, num_latent)
z_log_var: (batch_size, num_latent)
x_mu: (batch_size, num_features)
x: (batch_size, num_features)
"""
if analytic_kl_term:
kl_term = kl_normal2_stdnormal(z_mu, z_log_var).sum(axis=1)
log_px_given_z = log_bernoulli(x, x_mu).sum(axis=1)
LL = T.mean(-kl_term + log_px_given_z)
else:
log_qz_given_x = log_normal2(z, z_mu, z_log_var).sum(axis=1)
log_pz = log_stdnormal(z).sum(axis=1)
log_px_given_z = log_bernoulli(x, x_mu).sum(axis=1)
LL = T.mean(log_pz + log_px_given_z - log_qz_given_x)
return LL
def latent_gaussian_x_bernoulli(z, z_mu, z_log_var, x_mu, x, analytic_kl_term):
"""
Latent z : gaussian with standard normal prior
decoder output : bernoulli
When the output is bernoulli then the output from the decoder
should be sigmoid. The sizes of the inputs are
z: (batch_size, num_latent)
z_mu: (batch_size, num_latent)
z_log_var: (batch_size, num_latent)
x_mu: (batch_size, num_features)
x: (batch_size, num_features)
"""
if analytic_kl_term:
kl_term = kl_normal2_stdnormal(z_mu, z_log_var).sum(axis=1)
log_px_given_z = log_bernoulli(x, x_mu, eps=1e-6).sum(axis=1)
LL = T.mean(-kl_term + log_px_given_z)
else:
log_qz_given_x = log_normal2(z, z_mu, z_log_var).sum(axis=1)
log_pz = log_stdnormal(z).sum(axis=1)
log_px_given_z = log_bernoulli(x, x_mu, eps=1e-6).sum(axis=1)
LL = T.mean(log_pz + log_px_given_z - log_qz_given_x)
return LL
def latent_gaussian_x_bernoulli(z0, zk, z0_mu, z0_log_var, logdet_J_list, x_mu, x, eq_samples, iw_samples, epsilon=1e-6):
"""
Latent z : gaussian with standard normal prior
decoder output : bernoulli
When the output is bernoulli then the output from the decoder
should be sigmoid. The sizes of the inputs are
z0: (batch_size*eq_samples*iw_samples, num_latent)
zk: (batch_size*eq_samples*iw_samples, num_latent)
z0_mu: (batch_size, num_latent)
z0_log_var: (batch_size, num_latent)
logdet_J_list: list of `nflows` elements, each with shape (batch_size*eq_samples*iw_samples)
x_mu: (batch_size*eq_samples*iw_samples, num_features)
x: (batch_size, num_features)
Reference: Burda et al. 2015 "Importance Weighted Autoencoders"
"""
# reshape the variables so batch_size, eq_samples and iw_samples are separate dimensions
z0 = z0.reshape((-1, eq_samples, iw_samples, latent_size))
zk = zk.reshape((-1, eq_samples, iw_samples, latent_size))
x_mu = x_mu.reshape((-1, eq_samples, iw_samples, num_features))
for i in range(len(logdet_J_list)):
logdet_J_list[i] = logdet_J_list[i].reshape((-1, eq_samples, iw_samples))
# dimshuffle x, z_mu and z_log_var since we need to broadcast them when calculating the pdfs
x = x.dimshuffle(0, 'x', 'x', 1) # size: (batch_size, eq_samples, iw_samples, num_features)
z0_mu = z0_mu.dimshuffle(0, 'x', 'x', 1) # size: (batch_size, eq_samples, iw_samples, num_latent)
z0_log_var = z0_log_var.dimshuffle(0, 'x', 'x', 1) # size: (batch_size, eq_samples, iw_samples, num_latent)
# calculate LL components, note that the log_xyz() functions return log prob. for indepenedent components separately
# so we sum over feature/latent dimensions for multivariate pdfs
log_q0z0_given_x = log_normal2(z0, z0_mu, z0_log_var).sum(axis=3)
log_pzk = log_stdnormal(zk).sum(axis=3)
log_px_given_zk = log_bernoulli(x, x_mu, epsilon).sum(axis=3)
#normalizing flow loss
sum_logdet_J = 0
for logdet_J_k in logdet_J_list:
sum_logdet_J += logdet_J_k
# Calculate the LL using log-sum-exp to avoid underflow all log_*** -> shape: (batch_size, eq_samples, iw_samples)
LL = log_mean_exp(log_pzk + log_px_given_zk - log_q0z0_given_x + sum_logdet_J, axis=2) # log-mean-exp over iw_samples dimension -> shape: (batch_size, eq_samples)
LL = T.mean(LL) # average over eq_samples, batch_size dimensions -> shape: ()
return LL, T.mean(log_q0z0_given_x), T.mean(sum_logdet_J), T.mean(log_pzk), T.mean(log_px_given_zk)
def ELBO(z, z_mu, z_log_var, x_mu, x):
"""
Latent z : gaussian with standard normal prior
decoder output : bernoulli
When the output is bernoulli then the output from the decoder
should be sigmoid. The sizes of the inputs are
z: (batch_size, num_latent)
z_mu: (batch_size, num_latent)
z_log_var: (batch_size, num_latent)
x_mu: (batch_size, num_features)
x: (batch_size, num_features)
"""
kl_term = kl_normal2_stdnormal(z_mu, z_log_var).sum(axis=1)
log_px_given_z = log_bernoulli(x, x_mu, eps=1e-6).sum(axis=1)
LL = T.mean(-kl_term + log_px_given_z)
return LL
def lowerbound_for_reinforce(z,
z_mu,
z_log_var,
x_mu,
x,
num_features,
num_labelled,
num_classes,
epsilon=1e-6):
x = x.reshape((-1, num_features))
x_mu = x_mu.reshape((-1, num_features))
log_qz_given_xy = log_normal2(z, z_mu, z_log_var).sum(axis=1)
log_pz = log_stdnormal(z).sum(axis=1)
log_py = T.log(1.0 / num_classes)
log_px_given_zy = log_bernoulli(x, T.clip(x_mu, epsilon,
1 - epsilon)).sum(axis=1)
ll_xy = log_px_given_zy + log_pz + log_py - log_qz_given_xy
return ll_xy[num_labelled:]
def latent_gaussian_x_bernoulli(z, z_mu, z_log_var, x_mu, x, eq_samples, iw_samples, epsilon=1e-6):
"""
Latent z : gaussian with standard normal prior
decoder output : bernoulli
When the output is bernoulli then the output from the decoder
should be sigmoid. The sizes of the inputs are
z: (batch_size*eq_samples*iw_samples, num_latent)
z_mu: (batch_size, num_latent)
z_log_var: (batch_size, num_latent)
x_mu: (batch_size*eq_samples*iw_samples, num_features)
x: (batch_size, num_features)
Reference: Burda et al. 2015 "Importance Weighted Autoencoders"
"""
# reshape the variables so batch_size, eq_samples and iw_samples are separate dimensions
z = z.reshape((-1, eq_samples, iw_samples, latent_size))
x_mu = x_mu.reshape((-1, eq_samples, iw_samples, num_features))
# dimshuffle x, z_mu and z_log_var since we need to broadcast them when calculating the pdfs
x = x.dimshuffle(0, 'x', 'x', 1) # size: (batch_size, eq_samples, iw_samples, num_features)
z_mu = z_mu.dimshuffle(0, 'x', 'x', 1) # size: (batch_size, eq_samples, iw_samples, num_latent)
z_log_var = z_log_var.dimshuffle(0, 'x', 'x', 1) # size: (batch_size, eq_samples, iw_samples, num_latent)
# calculate LL components, note that the log_xyz() functions return log prob. for indepenedent components separately
# so we sum over feature/latent dimensions for multivariate pdfs
log_qz_given_x = log_normal2(z, z_mu, z_log_var).sum(axis=3)
log_pz = log_stdnormal(z).sum(axis=3)
log_px_given_z = log_bernoulli(x, x_mu, epsilon).sum(axis=3)
# Calculate the LL using log-sum-exp to avoid underflow all log_*** -> shape: (batch_size, eq_samples, iw_samples)
LL = log_mean_exp(log_pz + log_px_given_z - log_qz_given_x, axis=2) # log-mean-exp over iw_samples dimension -> shape: (batch_size, eq_samples)
LL = T.mean(LL) # average over eq_samples, batch_size dimensions -> shape: ()
return LL, T.mean(log_qz_given_x), T.mean(log_pz), T.mean(log_px_given_z)
k_max_indices = mean == k_max
mean[k_max_indices] += meanOfNegativeBinomialDistribution(
r[k_max_indices], log_r[k_max_indices])
return mean
reconstruction_distributions = {
"bernoulli": {
"parameters": ["p"],
"activation functions": {
"p": sigmoid,
},
"function": lambda x, x_theta, eps = 0.0: \
log_bernoulli(x, x_theta["p"], eps),
"mean": lambda x_theta: x_theta["p"],
# TODO Consider switching to Bernouilli sampling
"preprocess": lambda x: (x != 0).astype('float32')
},
"negative_binomial": {
"parameters": ["p", "log_r"],
"activation functions": {
"p": sigmoid,
"log_r": lambda x: T.clip(x, -10, 10)
},
"function": lambda x, x_theta, eps = 0.0: \
log_negative_binomial(x, x_theta["p"], x_theta["log_r"], eps),
"mean": lambda x_theta: \
meanOfNegativeBinomialDistribution(x_theta["p"], x_theta["log_r"]),
def latent_gaussian_x_bernoulli(z0,
zk,
z0_mu,
z0_log_var,
logdet_J_list,
x_mu,
x,
eq_samples,
iw_samples,
epsilon=1e-6):
"""
Latent z : gaussian with standard normal prior
decoder output : bernoulli
When the output is bernoulli then the output from the decoder
should be sigmoid. The sizes of the inputs are
z0: (batch_size*eq_samples*iw_samples, num_latent)
zk: (batch_size*eq_samples*iw_samples, num_latent)
z0_mu: (batch_size, num_latent)
z0_log_var: (batch_size, num_latent)
logdet_J_list: list of `nflows` elements, each with shape (batch_size*eq_samples*iw_samples)
x_mu: (batch_size*eq_samples*iw_samples, num_features)
x: (batch_size, num_features)
Reference: Burda et al. 2015 "Importance Weighted Autoencoders"
"""
# reshape the variables so batch_size, eq_samples and iw_samples are separate dimensions
z0 = z0.reshape((-1, eq_samples, iw_samples, latent_size))
zk = zk.reshape((-1, eq_samples, iw_samples, latent_size))
x_mu = x_mu.reshape((-1, eq_samples, iw_samples, num_features))
for i in range(len(logdet_J_list)):
logdet_J_list[i] = logdet_J_list[i].reshape(
(-1, eq_samples, iw_samples))
# dimshuffle x, z_mu and z_log_var since we need to broadcast them when calculating the pdfs
x = x.dimshuffle(
0, 'x', 'x',
1) # size: (batch_size, eq_samples, iw_samples, num_features)
z0_mu = z0_mu.dimshuffle(
0, 'x', 'x',
1) # size: (batch_size, eq_samples, iw_samples, num_latent)
z0_log_var = z0_log_var.dimshuffle(
0, 'x', 'x',
1) # size: (batch_size, eq_samples, iw_samples, num_latent)
# calculate LL components, note that the log_xyz() functions return log prob. for indepenedent components separately
# so we sum over feature/latent dimensions for multivariate pdfs
log_q0z0_given_x = log_normal2(z0, z0_mu, z0_log_var).sum(axis=3)
log_pzk = log_stdnormal(zk).sum(axis=3)
log_px_given_zk = log_bernoulli(x, x_mu, epsilon).sum(axis=3)
#normalizing flow loss
sum_logdet_J = 0
for logdet_J_k in logdet_J_list:
sum_logdet_J += logdet_J_k
# Calculate the LL using log-sum-exp to avoid underflow all log_*** -> shape: (batch_size, eq_samples, iw_samples)
LL = log_mean_exp(
log_pzk + log_px_given_zk - log_q0z0_given_x + sum_logdet_J, axis=2
) # log-mean-exp over iw_samples dimension -> shape: (batch_size, eq_samples)
LL = T.mean(
LL) # average over eq_samples, batch_size dimensions -> shape: ()
return LL, T.mean(log_q0z0_given_x), T.mean(sum_logdet_J), T.mean(
log_pzk), T.mean(log_px_given_zk)
