def lowerBound(self, x, x_theta, z_mu, z_log_var):
#note that we sum the latent dimension and mean over the samples
log_px_given_z = self.expectedNegativeReconstructionError(
x, x_theta, eps=1e-6).sum(axis=1).mean()
KL_qp = kl_normal2_stdnormal(z_mu, z_log_var).sum(axis=1).mean()
LL = -KL_qp + log_px_given_z
return LL, log_px_given_z, KL_qp
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, 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 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 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