def sample_and_log_prob(self, num_samples, context=None):
"""Generates samples from the distribution together with their log probability.
Args:
num_samples: int, number of samples to generate.
context: Tensor or None, conditioning variables. If None, the context is ignored.
Returns:
A tuple of:
* A Tensor containing the samples, with shape [num_samples, ...] if context is None,
or [context_size, num_samples, ...] if context is given.
* A Tensor containing the log probabilities of the samples, with shape
[num_samples, ...] if context is None, or [context_size, num_samples, ...] if
context is given.
"""
samples = self.sample(num_samples, context=context)
if context is not None:
# Merge the context dimension with sample dimension in order to call log_prob.
samples = utils.merge_leading_dims(samples, num_dims=2)
context = utils.repeat_rows(context, num_reps=num_samples)
assert samples.shape[0] == context.shape[0]
log_prob = self.log_prob(samples, context=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 _sample(self, num_samples, context):
if context is None:
return torch.randn(num_samples, *self._shape)
else:
# The value of the context is ignored, only its size is taken into account.
context_size = context.shape[0]
samples = torch.randn(context_size * num_samples, *self._shape)
return utils.split_leading_dim(samples, [context_size, num_samples])
def _sample(self, num_samples, context):
# Compute parameters.
logits = self._compute_params(context)
probs = torch.sigmoid(logits)
probs = utils.repeat_rows(probs, num_samples)
# Generate samples.
context_size = context.shape[0]
noise = torch.rand(context_size * num_samples, *self._shape)
samples = (noise < probs).float()
return utils.split_leading_dim(samples, [context_size, num_samples])
def _sample(self, num_samples, context):
# Compute parameters.
means, log_stds = self._compute_params(context)
stds = torch.exp(log_stds)
means = utils.repeat_rows(means, num_samples)
stds = utils.repeat_rows(stds, num_samples)
# Generate samples.
context_size = context.shape[0]
noise = torch.randn(context_size * num_samples, *self._shape)
samples = means + stds * noise
return utils.split_leading_dim(samples, [context_size, num_samples])
def sample_and_log_prob(self, num_samples, context=None):
"""Generates samples from the flow, together with their log probabilities.
For flows, this is more efficient that calling `sample` and `log_prob` separately.
"""
noise, log_prob = self._distribution.sample_and_log_prob(
num_samples, context=context)
if context is not None:
# Merge the context dimension with sample dimension in order to apply the transform.
noise = utils.merge_leading_dims(noise, num_dims=2)
context = utils.repeat_rows(context, num_reps=num_samples)
samples, logabsdet = self._transform.inverse(noise, context=context)
if context is not None:
# Split the context dimension from sample dimension.
samples = utils.split_leading_dim(samples, shape=[-1, num_samples])
logabsdet = utils.split_leading_dim(logabsdet,
shape=[-1, num_samples])
return samples, log_prob - logabsdet
def _sample(self, num_samples, context):
noise = self._distribution.sample(num_samples, context=context)
if context is not None:
# Merge the context dimension with sample dimension in order to apply the transform.
noise = utils.merge_leading_dims(noise, num_dims=2)
context = utils.repeat_rows(context, num_reps=num_samples)
samples, _ = self._transform.inverse(noise, context=context)
if context is not None:
# Split the context dimension from sample dimension.
samples = utils.split_leading_dim(samples, shape=[-1, num_samples])
return samples
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.
log_p_z = self._prior.log_prob(latents)
# Compute log prob of inputs under the decoder,
inputs = utils.repeat_rows(inputs, num_reps=num_samples)
log_p_x = self._likelihood.log_prob(inputs, context=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 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