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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Copyright 2019 The TensorFlow Probability Authors.
Licensed under the Apache License, Version 2.0 (the "License");
Step1:  TFP Probabilistic Layers
Step2:  Make things Fast!
Before we dive in, let's make sure we're using a GPU for this demo.  
To do this, select "Runtime" -> "Change runtime type" -> "Hardware accelerator" -> "GPU".
The following snippet will verify that we have access to a GPU.
Step3:  Note
Step4:  Note that preprocess() above returns image, image rather than just image because Keras is set up for discriminative models with an (example, label) input format, i.e. $p\theta(y|x)$. Since the goal of the VAE is to recover the input x from x itself (i.e. $p_\theta(x|x)$), the data pair is (example, example).
VAE Code Golf
Specify model.
Step5:  Do inference.
Step6:  Look Ma, No ~~Hands~~Tensors!
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Python Code:
#@title Licensed under the Apache License, Version 2.0 (the "License"); { display-mode: "form" }
# 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.
Explanation: Copyright 2019 The TensorFlow Probability Authors.
Licensed under the Apache License, Version 2.0 (the "License");
End of explanation
#@title Import { display-mode: "form" }
import numpy as np
import tensorflow.compat.v2 as tf
tf.enable_v2_behavior()
import tensorflow_datasets as tfds
import tensorflow_probability as tfp
tfk = tf.keras
tfkl = tf.keras.layers
tfpl = tfp.layers
tfd = tfp.distributions
Explanation: TFP Probabilistic Layers: Variational Auto Encoder
<table class="tfo-notebook-buttons" align="left">
  <td>
    <a target="_blank" href="https://www.tensorflow.org/probability/examples/Probabilistic_Layers_VAE"><img src="https://www.tensorflow.org/images/tf_logo_32px.png" />View on TensorFlow.org</a>
  </td>
  <td>
    <a target="_blank" href="https://colab.research.google.com/github/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Probabilistic_Layers_VAE.ipynb"><img src="https://www.tensorflow.org/images/colab_logo_32px.png" />Run in Google Colab</a>
  </td>
  <td>
    <a target="_blank" href="https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Probabilistic_Layers_VAE.ipynb"><img src="https://www.tensorflow.org/images/GitHub-Mark-32px.png" />View source on GitHub</a>
  </td>
  <td>
    <a href="https://storage.googleapis.com/tensorflow_docs/probability/tensorflow_probability/examples/jupyter_notebooks/Probabilistic_Layers_VAE.ipynb"><img src="https://www.tensorflow.org/images/download_logo_32px.png" />Download notebook</a>
  </td>
</table>
In this example we show how to fit a Variational Autoencoder using TFP's "probabilistic layers."
Dependencies & Prerequisites
End of explanation
if tf.test.gpu_device_name() != '/device:GPU:0':
  print('WARNING: GPU device not found.')
else:
  print('SUCCESS: Found GPU: {}'.format(tf.test.gpu_device_name()))
Explanation: Make things Fast!
Before we dive in, let's make sure we're using a GPU for this demo.  
To do this, select "Runtime" -> "Change runtime type" -> "Hardware accelerator" -> "GPU".
The following snippet will verify that we have access to a GPU.
End of explanation
datasets, datasets_info = tfds.load(name='mnist',
                                    with_info=True,
                                    as_supervised=False)
def _preprocess(sample):
  image = tf.cast(sample['image'], tf.float32) / 255.  # Scale to unit interval.
  image = image < tf.random.uniform(tf.shape(image))   # Randomly binarize.
  return image, image
train_dataset = (datasets['train']
                 .map(_preprocess)
                 .batch(256)
                 .prefetch(tf.data.AUTOTUNE)
                 .shuffle(int(10e3)))
eval_dataset = (datasets['test']
                .map(_preprocess)
                .batch(256)
                .prefetch(tf.data.AUTOTUNE))
Explanation: Note: if for some reason you cannot access a GPU, this colab will still work. (Training will just take longer.)
Load Dataset
End of explanation
input_shape = datasets_info.features['image'].shape
encoded_size = 16
base_depth = 32
prior = tfd.Independent(tfd.Normal(loc=tf.zeros(encoded_size), scale=1),
                        reinterpreted_batch_ndims=1)
encoder = tfk.Sequential([
    tfkl.InputLayer(input_shape=input_shape),
    tfkl.Lambda(lambda x: tf.cast(x, tf.float32) - 0.5),
    tfkl.Conv2D(base_depth, 5, strides=1,
                padding='same', activation=tf.nn.leaky_relu),
    tfkl.Conv2D(base_depth, 5, strides=2,
                padding='same', activation=tf.nn.leaky_relu),
    tfkl.Conv2D(2 * base_depth, 5, strides=1,
                padding='same', activation=tf.nn.leaky_relu),
    tfkl.Conv2D(2 * base_depth, 5, strides=2,
                padding='same', activation=tf.nn.leaky_relu),
    tfkl.Conv2D(4 * encoded_size, 7, strides=1,
                padding='valid', activation=tf.nn.leaky_relu),
    tfkl.Flatten(),
    tfkl.Dense(tfpl.MultivariateNormalTriL.params_size(encoded_size),
               activation=None),
    tfpl.MultivariateNormalTriL(
        encoded_size,
        activity_regularizer=tfpl.KLDivergenceRegularizer(prior)),
])
decoder = tfk.Sequential([
    tfkl.InputLayer(input_shape=[encoded_size]),
    tfkl.Reshape([1, 1, encoded_size]),
    tfkl.Conv2DTranspose(2 * base_depth, 7, strides=1,
                         padding='valid', activation=tf.nn.leaky_relu),
    tfkl.Conv2DTranspose(2 * base_depth, 5, strides=1,
                         padding='same', activation=tf.nn.leaky_relu),
    tfkl.Conv2DTranspose(2 * base_depth, 5, strides=2,
                         padding='same', activation=tf.nn.leaky_relu),
    tfkl.Conv2DTranspose(base_depth, 5, strides=1,
                         padding='same', activation=tf.nn.leaky_relu),
    tfkl.Conv2DTranspose(base_depth, 5, strides=2,
                         padding='same', activation=tf.nn.leaky_relu),
    tfkl.Conv2DTranspose(base_depth, 5, strides=1,
                         padding='same', activation=tf.nn.leaky_relu),
    tfkl.Conv2D(filters=1, kernel_size=5, strides=1,
                padding='same', activation=None),
    tfkl.Flatten(),
    tfpl.IndependentBernoulli(input_shape, tfd.Bernoulli.logits),
])
vae = tfk.Model(inputs=encoder.inputs,
                outputs=decoder(encoder.outputs[0]))
Explanation: Note that preprocess() above returns image, image rather than just image because Keras is set up for discriminative models with an (example, label) input format, i.e. $p\theta(y|x)$. Since the goal of the VAE is to recover the input x from x itself (i.e. $p_\theta(x|x)$), the data pair is (example, example).
VAE Code Golf
Specify model.
End of explanation
negloglik = lambda x, rv_x: -rv_x.log_prob(x)
vae.compile(optimizer=tf.optimizers.Adam(learning_rate=1e-3),
            loss=negloglik)
_ = vae.fit(train_dataset,
            epochs=15,
            validation_data=eval_dataset)
Explanation: Do inference.
End of explanation
# We'll just examine ten random digits.
x = next(iter(eval_dataset))[0][:10]
xhat = vae(x)
assert isinstance(xhat, tfd.Distribution)
#@title Image Plot Util
import matplotlib.pyplot as plt
def display_imgs(x, y=None):
  if not isinstance(x, (np.ndarray, np.generic)):
    x = np.array(x)
  plt.ioff()
  n = x.shape[0]
  fig, axs = plt.subplots(1, n, figsize=(n, 1))
  if y is not None:
    fig.suptitle(np.argmax(y, axis=1))
  for i in range(n):
    axs.flat[i].imshow(x[i].squeeze(), interpolation='none', cmap='gray')
    axs.flat[i].axis('off')
  plt.show()
  plt.close()
  plt.ion()
print('Originals:')
display_imgs(x)
print('Decoded Random Samples:')
display_imgs(xhat.sample())
print('Decoded Modes:')
display_imgs(xhat.mode())
print('Decoded Means:')
display_imgs(xhat.mean())
# Now, let's generate ten never-before-seen digits.
z = prior.sample(10)
xtilde = decoder(z)
assert isinstance(xtilde, tfd.Distribution)
print('Randomly Generated Samples:')
display_imgs(xtilde.sample())
print('Randomly Generated Modes:')
display_imgs(xtilde.mode())
print('Randomly Generated Means:')
display_imgs(xtilde.mean())
Explanation: Look Ma, No ~~Hands~~Tensors!
End of explanation
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