_notebooks/2021-09-14-01-Maximizing-the-ELBO.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Maximizing the ELBO\n",
    "\n",
    "> In this post, we will cover the complete implementation of Variational AutoEncoder, which can optimize the ELBO objective function. This is the summary of lecture \"Probabilistic Deep Learning with Tensorflow 2\" from Imperial College London.\n",
    "\n",
    "- toc: true \n",
    "- badges: true\n",
    "- comments: true\n",
    "- author: Chanseok Kang\n",
    "- categories: [Python, Coursera, Tensorflow_probability, ICL]\n",
    "- image: images/fashion_mnist_generated.png"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import tensorflow_probability as tfp\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Ellipse\n",
    "from IPython.display import HTML, Image\n",
    "\n",
    "tfd = tfp.distributions\n",
    "tfpl = tfp.layers\n",
    "tfb = tfp.bijectors\n",
    "\n",
    "plt.rcParams['figure.figsize'] = (10, 6)\n",
    "plt.rcParams[\"animation.html\"] = \"jshtml\" \n",
    "plt.rcParams['animation.embed_limit'] = 2**128"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tensorflow Version:  2.5.0\n",
      "Tensorflow Probability Version:  0.13.0\n"
     ]
    }
   ],
   "source": [
    "print(\"Tensorflow Version: \", tf.__version__)\n",
    "print(\"Tensorflow Probability Version: \", tfp.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overview"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prior Distribution\n",
    "\n",
    "$ \\text{latent variable } z \\sim N(0, I) = p(z) \\\\\n",
    " p(x \\vert z) = \\text{decoder}(z) \\\\\n",
    " x \\sim p(x \\vert z) $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Approximating True Posterior distribution\n",
    "\n",
    "$ \\text{encoder }(x) = q(z \\vert x) \\simeq p(z \\vert x) \\\\\n",
    " \\begin{aligned} \\log p(x) & \\ge \\mathbb{E}_{z \\sim q(z \\vert x)}[-\\log q(z \\vert x) + \\log p(x \\vert z)] \\quad \\leftarrow \\text{maximizing this lower bound} \\\\\n",
    "  &= - \\mathrm{KL} (q(z \\vert x) \\vert \\vert p(z)) + \\mathbb{E}_{z \\sim q(z \\vert x)}[\\log p(x \\vert z)] \\quad \\leftarrow \\text{Evidence Lower Bound (ELBO)} \\end{aligned}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sample Encoder Architecture"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```python\n",
    "latent_size = 2\n",
    "event_shape = (28, 28, 1)\n",
    "\n",
    "encoder = Sequential([\n",
    "    Conv2D(8, (5, 5), strides=2, activation='tanh', input_shape=event_shape),\n",
    "    Conv2D(8, (5, 5), strides=2, activatoin='tanh'),\n",
    "    Flatten(),\n",
    "    Dense(64, activation='tanh'),\n",
    "    Dense(2 * latent_size),\n",
    "    tfpl.DistributionLambda(lambda t: tfd.MultivariateNormalDiag(\n",
    "        loc=t[..., :latent_size], scale_diag=tf.math.exp(t[..., latent_size:]))),\n",
    "], name='encoder')\n",
    "\n",
    "encoder(X_train[:16])\n",
    "``` "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sample Decoder Architecture"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Almose reverse order of Encoder.\n",
    "\n",
    "```python\n",
    "decoder = Sequential([\n",
    "    Dense(64, activation='tanh', input_shape=(latent_size, )),\n",
    "    Dense(128, activation='tanh'),\n",
    "    Reshape((4, 4, 8)), # In order to put it in the form required by Conv2D layer\n",
    "    Conv2DTranspose(8, (5, 5), strides=2, output_padding=1, activation='tanh'),\n",
    "    Conv2DTranspose(8, (5, 5), strides=2, output_padding=1, activation='tanh'),\n",
    "    Conv2D(1, (3, 3), padding='SAME'),\n",
    "    Flatten(),\n",
    "    tfpl.IndependentBernoulli(event_shape)\n",
    "], name='decoder')\n",
    "\n",
    "decoder(tf.random.normal([16, latent_size])\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prior Distribution for zero-mean gaussian with identity covariance matrix\n",
    "```python\n",
    "prior = tfd.MultivariateNormalDiag(loc=tf.zeros(latent_size))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ELBO objective function\n",
    " One way to implement ELBO function is to use Analytical computation of KL divergence.\n",
    " \n",
    "```python\n",
    "def loss_fn(X_true, approx_posterior, X_pred, prior_dist):\n",
    "    \"\"\"\n",
    "    X_true: batch of data examples\n",
    "    approx_posterior: the output of encoder\n",
    "    X_pred: output of decoder\n",
    "    prior_dist: Prior distribution\n",
    "    \"\"\"\n",
    "    return tf.reduce_mean(tfd.kl_divergence(approx_posterior, prior_dist) - X_pred.log_prob(X_true))\n",
    "```\n",
    "\n",
    "The other way is using Monte Carlo Sampling instead of analyticall with the KL Divergence.\n",
    "\n",
    "```python\n",
    "def loss_fn(X_true, approx_posterior, X_pred, prior_dist):\n",
    "    reconstruction_loss = -X_pred.log_prob(X_true)\n",
    "    approx_posterior_sample = approx_posterior.sample()\n",
    "    kl_approx = (approx_posterior.log_prob(approx_posterior_sample) - prior_dist.log_prob(approx_posterior_sample))\n",
    "    return tf.reduce_mean(kl_approx + reconstruction_loss)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculating Gradient of Loss function\n",
    "```python\n",
    "@tf.function\n",
    "def get_loss_and_grads(x):\n",
    "    with tf.GradientTape() as tape:\n",
    "        approx_posterior = encoder(x)\n",
    "        approx_posterior_sample = approx_posterior.sample()\n",
    "        X_pred = decoder(approx_posterior_sample)\n",
    "        current_loss = loss_fn(x, approx_posterior, X_pred, prior)\n",
    "    grads = tape.gradient(current_loss, encoder.trainable_variables + decoder.trainable_variables)\n",
    "    return current_loss, grads\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training Loop\n",
    "\n",
    "```python\n",
    "optimizer = tf.keras.optimizers.Adam()\n",
    "for epoch in range(num_epochs):\n",
    "    for train_batch in train_data:\n",
    "        loss, grads = get_loss_and_grads(train_batch)\n",
    "        optimizer.apply_gradients(zip(grads, encoder.trainable_variables + decoder.trainable_variables))\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test\n",
    "```python\n",
    "z = prior.sample(1) # (1, 2)\n",
    "x = decoder(z).sample() # (1, 28, 28, 1)\n",
    "\n",
    "X_encoded = encoder(X_sample)\n",
    "\n",
    "def vae(inputs):\n",
    "    approx_posterior = encoder(inputs)\n",
    "    decoded = decoder(approx_posterior.sample())\n",
    "    return decoded.sample()\n",
    "\n",
    "reconstruction = vae(X_sample)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tutorial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Review of terminology:\n",
    "- $p(z)$ = prior\n",
    "- $q(z|x)$ = encoding distribution\n",
    "- $p(x|z)$ = decoding distribution\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\log p(x) &\\geq \\mathrm{E}_{Z \\sim q(z | x)}\\big[−\\log q(Z | x) + \\log p(x, Z)\\big]\\\\\n",
    "          &= - \\mathrm{KL}\\big[ \\ q(z | x) \\ || \\ p(z) \\ \\big] + \\mathrm{E}_{Z \\sim q(z | x)}\\big[\\log p(x | Z)\\big] \n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tensorflow.keras.models import Sequential, Model\n",
    "from tensorflow.keras.layers import Dense, Flatten, Reshape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import Fashion MNIST, make it a Tensorflow Dataset\n",
    "\n",
    "(X_train, _), (X_test, _) = tf.keras.datasets.fashion_mnist.load_data()\n",
    "X_train = X_train.astype('float32') / 255.\n",
    "X_test = X_test.astype('float32') / 255.\n",
    "example_X = X_test[:16]\n",
    "\n",
    "batch_size = 64\n",
    "X_train = tf.data.Dataset.from_tensor_slices(X_train).batch(batch_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From /home/chanseok/anaconda3/envs/torch/lib/python3.7/site-packages/tensorflow_probability/python/distributions/distribution.py:346: calling MultivariateNormalDiag.__init__ (from tensorflow_probability.python.distributions.mvn_diag) with scale_identity_multiplier is deprecated and will be removed after 2020-01-01.\n",
      "Instructions for updating:\n",
      "`scale_identity_multiplier` is deprecated; please combine it into `scale_diag` directly instead.\n"
     ]
    }
   ],
   "source": [
    "# Define the encoding distribution, q(z | x)\n",
    "\n",
    "latent_size = 2\n",
    "event_shape = (28, 28)\n",
    "\n",
    "encoder = Sequential([\n",
    "    Flatten(input_shape=event_shape),\n",
    "    Dense(256, activation='relu'),\n",
    "    Dense(128, activation='relu'),\n",
    "    Dense(64, activation='relu'),\n",
    "    Dense(32, activation='relu'),\n",
    "    Dense(2 * latent_size),\n",
    "    tfpl.DistributionLambda(\n",
    "        lambda t: tfd.MultivariateNormalDiag(\n",
    "            loc=t[..., :latent_size],\n",
    "            scale_diag=tf.math.exp(t[..., latent_size:])\n",
    "        )\n",
    "    )\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tfp.distributions.MultivariateNormalDiag 'sequential_distribution_lambda_MultivariateNormalDiag' batch_shape=[16] event_shape=[2] dtype=float32>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Pass an example image through the network - should return a batch of MultivariateNormalDiag\n",
    "\n",
    "encoder(example_X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the decoding distribution, p(x | z)\n",
    "\n",
    "decoder = Sequential([\n",
    "    Dense(32, activation='relu'),\n",
    "    Dense(64, activation='relu'),\n",
    "    Dense(128, activation='relu'),\n",
    "    Dense(256, activation='relu'),\n",
    "    Dense(tfpl.IndependentBernoulli.params_size(event_shape)),\n",
    "    tfpl.IndependentBernoulli(event_shape)\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tfp.distributions.Independent 'sequential_1_independent_bernoulli_IndependentBernoulli_Independentsequential_1_independent_bernoulli_IndependentBernoulli_Bernoulli' batch_shape=[16] event_shape=[28, 28] dtype=float32>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Pass a batch of examples to the decoder\n",
    "\n",
    "decoder(tf.random.normal([16, latent_size]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the prior, p(z) - a standard bivariate Gaussian\n",
    "prior = tfd.MultivariateNormalDiag(loc=tf.zeros(latent_size))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The loss function we need to estimate is\n",
    "$$\n",
    "-\\mathrm{ELBO} = \\mathrm{KL}[ \\ q(z|x) \\ || \\ p(z) \\ ] - \\mathrm{E}_{Z \\sim q(z|x)}[\\log p(x|Z)]\\\\\n",
    "$$\n",
    "where $x = (x_1, x_2, \\ldots, x_n)$ refers to all observations, $z = (z_1, z_2, \\ldots, z_n)$ refers to corresponding latent variables.\n",
    "\n",
    "Assumed independence of examples implies that we can write this as\n",
    "$$\n",
    "\\sum_j \\mathrm{KL}[ \\ q(z_j|x_j) \\ || \\ p(z_j) \\ ] - \\mathrm{E}_{Z_j \\sim q(z_j|x_j)}[\\log p(x_j|Z_j)]\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Specify the loss function, an estimate of the -ELBO\n",
    "\n",
    "def loss(x, encoding_dist, sampled_decoding_dist, prior):\n",
    "    return tf.reduce_sum(\n",
    "        tfd.kl_divergence(encoding_dist, prior) - sampled_decoding_dist.log_prob(x)\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a function that returns the loss and its gradients\n",
    "\n",
    "@tf.function\n",
    "def get_loss_and_grads(x):\n",
    "    with tf.GradientTape() as tape:\n",
    "        encoding_dist = encoder(x)\n",
    "        sampled_z = encoding_dist.sample()\n",
    "        sampled_decoding_dist = decoder(sampled_z)\n",
    "        current_loss = loss(x, encoding_dist, sampled_decoding_dist, prior)\n",
    "    grads = tape.gradient(current_loss, encoder.trainable_variables + decoder.trainable_variables)\n",
    "    return current_loss, grads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-ELBO after epoch 1: 8990\n",
      "-ELBO after epoch 2: 8858\n",
      "-ELBO after epoch 3: 8782\n",
      "-ELBO after epoch 4: 8820\n",
      "-ELBO after epoch 5: 8716\n",
      "-ELBO after epoch 6: 8664\n",
      "-ELBO after epoch 7: 8727\n",
      "-ELBO after epoch 8: 8667\n",
      "-ELBO after epoch 9: 8810\n",
      "-ELBO after epoch 10: 8675\n"
     ]
    }
   ],
   "source": [
    "# Compile and train the model\n",
    "num_epochs = 10\n",
    "optimizer = tf.keras.optimizers.Adam()\n",
    "\n",
    "for i in range(num_epochs):\n",
    "    for train_batch in X_train:\n",
    "        current_loss, grads = get_loss_and_grads(train_batch)\n",
    "        optimizer.apply_gradients(zip(grads, encoder.trainable_variables + decoder.trainable_variables))\n",
    "        \n",
    "    print('-ELBO after epoch {}: {:.0f}'.format(i + 1, current_loss.numpy()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Connect encoder and decoder, compute a reconstruction\n",
    "\n",
    "def vae(inputs):\n",
    "    approx_posterior = encoder(inputs)\n",
    "    decoding_dist = decoder(approx_posterior.sample())\n",
    "    return decoding_dist.sample()\n",
    "\n",
    "example_reconstruction = vae(example_X).numpy().squeeze()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot examples against reconstructions\n",
    "\n",
    "f, axs = plt.subplots(2, 6, figsize=(16, 5))\n",
    "\n",
    "for j in range(6):\n",
    "    axs[0, j].imshow(example_X[j, :, :].squeeze(), cmap='binary')\n",
    "    axs[1, j].imshow(example_reconstruction[j, :, :], cmap='binary')\n",
    "    axs[0, j].axis('off')\n",
    "    axs[1, j].axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the model has lack of reconstruction from grayscale image, So using mean for reconstruction gets more satisfied results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Connect encoder and decoder, compute a reconstruction with mean\n",
    "\n",
    "def vae_mean(inputs):\n",
    "    approx_posterior = encoder(inputs)\n",
    "    decoding_dist = decoder(approx_posterior.sample())\n",
    "    return decoding_dist.mean()\n",
    "\n",
    "example_reconstruction = vae_mean(example_X).numpy().squeeze()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot examples against reconstructions\n",
    "\n",
    "f, axs = plt.subplots(2, 6, figsize=(16, 5))\n",
    "\n",
    "for j in range(6):\n",
    "    axs[0, j].imshow(example_X[j, :, :].squeeze(), cmap='binary')\n",
    "    axs[1, j].imshow(example_reconstruction[j, :, :], cmap='binary')\n",
    "    axs[0, j].axis('off')\n",
    "    axs[1, j].axis('off')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate an example - sample a z value, then sample a reconstruction from p(x|z)\n",
    "\n",
    "z = prior.sample(6)\n",
    "generated_x = decoder(z).sample()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display generated_x\n",
    "\n",
    "f, axs = plt.subplots(1, 6, figsize=(16, 5))\n",
    "for j in range(6):\n",
    "    axs[j].imshow(generated_x[j, :, :].numpy().squeeze(), cmap='binary')\n",
    "    axs[j].axis('off')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate an example - sample a z value, then sample a reconstruction from p(x|z)\n",
    "\n",
    "z = prior.sample(6)\n",
    "generated_x = decoder(z).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display generated_x\n",
    "\n",
    "f, axs = plt.subplots(1, 6, figsize=(16, 5))\n",
    "for j in range(6):\n",
    "    axs[j].imshow(generated_x[j, :, :].numpy().squeeze(), cmap='binary')\n",
    "    axs[j].axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What if we use Monte Carlo Sampling for kl divergence?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "encoder = Sequential([\n",
    "    Flatten(input_shape=event_shape),\n",
    "    Dense(256, activation='relu'),\n",
    "    Dense(128, activation='relu'),\n",
    "    Dense(64, activation='relu'),\n",
    "    Dense(32, activation='relu'),\n",
    "    Dense(2 * latent_size),\n",
    "    tfpl.DistributionLambda(\n",
    "        lambda t: tfd.MultivariateNormalDiag(\n",
    "            loc=t[..., :latent_size],\n",
    "            scale_diag=tf.math.exp(t[..., latent_size:])\n",
    "        )\n",
    "    )\n",
    "])\n",
    "\n",
    "decoder = Sequential([\n",
    "    Dense(32, activation='relu'),\n",
    "    Dense(64, activation='relu'),\n",
    "    Dense(128, activation='relu'),\n",
    "    Dense(256, activation='relu'),\n",
    "    Dense(tfpl.IndependentBernoulli.params_size(event_shape)),\n",
    "    tfpl.IndependentBernoulli(event_shape)\n",
    "])\n",
    "\n",
    "# Define the prior, p(z) - a standard bivariate Gaussian\n",
    "prior = tfd.MultivariateNormalDiag(loc=tf.zeros(latent_size))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss(x, encoding_dist, sampled_decoding_dist, prior, sampled_z):\n",
    "    reconstruction_loss = -sampled_decoding_dist.log_prob(x)\n",
    "    kl_approx = (encoding_dist.log_prob(sampled_z) - prior.log_prob(sampled_z))\n",
    "    return tf.reduce_sum(kl_approx + reconstruction_loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "@tf.function\n",
    "def get_loss_and_grads(x):\n",
    "    with tf.GradientTape() as tape:\n",
    "        encoding_dist = encoder(x)\n",
    "        sampled_z = encoding_dist.sample()\n",
    "        sampled_decoding_dist = decoder(sampled_z)\n",
    "        current_loss = loss(x, encoding_dist, sampled_decoding_dist, prior, sampled_z)\n",
    "    grads = tape.gradient(current_loss, encoder.trainable_variables + decoder.trainable_variables)\n",
    "    return current_loss, grads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-ELBO after epoch 1: 8914\n",
      "-ELBO after epoch 2: 8802\n",
      "-ELBO after epoch 3: 8799\n",
      "-ELBO after epoch 4: 8743\n",
      "-ELBO after epoch 5: 8790\n",
      "-ELBO after epoch 6: 8716\n",
      "-ELBO after epoch 7: 8787\n",
      "-ELBO after epoch 8: 8686\n",
      "-ELBO after epoch 9: 8650\n",
      "-ELBO after epoch 10: 8813\n"
     ]
    }
   ],
   "source": [
    "# Compile and train the model\n",
    "num_epochs = 10\n",
    "optimizer = tf.keras.optimizers.Adam()\n",
    "\n",
    "for i in range(num_epochs):\n",
    "    for train_batch in X_train:\n",
    "        current_loss, grads = get_loss_and_grads(train_batch)\n",
    "        optimizer.apply_gradients(zip(grads, encoder.trainable_variables + decoder.trainable_variables))\n",
    "        \n",
    "    print('-ELBO after epoch {}: {:.0f}'.format(i + 1, current_loss.numpy()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Connect encoder and decoder, compute a reconstruction with mean\n",
    "\n",
    "def vae_mean(inputs):\n",
    "    approx_posterior = encoder(inputs)\n",
    "    decoding_dist = decoder(approx_posterior.sample())\n",
    "    return decoding_dist.mean()\n",
    "\n",
    "example_reconstruction = vae_mean(example_X).numpy().squeeze()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot examples against reconstructions\n",
    "\n",
    "f, axs = plt.subplots(2, 6, figsize=(16, 5))\n",
    "\n",
    "for j in range(6):\n",
    "    axs[0, j].imshow(example_X[j, :, :].squeeze(), cmap='binary')\n",
    "    axs[1, j].imshow(example_reconstruction[j, :, :], cmap='binary')\n",
    "    axs[0, j].axis('off')\n",
    "    axs[1, j].axis('off')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate an example - sample a z value, then sample a reconstruction from p(x|z)\n",
    "\n",
    "z = prior.sample(6)\n",
    "generated_x = decoder(z).mean()\n",
    "\n",
    "# Display generated_x\n",
    "\n",
    "f, axs = plt.subplots(1, 6, figsize=(16, 5))\n",
    "for j in range(6):\n",
    "    axs[j].imshow(generated_x[j, :, :].numpy().squeeze(), cmap='binary')\n",
    "    axs[j].axis('off')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}