def _resample_posterior(self, x, num_samples, context):
samples, log_q_z = self.model._approximate_posterior.sample_and_log_prob(
num_samples, context=context)
samples = utils.merge_leading_dims(samples, num_dims=2)
log_q_z = utils.merge_leading_dims(log_q_z, num_dims=2)
# Compute log prob of latents under the prior.
log_p_z = self.model._prior.log_prob(samples)
# Compute log prob of inputs under the decoder,
x = utils.repeat_rows(x, num_reps=num_samples)
log_p_x = self.model._likelihood.log_prob(x, context=samples)
# Compute ELBO.
log_w = log_p_x + log_p_z - log_q_z
log_w = utils.split_leading_dim(log_w, [-1, num_samples])
log_w -= torch.logsumexp(log_w, dim=-1)[:, None]
samples = utils.split_leading_dim(samples, [-1, num_samples])
idx = torch.distributions.Categorical(logits=log_w).sample(
[num_samples])
return samples[torch.arange(len(x), device=self.device)[:, None, None],
idx.T[:, :, None],
torch.arange(self.dimensions, device=self.device)[
None, None, :]]
def stochastic_elbo(self,
inputs,
num_samples=1,
kl_multiplier=1,
keepdim=False):
"""Calculates an unbiased Monte-Carlo estimate of the evidence lower bound.
Note: the KL term is also estimated via Monte Carlo.
Args:
inputs: Tensor of shape [batch_size, ...], the inputs.
num_samples: int, number of samples to use for the Monte-Carlo estimate.
Returns:
A Tensor of shape [batch_size], an ELBO estimate for each input.
"""
# Sample latents and calculate their log prob under the encoder.
if self._inputs_encoder is None:
posterior_context = inputs
else:
posterior_context = self._inputs_encoder(inputs)
latents, log_q_z = self._approximate_posterior.sample_and_log_prob(
num_samples, context=posterior_context)
latents = utils.merge_leading_dims(latents, num_dims=2)
log_q_z = utils.merge_leading_dims(log_q_z, num_dims=2)
# Compute log prob of latents under the prior.
inputs = utils.repeat_rows(inputs, num_reps=num_samples)
log_p_z = self._prior.log_prob(inputs, context=latents)
# Compute log prob of inputs under the decoder,
log_p_x = self._likelihood.log_prob(inputs[0] - latents)
# Compute ELBO.
# TODO: maybe compute KL analytically when possible?
elbo = log_p_x + kl_multiplier * (log_p_z - log_q_z)
elbo = utils.split_leading_dim(elbo, [-1, num_samples])
if keepdim:
return elbo
else:
return torch.sum(
elbo, dim=1) / num_samples # Average ELBO across samples.
def sample_and_log_prob(self, num_samples, context):
samples = self.sample(num_samples, context)
if context is not None:
samples = utils.merge_leading_dims(samples, num_dims=2)
context = utils.repeat_rows(context, num_reps=num_samples)
log_prob = self.log_prob(samples, context)
if context is not None:
# Split the context dimension from sample dimension.
samples = utils.split_leading_dim(samples, shape=[-1, num_samples])
log_prob = utils.split_leading_dim(log_prob,
shape=[-1, num_samples])
return samples, log_prob
def reconstruct(self, inputs, num_samples=None, mean=False):
"""Reconstruct given inputs.
Args:
inputs: Tensor of shape [batch_size, ...], the inputs to reconstruct.
num_samples: int or None, the number of reconstructions to generate per input. If None,
only one reconstruction is generated per input.
mean: bool, if True it uses the mean of the decoder instead of sampling from it.
Returns:
A Tensor of shape [batch_size, num_samples, ...] or [batch_size, ...] if num_samples
is None, the reconstructions for each input.
"""
latents = self.encode(inputs, num_samples)
if num_samples is not None:
latents = utils.merge_leading_dims(latents, num_dims=2)
recons = self._decode(latents, mean)
if num_samples is not None:
recons = utils.split_leading_dim(recons, [-1, num_samples])
return recons
def encode(self, inputs, num_samples=None):
"""Encodes inputs into the latent space.
Args:
inputs: Tensor of shape [batch_size, ...], the inputs to encode.
num_samples: int or None, the number of latent samples to generate per input. If None,
only one latent sample is generated per input.
Returns:
A Tensor of shape [batch_size, num_samples, ...] or [batch_size, ...] if num_samples
is None, the latent samples for each input.
"""
if num_samples is None:
latents = self._approximate_posterior.sample(num_samples=1,
context=inputs)
latents = utils.merge_leading_dims(latents, num_dims=2)
else:
latents = self._approximate_posterior.sample(
num_samples=num_samples, context=inputs)
return latents
def _decode(self, latents, mean):
if mean:
return self._likelihood.mean(context=latents)
else:
samples = self._likelihood.sample(num_samples=1, context=latents)
return utils.merge_leading_dims(samples, num_dims=2)
