Week 2 Programming Assignment.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Programming Assignment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian convolutional neural network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Instructions\n",
    "\n",
    "In this notebook, you will create a Bayesian convolutional neural network to classify the famous MNIST handwritten digits. This will be a probabilistic model, designed to capture both aleatoric and epistemic uncertainty. You will test the uncertainty quantifications against a corrupted version of the dataset.\n",
    "\n",
    "Some code cells are provided for you in the notebook. You should avoid editing provided code, and make sure to execute the cells in order to avoid unexpected errors. Some cells begin with the line: \n",
    "\n",
    "`#### GRADED CELL ####`\n",
    "\n",
    "Don't move or edit this first line - this is what the automatic grader looks for to recognise graded cells. These cells require you to write your own code to complete them, and are automatically graded when you submit the notebook. Don't edit the function name or signature provided in these cells, otherwise the automatic grader might not function properly.\n",
    "\n",
    "### How to submit\n",
    "\n",
    "Complete all the tasks you are asked for in the worksheet. When you have finished and are happy with your code, press the **Submit Assignment** button at the top of this notebook.\n",
    "\n",
    "### Let's get started!\n",
    "\n",
    "We'll start running some imports, and loading the dataset. Do not edit the existing imports in the following cell. If you would like to make further Tensorflow imports, you should add them here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [],
   "source": [
    "#### PACKAGE IMPORTS ####\n",
    "\n",
    "# Run this cell first to import all required packages. Do not make any imports elsewhere in the notebook\n",
    "\n",
    "import tensorflow as tf\n",
    "import tensorflow_probability as tfp\n",
    "import os\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from tensorflow.keras.models import Sequential\n",
    "from tensorflow.keras.layers import Dense, Flatten, Conv2D, MaxPooling2D\n",
    "\n",
    "from tensorflow.keras.losses import SparseCategoricalCrossentropy\n",
    "from tensorflow.keras.optimizers import RMSprop\n",
    "\n",
    "tfd = tfp.distributions\n",
    "tfpl = tfp.layers\n",
    "#from tensorflow_probability.layers import Convolution2DReparameterization\n",
    "# If you would like to make further imports from tensorflow, add them here\n",
    "#from tfpl.util import default_mean_field_normal_fn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![MNIST and MNIST-corrupted overview image](data/mnist_corrupted.png)\n",
    "\n",
    "#### The MNIST and MNIST-C datasets\n",
    "\n",
    "In this assignment, you will use the [MNIST](http://yann.lecun.com/exdb/mnist/) and [MNIST-C](https://github.com/google-research/mnist-c) datasets, which both consist of a training set of 60,000 handwritten digits with corresponding labels, and a test set of 10,000 images. The images have been normalised and centred. The MNIST-C dataset is a corrupted version of the MNIST dataset, to test out-of-distribution robustness of computer vision models.\n",
    "\n",
    "- Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner. \"Gradient-based learning applied to document recognition.\" Proceedings of the IEEE, 86(11):2278-2324, November 1998.\n",
    "- N. Mu and J. Gilmeer. \"MNIST-C: A Robustness Benchmark for Computer Vision\" https://arxiv.org/abs/1906.02337\n",
    "\n",
    "Your goal is to construct a neural network that classifies images of handwritten digits into one of 10 classes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Load the datasets\n",
    "\n",
    "We'll start by importing two datasets. The first is the MNIST dataset of handwritten digits, and the second is the MNIST-C dataset, which is a corrupted version of the MNIST dataset. This dataset is available on [TensorFlow datasets](https://www.tensorflow.org/datasets/catalog/mnist_corrupted). We'll be using the dataset with \"spatters\". We will load and inspect the datasets below. We'll use the notation `_c` to denote `corrupted`. The images are the same as in the original MNIST, but are \"corrupted\" by some grey spatters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to load training and testing data, with labels in integer and one-hot form\n",
    "\n",
    "def load_data(name):\n",
    "    data_dir = os.path.join('data', name)\n",
    "    x_train = 1 - np.load(os.path.join(data_dir, 'x_train.npy')) / 255.\n",
    "    x_train = x_train.astype(np.float32)\n",
    "    y_train = np.load(os.path.join(data_dir, 'y_train.npy'))\n",
    "    y_train_oh = tf.keras.utils.to_categorical(y_train)\n",
    "    x_test  = 1 - np.load(os.path.join(data_dir, 'x_test.npy')) / 255.\n",
    "    x_test = x_test.astype(np.float32)\n",
    "    y_test  = np.load(os.path.join(data_dir, 'y_test.npy'))\n",
    "    y_test_oh = tf.keras.utils.to_categorical(y_test)\n",
    "    \n",
    "    return (x_train, y_train, y_train_oh), (x_test, y_test, y_test_oh)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to inspect dataset digits\n",
    "\n",
    "def inspect_images(data, num_images):\n",
    "    fig, ax = plt.subplots(nrows=1, ncols=num_images, figsize=(2*num_images, 2))\n",
    "    for i in range(num_images):\n",
    "        ax[i].imshow(data[i, ..., 0], cmap='gray')\n",
    "        ax[i].axis('off')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 1600x200 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Load and inspect the MNIST dataset\n",
    "\n",
    "(x_train, y_train, y_train_oh), (x_test, y_test, y_test_oh) = load_data('MNIST')\n",
    "inspect_images(data=x_train, num_images=8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1600x200 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Load and inspect the MNIST-C dataset\n",
    "\n",
    "(x_c_train, y_c_train, y_c_train_oh), (x_c_test, y_c_test, y_c_test_oh) = load_data('MNIST_corrupted')\n",
    "inspect_images(data=x_c_train, num_images=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Create the deterministic model\n",
    "\n",
    "We will first train a standard deterministic CNN classifier model as a base model before implementing the probabilistic and Bayesian neural networks. You should now build the deterministic model using the Sequential API according to the following specifications:\n",
    "\n",
    "* The first layer should be Conv2D layer with 8 filters, 5x5 kernel size, ReLU activation and `'VALID'` padding.\n",
    "    * This layer should set the `input_shape` according to the function argument\n",
    "* The second layer should be a MaxPooling2D layer with a 6x6 window size.\n",
    "* The third layer should be a Flatten layer\n",
    "* The final layer should be a Dense layer with 10 units and softmax activation\n",
    "\n",
    "In total, the network should have 4 layers.\n",
    "\n",
    "The model should then be compiled with the loss function, optimiser and list of metrics supplied in the function arguments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [],
   "source": [
    "#### GRADED CELL ####\n",
    "\n",
    "# Complete the following function. \n",
    "# Make sure to not change the function name or arguments.\n",
    "\n",
    "def get_deterministic_model(input_shape, loss, optimizer, metrics):\n",
    "    \"\"\"\n",
    "    This function should build and compile a CNN model according to the above specification. \n",
    "    The function takes input_shape, loss, optimizer and metrics as arguments, which should be\n",
    "    used to define and compile the model.\n",
    "    Your function should return the compiled model.\n",
    "    \"\"\"\n",
    "    model = Sequential([\n",
    "        Conv2D(8,(5,5), input_shape = input_shape, activation='relu',padding='valid'),\n",
    "        MaxPooling2D(6),\n",
    "        Flatten(),\n",
    "        Dense(10, activation='softmax')\n",
    "    ])\n",
    "    model.compile(optimizer = optimizer, metrics=metrics, loss=loss)\n",
    "    return model\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Run your function to get the benchmark model\n",
    "\n",
    "tf.random.set_seed(0)\n",
    "deterministic_model = get_deterministic_model(\n",
    "    input_shape=(28, 28, 1), \n",
    "    loss=SparseCategoricalCrossentropy(), \n",
    "    optimizer=RMSprop(), \n",
    "    metrics=['accuracy']\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential_26\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "conv2d_3 (Conv2D)            (None, 24, 24, 8)         208       \n",
      "_________________________________________________________________\n",
      "max_pooling2d_26 (MaxPooling (None, 4, 4, 8)           0         \n",
      "_________________________________________________________________\n",
      "flatten_26 (Flatten)         (None, 128)               0         \n",
      "_________________________________________________________________\n",
      "dense_3 (Dense)              (None, 10)                1290      \n",
      "=================================================================\n",
      "Total params: 1,498\n",
      "Trainable params: 1,498\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Print the model summary\n",
    "\n",
    "deterministic_model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples\n",
      "Epoch 1/5\n",
      "60000/60000 [==============================] - 4s 70us/sample - loss: 0.5030 - accuracy: 0.8644\n",
      "Epoch 2/5\n",
      "60000/60000 [==============================] - 4s 68us/sample - loss: 0.1558 - accuracy: 0.9526\n",
      "Epoch 3/5\n",
      "60000/60000 [==============================] - 4s 66us/sample - loss: 0.1215 - accuracy: 0.9628\n",
      "Epoch 4/5\n",
      "60000/60000 [==============================] - 4s 69us/sample - loss: 0.1058 - accuracy: 0.9678\n",
      "Epoch 5/5\n",
      "60000/60000 [==============================] - 4s 68us/sample - loss: 0.0957 - accuracy: 0.9708\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x7f2265bc4f98>"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Train the model\n",
    "\n",
    "deterministic_model.fit(x_train, y_train, epochs=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on MNIST test set:  0.9732\n",
      "Accuracy on corrupted MNIST test set:  0.9444\n"
     ]
    }
   ],
   "source": [
    "# Evaluate the model\n",
    "\n",
    "print('Accuracy on MNIST test set: ',\n",
    "      str(deterministic_model.evaluate(x_test, y_test, verbose=False)[1]))\n",
    "print('Accuracy on corrupted MNIST test set: ',\n",
    "      str(deterministic_model.evaluate(x_c_test, y_c_test, verbose=False)[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you might expect, the pointwise performance on the corrupted MNIST set is worse. This makes sense, since this dataset is slightly different, and noisier, than the uncorrupted version. Furthermore, the model was trained on the uncorrupted MNIST data, so has no experience with the spatters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probabilistic CNN model\n",
    "\n",
    "You'll start by turning this deterministic network into a probabilistic one, by letting the model output a distribution instead of a deterministic tensor. This model will capture the aleatoric uncertainty on the image labels. You will do this by adding a probabilistic layer to the end of the model and training using the negative loglikelihood. \n",
    "\n",
    "You should first define the negative loss likelihood loss function below. This function has arguments `y_true` for the correct label (as a one-hot vector), and `y_pred` as the model prediction (a `OneHotCategorical` distribution). It should return the negative log-likelihood of each sample in `y_true` given the predicted distribution `y_pred`. If `y_true` is of shape `[B, E]` and `y_pred` has batch shape `[B]` and event shape `[E]`, the output should be a Tensor of shape `[B]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [],
   "source": [
    "#### GRADED CELL ####\n",
    "\n",
    "# Complete the following functions. \n",
    "# Make sure to not change the function name or arguments.\n",
    "\n",
    "def nll(y_true, y_pred):\n",
    "    return -y_pred.log_prob(y_true)\n",
    "    \"\"\"\n",
    "    This function should return the negative log-likelihood of each sample\n",
    "    in y_true given the predicted distribution y_pred. If y_true is of shape \n",
    "    [B, E] and y_pred has batch shape [B] and event_shape [E], the output \n",
    "    should be a Tensor of shape [B].\n",
    "    \"\"\" \n",
    "    # predictions = - tf.math.log(y_pred)\n",
    "    # p0 = tf.reduce_sum(predictions[y_true == 0][0]) \n",
    "    # p1 = tf.reduce_sum(predictions[y_true == 1][1]) \n",
    "    # p2 = tf.reduce_sum(predictions[y_true == 2][2]) \n",
    "    # p3 = tf.reduce_sum(predictions[y_true == 3][3]) \n",
    "    # p4 = tf.reduce_sum(predictions[y_true == 4][4]) \n",
    "    # p5 = tf.reduce_sum(predictions[y_true == 5][5]) \n",
    "    # p6 = tf.reduce_sum(predictions[y_true == 6][6]) \n",
    "    # p7 = tf.reduce_sum(predictions[y_true == 7][7]) \n",
    "    # p8 = tf.reduce_sum(predictions[y_true == 8][8]) \n",
    "    # p9 = tf.reduce_sum(predictions[y_true == 9][9])            \n",
    "    # return p0+p1+p2+p3+p4+p5+p6+p7+p8+p9\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You should now build your probabilistic model according to the following specification:\n",
    "\n",
    "* The first three layers are the same as for the deterministic model above\n",
    "* The fourth layer should be a Dense layer with no activation function, and the correct number of units needed to parameterise the probabilistic layer that follows\n",
    "* The final layer should be a probabilistic layer that outputs a `OneHotCategorical` distribution with an event shape of `[10]`, corresponding to the 10 digits\n",
    "* The `convert_to_tensor_fn` in the categorical layer should be set to the mode\n",
    "\n",
    "In total, your model should have 5 layers.\n",
    "\n",
    "The model should then be compiled with the loss function, optimiser and list of metrics supplied in the function arguments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#### GRADED CELL ####\n",
    "\n",
    "# Complete the following functions. \n",
    "# Make sure to not change the function name or arguments.\n",
    "\n",
    "def get_probabilistic_model(input_shape, loss, optimizer, metrics):\n",
    "    \"\"\"\n",
    "    This function should return the probabilistic model according to the \n",
    "    above specification.\n",
    "    The function takes input_shape, loss, optimizer and metrics as arguments, which should be\n",
    "    used to define and compile the model.\n",
    "    Your function should return the compiled model.\n",
    "    \"\"\"\n",
    "    \n",
    "    model = Sequential([\n",
    "        Conv2D(8,(5,5), input_shape = input_shape, activation='relu',padding='valid'),\n",
    "        MaxPooling2D(6),\n",
    "        Flatten(),\n",
    "        Dense(tfpl.OneHotCategorical.params_size(10)),\n",
    "        tfpl.OneHotCategorical([10], convert_to_tensor_fn=tfd.Distribution.mode),\n",
    "        \n",
    "    ])\n",
    "    model.compile(optimizer = optimizer, metrics=metrics, loss=loss)\n",
    "    return model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Run your function to get the probabilistic model\n",
    "\n",
    "tf.random.set_seed(0)\n",
    "probabilistic_model = get_probabilistic_model(\n",
    "    input_shape=(28, 28, 1), \n",
    "    loss=nll, \n",
    "    optimizer=RMSprop(), \n",
    "    metrics=['accuracy']\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential_27\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "conv2d_4 (Conv2D)            (None, 24, 24, 8)         208       \n",
      "_________________________________________________________________\n",
      "max_pooling2d_27 (MaxPooling (None, 4, 4, 8)           0         \n",
      "_________________________________________________________________\n",
      "flatten_27 (Flatten)         (None, 128)               0         \n",
      "_________________________________________________________________\n",
      "dense_4 (Dense)              (None, 10)                1290      \n",
      "_________________________________________________________________\n",
      "one_hot_categorical_25 (OneH ((None, 10), (None, 10))  0         \n",
      "=================================================================\n",
      "Total params: 1,498\n",
      "Trainable params: 1,498\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Print the model summary\n",
    "\n",
    "probabilistic_model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, you can train the probabilistic model on the MNIST data using the code below. \n",
    "\n",
    "Note that the target data now uses the one-hot version of the labels, instead of the sparse version. This is to match the categorical distribution you added at the end."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples\n",
      "Epoch 1/5\n",
      "60000/60000 [==============================] - 4s 73us/sample - loss: 0.5030 - accuracy: 0.8644\n",
      "Epoch 2/5\n",
      "60000/60000 [==============================] - 4s 67us/sample - loss: 0.1558 - accuracy: 0.9526\n",
      "Epoch 3/5\n",
      "60000/60000 [==============================] - 4s 73us/sample - loss: 0.1215 - accuracy: 0.9628\n",
      "Epoch 4/5\n",
      "60000/60000 [==============================] - 4s 66us/sample - loss: 0.1058 - accuracy: 0.9678\n",
      "Epoch 5/5\n",
      "60000/60000 [==============================] - 4s 66us/sample - loss: 0.0957 - accuracy: 0.9708\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x7f2265223470>"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Train the model\n",
    "\n",
    "probabilistic_model.fit(x_train, y_train_oh, epochs=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on MNIST test set:  0.9732\n",
      "Accuracy on corrupted MNIST test set:  0.9444\n"
     ]
    }
   ],
   "source": [
    "# Evaluate the model\n",
    "\n",
    "print('Accuracy on MNIST test set: ',\n",
    "      str(probabilistic_model.evaluate(x_test, y_test_oh, verbose=False)[1]))\n",
    "print('Accuracy on corrupted MNIST test set: ',\n",
    "      str(probabilistic_model.evaluate(x_c_test, y_c_test_oh, verbose=False)[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the test accuracy of the probabilistic model is identical to the deterministic model. This is because the model architectures for both are equivalent; the only difference being that the probabilistic model returns a distribution object. Since we have also set the same random seed for both models, the trained variables are in fact identical, as the following cell shows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "True\n",
      "True\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "# Check all the weights of the deterministic and probabilistic models are identical\n",
    "\n",
    "for deterministic_variable, probabilistic_variable in zip(deterministic_model.weights, probabilistic_model.weights):\n",
    "    print(np.allclose(deterministic_variable.numpy(), probabilistic_variable.numpy()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Analyse the model predictions\n",
    "\n",
    "We will now do some deeper analysis by looking at the probabilities the model assigns to each class instead of its single prediction. \n",
    "\n",
    "The function below will be useful to help us analyse the probabilistic model predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to make plots of the probabilities that the model estimates for an image\n",
    "\n",
    "def analyse_model_prediction(data, true_labels, model, image_num, run_ensemble=False):\n",
    "    if run_ensemble:\n",
    "        ensemble_size = 200\n",
    "    else:\n",
    "        ensemble_size = 1\n",
    "    image = data[image_num]\n",
    "    true_label = true_labels[image_num, 0]\n",
    "    predicted_probabilities = np.empty(shape=(ensemble_size, 10))\n",
    "    for i in range(ensemble_size):\n",
    "        predicted_probabilities[i] = model(image[np.newaxis, :]).mean().numpy()[0]\n",
    "    model_prediction = model(image[np.newaxis, :])\n",
    "    fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(10, 2),\n",
    "                                   gridspec_kw={'width_ratios': [2, 4]})\n",
    "    \n",
    "    # Show the image and the true label\n",
    "    ax1.imshow(image[..., 0], cmap='gray')\n",
    "    ax1.axis('off')\n",
    "    ax1.set_title('True label: {}'.format(str(true_label)))\n",
    "    \n",
    "    # Show a 95% prediction interval of model predicted probabilities\n",
    "    pct_2p5 = np.array([np.percentile(predicted_probabilities[:, i], 2.5) for i in range(10)])\n",
    "    pct_97p5 = np.array([np.percentile(predicted_probabilities[:, i], 97.5) for i in range(10)])    \n",
    "    bar = ax2.bar(np.arange(10), pct_97p5, color='red')\n",
    "    bar[int(true_label)].set_color('green')\n",
    "    ax2.bar(np.arange(10), pct_2p5-0.02, color='white', linewidth=1, edgecolor='white')\n",
    "    ax2.set_xticks(np.arange(10))\n",
    "    ax2.set_ylim([0, 1])\n",
    "    ax2.set_ylabel('Probability')\n",
    "    ax2.set_title('Model estimated probabilities')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Prediction examples on MNIST\n",
    "\n",
    "for i in [0, 1577]:\n",
    "    analyse_model_prediction(x_test, y_test, probabilistic_model, i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model is very confident that the first image is a 6, which is correct. For the second image, the model struggles, assigning nonzero probabilities to many different classes. \n",
    "\n",
    "Run the code below to do the same for 2 images from the corrupted MNIST test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Prediction examples on MNIST-C\n",
    "\n",
    "for i in [0, 3710]:\n",
    "    analyse_model_prediction(x_c_test, y_c_test, probabilistic_model, i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first is the same 6 as you saw above, but the second image is different. Notice how the model can still say with high certainty that the first image is a 6, but struggles for the second, assigning an almost uniform distribution to all possible labels.\n",
    "\n",
    "Finally, have a look at an image for which the model is very sure on MNIST data but very unsure on corrupted MNIST data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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olUr12KLbuKT8MpkMjRs3rtQpfYven5R0KFlOTg7q1KmDzz77DEFBQXBxcYGnpyd69uyJYcOGoWHDhpUVl6oQNhF60HV8YnGzMz39xAFA3cVv2bIFdevW1Rqv7ywbjx49QteuXXH//n1Mnz4dTZo0Qa1atXD16lWEhIQ8dzo4XVQqFerVq4fY2Fidvy/peEp9DR48GO+++y5+//13CCHQpk0b9SeIRU/KRGQ4Bg8ejJCQEKSnp6NHjx6oXbt2pVxv0XPle++9V+ybqFatWum9zm7duuHDDz/U+fui5zg7OzskJycjLi4OBw4cwIEDBxAbG4thw4bh66+/1us6n1bcuWvF1cX/PyH98uXL6Nq1K5o2bYolS5bAxcUFxsbG2L9/Pz7//PNSva6UdtsrW0nnF1TkLIuffvopZsyYgREjRmDu3LmoW7cujIyMEB4eXqbX5cpQlGvhwoXw8PDQOaao2RswYAA6dOiAnTt34scff8TChQuxYMEC7NixQ31OExkONhHlVKdOHRQUFODhw4caszQ9+wlG0adhDg4O6NixY7mvNykpCampqdiyZQsGDBigru/Zs0fn+IKCAly/fl3jE6qimZSKZn1o1KgRfv31V3Ts2LFSpg5UKBTqk7UA4NChQ5DJZOjSpcsLv24iqlr+85//YPTo0Th58iS2bNlS7DhXV1ccOnQIeXl5Gnsj/vnnH/Xvi/5VqVS4fPmyxqfbz86GVzRzk1KphK+vb4VsS6NGjXDv3r1Src/Y2Bj+/v7w9/eHSqXCuHHj8OWXX2LGjBk6P/l+kfbs2YOCggLs3r1b47VC16GsxeUq7ba7uroiISEB9+7d09gboe9shZcuXULnzp3Vl+/du4ebN2+iZ8+ez1226DFy6dIljZPVMzIykJ2drX4sFUlJSYEQQmPbn30d3b59Ozp37ox169ZpLJudnQ0bGxud+Z8mhEBKSorejasupX3sFL0/sbS0LNVj1tHREePGjcO4ceOQmZmJNm3aYN68eWwiDBDPiSinoj++ouM8ASA3Nxf//e9/Ncb17NkTZmZm+OSTTzSOPy2i71zoRZ8oiaemNFSpVFozmTxt+fLlGmNXrFgBExMT9bRvAwYMwMOHDzF//nytZR89evTc42FLO8WrLufPn8e6devw7rvvPncqOyJ6+Zibm2PVqlWYNWsW/P39ix3Xs2dPKJVKjeczAPj8888hk8nUb2SK/n32ObFodqAicrkc7777Lr7//nv8+eefWtd369YtvbdlwIABSExMRFxcnNbvsrOz1a8Bt2/f1vidkZGR+s1j0RSjZmZm6uVeNF2vKzk5OTr3TpuZmenMVNpt79mzJx4/fqwxfaxSqcSyZcv0yrxmzRo8evRIfXnVqlV4/Phxqd7QFjUazz4mlixZAgBaM3n9+++/GjM25ebmYuPGjfDw8ICDgwOAJ7eheGaq4W3btuHGjRs6M2zcuBF5eXnqy9u3b8fNmzcr5A15cffRszw9PdGoUSMsWrQI9+7d0/p90d+AUqnUeh9gZ2cHJyenYqfEpZcb90SUU+/eveHg4IBhw4Zh8uTJAJ5M5erk5ISbN2+qx1lbW+OLL77AqFGj4OXlhcDAQFhbW+Pq1avYu3cvunfvjkWLFpX6elu2bIn69etj/PjxSE1NhZmZGbZu3arxZPQ0CwsLbNu2DVlZWfD09MTevXtx6NAhzJkzR33YgJ+fH4KCghAVFYXffvsNXbt2hVwux8WLF7Ft2zasXbsWvXv3LjZTaad4ffjwIV5//XX069cPLi4uSElJwapVq+Do6Kj1xoCIDEdppvf09/dH586d8dFHH+Hq1atwd3fHjz/+iB9++AHh4eHqD3Y8PDwwaNAgrFy5Ejk5OWjXrh0SEhKQkpKitc758+fjyJEj8Pb2RkhICJo3b447d+7gzJkzOHToEO7cuaPXdkyZMgW7d+9G7969MXz4cHh6eiI/Px/nzp3D9u3bcfXqVdjY2GDUqFG4c+cOunTpgnr16uHatWtYtmwZPDw81J+Me3h4QC6XY8GCBcjJyYFCoVB/j0NF6969u3rPyOjRo3Hv3j2sXbsWdnZ2Gq9nwJM3nqtWrcInn3yCxo0bw87ODl26dCn1tvv7+6N9+/aYNm0arl69qv7OhdKcvP20wsJCdO3aFQMGDMCFCxewcuVKvPnmm+jTp89zl3V3d0dQUBDWrFmD7OxsdOrUCadOncLXX3+NgIAAjT0cwJNDsUaOHInTp0/D3t4e69evR0ZGhkaT1bt3b8yZMwfBwcFo164dzp07h2+//bbYcwbq1q2LN998E8HBwcjIyEBMTAwaN26MkJAQvW4HXYq7j55lZGSEr776Cj169ECLFi0QHBwMZ2dn3LhxA0eOHIGlpSX27NmDvLw81KtXD/369YO7uzvMzc1x6NAhnD59GosXLy53XqqGJJoVqsopzRSve/bs0fn7kydPCi8vL2FsbCzc3NzEsmXLtKZ4LRIfHy98fX2FpaWlMDU1FY0bNxYjR44UZ8+eLTGfrile//jjD9G5c2dhZmYmbG1txdixY8Xp06cFAPHdd9+pxwUGBgpra2tx4cIF0aVLF2FqaiocHR3FJ598ojGdmxBPpnpbuXKlaN26tTAxMRGWlpaiVatWIjIyUmPa2PJM8fro0SPRv39/4ezsLIyNjUW9evVEaGio1vSKRPTyenqK15I8O8WrEELk5eWJiRMnCicnJ1GzZk3xyiuviIULF2o9nz148ECMHz9eWFtbCzMzM+Hv7y/S0tK0pscUQoiMjAwRGhoqXFxcRM2aNYWDg4Po2rWrWLNmjXpMaad4LcoYGRkpGjduLIyNjYWNjY1o166dWLRokXpK0u3bt4vu3bsLOzs7YWxsLOrXry9Gjx6t9bqxdu1a0bBhQyGXyzWm5ixuitdt27ZpLF/cbR0VFSUAiFu3bqlru3fvFq1atRImJibCzc1NLFiwQKxfv15r+tD09HTRq1cvYWFhIQBo5CjNtgshxO3bt8XQoUOFpaWlsLKyEkOHDhVnz57Va4rXY8eOiffff1/UqVNHmJubiyFDhojbt29rjNX1GCry6NEjMXv2bNGgQQNRs2ZN4eLiIiIjI7Wmcy9aR1xcnGjVqpVQKBSiadOmWrf1w4cPxaRJk4Sjo6MwNTUV7du3F4mJicXeV999952IjIwUdnZ2wtTUVPTq1Utcu3ZNY51lneK1uPvo2Slei5w9e1a88847wtraWigUCuHq6ioGDBggEhIShBBCFBQUiClTpgh3d3dhYWEhzMzMhLu7u1i5cqXO25ZefjIhntnvRkRERFSFbdiwAcHBwTh9+jS8vLykjkNkkHhOBBERERER6YVNBBERERER6YVNBBERERER6YVNBBGV2fHjx+Hv7w8nJyfIZDLs2rXrucscPXoUbdq0gUKhQOPGjbFhw4YXH5SIXirDhw+HEILnQxBJiE0EEZVZfn4+3N3dsWLFilKNT01NRa9evdC5c2ckJycjPDwco0aN0jmnPBEREVVdnJ2JiCqETCbDzp07ERAQUOyYqVOnYt++fRpf6jVw4EBkZ2fj4MGDlRGTiIiIKgC/bI6IKk1iYiJ8fX01an5+fggPDy92mYKCAo1vQ1WpVLhz5w6sra0hk8leWFYiIiJDIIRAXl4enJycYGRU+oOU2EQQUaVJT0+Hvb29Rs3e3h65ubl48OABTE1NtZaJjo7G7NmzKysiERGRQUpLS0O9evVKPZ5NBBFVaZGRkYiIiFBfzsnJQf369ZGWlgZLS0sJkxERkSFIy0mD5xpPFDwueP7gSqCooUDS+0lwsXKpkPXl5ubCxcUFFhYWei3HJoKIKo2DgwMyMjI0ahkZGbC0tNS5FwIAFAoFFAqFVt3S0pJNBBERvXAF+QUoqFFQZd41F+BJnop+DdT3EOEqcnMQkSHw8fHB/v37NWrx8fHw8fGRKBEREdHzuVi6wKaWjdQxAABZ97OkjgCATQQRlcO9e/eQkpKivpyamork5GTUrVsX9evXR2RkJG7cuIGNGzcCAMaMGYPly5fjww8/xIgRI3D48GFs3boV+/btk2oTiIiISlTTqCYuhF2AaU3de8wr24NHD5ByJ+X5A18wfk8EEZXZb7/9htatW6N169YAgIiICLRu3RozZ84EANy8eRPXr19Xj2/QoAH27duH+Ph4uLu7Y/Hixfjqq6/g5+cnSX4iIqLnqWFUo8o0EABgWtMUNYyk3w/A74kgomolNzcXVlZWyMnJ4TkRRET0wp2/dR7NbJtJHUNDRWYq6+sq90QQEREREZFe2EQQEREREZFe2EQQEREREZFe2EQQEREREZFe2EQQEREREZFe2EQQEREREZFe2EQQEREREZFe2EQQEREREZFe2EQQEREREZFe2EQQEREREZFe2EQQEREREZFe2EQQEREREZFe2EQQEREREZFe2EQQEREREZFe2EQQEREREZFe2EQQEREREZFe2EQQEREREZFe2EQQEREREZFe2EQQEREREZFe2EQQEREREZFe2EQQUbmsWLECbm5uMDExgbe3N06dOlXi+JiYGDRp0gSmpqZwcXHBxIkT8fDhw0pKS0RERBWBTQQRldmWLVsQERGBqKgonDlzBu7u7vDz80NmZqbO8Zs2bcK0adMQFRWF8+fPY926ddiyZQumT59eycmJiIioPNhEEFGZLVmyBCEhIQgODkbz5s2xevVq1KpVC+vXr9c5/pdffkH79u0xePBguLm5oXv37hg0aNBz914QERFR1cImgojKpLCwEElJSfD19VXXjIyM4Ovri8TERJ3LtGvXDklJSeqm4cqVK9i/fz969uxZ7PUUFBQgNzdX44eIiIikVUPqAERUPWVlZUGpVMLe3l6jbm9vj3/++UfnMoMHD0ZWVhbefPNNCCHw+PFjjBkzpsTDmaKjozF79uwKzU5ERETlwz0RRFRpjh49ik8//RQrV67EmTNnsGPHDuzbtw9z584tdpnIyEjk5OSof9LS0ioxMREREenCPRFVxLlz57Rq3bp10znW1tZWq9avXz+dYydMmKCzXrt2bT3SEWmzsbGBXC5HRkaGRj0jIwMODg46l5kxYwaGDh2KUaNGAQBatmyJ/Px8vP/++/joo49gZKT9uYZCoYBCoaj4DSAiIqIy454IIioTY2NjeHp6IiEhQV1TqVRISEiAj4+PzmXu37+v1SjI5XIAgBDixYUlIiKiCsU9EURUZhEREQgKCoKXlxfatm2LmJgY5OfnIzg4GAAwbNgwODs7Izo6GgDg7++PJUuWoHXr1vD29kZKSgpmzJgBf39/dTNBREREVR+bCCIqs8DAQNy6dQszZ85Eeno6PDw8cPDgQfXJ1tevX9fY8/Dxxx9DJpPh448/xo0bN2Brawt/f3/MmzdPqk0gIiKiMmATQUTlEhYWhrCwMJ2/O3r0qMblGjVqICoqClFRUZWQjIiIiF4UNhGV7M6dOzrrI0aM0KoV962/uup//fWXzrHbt2/XWZ80aZJWrW/fvjrH1qlTR2ediIiIiAwTT6wmIiIiIiK9sIkgIiIiIiK9sIkgIiIiIiK9sIkgIiIiIiK9sIkgIiIiIiK9cHamSvbNN9/orCclJZV6HUVf3PW0ZcuW6Rxb3KxNumaDsrS01Dn21KlTWrVXX321pIhUxXXq1AkjR45E//79YWpqKnUcIiIiqma4J4LIALVu3RqTJ0+Gg4MDQkJCcPLkSakjERERUTXCJoLIAMXExODff/9FbGwsMjMz0bFjRzRv3hyLFi1CRkaG1PGIiIioimMTQWSgatSogXfeeQc//PAD/ve//2Hw4MGYMWMGXFxcEBAQgMOHD0sdkYiIiKooNhFEBu7UqVOIiorC4sWLYWdnh8jISNjY2KB3796YPHmy1PGIiIioCuKJ1ZVsyZIlpR7r6empsz5mzBitWt++fXWO7d+/v866rhOuc3NzdY7dt2+fVo0nVldvmZmZ+OabbxAbG4tLly7B398f3333Hfz8/CCTyQAAw4cPx9tvv41FixZJnJaIiIiqGjYRRAaoXr16aNSoEUaMGIHhw4fD1tZWa0yrVq3w+uuvS5COiIiIqjo2EUQGKCEhAR06dChxjKWlJY4cOVJJiYiIiKg64TkRRAbKrBmKAAAcOElEQVQoKioK2dnZWvXc3Fx06dJFgkRERERUnbCJIDJAx44dQ2FhoVb94cOH+OmnnyRIRERERNUJD2ciMiB//PEHAEAIgb///hvp6enq3ymVShw8eBDOzs5SxSMiIqJqgk3EC3TixAmt2u3bt0u9/KeffqqzbmVlVaoaAMjl8lJfX3GOHTumVZs4cWK510uVz8PDAzKZDDKZTOdhS6ampli2bJkEyYiIiKg6YRNBZEBSU1MhhEDDhg1x6tQpjVmZjI2NYWdnVyGNJxEREb3ceE4EkQFxdXWFm5sbVCoVvLy84Orqqv5xdHQsUwOxYsUKuLm5wcTEBN7e3jh16lSJ47OzsxEaGgpHR0coFAq8+uqr2L9/f1k3iYiIiCTAPRFEBmL37t3o0aMHatasid27d5c4tk+fPqVa55YtWxAREYHVq1fD29sbMTEx8PPzw4ULF2BnZ6c1vrCwEN26dYOdnR22b98OZ2dnXLt2DbVr1y7TNhEREZE02EQQGYiAgACkp6fDzs4OAQEBxY6TyWRQKpWlWueSJUsQEhKC4OBgAMDq1auxb98+rF+/HtOmTdMav379ety5cwe//PILatasCQBwc3PTf2OIiIhIUmwiXqCpU6dq1e7fv1/q5Rs1alTqsYmJiTrrf/31V6nXUZz69euXex0kPZVKpfP/ZVVYWIikpCRERkaqa0ZGRvD19S328bh79274+PggNDQUP/zwA2xtbTF48GBMnTqV52IQERFVI2wiiKhMsrKyoFQqYW9vr1G3t7fHP//8o3OZK1eu4PDhwxgyZAj279+PlJQUjBs3Do8ePUJUVJTOZQoKClBQUKC+nJubW3EbQURERGXCJoLIQHzxxRelHjt+/PgXkkGlUsHOzg5r1qyBXC6Hp6cnbty4gYULFxbbRERHR2P27NkvJA8RERGVDZsIIgPx+eefl2qcTCYrVRNhY2MDuVyOjIwMjXpGRgYcHBx0LuPo6IiaNWtqHLrUrFkzpKeno7CwEMbGxlrLREZGIiIiQn05NzcXLi4updoWIiIiejHYRBAZiNTU1Apdn7GxMTw9PZGQkKA+UVulUiEhIQFhYWE6l2nfvj02bdoElUoFI6MnM0xfvHgRjo6OOhsIAFAoFFAoFBWanYiIiMqH3xNBRGUWERGBtWvX4uuvv8b58+cxduxY5Ofnq2drGjZsmMaJ12PHjsWdO3cwYcIEXLx4Efv27cOnn36K0NBQqTaBiIiIyoB7Il6gS5culXpsUFCQVq24WZF0zfA0Z84cnWNLO1VnSTw8PMq9DpJeREQE5s6dCzMzM43Dg3RZsmRJqdYZGBiIW7duYebMmUhPT4eHhwcOHjyoPtn6+vXr6j0OAODi4oK4uDhMnDgRrVq1grOzMyZMmKBzJjMiIiKquthEEBmIs2fP4tGjR+r/F0cmk+m13rCwsGIPXzp69KhWzcfHBydPntTrOoiIiKhqYRNBZCCOHDmi8/9ERERE+uI5EUQGLi0tDWlpaVLHICIiomqETQSRAXr8+DFmzJgBKysruLm5wc3NDVZWVvj444/VhzwRERERFYeHM1URuk4srVFD990zdOhQrVpcXFyFZyry6quvvrB1kzQ++OAD7NixA5999hl8fHwAAImJiZg1axZu376NVatWSZyQiIiIqjI2EUQGaNOmTdi8eTN69OihrrVq1QouLi4YNGgQmwgiIiIqEQ9nIjJACoUCbm5uWvUGDRoU+6VvREREREXYRBAZoLCwMMydOxcFBQXqWkFBAebNm1fsdK1ERERERXg4E5GBeOeddzQuHzp0CPXq1YO7uzsA4Pfff0dhYSG6du0qRTwiIiKqRthEEBkIKysrjcvvvvuuxmUXF5fKjENERETVGJuIF6hVq1ZatcOHD+sce/XqVa3arFmzdI7duXNneWKRgYqNjZU6AhEREb0keE4EERERERHphXsiiAzU9u3bsXXrVly/fh2FhYUavztz5oxEqYiIiKg64J4IIgP0xRdfIDg4GPb29jh79izatm0La2trXLlyReO7I4iIiIh0YRNBZIBWrlyJNWvWYNmyZTA2NsaHH36I+Ph4jB8/Hjk5OVLHIyIioiqOhzO9QEFBQVq148eP6xzbs2fPFx2HSO369eto164dAMDU1BR5eXkAgKFDh+KNN97A8uXLpYxHREREVRz3RBAZIAcHB9y5cwcAUL9+fZw8eRIAkJqaCiGElNGIiIioGmATQWSAunTpgt27dwMAgoODMXHiRHTr1g2BgYH4z3/+I3E6IiIiqup4OBORAVqzZg1UKhUAIDQ0FNbW1vjll1/Qp08fjB49WuJ0REREVNWxiSAyQEZGRjAy+r8dkQMHDsTAgQMlTERERETVCZsIIgN19+5drFu3DufPnwcANG/eHMHBwahbt67EyYiIiKiqYxPxAg0dOlSrtnPnTp1jd+3aVa7rsrCw0FkvmnWnNAICAnTW27RpU6ZMVHUdP34cffr0gaWlJby8vAA8+e6IOXPmYM+ePejYsaNe61uxYgUWLlyI9PR0uLu7Y9myZWjbtu1zl9u8eTMGDRqEvn37lvtvgIiIiCoPT6wmMkChoaEYMGAAUlNTsWPHDuzYsQNXrlzBwIEDERoaqte6tmzZgoiICERFReHMmTNwd3eHn58fMjMzS1zu6tWrmDx5Mjp06FCeTSEiIiIJsIkgMkApKSmYNGkS5HK5uiaXyxEREYGUlBS91rVkyRKEhIQgODgYzZs3x+rVq1GrVi2sX7++2GWUSiWGDBmC2bNno2HDhmXeDiIiIpIGmwgiA9SmTRv1uRBPO3/+PNzd3Uu9nsLCQiQlJcHX11ddMzIygq+vLxITE4tdbs6cObCzs8PIkSP1C05ERERVAs+JIDIQf/zxh/r/48ePx4QJE5CSkoI33ngDAHDy5EmsWLEC8+fPL/U6s7KyoFQqYW9vr1G3t7fHP//8o3OZEydOYN26dUhOTi7VdRQUFKCgoEB9OTc3t9T5iIiI6MVgE1HJNm7cqLMeExOjVdu+fbvOsYMHD9aqXb9+XefYlStXljrbqVOndNZr1apV6nVQ1eXh4QGZTKbxjdQffvih1rjBgwcjMDDwhWTIy8vD0KFDsXbtWtjY2JRqmejoaMyePfuF5CEiIqKyYRNBZCBSU1MrfJ02NjaQy+XIyMjQqGdkZMDBwUFr/OXLl3H16lX4+/ura0VfelejRg1cuHABjRo10lgmMjISERER6su5ublwcXGpyM0gIiIiPbGJIDIQrq6uFb5OY2NjeHp6IiEhQT1FsEqlQkJCAsLCwrTGN23aFOfOndOoffzxx8jLy8PSpUt1NgcKhQIKhaLCsxMREVHZsYkgMlCXL19GTEyMxpfNTZgwQWtPwPNEREQgKCgIXl5eaNu2LWJiYpCfn4/g4GAAwLBhw+Ds7Izo6GiYmJjgtdde01i+du3aAKBVJyIioqqLTQSRAYqLi0OfPn3g4eGB9u3bAwB+/vlntGjRAnv27EG3bt1Kva7AwEDcunULM2fORHp6Ojw8PHDw4EH1ydbXr1+HkREngiMiInqZsIkgMkDTpk3DxIkTtWZimjZtGqZOnapXEwEAYWFhOg9fAoCjR4+WuOyGDRv0ui4iIiKSHpuISmZubq6z/vHHH5eqVpw5c+aUOVMRfd84UvV1/vx5bN26Vas+YsQInTOFERERET2NxxgQGSBbW1ud39OQnJwMOzs7CRIRERFRdcI9EUQGKCQkBO+//z6uXLmCdu3aAXhyTsSCBQs0plMlIiIi0oVNBJEBmjFjBiwsLLB48WJERkYCAJycnDBr1iyMHz9e4nRERERU1bGJIDIwQgikpaVh7NixmDhxIvLy8gAAFhYWEicjIiKi6oJNxEsiISGh3OuoU6dOBSShqk4IgcaNG+Ovv/7CK6+8wuaBiIiI9MYTq4kMjJGREV555RXcvn1b6ihERERUTbGJIDJA8+fPx5QpU/Dnn39KHYWIiIiqIR7ORGSAhg0bhvv378Pd3R3GxsYwNTXV+P2dO3ckSkZERETVAZsIIgPEL5QjIiKi8mATQWRAVCoVFi5ciN27d6OwsBBdu3ZFVFSU1p4IIiIiopKwiXhJVMRJso0bN66AJFSVzZs3D7NmzYKvry9MTU2xdOlSZGZmYv369VJHIyIiomqEJ1YTGZCNGzdi5cqViIuLw65du7Bnzx58++23UKlUUkcjIiKiaoRNBJEBuX79Onr27Km+7OvrC5lMhn///VfCVERERFTdsIkgMiCPHz+GiYmJRq1mzZp49OiRRImIiIioOuI5EUQGRAiB4cOHQ6FQqGsPHz7EmDFjYGZmpq7t2LFDinhERERUTbCJqIaUSmWpaiUxMtLeCdW2bdsyZ6LqISgoSKv23nvvSZCEiIiIqjM2EUQGJDY2VuoIRERE9BLgORFERERERKQXNhFERERERKQXNhFEVG4rVqyAm5sbTExM4O3tjVOnThU7du3atejQoQPq1KmDOnXqwNfXt8TxREREVPWwiSCictmyZQsiIiIQFRWFM2fOwN3dHX5+fsjMzNQ5/ujRoxg0aBCOHDmCxMREuLi4oHv37rhx40YlJyciIqKykgkhhNQhSD/JyclatTZt2ui1jrp162rV/v77b51j7ezs9Fo3GRZvb2+8/vrrWL58OQBApVLBxcUFH3zwAaZNm/bc5ZVKJerUqYPly5dj2LBhzx2fm5sLKysr5OTkwNLSstz5iYiISnL+1nk0s20mdQwNFZmprK+r3BNBRGVWWFiIpKQk+Pr6qmtGRkbw9fVFYmJiqdZx//59PHr0SGdjCwAFBQXIzc3V+CEiIiJpsYkgojLLysqCUqmEvb29Rt3e3h7p6emlWsfUqVPh5OSk0Yg8LTo6GlZWVuofFxeXcucmIiKi8mETQUSSmT9/PjZv3oydO3fCxMRE55jIyEjk5OSof9LS0io5JRERET2LXzZHRGVmY2MDuVyOjIwMjXpGRgYcHBxKXHbRokWYP38+Dh06hFatWhU7TqFQQKFQVEheIiIiqhhsIqqhHTt2lHpscefN6zqB1djYuMyZyDAZGxvD09MTCQkJCAgIAPDkxOqEhASEhYUVu9xnn32GefPmIS4uDl5eXpUVl4iIiCoImwgiKpeIiAgEBQXBy8sLbdu2RUxMDPLz8xEcHAzgScPq7OyM6OhoAMCCBQswc+ZMbNq0CW5ubupzJ8zNzWFubi7ZdhAREVHpsYkgonIJDAzErVu3MHPmTKSnp8PDwwMHDx5Un2x9/fp1GBn93+lXq1atQmFhIfr166exnqioKMyaNasyoxMREVEZsYkgonILCwsr9vClo0ePaly+evXqiw9ERERELxRnZyIiIiIiIr2wiSAiIiIiIr3wcCYD9dZbb2nVateuXflBiIiIiKja4Z4IIiIiIiLSC5sIIiIiIiLSC5sIIiIiIiLSC5sIIiIiIiLSC0+sroZcXFxKPbZt27Y66x06dKioOERERERkYLgngoiIiIiI9MImgoiIiIiI9MImgoiIiIiI9MImgoiIiIiI9MImgoiIiIiI9MLZmaqhkJCQUtWIiIiIiF4E7okgIiIiIiK9sIkgIiIiIiK9sIkgIiIiIiK9sIkgIiIiIiK9sIkgIiIiIiK9sIkgIiIiIiK9sIkgonJbsWIF3NzcYGJiAm9vb5w6darE8du2bUPTpk1hYmKCli1bYv/+/ZWUlIiIiCoCmwgiKpctW7YgIiICUVFROHPmDNzd3eHn54fMzEyd43/55RcMGjQII0eOxNmzZxEQEICAgAD8+eeflZyciIiIykomhBBShyCi6svb2xuvv/46li9fDgBQqVRwcXHBBx98gGnTpmmNDwwMRH5+Pvbu3auuvfHGG/Dw8MDq1aufe325ubmwsrJCTk4OLC0tK25DiIiIdDh/6zya2TaTOoaGisxU1tdVfmM1EZVZYWEhkpKSEBkZqa4ZGRnB19cXiYmJOpdJTExERESERs3Pzw+7du3SOb6goAAFBQXqyzk5OQCePOkREYDmzQFra6lTPPHTT1InIKpw9/LuIVdRtV5zKjJT0eupvvsV2EQQUZllZWVBqVTC3t5eo25vb49//vlH5zLp6ek6x6enp+scHx0djdmzZ2vVXVxcypia6CV044bUCZ6wspI6ARGVUV5eHqz0+BtmE0FEVVpkZKTGnguVSoU7d+7A2toaMplMwmTacnNz4eLigrS0tGpxqFV1yludsgLVK291ygpUr7zVKSvAvC9SVc4qhEBeXh6cnJz0Wo5NBBGVmY2NDeRyOTIyMjTqGRkZcHBw0LmMg4ODXuMVCgUUCoVGrXbt2uVI/eJZWlpWuReJklSnvNUpK1C98lanrED1yludsgLM+yJV1az67IEowtmZiKjMjI2N4enpiYSEBHVNpVIhISEBPj4+Opfx8fHRGA8A8fHxxY4nIiKiqod7IoioXCIiIhAUFAQvLy+0bdsWMTExyM/PR3BwMABg2LBhcHZ2RnR0NABgwoQJ6NSpExYvXoxevXph8+bN+O2337BmzRopN4OIiIj0IJ81a9YsqUMQUfX12muvoXbt2pg3bx4WLVoEAPj222/RpEkTAMDSpUtRo0YNBAQEAHhyQnSzZs2wcOFCzJ8/HxkZGVi3bh3at28v2TZUJLlcjrfeegs1alSPz2iqU97qlBWoXnmrU1ageuWtTlkB5n2RqlPW0uD3RBARERERkV54TgQREREREemFTQQREREREemFTQQREREREemFTQQREREREemFTQQRUQVZsWIF3NzcYGJiAm9vb5w6dUrqSDodP34c/v7+cHJygkwmw65du6SOVKzo6Gi8/vrrsLCwgJ2dHQICAnDhwgWpY+m0atUqtGrVSv1lUj4+Pjhw4IDUsUpt/vz5kMlkCA8PlzqKTrNmzYJMJtP4adq0qdSxinXjxg289957sLa2hqmpKVq2bInffvtN6lg6ubm5ad22MpkMoaGhUkfTolQqMWPGDDRo0ACmpqZo1KgR5s6di6o8T1BeXh7Cw8Ph6uoKU1NTtGvXDqdPn5Y6VrmxiSAiqgBbtmxBREQEoqKicObMGbi7u8PPzw+ZmZlSR9OSn58Pd3d3rFixQuooz3Xs2DGEhobi5MmTiI+Px6NHj9C9e3fk5+dLHU1LvXr1MH/+fCQlJeG3335Dly5d0LdvX/z1119SR3uu06dP48svv0SrVq2kjlKiFi1a4ObNm+qfEydOSB1Jp7t376J9+/aoWbMmDhw4gL///huLFy9GnTp1pI6m0+nTpzVu1/j4eABA//79JU6mbcGCBVi1ahWWL1+O8+fPY8GCBfjss8+wbNkyqaMVa9SoUYiPj8c333yDc+fOoXv37vD19cWNGzekjlY+goiIyq1t27YiNDRUfVmpVAonJycRHR0tYarnAyB27twpdYxSy8zMFADEsWPHpI5SKnXq1BFfffWV1DFKlJeXJ1555RURHx8vOnXqJCZMmCB1JJ2ioqKEu7u71DFKZerUqeLNN9+UOkaZTZgwQTRq1EioVCqpo2jp1auXGDFihEbtnXfeEUOGDJEoUcnu378v5HK52Lt3r0a9TZs24qOPPpIoVcXgnggionIqLCxEUlISfH191TUjIyP4+voiMTFRwmQvn5ycHABA3bp1JU5SMqVSic2bNyM/Px8+Pj5SxylRaGgoevXqpfH4raouXboEJycnNGzYEEOGDMH169eljqTT7t274eXlhf79+8POzg6tW7fG2rVrpY5VKoWFhfjvf/+LESNGQCaTSR1HS7t27ZCQkICLFy8CAH7//XecOHECPXr0kDiZbo8fP4ZSqYSJiYlG3dTUtMruSSutl+Mr84iIJJSVlQWlUgl7e3uNur29Pf755x+JUr18VCoVwsPD0b59e7z22mtSx9Hp3Llz8PHxwcOHD2Fubo6dO3eiefPmUscq1ubNm3HmzJlqcXy2t7c3NmzYgCZNmuDmzZuYPXs2OnTogD///BMWFhZSx9Nw5coVrFq1ChEREZg+fTpOnz6N8ePHw9jYGEFBQVLHK9GuXbuQnZ2N4cOHSx1Fp2nTpiE3NxdNmzaFXC6HUqnEvHnzMGTIEKmj6WRhYQEfHx/MnTsXzZo1g729Pb777jskJiaicePGUscrFzYRRERULYSGhuLPP/+s0p/eNWnSBMnJycjJycH27dsRFBSEY8eOVclGIi0tDRMmTEB8fLzWp6RV0dOfNLdq1Qre3t5wdXXF1q1bMXLkSAmTaVOpVPDy8sKnn34KAGjdujX+/PNPrF69uso3EevWrUOPHj3g5OQkdRSdtm7dim+//RabNm1CixYtkJycjPDwcDg5OVXZ2/abb77BiBEj4OzsDLlcjjZt2mDQoEFISkqSOlq5sIkgIionGxsbyOVyZGRkaNQzMjLg4OAgUaqXS1hYGPbu3Yvjx4+jXr16UscplrGxsfrTRU9PT5w+fRpLly7Fl19+KXEybUlJScjMzESbNm3UNaVSiePHj2P58uUoKCiAXC6XMGHJateujVdffRUpKSlSR9Hi6Oio1Tg2a9YM33//vUSJSufatWs4dOgQduzYIXWUYk2ZMgXTpk3DwIEDAQAtW7bEtWvXEB0dXWWbiEaNGuHYsWPIz89Hbm4uHB0dERgYiIYNG0odrVx4TgQRUTkZGxvD09MTCQkJ6ppKpUJCQkKVPx6+qhNCICwsDDt37sThw4fRoEEDqSPpRaVSoaCgQOoYOnXt2hXnzp1DcnKy+sfLywtDhgxBcnJylW4gAODevXu4fPkyHB0dpY6ipX379lpTEV+8eBGurq4SJSqd2NhY2NnZoVevXlJHKdb9+/dhZKT59lUul0OlUkmUqPTMzMzg6OiIu3fvIi4uDn379pU6UrlwTwQRUQWIiIhAUFAQvLy80LZtW8TExCA/Px/BwcFSR9Ny7949jU9vU1NTkZycjLp166J+/foSJtMWGhqKTZs24YcffoCFhQXS09MBAFZWVjA1NZU4nabIyEj06NED9evXR15eHjZt2oSjR48iLi5O6mg6WVhYaJ1bYmZmBmtr6yp5zsnkyZPh7+8PV1dX/Pvvv4iKioJcLsegQYOkjqZl4sSJaNeuHT799FMMGDAAp06dwpo1a7BmzRqpoxVLpVIhNjYWQUFBqFGj6r499Pf3x7x581C/fn20aNECZ8+exZIlSzBixAipoxUrLi4OQgg0adIEKSkpmDJlCpo2bVolXx/0IvX0UEREL4tly5aJ+vXrC2NjY9G2bVtx8uRJqSPpdOTIEQFA6ycoKEjqaFp05QQgYmNjpY6mZcSIEcLV1VUYGxsLW1tb0bVrV/Hjjz9KHUsvVXmK18DAQOHo6CiMjY2Fs7OzCAwMFCkpKVLHKtaePXvEa6+9JhQKhWjatKlYs2aN1JFKFBcXJwCICxcuSB2lRLm5uWLChAmifv36wsTERDRs2FB89NFHoqCgQOpoxdqyZYto2LChMDY2Fg4ODiI0NFRkZ2dLHavcZEJU4a/4IyIiIiKiKofnRBARERERkV7YRBARERERkV7YRBARERERkV7YRBARERERkV7YRBARERERkV7YRBARERERkV7YRBARERERkV7YRBARERERkV7YRBARERERkV7YRBARERERkV7YRBARERERkV7YRBARERERkV7+HxBKEjej/ijUAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1000x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Prediction examples from both datasets\n",
    "\n",
    "for i in [9241]:\n",
    "    analyse_model_prediction(x_test, y_test, probabilistic_model, i)\n",
    "    analyse_model_prediction(x_c_test, y_c_test, probabilistic_model, i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's not surprising what's happening here: the spatters cover up most of the number. You would hope a model indicates that it's unsure here, since there's very little information to go by. This is exactly what's happened."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Uncertainty quantification using entropy\n",
    "\n",
    "We can also make some analysis of the model's uncertainty across the full test set, instead of for individual values. One way to do this is to calculate the [entropy](https://en.wikipedia.org/wiki/Entropy_%28information_theory%29) of the distribution. The entropy is the expected information (or informally, the expected 'surprise') of a random variable, and is a measure of the uncertainty of the random variable. The entropy of the estimated probabilities for sample $i$ is defined as\n",
    "\n",
    "$$\n",
    "H_i = -\\sum_{j=1}^{10} p_{ij} \\text{log}_{2}(p_{ij})\n",
    "$$\n",
    "\n",
    "where $p_{ij}$ is the probability that the model assigns to sample $i$ corresponding to label $j$. The entropy as above is measured in _bits_. If the natural logarithm is used instead, the entropy is measured in _nats_.\n",
    "\n",
    "The key point is that the higher the value, the more unsure the model is. Let's see the distribution of the entropy of the model's predictions across the MNIST and corrupted MNIST test sets. The plots will be split between predictions the model gets correct and incorrect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Functions to plot the distribution of the information entropy across samples,\n",
    "# split into whether the model prediction is correct or incorrect\n",
    "\n",
    "\n",
    "def get_correct_indices(model, x, labels):\n",
    "    y_model = model(x)\n",
    "    correct = np.argmax(y_model.mean(), axis=1) == np.squeeze(labels)\n",
    "    correct_indices = [i for i in range(x.shape[0]) if correct[i]]\n",
    "    incorrect_indices = [i for i in range(x.shape[0]) if not correct[i]]\n",
    "    return correct_indices, incorrect_indices\n",
    "\n",
    "\n",
    "def plot_entropy_distribution(model, x, labels):\n",
    "    probs = model(x).mean().numpy()\n",
    "    entropy = -np.sum(probs * np.log2(probs), axis=1)\n",
    "    fig, axes = plt.subplots(1, 2, figsize=(10, 4))\n",
    "    for i, category in zip(range(2), ['Correct', 'Incorrect']):\n",
    "        entropy_category = entropy[get_correct_indices(model, x, labels)[i]]\n",
    "        mean_entropy = np.mean(entropy_category)\n",
    "        num_samples = entropy_category.shape[0]\n",
    "        title = category + 'ly labelled ({:.1f}% of total)'.format(num_samples / x.shape[0] * 100)\n",
    "        axes[i].hist(entropy_category, weights=(1/num_samples)*np.ones(num_samples))\n",
    "        axes[i].annotate('Mean: {:.3f} bits'.format(mean_entropy), (0.4, 0.9), ha='center')\n",
    "        axes[i].set_xlabel('Entropy (bits)')\n",
    "        axes[i].set_ylim([0, 1])\n",
    "        axes[i].set_ylabel('Probability')\n",
    "        axes[i].set_title(title)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MNIST test set:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Entropy plots for the MNIST dataset\n",
    "\n",
    "print('MNIST test set:')\n",
    "plot_entropy_distribution(probabilistic_model, x_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Corrupted MNIST test set:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Entropy plots for the MNIST-C dataset\n",
    "\n",
    "print('Corrupted MNIST test set:')\n",
    "plot_entropy_distribution(probabilistic_model, x_c_test, y_c_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two main conclusions:\n",
    "- The model is more unsure on the predictions it got wrong: this means it \"knows\" when the prediction may be wrong.\n",
    "- The model is more unsure for the corrupted MNIST test than for the uncorrupted version. Futhermore, this is more pronounced for correct predictions than for those it labels incorrectly.\n",
    "\n",
    "In this way, the model seems to \"know\" when it is unsure. This is a great property to have in a machine learning model, and is one of the advantages of probabilistic modelling."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian CNN model\n",
    "\n",
    "The probabilistic model you just created considered only aleatoric uncertainty, assigning probabilities to each image instead of deterministic labels. The model still had deterministic weights. However, as you've seen, there is also 'epistemic' uncertainty over the weights, due to uncertainty about the parameters that explain the training data. \n",
    "\n",
    "You'll now be adding weight uncertainty to the model you just created. Your new model will again have the following layers:\n",
    "- 2D convolution\n",
    "- Max pooling\n",
    "- Flatten\n",
    "- Dense\n",
    "- OneHotCategorical\n",
    "\n",
    "but where the convolutional and dense layers include weight uncertainty. You'll embed weight uncertainty as follows:\n",
    "- The 2D convolution layer will be replaced by a `Convolution2DReparameterization` layer\n",
    "- The Dense layer will be replaced by a `DenseVariational` layer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You should start by creating the convolutional layer in the function below. The function should return an instance of the `Convolution2DReparameterization` layer, according to the following specification: \n",
    "\n",
    "* The function takes the `input_shape` and `divergence_fn` as arguments\n",
    "* The layer should set the input shape in its constructor using the `input_shape` argument\n",
    "* This layer should have 8 filters, a kernel size of `(5, 5)`, a ReLU activation, and `\"VALID\"` padding\n",
    "* The prior for both the kernel and bias should be the standard `default_multivariate_normal_fn`, as seen in the coding tutorial\n",
    "* The posterior for each parameter in both the kernel and bias should be an independent normal distribution with trainable mean and variance (_hint: use the_ `default_mean_field_normal_fn`_)_\n",
    "* The divergence function should be set using the `divergence_fn` argument for both the kernel and the bias\n",
    "\n",
    "_HINT: Review the arguments you used in the coding tutorial on Reparameterization layers._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [],
   "source": [
    "#### GRADED CELL ####\n",
    "\n",
    "# Complete the following functions. \n",
    "# Make sure to not change the function name or arguments.\n",
    "\n",
    "def get_convolutional_reparameterization_layer(input_shape, divergence_fn):\n",
    "    \"\"\"\n",
    "    This function should create an instance of a Convolution2DReparameterization \n",
    "    layer according to the above specification. \n",
    "    The function takes the input_shape and divergence_fn as arguments, which should \n",
    "    be used to define the layer.\n",
    "    Your function should then return the layer instance.\n",
    "    \"\"\"\n",
    "    return tfp.layers.Convolution2DReparameterization(input_shape = input_shape, padding='valid', activation='relu', kernel_size=(5,5), filters=8, \n",
    "    kernel_prior_fn=tfpl.default_multivariate_normal_fn,\n",
    "        kernel_posterior_fn = tfpl.default_mean_field_normal_fn(is_singular=False),\n",
    "        kernel_divergence_fn=divergence_fn,\n",
    "        bias_prior_fn=tfpl.default_multivariate_normal_fn,\n",
    "        bias_posterior_fn = tfpl.default_mean_field_normal_fn(is_singular=False),\n",
    "        bias_divergence_fn=divergence_fn,\n",
    "    \n",
    "                                           )\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You'll use this function to create your model a little bit later on. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Custom prior\n",
    "\n",
    "For the parameters of the `DenseVariational` layer, we will use a custom prior: the \"spike and slab\" (also called a *scale mixture prior*) distribution. This distribution has a density that is the weighted sum of two normally distributed ones: one with a standard deviation of 1 and one with a standard deviation of 10. In this way, it has a sharp spike around 0 (from the normal distribution with standard deviation 1), but is also more spread out towards far away values (from the contribution from the normal distribution with standard deviation 10). The reason for using such a prior is that it is like a standard unit normal, but makes values far away from 0 more likely, allowing the model to explore a larger weight space. Run the code below to create a \"spike and slab\" distribution and plot its probability density function, compared with a standard unit normal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to define the spike and slab distribution\n",
    "\n",
    "def spike_and_slab(event_shape, dtype):\n",
    "    distribution = tfd.Mixture(\n",
    "        cat=tfd.Categorical(probs=[0.5, 0.5]),\n",
    "        components=[\n",
    "            tfd.Independent(tfd.Normal(\n",
    "                loc=tf.zeros(event_shape, dtype=dtype), \n",
    "                scale=1.0*tf.ones(event_shape, dtype=dtype)),\n",
    "                            reinterpreted_batch_ndims=1),\n",
    "            tfd.Independent(tfd.Normal(\n",
    "                loc=tf.zeros(event_shape, dtype=dtype), \n",
    "                scale=10.0*tf.ones(event_shape, dtype=dtype)),\n",
    "                            reinterpreted_batch_ndims=1)],\n",
    "    name='spike_and_slab')\n",
    "    return distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the spike and slab distribution pdf\n",
    "\n",
    "x_plot = np.linspace(-5, 5, 1000)[:, np.newaxis]\n",
    "plt.plot(x_plot, tfd.Normal(loc=0, scale=1).prob(x_plot).numpy(), label='unit normal', linestyle='--')\n",
    "plt.plot(x_plot, spike_and_slab(1, dtype=tf.float32).prob(x_plot).numpy(), label='spike and slab')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Density')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You should now complete the function below to create the prior distribution for the `DenseVariational` layer, using the spike and slab distribution above.\n",
    "\n",
    "* The function has the required signature for the `make_prior_fn` argument of the `DenseVariational` layer\n",
    "* The prior will have no trainable parameters\n",
    "* It should use the spike and slab distribution for both the kernel and the bias, setting the `dtype` according to the function argument\n",
    "* The distribution should have the correct event shape, according to the `kernel_size` and `bias_size` arguments\n",
    "* The function should return a callable, that returns the spike and slab distribution\n",
    "\n",
    "_Hints:_ \n",
    "* _Refer to the lecture video and/or coding tutorial to review the_ `DenseVariational` _layer arguments_\n",
    "* _Use the_ `Sequential` _API with a_ `DistributionLambda` _layer to create the callable that is returned by the function_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [],
   "source": [
    "#### GRADED CELL ####\n",
    "\n",
    "# Complete the following functions. \n",
    "# Make sure to not change the function name or arguments.\n",
    "\n",
    "def get_prior(kernel_size, bias_size, dtype=None):\n",
    "    \"\"\"\n",
    "    This function should create the prior distribution, consisting of the \n",
    "    \"spike and slab\" distribution that is described above. \n",
    "    The distribution should be created using the kernel_size, bias_size and dtype\n",
    "    function arguments above.\n",
    "    The function should then return a callable, that returns the prior distribution.\n",
    "    \"\"\"\n",
    "    \n",
    "    n=kernel_size+bias_size  # event_shape\n",
    "\n",
    "    prior_model = Sequential([tfpl.DistributionLambda(  lambda       t : spike_and_slab(n, dtype))    ])    \n",
    "\n",
    "    return prior_model   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You'll use this function when you create the `DenseVariational` layer later on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You should now complete the function below to create the variational posterior distribution for the `DenseVariational` layer. This distribution will be an independent Gaussian with trainable mean and standard deviation for each parameter in the layer.\n",
    "\n",
    "* The function has the required signature for the `make_posterior_fn` argument of the `DenseVariational` layer\n",
    "* The posterior will have 2 trainable variables for each layer parameter, one for the mean and one for the standard deviation\n",
    "* The distribution should have the correct event shape, according to the `kernel_size` and `bias_size` arguments\n",
    "* The function should return a callable, that returns the trainable independent Gaussian distribution\n",
    "\n",
    "_Hints:_ \n",
    "* _Refer to the lecture video and/or coding tutorial to review the_ `DenseVariational` _layer arguments_\n",
    "* _Use the_ `Sequential` _API with a_ `VariableLayer` and an `IndependentNormal` _layer to create the callable that is returned by the function_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [],
   "source": [
    "#### GRADED CELL ####\n",
    "\n",
    "# Complete the following functions. \n",
    "# Make sure to not change the function name or arguments.\n",
    "\n",
    "def get_posterior(kernel_size, bias_size, dtype=None):\n",
    "    \"\"\"\n",
    "    This function should create the posterior distribution as specified above.\n",
    "    The distribution should be created using the kernel_size, bias_size and dtype\n",
    "    function arguments above.\n",
    "    The function should then return a callable, that returns the posterior distribution.\n",
    "    \"\"\"\n",
    "    n=kernel_size+bias_size  # event_shape\n",
    "\n",
    "                              \n",
    "    post_model = Sequential([tfpl.VariableLayer(tfpl.IndependentNormal.params_size(n), dtype =dtype) ,\n",
    "                              tfpl.IndependentNormal(\n",
    "                                 n\n",
    "                              )\n",
    "                              ])    \n",
    "\n",
    "    return post_model   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You should now use your `prior` and `posterior` functions to complete the function below to create the `DenseVariational` layer. \n",
    "\n",
    "* The function has `prior_fn`, `posterior_fn` and `kl_weight` arguments, to be used in the constructor of the `DenseVariational` layer\n",
    "* The layer should have the correct number of units in order to parameterize a `OneHotCategorical` layer with 10 categories\n",
    "* The `make_prior_fn`, `make_posterior_fn` and `kl_weight` arguments should be set with the corresponding function arguments\n",
    "* An exact KL-divergence is unavailable for this choice of prior and posterior, so the layer should not attempt to use an analytical expression for this\n",
    "* Your function should then return an instance of the `DenseVariational` layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [],
   "source": [
    "#### GRADED CELL ####\n",
    "\n",
    "# Complete the following functions. \n",
    "# Make sure to not change the function name or arguments.\n",
    "\n",
    "def get_dense_variational_layer(prior_fn, posterior_fn, kl_weight):\n",
    "    \"\"\"\n",
    "    This function should create an instance of a DenseVariational layer according \n",
    "    to the above specification. \n",
    "    The function takes the prior_fn, posterior_fn and kl_weight as arguments, which should \n",
    "    be used to define the layer.\n",
    "    Your function should then return the layer instance.\n",
    "    \"\"\"\n",
    "    dl = tfpl.DenseVariational(\n",
    "        units=tfpl.OneHotCategorical.params_size(10),  \n",
    "        make_posterior_fn = posterior_fn,\n",
    "        make_prior_fn = prior_fn,\n",
    "        kl_weight=kl_weight\n",
    "    ) \n",
    "\n",
    "    return dl   \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, you're ready to use the functions you defined to create the convolutional reparameterization and dense variational layers, and use them in your Bayesian convolutional neural network model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create the layers\n",
    "\n",
    "tf.random.set_seed(0)\n",
    "divergence_fn = lambda q, p, _ : tfd.kl_divergence(q, p) / x_train.shape[0]\n",
    "convolutional_reparameterization_layer = get_convolutional_reparameterization_layer(\n",
    "    input_shape=(28, 28, 1), divergence_fn=divergence_fn\n",
    ")\n",
    "dense_variational_layer = get_dense_variational_layer(\n",
    "    get_prior, get_posterior, kl_weight=1/x_train.shape[0]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Build and compile the Bayesian CNN model\n",
    "\n",
    "bayesian_model = Sequential([\n",
    "    convolutional_reparameterization_layer,\n",
    "    MaxPooling2D(pool_size=(6, 6)),\n",
    "    Flatten(),\n",
    "    dense_variational_layer,\n",
    "    tfpl.OneHotCategorical(10, convert_to_tensor_fn=tfd.Distribution.mode)\n",
    "])\n",
    "bayesian_model.compile(loss=nll,\n",
    "              optimizer=RMSprop(),\n",
    "              metrics=['accuracy'],\n",
    "              experimental_run_tf_function=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential_28\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "conv2d_reparameterization_17 (None, 24, 24, 8)         416       \n",
      "_________________________________________________________________\n",
      "max_pooling2d_28 (MaxPooling (None, 4, 4, 8)           0         \n",
      "_________________________________________________________________\n",
      "flatten_28 (Flatten)         (None, 128)               0         \n",
      "_________________________________________________________________\n",
      "dense_variational_17 (DenseV (None, 10)                2580      \n",
      "_________________________________________________________________\n",
      "one_hot_categorical_26 (OneH ((None, 10), (None, 10))  0         \n",
      "=================================================================\n",
      "Total params: 2,996\n",
      "Trainable params: 2,996\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Print the model summary\n",
    "\n",
    "bayesian_model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples\n",
      "Epoch 1/10\n",
      "60000/60000 [==============================] - 4s 72us/sample - loss: 1.9676 - accuracy: 0.3259\n",
      "Epoch 2/10\n",
      "60000/60000 [==============================] - 4s 75us/sample - loss: 0.7180 - accuracy: 0.7713\n",
      "Epoch 3/10\n",
      "60000/60000 [==============================] - 4s 72us/sample - loss: 0.3832 - accuracy: 0.8845\n",
      "Epoch 4/10\n",
      "60000/60000 [==============================] - 4s 69us/sample - loss: 0.2810 - accuracy: 0.9189\n",
      "Epoch 5/10\n",
      "60000/60000 [==============================] - 4s 73us/sample - loss: 0.2354 - accuracy: 0.9344\n",
      "Epoch 6/10\n",
      "60000/60000 [==============================] - 4s 69us/sample - loss: 0.2068 - accuracy: 0.9428\n",
      "Epoch 7/10\n",
      "60000/60000 [==============================] - 4s 71us/sample - loss: 0.1905 - accuracy: 0.9488\n",
      "Epoch 8/10\n",
      "60000/60000 [==============================] - 4s 69us/sample - loss: 0.1774 - accuracy: 0.9525\n",
      "Epoch 9/10\n",
      "60000/60000 [==============================] - 4s 70us/sample - loss: 0.1689 - accuracy: 0.9560\n",
      "Epoch 10/10\n",
      "60000/60000 [==============================] - 4s 69us/sample - loss: 0.1623 - accuracy: 0.9588\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x7f22641a9cf8>"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Train the model\n",
    "\n",
    "bayesian_model.fit(x=x_train, y=y_train_oh, epochs=10, verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on MNIST test set:  0.9658\n",
      "Accuracy on corrupted MNIST test set:  0.9257\n"
     ]
    }
   ],
   "source": [
    "# Evaluate the model\n",
    "\n",
    "print('Accuracy on MNIST test set: ',\n",
    "      str(bayesian_model.evaluate(x_test, y_test_oh, verbose=False)[1]))\n",
    "print('Accuracy on corrupted MNIST test set: ',\n",
    "      str(bayesian_model.evaluate(x_c_test, y_c_test_oh, verbose=False)[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Analyse the model predictions\n",
    "\n",
    "Now that the model has trained, run the code below to create the same plots as before, starting with an analysis of the predicted probabilities for the same images. \n",
    "\n",
    "This model now has weight uncertainty, so running the forward pass multiple times will not generate the same estimated probabilities. For this reason, the estimated probabilities do not have single values. The plots are adjusted to show a 95% prediction interval for the model's estimated probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Prediction examples on MNIST\n",
    "\n",
    "for i in [0, 1577]:\n",
    "    analyse_model_prediction(x_test, y_test, bayesian_model, i, run_ensemble=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the first image, the model assigns a probability of almost one for the 6 label. Furthermore, it is confident in this probability: this probability remains close to one for every sample from the posterior weight distribution (as seen by the horizontal green line having very small height, indicating a narrow prediction interval). This means that the epistemic uncertainty on this probability is very low. \n",
    "\n",
    "For the second image, the epistemic uncertainty on the probabilities is much larger, which indicates that the estimated probabilities may be unreliable. In this way, the model indicates whether estimates may be inaccurate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Prediction examples on MNIST-C\n",
    "\n",
    "for i in [0, 3710]:\n",
    "    analyse_model_prediction(x_c_test, y_c_test, bayesian_model, i, run_ensemble=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even with the spatters, the Bayesian model is confident in predicting the correct label for the first image above. The model struggles with the second image, which is reflected in the range of probabilities output by the network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Prediction examples from both datasets\n",
    "\n",
    "for i in [9241]:\n",
    "    analyse_model_prediction(x_test, y_test, bayesian_model, i, run_ensemble=True)\n",
    "    analyse_model_prediction(x_c_test, y_c_test, bayesian_model, i, run_ensemble=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similar to before, the model struggles with the second number, as it is mostly covered up by the spatters. However, this time is clear to see the epistemic uncertainty in the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Uncertainty quantification using entropy\n",
    "\n",
    "We also again plot the distribution of distribution entropy across the different test sets below. In these plots, no consideration has been made for the epistemic uncertainty, and the conclusions are broadly similar to those for the previous model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MNIST test set:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Entropy plots for the MNIST dataset\n",
    "\n",
    "print('MNIST test set:')\n",
    "plot_entropy_distribution(bayesian_model, x_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Corrupted MNIST test set:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Entropy plots for the MNIST-C dataset\n",
    "\n",
    "print('Corrupted MNIST test set:')\n",
    "plot_entropy_distribution(bayesian_model, x_c_test, y_c_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Congratulations on completing this programming assignment! In the next week of the course we will look at the bijectors module and normalising flows."
   ]
  }
 ],
 "metadata": {
  "coursera": {
   "course_slug": "probabilistic-deep-learning-with-tensorflow2",
   "graded_item_id": "QPF47",
   "launcher_item_id": "psszg"
  },
  "kernelspec": {
   "display_name": "tfp7",
   "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}