5 - Basic neural network in TensorFlow 2.0 -- DenseVariational layer.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5 - Deep probabilistic neural network in TensorFlow 2.0\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we've seen how easy it is to train an image classification network in TensorFlow `keras`, let's explore making that network probabilistic using TensorFlow Probability."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.0.0\n"
     ]
    }
   ],
   "source": [
    "from __future__ import absolute_import, division, print_function, unicode_literals\n",
    "from typing import Optional\n",
    "\n",
    "# TensorFlow and tf.keras\n",
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "import tensorflow_probability as tfp\n",
    "from tensorflow_probability import distributions as tfd\n",
    "\n",
    "# Helper libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "\n",
    "print(tf.__version__)\n",
    "tf.get_logger().setLevel('ERROR')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "checkpoint_path = 'saved_models/mnist_fashion.ckpt'  # Ignore for now."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Image Classification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We've seen how to solve simple regression problems in TensorFlow 2.0 and the Keras layers library, but how about doing something deeper? What about image classification?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "fashion_mnist = keras.datasets.fashion_mnist\n",
    "\n",
    "(train_images, train_labels), (test_images, test_labels) = fashion_mnist.load_data()\n",
    "class_names = ['T-shirt/top', 'Trouser', 'Pullover', 'Dress', 'Coat','Sandal', \n",
    "               'Shirt', 'Sneaker', 'Bag', 'Ankle boot']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's verify that this is the same data that we saw a moment ago."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.imshow(train_images[0])\n",
    "plt.colorbar()\n",
    "plt.grid(False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Standardize the r/g/b pixel values to between zero and one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_images = train_images / 255.0  # Divide by float to ensure that we don't suffer from default integer casting.\n",
    "test_images = test_images / 255.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "for i in range(25):\n",
    "    plt.subplot(5,5,i+1)\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "    plt.grid(False)\n",
    "    plt.imshow(train_images[i], cmap=plt.cm.binary)\n",
    "    plt.xlabel(class_names[train_labels[i]])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We've already built a deep neural network for these data -- let's adjust it to be probabilistic this time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def posterior_mean_field(kernel_size: int, bias_size: Optional[int] = 0, dtype: Optional[str] = None) -> tf.keras.Model:\n",
    "    \"\"\"Specify the surrogate posterior over `keras.layers.Dense` `kernel` and `bias`.\"\"\"\n",
    "    n = kernel_size + bias_size\n",
    "    c = np.log(np.expm1(1.))\n",
    "    \n",
    "    return tf.keras.Sequential([\n",
    "      tfp.layers.VariableLayer(2 * n, dtype=dtype),\n",
    "      tfp.layers.DistributionLambda(lambda t: tfd.Independent(\n",
    "          tfd.Normal(loc=t[..., :n],\n",
    "                     scale=1e-5 + tf.nn.softplus(c + t[..., n:])),\n",
    "          reinterpreted_batch_ndims=1)),\n",
    "  ])\n",
    "\n",
    "\n",
    "def prior_trainable(kernel_size: int, bias_size: Optional[int] = 0, dtype: Optional[str] = None) -> tf.keras.Model:\n",
    "    \"\"\"Specify the prior over `keras.layers.Dense` `kernel` and `bias`.\"\"\"\n",
    "    n = kernel_size + bias_size\n",
    "    \n",
    "    return tf.keras.Sequential([\n",
    "      tfp.layers.VariableLayer(n, dtype=dtype),\n",
    "      tfp.layers.DistributionLambda(lambda t: tfd.Independent(\n",
    "          tfd.Normal(loc=t, scale=1),\n",
    "          reinterpreted_batch_ndims=1)),\n",
    "    ])\n",
    "\n",
    "\n",
    "model = keras.Sequential([\n",
    "    keras.layers.Flatten(input_shape=(28, 28)),\n",
    "    tfp.layers.DenseVariational(128, \n",
    "                                activation='relu', \n",
    "                                make_posterior_fn=posterior_mean_field, \n",
    "                                make_prior_fn=prior_trainable),\n",
    "    keras.layers.Dense(10, activation='softmax')\n",
    "])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a loss function, we'll choose categorical cross entropy loss between logit outputs and labels -- this is a great loss function for mutually exclusive discrete classification tasks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.compile(optimizer=tf.optimizers.Adam(learning_rate=0.01),\n",
    "              loss='categorical_crossentropy',\n",
    "              metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because I'm using the `categorical_crossentropy` loss here, I need to binarize my training labels. Fortunately, TensorFlow Keras provides an easy utility function for that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., ..., 0., 0., 1.],\n",
       "       [1., 0., 0., ..., 0., 0., 0.],\n",
       "       [1., 0., 0., ..., 0., 0., 0.],\n",
       "       ...,\n",
       "       [0., 0., 0., ..., 0., 0., 0.],\n",
       "       [1., 0., 0., ..., 0., 0., 0.],\n",
       "       [0., 0., 0., ..., 0., 0., 0.]], dtype=float32)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binary_train_labels = tf.keras.utils.to_categorical(train_labels)\n",
    "binary_train_labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "flatten (Flatten)            (None, 784)               0         \n",
      "_________________________________________________________________\n",
      "dense_variational (DenseVari (None, 128)               301440    \n",
      "_________________________________________________________________\n",
      "dense (Dense)                (None, 10)                1290      \n",
      "=================================================================\n",
      "Total params: 302,730\n",
      "Trainable params: 302,730\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Almost triple the number of parameters that were in our previous model. This might be a use case for hardware acceleration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples\n",
      "Epoch 1/15\n",
      "60000/60000 [==============================] - 7s 111us/sample - loss: 726.3499 - accuracy: 0.6223\n",
      "Epoch 2/15\n",
      "60000/60000 [==============================] - 7s 111us/sample - loss: 726.5054 - accuracy: 0.6221\n",
      "Epoch 3/15\n",
      "60000/60000 [==============================] - 7s 118us/sample - loss: 726.9353 - accuracy: 0.6197\n",
      "Epoch 4/15\n",
      "60000/60000 [==============================] - 7s 119us/sample - loss: 726.6211 - accuracy: 0.6230\n",
      "Epoch 5/15\n",
      "60000/60000 [==============================] - 7s 120us/sample - loss: 726.3349 - accuracy: 0.6229\n",
      "Epoch 6/15\n",
      "60000/60000 [==============================] - 7s 119us/sample - loss: 726.5949 - accuracy: 0.6232\n",
      "Epoch 7/15\n",
      "60000/60000 [==============================] - 7s 116us/sample - loss: 726.3547 - accuracy: 0.6228\n",
      "Epoch 8/15\n",
      "60000/60000 [==============================] - 7s 118us/sample - loss: 726.8379 - accuracy: 0.6254\n",
      "Epoch 9/15\n",
      "60000/60000 [==============================] - 8s 127us/sample - loss: 727.2530 - accuracy: 0.6271\n",
      "Epoch 10/15\n",
      "60000/60000 [==============================] - 8s 130us/sample - loss: 727.0207 - accuracy: 0.6270\n",
      "Epoch 11/15\n",
      "60000/60000 [==============================] - 7s 123us/sample - loss: 725.6426 - accuracy: 0.6273\n",
      "Epoch 12/15\n",
      "60000/60000 [==============================] - 7s 121us/sample - loss: 727.5073 - accuracy: 0.6297\n",
      "Epoch 13/15\n",
      "60000/60000 [==============================] - 8s 127us/sample - loss: 726.5032 - accuracy: 0.6291\n",
      "Epoch 14/15\n",
      "60000/60000 [==============================] - 8s 129us/sample - loss: 726.5368 - accuracy: 0.6279\n",
      "Epoch 15/15\n",
      "60000/60000 [==============================] - 8s 132us/sample - loss: 727.7268 - accuracy: 0.6255\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.keras.callbacks.History at 0x10ac84c18>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cp_callback = tf.keras.callbacks.ModelCheckpoint(filepath=checkpoint_path,\n",
    "                                                 save_weights_only=True,\n",
    "                                                 verbose=1)\n",
    "\n",
    "model.fit(train_images, binary_train_labels, epochs=15, callbacks=[])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The last time we ran this (non-probabilistically), each epoch took about 5 seconds to train. This time, it looks like 4-5x that."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since nobody's boss paid for them to be here to watch a model train on my laptop's CPU, I went ahead and pre-trained this one for ~40 epochs and saved it to disk. Let's load that instead."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tensorflow.python.training.tracking.util.CheckpointLoadStatus at 0x16fd12400>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.load_weights(checkpoint_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000/1 - 1s - loss: 700.9537 - accuracy: 0.6096\n",
      "\n",
      "Test accuracy: 0.6096\n"
     ]
    }
   ],
   "source": [
    "test_loss, test_acc = model.evaluate(test_images,  tf.keras.utils.to_categorical(test_labels), verbose=2)\n",
    "\n",
    "print('\\nTest accuracy:', test_acc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, even though the model trained slowly, we've at least got something that we can work with that's right over half the time. Note that we're still not performing quite at the level that we reached with the simple densely-connected model. That likely has to do with the intense regularization we're applying in the form of Bayesian priors on the model weights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([2.1634940e-11, 6.8648895e-15, 5.5669627e-12, 2.0013838e-13,\n",
       "        1.9385935e-14, 9.4213383e-03, 2.7353196e-11, 1.4116478e-02,\n",
       "        1.3064804e-05, 9.7644913e-01], dtype=float32),\n",
       " array([8.7778653e-06, 1.7605881e-04, 5.3709757e-01, 5.0561321e-05,\n",
       "        4.3041095e-01, 7.0179590e-10, 2.7603244e-02, 3.8150920e-16,\n",
       "        4.6528531e-03, 3.1365407e-19], dtype=float32))"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictions = model.predict(test_images)\n",
    "predictions[0], predictions[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Predictions work the same as in the regular dense model -- we get a softmax output of activations for each potential class in the problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our softmax function effectively squished the model outputs into a distribution and seems to be most heavily activated on class 9 for the first test image. Let's verify that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmax(predictions[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alright, and what was the true label?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_labels[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Success! At least from this draw, we got this one correct. Let's visualize this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_image(i: int, predictions_array: np.ndarray, true_label: np.ndarray, img: np.ndarray):\n",
    "    \"\"\"\n",
    "    Plot an image from the passed set, along with its true and predicted label.\n",
    "    \"\"\"\n",
    "    predictions_array, true_label, img = predictions_array, true_label[i], img[i]\n",
    "    plt.grid(False)\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])\n",
    "\n",
    "    plt.imshow(img, cmap=plt.cm.binary)\n",
    "\n",
    "    predicted_label = np.argmax(predictions_array)\n",
    "    if predicted_label == true_label:\n",
    "        color = 'blue'\n",
    "    else:\n",
    "        color = 'red'\n",
    "\n",
    "    plt.xlabel(\"{} {:2.0f}% ({})\".format(class_names[predicted_label],\n",
    "                                100*np.max(predictions_array),\n",
    "                                class_names[true_label]),\n",
    "                                color=color)\n",
    "\n",
    "def plot_value_array(i: int, predictions_array: np.ndarray, true_label: np.ndarray):\n",
    "    \"\"\"\n",
    "    Plot a bar chart of the model activations for each class pertaining to a given image.\n",
    "    \"\"\"\n",
    "    predictions_array, true_label = predictions_array, true_label[i]\n",
    "    plt.grid(False)\n",
    "    plt.xticks(range(10))\n",
    "    plt.yticks([])\n",
    "    thisplot = plt.bar(range(10), predictions_array, color=\"#777777\")\n",
    "    plt.ylim([0, 1])\n",
    "    predicted_label = np.argmax(predictions_array)\n",
    "\n",
    "    thisplot[predicted_label].set_color('red')\n",
    "    thisplot[true_label].set_color('blue')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "i = 0\n",
    "plt.figure(figsize=(6,3))\n",
    "plt.subplot(1,2,1)\n",
    "plot_image(i, predictions[i], test_labels, test_images)\n",
    "plt.subplot(1,2,2)\n",
    "plot_value_array(i, predictions[i],  test_labels)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try that again, given our model's propensity to overstate its confidence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "predictions = model.predict(test_images)\n",
    "predictions[0], predictions[1]\n",
    "\n",
    "i = 0\n",
    "plt.figure(figsize=(6,3))\n",
    "plt.subplot(1,2,1)\n",
    "plot_image(i, predictions[i], test_labels, test_images)\n",
    "plt.subplot(1,2,2)\n",
    "plot_value_array(i, predictions[i],  test_labels)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we suspected, the confidence value changed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check out the rest of the first 15 images in the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 30 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_rows = 5\n",
    "num_cols = 3\n",
    "num_images = num_rows * num_cols\n",
    "plt.figure(figsize=(2 * 2 * num_cols, 2 * num_rows))\n",
    "\n",
    "for i in range(num_images):\n",
    "    plt.subplot(num_rows, 2 * num_cols, 2 * i + 1)\n",
    "    plot_image(i, predictions[i], test_labels, test_images)\n",
    "    plt.subplot(num_rows, 2 * num_cols, 2 * i + 2)\n",
    "    plot_value_array(i, predictions[i], test_labels)\n",
    "    \n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the model missed on a solid chunk of these (at least in this draw). Let's explore the special capability that this probabilistic model has over a point-estimate, though -- epistemic uncertainty."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluate uncertainties"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remember, we instantiated this model using a probabilistic layer, so we running multiple prediction instances through the model leads to multiple output results. Let's demonstrate this to find the least-certain item of clothing in the first two hundred images."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we'll generate 100 predictions for each of the first 500 images in the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "yhats = [model.predict(test_images[:500]) for _ in range(100)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's group the predictions for each test image together and cast to a Pandas `DataFrame`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "first_five_hundred_preds = [pd.DataFrame([yhat[i] for yhat in yhats]) for i in range(500)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>3.377748e-10</td>\n",
       "      <td>5.850212e-14</td>\n",
       "      <td>5.419863e-12</td>\n",
       "      <td>3.362844e-12</td>\n",
       "      <td>6.235161e-14</td>\n",
       "      <td>0.021729</td>\n",
       "      <td>1.391449e-10</td>\n",
       "      <td>0.081391</td>\n",
       "      <td>1.560951e-03</td>\n",
       "      <td>0.895319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>2.752607e-11</td>\n",
       "      <td>7.424823e-12</td>\n",
       "      <td>6.637347e-13</td>\n",
       "      <td>8.148870e-11</td>\n",
       "      <td>4.592342e-13</td>\n",
       "      <td>0.007091</td>\n",
       "      <td>3.021748e-10</td>\n",
       "      <td>0.073243</td>\n",
       "      <td>6.341593e-03</td>\n",
       "      <td>0.913324</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>2.787761e-06</td>\n",
       "      <td>2.078465e-07</td>\n",
       "      <td>1.423009e-08</td>\n",
       "      <td>1.294055e-06</td>\n",
       "      <td>2.726563e-08</td>\n",
       "      <td>0.017312</td>\n",
       "      <td>3.101347e-06</td>\n",
       "      <td>0.059027</td>\n",
       "      <td>1.716941e-01</td>\n",
       "      <td>0.751960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1.066665e-12</td>\n",
       "      <td>2.192563e-14</td>\n",
       "      <td>3.148017e-15</td>\n",
       "      <td>1.972714e-13</td>\n",
       "      <td>5.127075e-15</td>\n",
       "      <td>0.000187</td>\n",
       "      <td>3.400442e-12</td>\n",
       "      <td>0.003108</td>\n",
       "      <td>3.851524e-04</td>\n",
       "      <td>0.996320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>1.217317e-14</td>\n",
       "      <td>1.579388e-21</td>\n",
       "      <td>7.367528e-17</td>\n",
       "      <td>5.415037e-23</td>\n",
       "      <td>3.868343e-16</td>\n",
       "      <td>0.000945</td>\n",
       "      <td>1.387236e-13</td>\n",
       "      <td>0.001806</td>\n",
       "      <td>2.266586e-04</td>\n",
       "      <td>0.997023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>95</td>\n",
       "      <td>2.619868e-15</td>\n",
       "      <td>4.061313e-20</td>\n",
       "      <td>7.289464e-18</td>\n",
       "      <td>2.969214e-19</td>\n",
       "      <td>3.617056e-22</td>\n",
       "      <td>0.001823</td>\n",
       "      <td>2.605950e-17</td>\n",
       "      <td>0.003415</td>\n",
       "      <td>3.009239e-07</td>\n",
       "      <td>0.994761</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>96</td>\n",
       "      <td>1.225216e-15</td>\n",
       "      <td>2.855447e-16</td>\n",
       "      <td>7.747553e-18</td>\n",
       "      <td>1.087280e-15</td>\n",
       "      <td>1.280263e-17</td>\n",
       "      <td>0.001670</td>\n",
       "      <td>1.341383e-15</td>\n",
       "      <td>0.001389</td>\n",
       "      <td>1.522658e-05</td>\n",
       "      <td>0.996926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>97</td>\n",
       "      <td>2.522918e-14</td>\n",
       "      <td>2.912896e-15</td>\n",
       "      <td>6.148655e-15</td>\n",
       "      <td>6.889188e-15</td>\n",
       "      <td>1.035115e-17</td>\n",
       "      <td>0.006325</td>\n",
       "      <td>1.047273e-13</td>\n",
       "      <td>0.003650</td>\n",
       "      <td>3.514881e-05</td>\n",
       "      <td>0.989990</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>98</td>\n",
       "      <td>4.569917e-18</td>\n",
       "      <td>1.647594e-24</td>\n",
       "      <td>1.171616e-18</td>\n",
       "      <td>1.015183e-20</td>\n",
       "      <td>1.313648e-22</td>\n",
       "      <td>0.040721</td>\n",
       "      <td>3.106574e-17</td>\n",
       "      <td>0.002003</td>\n",
       "      <td>5.518408e-04</td>\n",
       "      <td>0.956725</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>99</td>\n",
       "      <td>8.934898e-11</td>\n",
       "      <td>3.325913e-15</td>\n",
       "      <td>2.406999e-14</td>\n",
       "      <td>9.062205e-13</td>\n",
       "      <td>4.654014e-14</td>\n",
       "      <td>0.230517</td>\n",
       "      <td>2.855553e-11</td>\n",
       "      <td>0.378404</td>\n",
       "      <td>4.696325e-03</td>\n",
       "      <td>0.386383</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               0             1             2             3             4  \\\n",
       "0   3.377748e-10  5.850212e-14  5.419863e-12  3.362844e-12  6.235161e-14   \n",
       "1   2.752607e-11  7.424823e-12  6.637347e-13  8.148870e-11  4.592342e-13   \n",
       "2   2.787761e-06  2.078465e-07  1.423009e-08  1.294055e-06  2.726563e-08   \n",
       "3   1.066665e-12  2.192563e-14  3.148017e-15  1.972714e-13  5.127075e-15   \n",
       "4   1.217317e-14  1.579388e-21  7.367528e-17  5.415037e-23  3.868343e-16   \n",
       "..           ...           ...           ...           ...           ...   \n",
       "95  2.619868e-15  4.061313e-20  7.289464e-18  2.969214e-19  3.617056e-22   \n",
       "96  1.225216e-15  2.855447e-16  7.747553e-18  1.087280e-15  1.280263e-17   \n",
       "97  2.522918e-14  2.912896e-15  6.148655e-15  6.889188e-15  1.035115e-17   \n",
       "98  4.569917e-18  1.647594e-24  1.171616e-18  1.015183e-20  1.313648e-22   \n",
       "99  8.934898e-11  3.325913e-15  2.406999e-14  9.062205e-13  4.654014e-14   \n",
       "\n",
       "           5             6         7             8         9  \n",
       "0   0.021729  1.391449e-10  0.081391  1.560951e-03  0.895319  \n",
       "1   0.007091  3.021748e-10  0.073243  6.341593e-03  0.913324  \n",
       "2   0.017312  3.101347e-06  0.059027  1.716941e-01  0.751960  \n",
       "3   0.000187  3.400442e-12  0.003108  3.851524e-04  0.996320  \n",
       "4   0.000945  1.387236e-13  0.001806  2.266586e-04  0.997023  \n",
       "..       ...           ...       ...           ...       ...  \n",
       "95  0.001823  2.605950e-17  0.003415  3.009239e-07  0.994761  \n",
       "96  0.001670  1.341383e-15  0.001389  1.522658e-05  0.996926  \n",
       "97  0.006325  1.047273e-13  0.003650  3.514881e-05  0.989990  \n",
       "98  0.040721  3.106574e-17  0.002003  5.518408e-04  0.956725  \n",
       "99  0.230517  2.855553e-11  0.378404  4.696325e-03  0.386383  \n",
       "\n",
       "[100 rows x 10 columns]"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "first_five_hundred_preds[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So here we have 100 class softmax outputs for each of the ten potential classes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we take the mean of this `DataFrame`, we can use that as a more stable indicator of model confidence than any single random draw."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    2.359152e-07\n",
       "1    8.269638e-09\n",
       "2    6.382639e-09\n",
       "3    8.593019e-08\n",
       "4    4.681631e-09\n",
       "5    2.448622e-02\n",
       "6    3.107235e-07\n",
       "7    9.540941e-02\n",
       "8    2.879626e-02\n",
       "9    8.513075e-01\n",
       "dtype: float64"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "first_five_hundred_preds[0].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmax(first_five_hundred_preds[0].mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Were we correct?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similar to the mean, we can also calculate the _variance_ (or standard deviation) for each of the classes to see where the uncertainties lie."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1.130860e-06\n",
       "1    4.259474e-08\n",
       "2    5.774342e-08\n",
       "3    5.781170e-07\n",
       "4    3.849502e-08\n",
       "5    6.276223e-02\n",
       "6    2.203529e-06\n",
       "7    1.819112e-01\n",
       "8    8.571158e-02\n",
       "9    2.308109e-01\n",
       "dtype: float64"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "first_five_hundred_preds[0].std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although we're most confident that the correct class is \"shoe\", we also seem to have the most uncertainty for that class across our 100 draws.\n",
    "\n",
    "If we take the mean of the standard deviation, we'll find a measure of uncertainty across all classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07046955476021521"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "first_five_hundred_preds[0].std().mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then use this uncertainty measure to find the single image (of these 500) that has the greatest uncertainty across all classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "209"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "most_uncertain = np.argmax([pred.std().mean() for pred in first_five_hundred_preds])\n",
    "most_uncertain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    0.146000\n",
       "1    0.013482\n",
       "2    0.044604\n",
       "3    0.106206\n",
       "4    0.016378\n",
       "5    0.254666\n",
       "6    0.096015\n",
       "7    0.003074\n",
       "8    0.315423\n",
       "9    0.004153\n",
       "dtype: float64"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "first_five_hundred_preds[most_uncertain].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    0.210297\n",
       "1    0.033988\n",
       "2    0.106833\n",
       "3    0.181224\n",
       "4    0.039408\n",
       "5    0.349011\n",
       "6    0.129045\n",
       "7    0.009167\n",
       "8    0.321171\n",
       "9    0.014792\n",
       "dtype: float64"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "first_five_hundred_preds[most_uncertain].std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using uncertainty to allow a model to opt-out of predictions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The standard deviation of that confidence value is as large as the value itself!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can take a random prediction for this most uncertain image and see the variance in action on those confidence values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    2.122286e-01\n",
       "1    2.862234e-02\n",
       "2    1.110139e-01\n",
       "3    2.326734e-01\n",
       "4    1.287911e-01\n",
       "5    5.411891e-03\n",
       "6    2.402852e-01\n",
       "7    5.585978e-07\n",
       "8    4.097029e-02\n",
       "9    2.596843e-06\n",
       "Name: 7, dtype: float64"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "first_five_hundred_preds[most_uncertain].iloc[7]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see what this image actually is."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "i = most_uncertain\n",
    "row = 3\n",
    "plt.figure(figsize=(6,3))\n",
    "plt.subplot(1,2,1)\n",
    "plot_image(i, first_five_hundred_preds[i].mean(), test_labels, test_images)\n",
    "plt.subplot(1,2,2)\n",
    "plot_value_array(i, first_five_hundred_preds[i].mean(),  test_labels)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see why a model might have some uncertainty there!\n",
    "\n",
    "Let's allow the model now to use the uncertainty as an attribute in whether it makes a prediction. Now, instead of always outputting a class, we'll only make a prediction if the mean value minus twice the standard deviation is greater than some guard value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "guard_value = 0.25\n",
    "\n",
    "max_preds = [max(pred.mean() - (pred.std() * 2)) for pred in first_five_hundred_preds]\n",
    "predicted_preds = [(i, val) for i, val in enumerate(max_preds) if val > guard_value]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "244"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(predicted_preds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "evaluate_indices = [predicted_pred[0] for predicted_pred in predicted_preds]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "244/1 - 0s - loss: 714.9393 - accuracy: 0.8566\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[712.9726152263704, 0.85655737]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.evaluate(test_images[evaluate_indices],  tf.keras.utils.to_categorical(test_labels[evaluate_indices]), verbose=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model was able to boost its baseline accuracy significantly by recognizing those cases on which it's not confident and refusing to make a prediction! We can try higher values for this guard figure to see how being more stringent on permissable uncertainty affects the model's ultimate accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "129/1 - 0s - loss: 746.4554 - accuracy: 0.9302\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[768.4939646166424, 0.9302326]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "guard_value = 0.5\n",
    "\n",
    "max_preds = [max(pred.mean() - (pred.std() * 2)) for pred in first_five_hundred_preds]\n",
    "predicted_preds = [(i, val) for i, val in enumerate(max_preds) if val > guard_value]\n",
    "\n",
    "evaluate_indices = [predicted_pred[0] for predicted_pred in predicted_preds]\n",
    "\n",
    "model.evaluate(test_images[evaluate_indices],  tf.keras.utils.to_categorical(test_labels[evaluate_indices]), verbose=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Takeaways\n",
    "\n",
    "- We can use epistemic uncertainty in deep neural networks for tasks like image classification just as easily as we can for regresssion.\n",
    "- Probabilistic uncertainty can be quantified directly by the variance in a large number of predictions from a model's potential classes\n",
    "- A model can use this uncertainty itself to weed out instances it would rather not predict over and thereby raise its precision for the remaining instances."
   ]
  }
 ],
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