model.py

################################################################################
# Copyright 2019 DeepMind Technologies Limited
#
#     Licensed under the Apache License, Version 2.0 (the "License");
#     you may not use this file except in compliance with the License.
#     You may obtain a copy of the License at
#
#         https://www.apache.org/licenses/LICENSE-2.0
#
#     Unless required by applicable law or agreed to in writing, software
#     distributed under the License is distributed on an "AS IS" BASIS,
#     WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
#     See the License for the specific language governing permissions and
#     limitations under the License.
################################################################################
"""Implementation of Continual Unsupervised Representation Learning model."""

from absl import logging
import numpy as np
import sonnet as snt
import tensorflow as tf
import tensorflow_probability as tfp

from curl import layers
from curl import utils

tfc = tf.compat.v1

# pylint: disable=g-long-lambda
# pylint: disable=redefined-outer-name


class SharedEncoder(snt.AbstractModule):
  """The shared encoder module, mapping input x to hiddens."""

  def __init__(self, encoder_type, n_enc, enc_strides, name='shared_encoder'):
    """The shared encoder function, mapping input x to hiddens.

    Args:
      encoder_type: str, type of encoder, either 'conv' or 'multi'
      n_enc: list, number of hidden units per layer in the encoder
      enc_strides: list, stride in each layer (only for 'conv' encoder_type)
      name: str, module name used for tf scope.
    """
    super(SharedEncoder, self).__init__(name=name)
    self._encoder_type = encoder_type

    if encoder_type == 'conv':
      self.shared_encoder = layers.SharedConvModule(
          filters=n_enc,
          strides=enc_strides,
          kernel_size=3,
          activation=tf.nn.relu)
    elif encoder_type == 'multi':
      self.shared_encoder = snt.nets.MLP(
          name='mlp_shared_encoder',
          output_sizes=n_enc,
          activation=tf.nn.relu,
          activate_final=True)
    else:
      raise ValueError('Unknown encoder_type {}'.format(encoder_type))

  def _build(self, x, is_training):
    if self._encoder_type == 'multi':
      self.conv_shapes = None
      x = snt.BatchFlatten()(x)
      return self.shared_encoder(x)
    else:
      output = self.shared_encoder(x)
      self.conv_shapes = self.shared_encoder.conv_shapes
      return output


def cluster_encoder_fn(hiddens, n_y_active, n_y, is_training=True):
  """The cluster encoder function, modelling q(y | x).

  Args:
    hiddens: The shared encoder activations, 2D `Tensor` of size `[B, ...]`.
    n_y_active: Tensor, the number of active components.
    n_y: int, number of maximum components allowed (used for tensor size)
    is_training: Boolean, whether to build the training graph or an evaluation
      graph.

  Returns:
    The distribution `q(y | x)`.
  """
  del is_training  # unused for now
  with tf.control_dependencies([tfc.assert_rank(hiddens, 2)]):
    lin = snt.Linear(n_y, name='mlp_cluster_encoder_final')
    logits = lin(hiddens)

  # Only use the first n_y_active components, and set the remaining to zero.
  if n_y > 1:
    probs = tf.nn.softmax(logits[:, :n_y_active])
    logging.info('Cluster softmax active probs shape: %s', str(probs.shape))
    paddings1 = tf.stack([tf.constant(0), tf.constant(0)], axis=0)
    paddings2 = tf.stack([tf.constant(0), n_y - n_y_active], axis=0)
    paddings = tf.stack([paddings1, paddings2], axis=1)
    probs = tf.pad(probs, paddings) + 0.0 * logits + 1e-12
  else:
    probs = tf.ones_like(logits)
  logging.info('Cluster softmax probs shape: %s', str(probs.shape))

  return tfp.distributions.OneHotCategorical(probs=probs)


def latent_encoder_fn(hiddens, y, n_y, n_z, is_training=True):
  """The latent encoder function, modelling q(z | x, y).

  Args:
    hiddens: The shared encoder activations, 2D `Tensor` of size `[B, ...]`.
    y: Categorical cluster variable, `Tensor` of size `[B, n_y]`.
    n_y: int, number of dims of y.
    n_z: int, number of dims of z.
    is_training: Boolean, whether to build the training graph or an evaluation
      graph.

  Returns:
    The Gaussian distribution `q(z | x, y)`.
  """
  del is_training  # unused for now

  with tf.control_dependencies([tfc.assert_rank(hiddens, 2)]):
    # Logits for both mean and variance
    n_logits = 2 * n_z

    all_logits = []
    for k in range(n_y):
      lin = snt.Linear(n_logits, name='mlp_latent_encoder_' + str(k))
      all_logits.append(lin(hiddens))

  # Sum over cluster components.
  all_logits = tf.stack(all_logits)  # [n_y, B, n_logits]
  logits = tf.einsum('ij,jik->ik', y, all_logits)

  # Compute distribution from logits.
  return utils.generate_gaussian(
      logits=logits, sigma_nonlin='softplus', sigma_param='var')


def data_decoder_fn(z,
                    y,
                    output_type,
                    output_shape,
                    decoder_type,
                    n_dec,
                    dec_up_strides,
                    n_x,
                    n_y,
                    shared_encoder_conv_shapes=None,
                    is_training=True,
                    test_local_stats=True):
  """The data decoder function, modelling p(x | z).

  Args:
    z: Latent variables, `Tensor` of size `[B, n_z]`.
    y: Categorical cluster variable, `Tensor` of size `[B, n_y]`.
    output_type: str, output distribution ('bernoulli' or 'quantized_normal').
    output_shape: list, shape of output (not including batch dimension).
    decoder_type: str, 'single', 'multi', or 'deconv'.
    n_dec: list, number of hidden units per layer in the decoder
    dec_up_strides: list, stride in each layer (only for 'deconv' decoder_type).
    n_x: int, number of dims of x.
    n_y: int, number of dims of y.
    shared_encoder_conv_shapes: the shapes of the activations of the
      intermediate layers of the encoder,
    is_training: Boolean, whether to build the training graph or an evaluation
      graph.
    test_local_stats: Boolean, whether to use the test batch statistics at test
      time for batch norm (default) or the moving averages.

  Returns:
    The Bernoulli distribution `p(x | z)`.
  """

  if output_type == 'bernoulli':
    output_dist = lambda x: tfp.distributions.Bernoulli(logits=x)
    n_out_factor = 1
    out_shape = list(output_shape)
  else:
    raise NotImplementedError
  if len(z.shape) != 2:
    raise NotImplementedError('The data decoder function expects `z` to be '
                              '2D, but its shape was %s instead.' %
                              str(z.shape))
  if len(y.shape) != 2:
    raise NotImplementedError('The data decoder function expects `y` to be '
                              '2D, but its shape was %s instead.' %
                              str(y.shape))

  # Upsample layer (deconvolutional, bilinear, ..).
  if decoder_type == 'deconv':

    # First, check that the encoder is convolutional too (needed for batchnorm)
    if shared_encoder_conv_shapes is None:
      raise ValueError('Shared encoder does not contain conv_shapes.')

    num_output_channels = output_shape[-1]
    conv_decoder = UpsampleModule(
        filters=n_dec,
        kernel_size=3,
        activation=tf.nn.relu,
        dec_up_strides=dec_up_strides,
        enc_conv_shapes=shared_encoder_conv_shapes,
        n_c=num_output_channels * n_out_factor,
        method=decoder_type)
    logits = conv_decoder(
        z, is_training=is_training, test_local_stats=test_local_stats)
    logits = tf.reshape(logits, [-1] + out_shape)  # n_out_factor in last dim

  # Multiple MLP decoders, one for each component.
  elif decoder_type == 'multi':
    all_logits = []
    for k in range(n_y):
      mlp_decoding = snt.nets.MLP(
          name='mlp_latent_decoder_' + str(k),
          output_sizes=n_dec + [n_x * n_out_factor],
          activation=tf.nn.relu,
          activate_final=False)
      logits = mlp_decoding(z)
      all_logits.append(logits)

    all_logits = tf.stack(all_logits)
    logits = tf.einsum('ij,jik->ik', y, all_logits)
    logits = tf.reshape(logits, [-1] + out_shape)  # Back to 4D

  # Single (shared among components) MLP decoder.
  elif decoder_type == 'single':
    mlp_decoding = snt.nets.MLP(
        name='mlp_latent_decoder',
        output_sizes=n_dec + [n_x * n_out_factor],
        activation=tf.nn.relu,
        activate_final=False)
    logits = mlp_decoding(z)
    logits = tf.reshape(logits, [-1] + out_shape)  # Back to 4D
  else:
    raise ValueError('Unknown decoder_type {}'.format(decoder_type))

  return output_dist(logits)


def latent_decoder_fn(y, n_z, is_training=True):
  """The latent decoder function, modelling p(z | y).

  Args:
    y: Categorical cluster variable, `Tensor` of size `[B, n_y]`.
    n_z: int, number of dims of z.
    is_training: Boolean, whether to build the training graph or an evaluation
      graph.

  Returns:
    The Gaussian distribution `p(z | y)`.
  """
  del is_training  # Unused for now.
  if len(y.shape) != 2:
    raise NotImplementedError('The latent decoder function expects `y` to be '
                              '2D, but its shape was %s instead.' %
                              str(y.shape))

  lin_mu = snt.Linear(n_z, name='latent_prior_mu')
  lin_sigma = snt.Linear(n_z, name='latent_prior_sigma')

  mu = lin_mu(y)
  sigma = lin_sigma(y)

  logits = tf.concat([mu, sigma], axis=1)

  return utils.generate_gaussian(
      logits=logits, sigma_nonlin='softplus', sigma_param='var')


class Curl(object):
  """CURL model class."""

  def __init__(self,
               prior,
               latent_decoder,
               data_decoder,
               shared_encoder,
               cluster_encoder,
               latent_encoder,
               n_y_active,
               kly_over_batch=False,
               is_training=True,
               name='curl'):
    self.scope_name = name
    self._shared_encoder = shared_encoder
    self._prior = prior
    self._latent_decoder = latent_decoder
    self._data_decoder = data_decoder
    self._cluster_encoder = cluster_encoder
    self._latent_encoder = latent_encoder
    self._n_y_active = n_y_active
    self._kly_over_batch = kly_over_batch
    self._is_training = is_training
    self._cache = {}

  def sample(self, sample_shape=(), y=None, mean=False):
    """Draws a sample from the learnt distribution p(x).

    Args:
      sample_shape: `int` or 0D `Tensor` giving the number of samples to return.
        If  empty tuple (default value), 1 sample will be returned.
      y: Optional, the one hot label on which to condition the sample.
      mean: Boolean, if True the expected value of the output distribution is
        returned, otherwise samples from the output distribution.

    Returns:
      Sample tensor of shape `[B * N, ...]` where `B` is the batch size of
      the prior, `N` is the number of samples requested, and `...` represents
      the shape of the observations.

    Raises:
      ValueError: If both `sample_shape` and `n` are provided.
      ValueError: If `sample_shape` has rank > 0 or if `sample_shape`
      is an int that is < 1.
    """
    with tf.name_scope('{}_sample'.format(self.scope_name)):
      if y is None:
        y = tf.to_float(self.compute_prior().sample(sample_shape))

      if y.shape.ndims > 2:
        y = snt.MergeDims(start=0, size=y.shape.ndims - 1, name='merge_y')(y)

      z = self._latent_decoder(y, is_training=self._is_training)
      if mean:
        samples = self.predict(z.sample(), y).mean()
      else:
        samples = self.predict(z.sample(), y).sample()
    return samples

  def reconstruct(self, x, use_mode=True, use_mean=False):
    """Reconstructs the given observations.

    Args:
      x: Observed `Tensor`.
      use_mode: Boolean, if true, take the argmax over q(y|x)
      use_mean: Boolean, if true, use pixel-mean for reconstructions.

    Returns:
      The reconstructed samples x ~ p(x | y~q(y|x), z~q(z|x, y)).
    """

    hiddens = self._shared_encoder(x, is_training=self._is_training)
    qy = self.infer_cluster(hiddens)
    y_sample = qy.mode() if use_mode else qy.sample()
    y_sample = tf.to_float(y_sample)
    qz = self.infer_latent(hiddens, y_sample)
    p = self.predict(qz.sample(), y_sample)

    if use_mean:
      return p.mean()
    else:
      return p.sample()

  def log_prob(self, x):
    """Redirects to log_prob_elbo with a warning."""
    logging.warn('log_prob is actually a lower bound')
    return self.log_prob_elbo(x)

  def log_prob_elbo(self, x):
    """Returns evidence lower bound."""
    log_p_x, kl_y, kl_z = self.log_prob_elbo_components(x)[:3]
    return log_p_x - kl_y - kl_z

  def log_prob_elbo_components(self, x, y=None, reduce_op=tf.reduce_sum):
    """Returns the components used in calculating the evidence lower bound.

    Args:
      x: Observed variables, `Tensor` of size `[B, I]` where `I` is the size of
        a flattened input.
      y: Optional labels, `Tensor` of size `[B, I]` where `I` is the size of a
        flattened input.
      reduce_op: The op to use for reducing across non-batch dimensions.
        Typically either `tf.reduce_sum` or `tf.reduce_mean`.

    Returns:
      `log p(x|y,z)` of shape `[B]` where `B` is the batch size.
      `KL[q(y|x) || p(y)]` of shape `[B]` where `B` is the batch size.
      `KL[q(z|x,y) || p(z|y)]` of shape `[B]` where `B` is the batch size.
    """
    cache_key = (x,)

    # Checks if the output graph for this inputs has already been computed.
    if cache_key in self._cache:
      return self._cache[cache_key]

    with tf.name_scope('{}_log_prob_elbo'.format(self.scope_name)):

      hiddens = self._shared_encoder(x, is_training=self._is_training)
      # 1) Compute KL[q(y|x) || p(y)] from x, and keep distribution q_y around
      kl_y, q_y = self._kl_and_qy(hiddens)  # [B], distribution

      # For the next two terms, we need to marginalise over all y.

      # First, construct every possible y indexing (as a one hot) and repeat it
      # for every element in the batch [n_y_active, B, n_y].
      # Note that the onehot have dimension of all y, while only the codes
      # corresponding to active components are instantiated
      bs, n_y = q_y.probs.shape
      all_y = tf.tile(
          tf.expand_dims(tf.one_hot(tf.range(self._n_y_active),
                                    n_y), axis=1),
          multiples=[1, bs, 1])

      # 2) Compute KL[q(z|x,y) || p(z|y)] (for all possible y), and keep z's
      # around [n_y, B] and [n_y, B, n_z]
      kl_z_all, z_all = tf.map_fn(
          fn=lambda y: self._kl_and_z(hiddens, y),
          elems=all_y,
          dtype=(tf.float32, tf.float32),
          name='elbo_components_z_map')
      kl_z_all = tf.transpose(kl_z_all, name='kl_z_all')

      # Now take the expectation over y (scale by q(y|x))
      y_logits = q_y.logits[:, :self._n_y_active]  # [B, n_y]
      y_probs = q_y.probs[:, :self._n_y_active]  # [B, n_y]
      y_probs = y_probs / tf.reduce_sum(y_probs, axis=1, keepdims=True)
      kl_z = tf.reduce_sum(y_probs * kl_z_all, axis=1)

      # 3) Evaluate logp and recon, i.e., log and mean of p(x|z,[y])
      # (conditioning on y only in the `multi` decoder_type case, when
      # train_supervised is True). Here we take the reconstruction from each
      # possible component y and take its log prob. [n_y, B, Ix, Iy, Iz]
      log_p_x_all = tf.map_fn(
          fn=lambda val: self.predict(val[0], val[1]).log_prob(x),
          elems=(z_all, all_y),
          dtype=tf.float32,
          name='elbo_components_logpx_map')

      # Sum log probs over all dimensions apart from the first two (n_y, B),
      # i.e., over I. Use einsum to construct higher order multiplication.
      log_p_x_all = snt.BatchFlatten(preserve_dims=2)(log_p_x_all)  # [n_y,B,I]
      # Note, this is E_{q(y|x)} [ log p(x | z, y)], i.e., we scale log_p_x_all
      # by q(y|x).
      log_p_x = tf.einsum('ij,jik->ik', y_probs, log_p_x_all)  # [B, I]

      # We may also use a supervised loss for some samples [B, n_y]
      if y is not None:
        self.y_label = tf.one_hot(y, n_y)
      else:
        self.y_label = tfc.placeholder(
            shape=[bs, n_y], dtype=tf.float32, name='y_label')

      # This is computing log p(x | z, y=true_y)], which is basically equivalent
      # to indexing into the correct element of `log_p_x_all`.
      log_p_x_sup = tf.einsum('ij,jik->ik',
                              self.y_label[:, :self._n_y_active],
                              log_p_x_all)  # [B, I]
      kl_z_sup = tf.einsum('ij,ij->i',
                           self.y_label[:, :self._n_y_active],
                           kl_z_all)  # [B]
      # -log q(y=y_true | x)
      kl_y_sup = tf.nn.sparse_softmax_cross_entropy_with_logits(  # [B]
          labels=tf.argmax(self.y_label[:, :self._n_y_active], axis=1),
          logits=y_logits)

      # Reduce over all dimension except batch.
      dims_x = [k for k in range(1, log_p_x.shape.ndims)]
      log_p_x = reduce_op(log_p_x, dims_x, name='log_p_x')
      log_p_x_sup = reduce_op(log_p_x_sup, dims_x, name='log_p_x_sup')

      # Store values needed externally
      self.q_y = q_y
      self.log_p_x_all = tf.transpose(
          reduce_op(
              log_p_x_all,
              -1,  # [B, n_y]
              name='log_p_x_all'))
      self.kl_z_all = kl_z_all
      self.y_probs = y_probs

    self._cache[cache_key] = (log_p_x, kl_y, kl_z, log_p_x_sup, kl_y_sup,
                              kl_z_sup)
    return log_p_x, kl_y, kl_z, log_p_x_sup, kl_y_sup, kl_z_sup

  def _kl_and_qy(self, hiddens):
    """Returns analytical or sampled KL div and the distribution q(y | x).

    Args:
      hiddens: The shared encoder activations, 2D `Tensor` of size `[B, ...]`.

    Returns:
      Pair `(kl, y)`, where `kl` is the KL divergence (a `Tensor` with shape
      `[B]`, where `B` is the batch size), and `y` is a sample from the
      categorical encoding distribution.
    """
    with tf.control_dependencies([tfc.assert_rank(hiddens, 2)]):
      q = self.infer_cluster(hiddens)  # q(y|x)
    p = self.compute_prior()  # p(y)
    try:
      # Take the average proportions over whole batch then repeat it in each row
      # before computing the KL
      if self._kly_over_batch:
        probs = tf.reduce_mean(
            q.probs, axis=0, keepdims=True) * tf.ones_like(q.probs)
        qmean = tfp.distributions.OneHotCategorical(probs=probs)
        kl = tfp.distributions.kl_divergence(qmean, p)
      else:
        kl = tfp.distributions.kl_divergence(q, p)
    except NotImplementedError:
      y = q.sample(name='y_sample')
      logging.warn('Using sampling KLD for y')
      log_p_y = p.log_prob(y, name='log_p_y')
      log_q_y = q.log_prob(y, name='log_q_y')

      # Reduce over all dimension except batch.
      sum_axis_p = [k for k in range(1, log_p_y.get_shape().ndims)]
      log_p_y = tf.reduce_sum(log_p_y, sum_axis_p)
      sum_axis_q = [k for k in range(1, log_q_y.get_shape().ndims)]
      log_q_y = tf.reduce_sum(log_q_y, sum_axis_q)

      kl = log_q_y - log_p_y

    # Reduce over all dimension except batch.
    sum_axis_kl = [k for k in range(1, kl.get_shape().ndims)]
    kl = tf.reduce_sum(kl, sum_axis_kl, name='kl')
    return kl, q

  def _kl_and_z(self, hiddens, y):
    """Returns KL[q(z|y,x) || p(z|y)] and a sample for z from q(z|y,x).

    Returns the analytical KL divergence KL[q(z|y,x) || p(z|y)] if one is
    available (as registered with `kullback_leibler.RegisterKL`), or a sampled
    KL divergence otherwise (in this case the returned sample is the one used
    for the KL divergence).

    Args:
      hiddens: The shared encoder activations, 2D `Tensor` of size `[B, ...]`.
      y: Categorical cluster random variable, `Tensor` of size `[B, n_y]`.

    Returns:
      Pair `(kl, z)`, where `kl` is the KL divergence (a `Tensor` with shape
      `[B]`, where `B` is the batch size), and `z` is a sample from the encoding
      distribution.
    """
    with tf.control_dependencies([tfc.assert_rank(hiddens, 2)]):
      q = self.infer_latent(hiddens, y)  # q(z|x,y)
    p = self.generate_latent(y)  # p(z|y)
    z = q.sample(name='z')
    try:
      kl = tfp.distributions.kl_divergence(q, p)
    except NotImplementedError:
      logging.warn('Using sampling KLD for z')
      log_p_z = p.log_prob(z, name='log_p_z_y')
      log_q_z = q.log_prob(z, name='log_q_z_xy')

      # Reduce over all dimension except batch.
      sum_axis_p = [k for k in range(1, log_p_z.get_shape().ndims)]
      log_p_z = tf.reduce_sum(log_p_z, sum_axis_p)
      sum_axis_q = [k for k in range(1, log_q_z.get_shape().ndims)]
      log_q_z = tf.reduce_sum(log_q_z, sum_axis_q)

      kl = log_q_z - log_p_z

    # Reduce over all dimension except batch.
    sum_axis_kl = [k for k in range(1, kl.get_shape().ndims)]
    kl = tf.reduce_sum(kl, sum_axis_kl, name='kl')
    return kl, z

  def infer_latent(self, hiddens, y=None, use_mean_y=False):
    """Performs inference over the latent variable z.

    Args:
      hiddens: The shared encoder activations, 4D `Tensor` of size `[B, ...]`.
      y: Categorical cluster variable, `Tensor` of size `[B, ...]`.
      use_mean_y: Boolean, whether to take the mean encoding over all y.

    Returns:
      The distribution `q(z|x, y)`, which on sample produces tensors of size
      `[N, B, ...]` where `B` is the batch size of `x` and `y`, and `N` is the
      number of samples and `...` represents the shape of the latent variables.
    """
    with tf.control_dependencies([tfc.assert_rank(hiddens, 2)]):
      if y is None:
        y = tf.to_float(self.infer_cluster(hiddens).mode())

    if use_mean_y:
      # If use_mean_y, then y must be probabilities
      all_y = tf.tile(
          tf.expand_dims(tf.one_hot(tf.range(y.shape[1]), y.shape[1]), axis=1),
          multiples=[1, y.shape[0], 1])

      # Compute z KL from x (for all possible y), and keep z's around
      z_all = tf.map_fn(
          fn=lambda y: self._latent_encoder(
              hiddens, y, is_training=self._is_training).mean(),
          elems=all_y,
          dtype=tf.float32)
      return tf.einsum('ij,jik->ik', y, z_all)
    else:
      return self._latent_encoder(hiddens, y, is_training=self._is_training)

  def generate_latent(self, y):
    """Use the generative model to compute latent variable z, given a y.

    Args:
      y: Categorical cluster variable, `Tensor` of size `[B, ...]`.

    Returns:
      The distribution `p(z|y)`, which on sample produces tensors of size
      `[N, B, ...]` where `B` is the batch size of `x`, and `N` is the number of
      samples asked and `...` represents the shape of the latent variables.
    """
    return self._latent_decoder(y, is_training=self._is_training)

  def get_shared_rep(self, x, is_training):
    """Gets the shared representation from a given input x.

    Args:
      x: Observed variables, `Tensor` of size `[B, I]` where `I` is the size of
        a flattened input.
      is_training: bool, whether this constitutes training data or not.

    Returns:
      `log p(x|y,z)` of shape `[B]` where `B` is the batch size.
      `KL[q(y|x) || p(y)]` of shape `[B]` where `B` is the batch size.
      `KL[q(z|x,y) || p(z|y)]` of shape `[B]` where `B` is the batch size.
    """
    return self._shared_encoder(x, is_training)

  def infer_cluster(self, hiddens):
    """Performs inference over the categorical variable y.

    Args:
      hiddens: The shared encoder activations, 2D `Tensor` of size `[B, ...]`.

    Returns:
      The distribution `q(y|x)`, which on sample produces tensors of size
      `[N, B, ...]` where `B` is the batch size of `x`, and `N` is the number of
      samples asked and `...` represents the shape of the latent variables.
    """
    with tf.control_dependencies([tfc.assert_rank(hiddens, 2)]):
      return self._cluster_encoder(hiddens, is_training=self._is_training)

  def predict(self, z, y):
    """Computes prediction over the observed variables.

    Args:
      z: Latent variables, `Tensor` of size `[B, ...]`.
      y: Categorical cluster variable, `Tensor` of size `[B, ...]`.

    Returns:
      The distribution `p(x|z)`, which on sample produces tensors of size
      `[N, B, ...]` where `N` is the number of samples asked.
    """
    encoder_conv_shapes = getattr(self._shared_encoder, 'conv_shapes', None)
    return self._data_decoder(
        z,
        y,
        shared_encoder_conv_shapes=encoder_conv_shapes,
        is_training=self._is_training)

  def compute_prior(self):
    """Computes prior over the latent variables.

    Returns:
      The distribution `p(y)`, which on sample produces tensors of size
      `[N, ...]` where `N` is the number of samples asked and `...` represents
      the shape of the latent variables.
    """
    return self._prior()


class UpsampleModule(snt.AbstractModule):
  """Convolutional decoder.

  If `method` is 'deconv' apply transposed convolutions with stride 2,
  otherwise apply the `method` upsampling function and then smooth with a
  stride 1x1 convolution.

  Params:
  -------
  filters: list, where the first element is the number of filters of the initial
    MLP layer and the remaining elements are the number of filters of the
    upsampling layers.
  kernel_size: the size of the convolutional kernels. The same size will be
    used in all convolutions.
  activation: an activation function, applied to all layers but the last.
  dec_up_strides: list, the upsampling factors of each upsampling convolutional
    layer.
  enc_conv_shapes: list, the shapes of the input and of all the intermediate
    feature maps of the convolutional layers in the encoder.
  n_c: the number of output channels.
  """

  def __init__(self,
               filters,
               kernel_size,
               activation,
               dec_up_strides,
               enc_conv_shapes,
               n_c,
               method='nn',
               name='upsample_module'):
    super(UpsampleModule, self).__init__(name=name)

    assert len(filters) == len(dec_up_strides) + 1, (
        'The decoder\'s filters should contain one element more than the '
        'decoder\'s up stride list, but has %d elements instead of %d.\n'
        'Decoder filters: %s\nDecoder up strides: %s' %
        (len(filters), len(dec_up_strides) + 1, str(filters),
         str(dec_up_strides)))

    self._filters = filters
    self._kernel_size = kernel_size
    self._activation = activation

    self._dec_up_strides = dec_up_strides
    self._enc_conv_shapes = enc_conv_shapes
    self._n_c = n_c
    if method == 'deconv':
      self._conv_layer = tf.layers.Conv2DTranspose
      self._method = method
    else:
      self._conv_layer = tf.layers.Conv2D
      self._method = getattr(tf.image.ResizeMethod, method.upper())
    self._method_str = method.capitalize()

  def _build(self, z, is_training=True, test_local_stats=True, use_bn=False):
    batch_norm_args = {
        'is_training': is_training,
        'test_local_stats': test_local_stats
    }

    method = self._method
    # Cycle over the encoder shapes backwards, to build a symmetrical decoder.
    enc_conv_shapes = self._enc_conv_shapes[::-1]
    strides = self._dec_up_strides
    # We store the heights and widths of the encoder feature maps that are
    # unique, i.e., the ones right after a layer with stride != 1. These will be
    # used as a target to potentially crop the upsampled feature maps.
    unique_hw = np.unique([(el[1], el[2]) for el in enc_conv_shapes], axis=0)
    unique_hw = unique_hw.tolist()[::-1]
    unique_hw.pop()  # Drop the initial shape

    # The first filter is an MLP.
    mlp_filter, conv_filters = self._filters[0], self._filters[1:]
    # The first shape is used after the MLP to go to 4D.

    layers = [z]
    # The shape of the first enc is used after the MLP to go back to 4D.
    dec_mlp = snt.nets.MLP(
        name='dec_mlp_projection',
        output_sizes=[mlp_filter, np.prod(enc_conv_shapes[0][1:])],
        use_bias=not use_bn,
        activation=self._activation,
        activate_final=True)

    upsample_mlp_flat = dec_mlp(z)
    if use_bn:
      upsample_mlp_flat = snt.BatchNorm(scale=True)(upsample_mlp_flat,
                                                    **batch_norm_args)
    layers.append(upsample_mlp_flat)
    upsample = tf.reshape(upsample_mlp_flat, enc_conv_shapes[0])
    layers.append(upsample)

    for i, (filter_i, stride_i) in enumerate(zip(conv_filters, strides), 1):
      if method != 'deconv' and stride_i > 1:
        upsample = tf.image.resize_images(
            upsample, [stride_i * el for el in upsample.shape.as_list()[1:3]],
            method=method,
            name='upsample_' + str(i))
      upsample = self._conv_layer(
          filters=filter_i,
          kernel_size=self._kernel_size,
          padding='same',
          use_bias=not use_bn,
          activation=self._activation,
          strides=stride_i if method == 'deconv' else 1,
          name='upsample_conv_' + str(i))(
              upsample)
      if use_bn:
        upsample = snt.BatchNorm(scale=True)(upsample, **batch_norm_args)
      if stride_i > 1:
        hw = unique_hw.pop()
        upsample = utils.maybe_center_crop(upsample, hw)
      layers.append(upsample)

    # Final layer, no upsampling.
    x_logits = tf.layers.Conv2D(
        filters=self._n_c,
        kernel_size=self._kernel_size,
        padding='same',
        use_bias=not use_bn,
        activation=None,
        strides=1,
        name='logits')(
            upsample)
    if use_bn:
      x_logits = snt.BatchNorm(scale=True)(x_logits, **batch_norm_args)
    layers.append(x_logits)

    logging.info('%s upsampling module layer shapes', self._method_str)
    logging.info('\n'.join([str(v.shape.as_list()) for v in layers]))

    return x_logits