def negative_iwae_bound(self, x, iw):
"""
Computes the Importance Weighted Autoencoder Bound
Additionally, we also compute the ELBO KL and reconstruction terms
Args:
x: tensor: (batch, dim): Observations
iw: int: (): Number of importance weighted samples
Returns:
niwae: tensor: (): Negative IWAE bound
kl: tensor: (): ELBO KL divergence to prior
rec: tensor: (): ELBO Reconstruction term
"""
################################################################################
# TODO: Modify/complete the code here
# Compute niwae (negative IWAE) with iw importance samples, and the KL
# and Rec decomposition of the Evidence Lower Bound
#
# Outputs should all be scalar
################################################################################
# Compute the mixture of Gaussian prior
pm, pv = ut.gaussian_parameters(self.z_pre, dim=1)
#
# Generate samples.
qm, qv = self.enc.encode(x)
niwaes = []
recs = []
kls = []
for i in range(iw):
z_sample = ut.sample_gaussian(qm, qv).view(-1, qm.shape[1])
rec = self.dec.decode(z_sample)
logptheta_x_g_z = ut.log_bernoulli_with_logits(x, rec)
logptheta_z = ut.log_normal_mixture(z_sample, pm, pv)
logqphi_z_g_x = ut.log_normal(z_sample, qm, qv)
niwae = logptheta_x_g_z + logptheta_z - logqphi_z_g_x
#
# Normal variables.
rec = -ut.log_bernoulli_with_logits(x, rec)
kl = ut.log_normal(z_sample, qm, qv) - ut.log_normal_mixture(
z_sample, pm, pv)
niwaes.append(niwae)
recs.append(rec)
kls.append(kl)
niwaes = torch.stack(niwaes, -1)
niwae = ut.log_mean_exp(niwaes, -1)
kl = torch.stack(kls, -1)
rec = torch.stack(recs, -1)
################################################################################
# End of code modification
################################################################################
return -niwae.mean(), kl.mean(), rec.mean()
def negative_elbo_bound(self, x):
"""
Computes the Evidence Lower Bound, KL and, Reconstruction costs
Args:
x: tensor: (batch, dim): Observations
Returns:
nelbo: tensor: (): Negative evidence lower bound
kl: tensor: (): ELBO KL divergence to prior
rec: tensor: (): ELBO Reconstruction term
"""
print(x)
m, v = self.enc.encode(x)
z = ut.sample_gaussian(m, v)
logits = self.dec.decode(z)
batch_size, dim = m.shape
# Compute KL term
# km = torch.zeros(batch_size,self.k,dim)
# kv = torch.ones(batch_size,self.k,dim)
km = self.km.repeat(batch_size, 1, 1)
kv = self.kv.repeat(batch_size, 1, 1)
kl_vec = ut.log_normal(z, m, v) - ut.log_normal_mixture(z, km, kv)
kl = torch.mean(kl_vec)
# Compute reconstruction loss
rec_vec = torch.neg(ut.log_bernoulli_with_logits(x, logits))
rec = torch.mean(rec_vec)
# Compute nelbo
nelbo = rec + kl
return nelbo, kl, rec
def kl_elem(self, z, qm, qv):
# Compute the mixture of Gaussian prior
prior_m, prior_v = ut.gaussian_parameters(self.z_pre, dim=1)
log_prob_net = ut.log_normal(z, qm, qv)
log_prob_prior = ut.log_normal_mixture(z, prior_m, prior_v)
# print("log_prob_net:", log_prob_net.mean(), "log_prob_prior:", log_prob_prior.mean())
kl_elem = log_prob_net - log_prob_prior
return kl_elem
def negative_iwae_bound(self, x, iw):
"""
Computes the Importance Weighted Autoencoder Bound
Additionally, we also compute the ELBO KL and reconstruction terms
Args:
x: tensor: (batch, dim): Observations
iw: int: (): Number of importance weighted samples
Returns:
niwae: tensor: (): Negative IWAE bound
kl: tensor: (): ELBO KL divergence to prior
rec: tensor: (): ELBO Reconstruction term
"""
################################################################################
# TODO: Modify/complete the code here
# Compute niwae (negative IWAE) with iw importance samples, and the KL
# and Rec decomposition of the Evidence Lower Bound
#
# Outputs should all be scalar
################################################################################
# Compute the mixture of Gaussian prior
prior = ut.gaussian_parameters(self.z_pre, dim=1)
m, v = self.enc.encode(x)
dist = Normal(loc=m, scale=torch.sqrt(v))
z_sample = dist.rsample(sample_shape=torch.Size([iw]))
log_batch_z_sample_prob = []
kl_batch_z_sample = []
for i in range(iw):
recon_logits = self.dec.decode(z_sample[i])
log_batch_z_sample_prob.append(
ut.log_bernoulli_with_logits(
x, recon_logits)) # [batch, z_sample]
kl_batch_z_sample.append(
ut.log_normal(z_sample[i], m, v) -
ut.log_normal_mixture(z_sample[i], prior[0], prior[1]))
log_batch_z_sample_prob = torch.stack(log_batch_z_sample_prob, dim=1)
kl_batch_z_sample = torch.stack(kl_batch_z_sample, dim=1)
niwae = -ut.log_mean_exp(log_batch_z_sample_prob - kl_batch_z_sample,
dim=1).mean(dim=0)
rec = -torch.mean(log_batch_z_sample_prob, dim=0)
kl = torch.mean(kl_batch_z_sample, dim=0)
################################################################################
# End of code modification
################################################################################
return niwae, kl, rec
def negative_iwae_bound(self, x, iw):
"""
Computes the Importance Weighted Autoencoder Bound
Additionally, we also compute the ELBO KL and reconstruction terms
Args:
x: tensor: (batch, dim): Observations
iw: int: (): Number of importance weighted samples
Returns:
niwae: tensor: (): Negative IWAE bound
kl: tensor: (): ELBO KL divergence to prior
rec: tensor: (): ELBO Reconstruction term
"""
m, v = self.enc.encode(x)
batch_size, dim = m.shape
# Duplicate
m = ut.duplicate(m, iw)
v = ut.duplicate(v, iw)
x = ut.duplicate(x, iw)
z = ut.sample_gaussian(m, v)
logits = self.dec.decode(z)
km = self.km.repeat(batch_size, 1, 1)
kv = self.kv.repeat(batch_size, 1, 1)
km = ut.duplicate(km, iw)
kv = ut.duplicate(kv, iw)
kl_vec = ut.log_normal(z, m, v) - ut.log_normal_mixture(z, km, kv)
kl = torch.mean(kl_vec)
# TODO: compute the values below
rec_vec = ut.log_bernoulli_with_logits(x, logits)
rec = torch.neg(torch.mean(rec_vec))
if iw > 1:
iwtensor = torch.zeros(iw)
j = 0
while j < iw:
i = 0
sum = 0
while i < batch_size:
sum += rec_vec[j * batch_size + i]
i += 1
iwtensor[j] = sum / batch_size - kl
j += 1
niwae = torch.neg(ut.log_mean_exp(iwtensor, 0))
else:
niwae = rec + kl
return niwae, kl, rec
def negative_elbo_bound(self, x):
"""
Computes the Evidence Lower Bound, KL and, Reconstruction costs
Args:
x: tensor: (batch, dim): Observations
Returns:
nelbo: tensor: (): Negative evidence lower bound
kl: tensor: (): ELBO KL divergence to prior
rec: tensor: (): ELBO Reconstruction term
"""
################################################################################
# TODO: Modify/complete the code here
# Compute negative Evidence Lower Bound and its KL and Rec decomposition
#
# To help you start, we have computed the mixture of Gaussians prior
# prior = (m_mixture, v_mixture) for you, where
# m_mixture and v_mixture each have shape (1, self.k, self.z_dim)
#
# Note that nelbo = kl + rec
#
# Outputs should all be scalar
################################################################################
# Compute the mixture of Gaussian prior
(m, v) = self.enc.encode(x) # compute the encoder output
#print(" ***** \n")
#print("x xhape ", x.shape)
#print("m and v shapes = ", m.shape, v.shape)
prior = ut.gaussian_parameters(self.z_pre, dim=1)
#print("prior shapes = ", prior[0].shape, prior[1].shape)
z = ut.sample_gaussian(m, v) # sample a point from the multivariate Gaussian
#print("shape of z = ",z.shape)
logits = self.dec.decode(z) # pass the sampled "Z" through the decoder
#print("logits shape = ", logits.shape)
rec = -torch.mean(ut.log_bernoulli_with_logits(x, logits), -1) # Calculate log Prob of the output
log_prob = ut.log_normal(z, m, v)
log_prob -= ut.log_normal_mixture(z, prior[0], prior[1])
kl = torch.mean(log_prob)
rec = torch.mean(rec)
nelbo = kl + rec
################################################################################
# End of code modification
################################################################################
return nelbo, kl, rec
def negative_elbo_bound(self, x):
"""
Computes the Evidence Lower Bound, KL and, Reconstruction costs
Args:
x: tensor: (batch, dim): Observations
Returns:
nelbo: tensor: (): Negative evidence lower bound
kl: tensor: (): ELBO KL divergence to prior
rec: tensor: (): ELBO Reconstruction term
"""
################################################################################
# TODO: Modify/complete the code here
# Compute negative Evidence Lower Bound and its KL and Rec decomposition
#
# To help you start, we have computed the mixture of Gaussians prior
# prior = (m_mixture, v_mixture) for you, where
# m_mixture and v_mixture each have shape (1, self.k, self.z_dim)
#
# Note that nelbo = kl + rec
#
# Outputs should all be scalar
################################################################################
# Compute the mixture of Gaussian prior
prior = ut.gaussian_parameters(self.z_pre, dim=1)
prior_m, prior_v = prior
batch = x.shape[0]
qm, qv = self.enc.encode(x)
# Now draw Zs from the posterior qm/qv
z = ut.sample_gaussian(qm, qv)
l_posterior = ut.log_normal(z, qm, qv)
multi_m = prior_m.expand(batch, *prior_m.shape[1:])
multi_v = prior_v.expand(batch, *prior_v.shape[1:])
l_prior = ut.log_normal_mixture(z, multi_m, multi_v)
kls = l_posterior - l_prior
kl = torch.mean(kls)
probs = self.dec.decode(z)
recs = ut.log_bernoulli_with_logits(x, probs)
rec = -1.0 * torch.mean(recs)
nelbo = kl + rec
################################################################################
# End of code modification
################################################################################
return nelbo, kl, rec
def negative_iwae_bound(self, x, iw):
"""
Computes the Importance Weighted Autoencoder Bound
Additionally, we also compute the ELBO KL and reconstruction terms
Args:
x: tensor: (batch, dim): Observations
iw: int: (): Number of importance weighted samples
Returns:
niwae: tensor: (): Negative IWAE bound
kl: tensor: (): ELBO KL divergence to prior
rec: tensor: (): ELBO Reconstruction term
"""
################################################################################
# TODO: Modify/complete the code here
# Compute niwae (negative IWAE) with iw importance samples, and the KL
# and Rec decomposition of the Evidence Lower Bound
#
# Outputs should all be scalar
################################################################################
# Compute the mixture of Gaussian prior
prior = ut.gaussian_parameters(self.z_pre, dim=1)
q_m, q_v = self.enc.encode(x)
q_m_, q_v_ = ut.duplicate(q_m, rep=iw), ut.duplicate(q_v, rep=iw)
z_given_x = ut.sample_gaussian(q_m_, q_v_)
decoded_bernoulli_logits = self.dec.decode(z_given_x)
#duplicate x
x_dup = ut.duplicate(x, rep=iw)
rec = ut.log_bernoulli_with_logits(x_dup, decoded_bernoulli_logits)
log_p_theta = ut.log_normal_mixture(z_given_x, prior[0], prior[1])
log_q_phi = ut.log_normal(z_given_x, q_m_, q_v_)
kl = log_q_phi - log_p_theta
niwae = rec - kl
niwae = ut.log_mean_exp(niwae.reshape(iw, -1), dim=0)
niwae = -torch.mean(niwae)
#yay!
################################################################################
# End of code modification
################################################################################
return niwae, kl, rec
def negative_elbo_bound(self, x):
"""
Computes the Evidence Lower Bound, KL and, Reconstruction costs
Args:
x: tensor: (batch, dim): Observations
Returns:
nelbo: tensor: (): Negative evidence lower bound
kl: tensor: (): ELBO KL divergence to prior
rec: tensor: (): ELBO Reconstruction term
"""
################################################################################
# TODO: Modify/complete the code here
# Compute negative Evidence Lower Bound and its KL and Rec decomposition
#
# To help you start, we have computed the mixture of Gaussians prior
# prior = (m_mixture, v_mixture) for you, where
# m_mixture and v_mixture each have shape (1, self.k, self.z_dim)
#
# Note that nelbo = kl + rec
#
# Outputs should all be scalar
################################################################################
# Compute the mixture of Gaussian prior
prior = ut.gaussian_parameters(self.z_pre, dim=1)
q_m, q_v = self.enc.encode(x)
#print("q_m", q_m.size())
z_given_x = ut.sample_gaussian(q_m, q_v)
decoded_bernoulli_logits = self.dec.decode(z_given_x)
rec = -ut.log_bernoulli_with_logits(x, decoded_bernoulli_logits)
#rec = -torch.mean(rec)
#terms for KL divergence
log_q_phi = ut.log_normal(z_given_x, q_m, q_v)
#print("log_q_phi", log_q_phi.size())
log_p_theta = ut.log_normal_mixture(z_given_x, prior[0], prior[1])
#print("log_p_theta", log_p_theta.size())
kl = log_q_phi - log_p_theta
#print("kl", kl.size())
nelbo = torch.mean(kl + rec)
rec = torch.mean(rec)
kl = torch.mean(kl)
################################################################################
# End of code modification
################################################################################
return nelbo, kl, rec
def negative_iwae_bound(self, x, iw):
"""
Computes the Importance Weighted Autoencoder Bound
Additionally, we also compute the ELBO KL and reconstruction terms
Args:
x: tensor: (batch, dim): Observations
iw: int: (): Number of importance weighted samples
Returns:
niwae: tensor: (): Negative IWAE bound
kl: tensor: (): ELBO KL divergence to prior
rec: tensor: (): ELBO Reconstruction term
"""
################################################################################
# TODO: Modify/complete the code here
# Compute niwae (negative IWAE) with iw importance samples, and the KL
# and Rec decomposition of the Evidence Lower Bound
#
# Outputs should all be scalar
################################################################################
# Compute the mixture of Gaussian prior
prior = ut.gaussian_parameters(self.z_pre, dim=1)
N_batches, dims = x.size()
x = ut.duplicate(x, iw)
q_mu, q_var = self.enc.encode(x)
z_samp = ut.sample_gaussian(q_mu, q_var)
logits = self.dec.decode(z_samp)
probs = ut.log_bernoulli_with_logits(x, logits)
kl_vals = -ut.log_normal(z_samp, q_mu, q_var) + ut.log_normal_mixture(z_samp, *prior)
probs = probs + kl_vals
niwae = torch.mean(-ut.log_mean_exp(probs.reshape(N_batches, iw), 1))
kl = torch.tensor(0)
rec = torch.tensor(0)
################################################################################
# End of code modification
################################################################################
return niwae, kl, rec
def negative_elbo_bound(self, x):
"""
Computes the Evidence Lower Bound, KL and, Reconstruction costs
Args:
x: tensor: (batch, dim): Observations
Returns:
nelbo: tensor: (): Negative evidence lower bound
kl: tensor: (): ELBO KL divergence to prior
rec: tensor: (): ELBO Reconstruction term
"""
################################################################################
# TODO: Modify/complete the code here
# Compute negative Evidence Lower Bound and its KL and Rec decomposition
#
# To help you start, we have computed the mixture of Gaussians prior
# prior = (m_mixture, v_mixture) for you, where
# m_mixture and v_mixture each have shape (1, self.k, self.z_dim)
#
# Note that nelbo = kl + rec
#
# Outputs should all be scalar
################################################################################
#
# Compute the mixture of Gaussian prior
pm, pv = ut.gaussian_parameters(self.z_pre, dim=1)
#
# Generate samples.
qm, qv = self.enc.encode(x)
z_sample = ut.sample_gaussian(qm, qv)
rec = self.dec.decode(z_sample)
#
# Compute loss.
# KL divergence between the latent distribution and the prior.
rec = -ut.log_bernoulli_with_logits(x, rec)
# kl = ut.kl_normal(qm, qv, pm, pv)
kl = ut.log_normal(z_sample, qm, qv) - ut.log_normal_mixture(
z_sample, pm, pv)
#
# The liklihood of reproducing the sample image given the parameters.
# Would need to take the average of this otherwise.
nelbo = (kl + rec).mean()
# NELBO: 89.24684143066406. KL: 10.346451759338379. Rec: 78.90038299560547
################################################################################
# End of code modification
################################################################################
return nelbo, kl.mean(), rec.mean()
def negative_elbo_bound(self, x):
"""
Computes the Evidence Lower Bound, KL and, Reconstruction costs
Args:
x: tensor: (batch, dim): Observations
Returns:
nelbo: tensor: (): Negative evidence lower bound
kl: tensor: (): ELBO KL divergence to prior
rec: tensor: (): ELBO Reconstruction term
"""
################################################################################
# TODO: Modify/complete the code here
# Compute negative Evidence Lower Bound and its KL and Rec decomposition
#
# To help you start, we have computed the mixture of Gaussians prior
# prior = (m_mixture, v_mixture) for you, where
# m_mixture and v_mixture each have shape (1, self.k, self.z_dim)
#
# Note that nelbo = kl + rec
#
# Outputs should all be scalar
################################################################################
# Compute the mixture of Gaussian prior
prior = ut.gaussian_parameters(self.z_pre, dim=1)
N_samp, dim = x.size()
q_mu, q_var = self.enc.encode(x)
z_samp = ut.sample_gaussian(q_mu, q_var)
logits = self.dec.decode(z_samp)
rec = -torch.mean(ut.log_bernoulli_with_logits(x, logits))
kl = torch.mean(ut.log_normal(z_samp, q_mu, q_var) - ut.log_normal_mixture(z_samp, *prior))
nelbo = kl + rec
################################################################################
# End of code modification
################################################################################
return nelbo, kl, rec
def negative_iwae_bound(self, x, iw):
"""
Computes the Importance Weighted Autoencoder Bound
Additionally, we also compute the ELBO KL and reconstruction terms
Args:
x: tensor: (batch, dim): Observations
iw: int: (): Number of importance weighted samples
Returns:
niwae: tensor: (): Negative IWAE bound
kl: tensor: (): ELBO KL divergence to prior
rec: tensor: (): ELBO Reconstruction term
"""
################################################################################
# TODO: Modify/complete the code here
# Compute niwae (negative IWAE) with iw importance samples, and the KL
# and Rec decomposition of the Evidence Lower Bound
#
# Outputs should all be scalar
################################################################################
# Compute the mixture of Gaussian prior
prior = ut.gaussian_parameters(self.z_pre, dim=1)
m, v = self.enc.encode(x)
m = ut.duplicate(m, iw)
v = ut.duplicate(v, iw)
x = ut.duplicate(x, iw)
z = ut.sample_gaussian(m, v)
logits = self.dec.decode(z)
kl = ut.log_normal(z, m, v) - ut.log_normal_mixture(z, *prior)
rec = -ut.log_bernoulli_with_logits(x, logits)
nelbo = kl + rec
niwae = -ut.log_mean_exp(-nelbo.reshape(iw, -1), dim=0)
niwae, kl, rec = niwae.mean(), kl.mean(), rec.mean()
################################################################################
# End of code modification
################################################################################
return niwae, kl, rec
def negative_iwae_bound(self, x, iw):
"""
Computes the Importance Weighted Autoencoder Bound
Additionally, we also compute the ELBO KL and reconstruction terms
Args:
x: tensor: (batch, dim): Observations
iw: int: (): Number of importance weighted samples
Returns:
niwae: tensor: (): Negative IWAE bound
kl: tensor: (): ELBO KL divergence to prior
rec: tensor: (): ELBO Reconstruction term
"""
################################################################################
# TODO: Modify/complete the code here
# Compute niwae (negative IWAE) with iw importance samples, and the KL
# and Rec decomposition of the Evidence Lower Bound
#
# Outputs should all be scalar
################################################################################
# Compute the mixture of Gaussian prior
prior = ut.gaussian_parameters(self.z_pre, dim=1)
prior_m, prior_v = prior
batch = x.shape[0]
multi_x = ut.duplicate(x, iw)
qm, qv = self.enc.encode(x)
multi_qm = ut.duplicate(qm, iw)
multi_qv = ut.duplicate(qv, iw)
# z will be (batch*iw x z_dim)
# with sampled z's for a given x non-contiguous!
z = ut.sample_gaussian(multi_qm, multi_qv)
probs = self.dec.decode(z)
recs = ut.log_bernoulli_with_logits(multi_x, probs)
rec = -1.0 * torch.mean(recs)
multi_m = prior_m.expand(batch * iw, *prior_m.shape[1:])
multi_v = prior_v.expand(batch * iw, *prior_v.shape[1:])
z_priors = ut.log_normal_mixture(z, multi_m, multi_v)
x_posteriors = recs
z_posteriors = ut.log_normal(z, multi_qm, multi_qv)
kls = z_posteriors - z_priors
kl = torch.mean(kls)
log_ratios = z_priors + x_posteriors - z_posteriors
# Should be (batch*iw, z_dim), batch ratios non contiguous
unflat_log_ratios = log_ratios.reshape(iw, batch)
niwaes = ut.log_mean_exp(unflat_log_ratios, 0)
niwae = -1.0 * torch.mean(niwaes)
################################################################################
# End of code modification
################################################################################
return niwae, kl, rec