Copy_of_Part2_Debiasing.ipynb

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      "name": "Copy of Part2_Debiasing.ipynb",
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      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/github/GoelPratyush/Face_Recognition/blob/master/Copy_of_Part2_Debiasing.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ag_e7xtTzT1W",
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      "source": [
        "<table align=\"center\">\n",
        "  <td align=\"center\"><a target=\"_blank\" href=\"http://introtodeeplearning.com\">\n",
        "        <img src=\"http://introtodeeplearning.com/images/colab/mit.png\" style=\"padding-bottom:5px;\" />\n",
        "      Visit MIT Deep Learning</a></td>\n",
        "  <td align=\"center\"><a target=\"_blank\" href=\"https://colab.research.google.com/github/aamini/introtodeeplearning/blob/master/lab2/Part2_Debiasing.ipynb\">\n",
        "        <img src=\"http://introtodeeplearning.com/images/colab/colab.png?v2.0\"  style=\"padding-bottom:5px;\" />Run in Google Colab</a></td>\n",
        "  <td align=\"center\"><a target=\"_blank\" href=\"https://github.com/aamini/introtodeeplearning/blob/master/lab2/Part2_Debiasing.ipynb\">\n",
        "        <img src=\"http://introtodeeplearning.com/images/colab/github.png\"  height=\"70px\" style=\"padding-bottom:5px;\"  />View Source on GitHub</a></td>\n",
        "</table>\n",
        "\n",
        "# Copyright Information"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rNbf1pRlSDby",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved.\n",
        "# \n",
        "# Licensed under the MIT License. You may not use this file except in compliance\n",
        "# with the License. Use and/or modification of this code outside of 6.S191 must\n",
        "# reference:\n",
        "#\n",
        "# © MIT 6.S191: Introduction to Deep Learning\n",
        "# http://introtodeeplearning.com\n",
        "#"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QOpPUH3FR179",
        "colab_type": "text"
      },
      "source": [
        "# Laboratory 2: Computer Vision\n",
        "\n",
        "# Part 2: Debiasing Facial Detection Systems\n",
        "\n",
        "In the second portion of the lab, we'll explore two prominent aspects of applied deep learning: facial detection and algorithmic bias. \n",
        "\n",
        "Deploying fair, unbiased AI systems is critical to their long-term acceptance. Consider the task of facial detection: given an image, is it an image of a face?  This seemingly simple, but extremely important, task is subject to significant amounts of algorithmic bias among select demographics. \n",
        "\n",
        "In this lab, we'll investigate [one recently published approach](http://introtodeeplearning.com/AAAI_MitigatingAlgorithmicBias.pdf) to addressing algorithmic bias. We'll build a facial detection model that learns the *latent variables* underlying face image datasets and uses this to adaptively re-sample the training data, thus mitigating any biases that may be present in order  to train a *debiased* model.\n",
        "\n",
        "\n",
        "Run the next code block for a short video from Google that explores how and why it's important to consider bias when thinking about machine learning:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XQh5HZfbupFF",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import IPython\n",
        "IPython.display.YouTubeVideo('59bMh59JQDo')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3Ezfc6Yv6IhI",
        "colab_type": "text"
      },
      "source": [
        "Let's get started by installing the relevant dependencies:"
      ]
    },
    {
      "cell_type": "code",
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        "id": "E46sWVKK6LP9",
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        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 353
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      },
      "source": [
        "# Import Tensorflow 2.0\n",
        "%tensorflow_version 2.x\n",
        "import tensorflow as tf\n",
        "\n",
        "import IPython\n",
        "import functools\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from tqdm import tqdm\n",
        "\n",
        "# Download and import the MIT 6.S191 package\n",
        "!pip install mitdeeplearning\n",
        "import mitdeeplearning as mdl"
      ],
      "execution_count": 0,
      "outputs": [
        {
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            "TensorFlow 2.x selected.\n",
            "Collecting mitdeeplearning\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/8b/3b/b9174b68dc10832356d02a2d83a64b43a24f1762c172754407d22fc8f960/mitdeeplearning-0.1.2.tar.gz (2.1MB)\n",
            "\u001b[K     |████████████████████████████████| 2.1MB 52kB/s \n",
            "\u001b[?25hRequirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (1.18.2)\n",
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            "Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0)\n",
            "Building wheels for collected packages: mitdeeplearning\n",
            "  Building wheel for mitdeeplearning (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for mitdeeplearning: filename=mitdeeplearning-0.1.2-cp36-none-any.whl size=2114586 sha256=53990985648441d31ed1f31ac8158870a0f491d58d50b0d28011737998c5eb77\n",
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            "Successfully built mitdeeplearning\n",
            "Installing collected packages: mitdeeplearning\n",
            "Successfully installed mitdeeplearning-0.1.2\n"
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          "name": "stdout"
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      "source": [
        "## 2.1 Datasets\n",
        "\n",
        "We'll be using three datasets in this lab. In order to train our facial detection models, we'll need a dataset of positive examples (i.e., of faces) and a dataset of negative examples (i.e., of things that are not faces). We'll use these data to train our models to classify images as either faces or not faces. Finally, we'll need a test dataset of face images. Since we're concerned about the potential *bias* of our learned models against certain demographics, it's important that the test dataset we use has equal representation across the demographics or features of interest. In this lab, we'll consider skin tone and gender. \n",
        "\n",
        "1.   **Positive training data**: [CelebA Dataset](http://mmlab.ie.cuhk.edu.hk/projects/CelebA.html). A large-scale (over 200K images) of celebrity faces.   \n",
        "2.   **Negative training data**: [ImageNet](http://www.image-net.org/). Many images across many different categories. We'll take negative examples from a variety of non-human categories. \n",
        "[Fitzpatrick Scale](https://en.wikipedia.org/wiki/Fitzpatrick_scale) skin type classification system, with each image labeled as \"Lighter'' or \"Darker''.\n",
        "\n",
        "Let's begin by importing these datasets. We've written a class that does a bit of data pre-processing to import the training data in a usable format."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RWXaaIWy6jVw",
        "colab_type": "code",
        "outputId": "074d995c-3dd2-47c3-dc15-3fb35aa3d91b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 84
        }
      },
      "source": [
        "# Get the training data: both images from CelebA and ImageNet\n",
        "path_to_training_data = tf.keras.utils.get_file('train_face.h5', 'https://www.dropbox.com/s/l5iqduhe0gwxumq/train_face.h5?dl=1')\n",
        "# Instantiate a TrainingDatasetLoader using the downloaded dataset\n",
        "loader = mdl.lab2.TrainingDatasetLoader(path_to_training_data)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Downloading data from https://www.dropbox.com/s/l5iqduhe0gwxumq/train_face.h5?dl=1\n",
            "1263894528/1263889489 [==============================] - 81s 0us/step\n",
            "Opening /root/.keras/datasets/train_face.h5\n",
            "Loading data into memory...\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yIE321rxa_b3",
        "colab_type": "text"
      },
      "source": [
        "We can look at the size of the training dataset and grab a batch of size 100:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DjPSjZZ_bGqe",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "number_of_training_examples = loader.get_train_size()\n",
        "(images, labels) = loader.get_batch(100)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sxtkJoqF6oH1",
        "colab_type": "text"
      },
      "source": [
        "Play around with displaying images to get a sense of what the training data actually looks like!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Jg17jzwtbxDA",
        "colab_type": "code",
        "outputId": "931e6ef9-2e94-4704-80ef-a0cfc40ea03f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 191
        }
      },
      "source": [
        "### Examining the CelebA training dataset ###\n",
        "\n",
        "#@title Change the sliders to look at positive and negative training examples! { run: \"auto\" }\n",
        "\n",
        "face_images = images[np.where(labels==1)[0]]\n",
        "not_face_images = images[np.where(labels==0)[0]]\n",
        "\n",
        "idx_face = 23 #@param {type:\"slider\", min:0, max:50, step:1}\n",
        "idx_not_face = 9 #@param {type:\"slider\", min:0, max:50, step:1}\n",
        "\n",
        "plt.figure(figsize=(5,5))\n",
        "plt.subplot(1, 2, 1)\n",
        "plt.imshow(face_images[idx_face])\n",
        "plt.title(\"Face\"); plt.grid(False)\n",
        "\n",
        "plt.subplot(1, 2, 2)\n",
        "plt.imshow(not_face_images[idx_not_face])\n",
        "plt.title(\"Not Face\"); plt.grid(False)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ie4EiIvQpkqeJbMZ+ymyHgYurS/quY7VeUZJC3RCk8TniQa2qoGIteHwFplw+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\nYII=\n",
            "text/plain": [
              "<Figure size 360x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NDj7KBaW8Asz",
        "colab_type": "text"
      },
      "source": [
        "### Thinking about bias\n",
        "\n",
        "Remember we'll be training our facial detection classifiers on the large, well-curated CelebA dataset (and ImageNet), and then evaluating their accuracy by testing them on an independent test dataset. Our goal is to build a model that trains on CelebA *and* achieves high classification accuracy on the the test dataset across all demographics, and to thus show that this model does not suffer from any hidden bias. \n",
        "\n",
        "What exactly do we mean when we say a classifier is biased? In order to formalize this, we'll need to think about [*latent variables*](https://en.wikipedia.org/wiki/Latent_variable), variables that define a dataset but are not strictly observed. As defined in the generative modeling lecture, we'll use the term *latent space* to refer to the probability distributions of the aforementioned latent variables. Putting these ideas together, we consider a classifier *biased* if its classification decision changes after it sees some additional latent features. This notion of bias may be helpful to keep in mind throughout the rest of the lab. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AIFDvU4w8OIH",
        "colab_type": "text"
      },
      "source": [
        "## 2.2 CNN for facial detection \n",
        "\n",
        "First, we'll define and train a CNN on the facial classification task, and evaluate its accuracy. Later, we'll evaluate the performance of our debiased models against this baseline CNN. The CNN model has a relatively standard architecture consisting of a series of convolutional layers with batch normalization followed by two fully connected layers to flatten the convolution output and generate a class prediction. \n",
        "\n",
        "### Define and train the CNN model\n",
        "\n",
        "Like we did in the first part of the lab, we'll define our CNN model, and then train on the CelebA and ImageNet datasets using the `tf.GradientTape` class and the `tf.GradientTape.gradient` method."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "82EVTAAW7B_X",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "### Define the CNN model ###\n",
        "\n",
        "n_filters = 12 # base number of convolutional filters\n",
        "\n",
        "'''Function to define a standard CNN model'''\n",
        "def make_standard_classifier(n_outputs=1):\n",
        "  Conv2D = functools.partial(tf.keras.layers.Conv2D, padding='same', activation='relu')\n",
        "  BatchNormalization = tf.keras.layers.BatchNormalization\n",
        "  Flatten = tf.keras.layers.Flatten\n",
        "  Dense = functools.partial(tf.keras.layers.Dense, activation='relu')\n",
        "\n",
        "  model = tf.keras.Sequential([\n",
        "    Conv2D(filters=1*n_filters, kernel_size=5,  strides=2),\n",
        "    BatchNormalization(),\n",
        "    \n",
        "    Conv2D(filters=2*n_filters, kernel_size=5,  strides=2),\n",
        "    BatchNormalization(),\n",
        "\n",
        "    Conv2D(filters=4*n_filters, kernel_size=3,  strides=2),\n",
        "    BatchNormalization(),\n",
        "\n",
        "    Conv2D(filters=6*n_filters, kernel_size=3,  strides=2),\n",
        "    BatchNormalization(),\n",
        "\n",
        "    Flatten(),\n",
        "    Dense(512),\n",
        "    Dense(n_outputs, activation=None),\n",
        "  ])\n",
        "  return model\n",
        "\n",
        "standard_classifier = make_standard_classifier()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c-eWf3l_lCri",
        "colab_type": "text"
      },
      "source": [
        "Now let's train the standard CNN!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "eJlDGh1o31G1",
        "outputId": "ed4c8627-306c-4ed7-ef87-d1b4b38e8a98",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 530
        }
      },
      "source": [
        "### Train the standard CNN ###\n",
        "\n",
        "# Training hyperparameters\n",
        "batch_size = 32\n",
        "num_epochs = 2  # keep small to run faster\n",
        "learning_rate = 5e-4\n",
        "\n",
        "optimizer = tf.keras.optimizers.Adam(learning_rate) # define our optimizer\n",
        "loss_history = mdl.util.LossHistory(smoothing_factor=0.99) # to record loss evolution\n",
        "plotter = mdl.util.PeriodicPlotter(sec=2, scale='semilogy')\n",
        "if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists\n",
        "\n",
        "@tf.function\n",
        "def standard_train_step(x, y):\n",
        "  with tf.GradientTape() as tape:\n",
        "    # feed the images into the model\n",
        "    logits = standard_classifier(x) \n",
        "    # Compute the loss\n",
        "    loss = tf.nn.sigmoid_cross_entropy_with_logits(labels=y, logits=logits)\n",
        "\n",
        "  # Backpropagation\n",
        "  grads = tape.gradient(loss, standard_classifier.trainable_variables)\n",
        "  optimizer.apply_gradients(zip(grads, standard_classifier.trainable_variables))\n",
        "  return loss\n",
        "\n",
        "# The training loop!\n",
        "for epoch in range(num_epochs):\n",
        "  for idx in tqdm(range(loader.get_train_size()//batch_size)):\n",
        "    # Grab a batch of training data and propagate through the network\n",
        "    x, y = loader.get_batch(batch_size)\n",
        "    loss = standard_train_step(x, y)\n",
        "\n",
        "    # Record the loss and plot the evolution of the loss as a function of training\n",
        "    loss_history.append(loss.numpy().mean())\n",
        "    plotter.plot(loss_history.get())"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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r0+KjvFYZffDKYQCAT3ce83psKSXKaxpdtYei1f6FSKfDNZEt/76FyJ29wKO557vPr/E4\n3r7jvnVEE1HPYsskEE5uHDcAlbVNkFIiOsL96zjZRsftZeq6Bu9uclcmbWxuRe7sBbjhpbW4ff5G\nPLV4N0Z7afcfkZ1seP7CygOG51ppix+NH+Da9ocPv8bfl+3Fx9u+cW1rbZXsLyDq4ThPIMjO7NML\n1Q3NOFReiwZduQjzRDE9h0MgPyMeO49UYXtpJYZnJ2GT2oSzap82pNN9l/Ct3BTD+7UZyxrzmsgF\nA1Lxxd4yPDhjGFbsPoFD5bXYWFyOL/cpcw02FVfg2jHZmPbMF673bP79ZUiJb3/eAhHZC+8Egixf\nnShmbnf/+cVntPm+A+oIohl//xIAcF0bQzlP1RqHoA4wrX2QHBvpevzWxhL85dM9AACnQ+BXlw0C\nANQ3uRPUK6sOGhIAACz92nvTFBHZF5NAkGmzgPX+O/NcDEjz3K5nLkzXFvMn/egIJz762fn4xSXK\nBf7DrUoTz8nTDR6lLL49Mgtp8VHIt4hTb4PFugdEZH9MAkGWmRhjeL7m3osxYWC6l73dLhvqXu+4\npqHZUKLaF8Ozk/Dry84EAByvbsBzK/bjxpfXe+wnhMDlZ2fiQDsjkd4uLHWtp9zVfoJFO47i3cLS\nLh2DiHzDPoEgM48AMicFb7KSY12Phz24GAAwIjsJW0uVYbW/uvRMjM1LxfUv+jbj9wm1XpGVJF1z\nkVlmYgyOqkteFjz6qWv7n747AteY+jWKymowf20xZk8dgkin988fs15TFtQxv5+I/I9JwEae/v5I\nCItZwlb6WCSLqAgHPvjpedhYfAo/OT8PALDozoltJpbXZ46zTBQr7p7kepyT4rl+8lUj++HuyYOR\nkxqHZ5fvw1OLdxtev+vtrRibl4rmVulq8npqyW4s2HYEmYkxmOlDc1ZjcyuiIqyTxfbSSpzRuxdi\no5yWrxORb9gcZANR6qfiq0b28/k9TofA57+ZZNh2+FQdRuQkuxIAAAzJTGyz2uj4gWn4hakTesmv\nLkCurg/g0qHuJS0vPasPHEJJWDmpSnJItRgVNHFQOiY+uRwX/XGFq4id9n0+tnAncmcvwJyFO9v8\nHr3NVK5rbMGMv3+J21+zXoKTiHzHJGADy38zCa/++Fs+3wVozJ3H31R2rkS0eWjnmX0SDM97J8Tg\nwOPTsGr2xXjppgIcmDPdEOv4/DSPY+pLV1/17CoAwPAs4+Q/8/wEs4Ne+iG0ZTlX7jmBa59bjdzZ\nC7DraFWbxwoVx6vqkTt7AXJnLwh2KBQimARsICs5Fhd1cgH5m3QTujrrjN7u9QzMcwo0Docw9EPo\n5abHY8dDl+O8MzyTgd7DH3/dbixrdaWrD5ZZV0rVz6fYWKzMj7jhxXXtHjsUzPy3u6xIZ1eYI9Jj\nEujhHpwxzDWn4FZdM1BHnH+Ge2TRv285t1PH6BUdgcq6Jq+vH6+2vksx1y8q0TUBzbO4U/jd/7bj\n3Mc/89h+sqYRx6tCf7Gc7FR3/8zOI+Fx90Pdi0mgh3M4hKsvYeKZGZ06hr5ppysdrU+oayRM1g1f\n1Yx9zPPCDSj1i77/whoUn1SafvRF88pON2L1vjLD/v9Z531pzLGPf4ZG3V1CKBqo66vxdWEhorYw\nCYSAM3on4OCcabiwk0kAUKqMbv/D5C7FMaxfEormTsdzPxzT5n5PXXsO5t3o3mfdwXJc+NQKVNY1\n4bW1xov8D15yN/P4MnfgSGVdB6PuWeqbWxEd4UCv6AjsOcYkQF3HJBAiOtqpbBYT6URCjPf5AB3h\n1M19ePiqYbjdNBz0uwU5ljOiRzy0xFWf6IZzjesxN7W04q63t7Z77pLy0E4C1fVNcDoE4qOdeGtj\nSbDDoRDAJEDdomjudBTNnY4fjc/FufnutZL/et1IAMAgXWe0lR/okkBtYzMeW+B9OOnlw9zNTw98\nsAOvrS3Gza96zn4OBa+vL0FtYwuOVTWgvqnVsgw5UUfYMgmEy6Iy4SI/3X3BT1RnH3tbKwEArhzR\nDwMz3O8Z+sBi/HN1kev5iz8qQNHc6Zh34xhEOgX+9L2RePeO8QCAA2U1uP/9HVi++wSaWnpu/8A3\nFXW45rnVOFHd0O5+RF1hyyQQLovKhIvsFPfQ0ihduYj7p5+Fq0dnYe9jUzFzYp5he0ykE/dPP8vy\neFrdpMnDMrH3sWnoFR2BMQNSPfZ7dvk+f30LHnYfrfY64skfXltbjMLiU/jPOuNSo3np8Rifn4an\nv6/cUZWeYhKgrrFlEqDQEuF04LYL8jE2LxUTBrrnEtw6MR9//t5IRDod6K/rI4hQE4V5chkAHJwz\nzet5zHMcnv50b1dDtySlxOVPr/Q64qkzx9ttGunTV11C9LDpIi8EkNorCmPzlKTHJEBdxSRAAXHf\ntLPw1u3jvXZgp8S5O6UjnMo+Y/NS8fBVw1zbR/VPbrMD/F+3jPVTtG3TT1bzx8pqD374FS5/eiW+\n2HvC47U9pjLgTS2tiHY60CcxBhEOgdJT1qU1AGDeyv2GeRdEVpgEyBbOzVPuEO6YNBCJ6iglIQR+\nND7X9Qk/rZ2Vy7Q1mzVWNY38QZ8ETpxuu83eF/9eozT5uFeFA37/wVcAgK0lFYYLfVl1IyKdDjgd\nAv2SY73eCVTWNeHxhbsw8cnlrjIbRFaYBMgWMhKiUTR3Ou6ZMsTjtYeuPBuA50Xeys3n5boel9c0\norre+yxmMyklXlx5AH9asrvN/fQX1ZLyWvx5yW7cpivn0FE/npALAPiXrvNbb/MhpQDfhqJy1DW1\nuO4YslNivd4JFOnqLr385cFOx6a3taTCVbcod/YCvLqq88fddOgUnlux3y9xUdcwCZDtDe2XiGeu\nH2VoGvLGvFLbe5sO+3yevyzdg8cW7sTflu2zbOaRUqKittEwK3nzoQo8s2wflnx9rENNQ6v3l+HO\nNzZjx+FK18inOt1wz4t1taSOqeUwvvv8GgDuQoFZybHYdKgCf/vMs+9DP1fjnY0dW6CnsrbJctTR\nsl3HDc8f+qj9WlDeXP2P1Xhi0S4OcbUBJgHqEa4c0a/NktiaXNMkNKv6Q1Z2HK7EM8vco4ms6iD9\nc3URRj68FIVq0ToAeFQ3f+H9LcaE01ZS+PErG/D+lm9wxd++NGzX7jL0F9zymkbDPnepK8JlqaOu\n/rR0D1pMNZj0p06Oi+zQTOoZf/8SE+YuMx1P4q8WyUYr99FZRV18P3UdkwCFFC0J9E2KQUykA0P7\nJfr0PvMnUqu1DLRPvo96mbj2/Ap3wrn3ve3Iu3eh1/Pph83qrTLVShqQFucRy/nqUqL9dFVdj5qK\n50m4s8CmQxUYP8d4UW+Ldj5tHQgAOO2lYunv/rfD5+NaWbHbszOcAotJgEJKVkos4qKcuGvyYJw3\nMN3nIZQxkcbCeebyE/ok4W0C1/Bs95DW19crNZBW7rG+yPVPM67WNkB9vuSrY3hEV3K7f2qcxwif\n+ialOUq/utyhk8Z9tDsB/airjtLWgQCA5hbjncaTarFAb+XF26K/Q5r7ifdlTSkwmAQopDgdAl8/\nPAXXjslGUlwkdh6p8ihXbaXV1HTz8pcHIKXEV98os9Z/+JLnegX6OQ8A8E5hKarUjmhtWcwfvbIe\n20orDPs9vnAn9h4zDv18744JAIA3NpQYOnL7p3reCaTEKxf2jF7Rrm3mJUK1Gkz6BYJ8qbBq1YRV\n09CMdzcZ+xWuGZON7JRYQz+Gr3z4dVAAMQlQyPp42xEAwEfbvml3X+3C9OqPvwVAaULJu3chpj/z\nJeavLXYtXqN3z5QhyM8w9kGc84clAIwXXH2zCqD0Uxw2dbxaDWf9zqgs9E+Nw6naJlTVNyG9VxSm\nDMvEkEyliWtwZoKh0F5do/uCrK35rF8wyJd+gcVfHfPYNveTXa4msDlXD8eWBy6D0yGQmRiDT3d6\n7t8ec9MVh7AGF5MAhaznfzgagHGkjDdLvz4KAJZDLp/QNVmM6p/sehzpdGDZXZOw+9EpePTbZ3s9\n9gEvy2TqWU2Cm3J2pquZ6NDJWjS3SvRJdH/6dzoEHvvOcNfzBz7Y4VEqQ9+M40uF1VmmdZvnLNyJ\n+WvdpSviopyuDvqNxadQ29iCU6aO6/aUnzbu/4vXNxuGtFJgMQlQyCrIVUormEsvWHl2uTJmPSsl\nFmMGGMtP1DS6O0V3HalGkloEL1Kd2Rwd4UR/3YpfVfVNhpIX7RV5O7OP8mndXFlVAMhRj7v/xGlU\n1DZhS6lnUUVtOOnbhaV4avFuLNpxxPXaVaP6uR63NbsYsO78Na8Drb/gazWcOlqjqZe6cNAv1BXx\nFn91DJP+uKJDx+hu7f2srLy+/hByZy/occt+MglQyEqMiURSbCTWHSz3us8drxXiiUXuT/pjBqRi\n7tXDDfvom8kf+fbZyFQ7ZBt1VUoHZ7rb3mfNLzRcCNrrnH7xRwUAgHdmTTBsdwjhSi6r1dnE5qYl\nAIYFegBg1mubAAATB6VjwsB0rJ59MQDg053HPd5reN98913Ary4903KfIl0H9N2TBwOAR3+B2Ynq\nBuTOXoD3NytDaLV+h4GmpNdsk6qvOw5X4vwnlmP+2mJ8+vUxLP7qqE/v04r99bTFfpgEKKRV1jVh\n2a7jWLDtiOXrn+w4api5mhQbiUF9EvDH747w2PfN28bh2jHZuGeqcvHLTnZ/+u+TGOO6mK/ef9LV\nBPTjCbkoKqux7HC9fFgfHJwzzbXATpJpJI8QcC3086a6gMy1Y7I9jhPhdGB8fprH9g1FSvLThpJ+\nuvOY16Gejc2trs5kAK51q830fRCDMxMQH+XExEFtr2injaZ68EOlFIa+Y/inFw10PT7jd5+0eZxA\nWbBd+Vv5/fs7cOu/N+L2+YXtvEOhjZT6pkLp83insBSLdrSdQOqbWjDnk51BvXtgEqCw8OW+jo1H\n75cU47FNa7e/eEgfFM2d7nHRHpvrWc46PyMeNY0tHsNKhQDmXH1OmwXxrF5q8DLCJy/Dc6U2bSip\n3tkPLrZ8/zO6iWDXjsmGwyEsv5+cVOPQ1nOykz06uc3i1HWrtQl4WkLU3+lolu9u+26lPfVNLR4T\n5zpq+a7OxaAl2xW7j2NDUTnufnurRx+L2a/e3IIXPj+Am1/d0Klz+gOTAIU07QJ0uKK+Q2Udeida\nJYG232NOCj+/+AxXGYv9J2pMrw2yHBG05YHLcFZfZfSPVUeutz5u/XBRTabF92Bl86FT+LuuXf+n\nFyl3AZlqItSv6+Aw/RCyUmLb7XPR/9T/uHg3mlvdScCcVLp6MRzy+0UY8+jSLh1j11HP5hyrGeRm\n6erv4O3CUleJj/Z8ot4prC8qx+r9Ze3s3T2YBCikPfsDZYTQyj0n8NznvhcsG2CazAUoHbUd8bdl\n+5CvrpB2UG0ecn8Ktn5PclwU7p2qFNHTJpQ9/0N3m/8t5+VZvm/fidMe25b8+gLX45W/uchrnCW6\ni/h/Z57rSlzamgYNza347K4Lce/UIa75D5qs5FgcrarHSVM11TX7T+L+97d7JN6/L9/nKtAnIT3u\nBAbr5jX44tZ/bcA/Vhg7pitqfS8aaEVfhFDjS0extw8JbdVH0lfG3WbR6R8ITAIU0i4a0hsD1aaS\nV1cVebyekxrrKlWt/+Qc6XSgaO50fPDT81zb2rsTMO9zz5Qh6JuolK84WKZcpFt0n4K9ueDMDGy8\n/1JcNFgZ9TPl7EwUqCOW9COV9GZbVF/VSnIDSkK589JBADzH5SfHuvdLi3ffUWgzko9V1WNgRi/c\nfuFAmGnt4GMe/dRw3McWfo3X1h5C0claj0SgdVBvLalA36RY1/c8cVA6oiM7dkn6dOdxPLnIs+pr\nrZefky+sbhi1zn0pJf6ydI/lOg3ebjTbWtNhxgj36K0jQVoqlEmAQp7W5OCt3ENOShx2PTIFK3/r\n+Wl5RI57XkBVXfsXlk9+OdH1+I5JA+FwCOSmxeOA2hykNVe3N3ch3dS8c8/UIYiNdHr9pGwu35CT\n6lnOQWuzPlppnKzVort66cPS7gTM+xvOq6uB9NFWd+f78SrlZ33fe9vhrRHu26Oy4HQIfHbXhfjH\nDaOR7UPTkjetrdKQbO57b3unjgN4zh4H3Bfyo1X1+Otne3HTq+tdrzW3tHrtcAeA4pPek4CUErFq\nyZK2+oe6U/sF2ol6uMIiz9m+Gu3/u7l2kBVvnbJ6QzITsfWByTit+ySanxGP7YeVW33tAtPR/+/f\nyk3FzkemeH3doV69h2cl4QMbdt4AABJcSURBVO7LB3vMOQCAbDUJHK6oc41IAoAW3YQyfVxD1L4J\n7V8r+uSjDfGUUuK4mnAH9o73+gl5UG8loQ1Um8yykmNxsqYRtY3NOFbVgDteK8Rrt57rkRCtvPjF\nAcycmO96/v6Wb/D0daPafZ8VKZUZ3PrqrdqdwEl1opv+0/1v39mG9zZ7L1le3MadwBf7ylDX1IIh\nmQlBWyqUdwIU8h7SrUOg1QLSSIl2G/u1dvDJ6uSo9iTFRRoujjkpcSgpr8Px6npXEmirOaizdj48\nBe/eMQEXnplhqDCq6WcawqjR3wnoh+rnpcdj+d2TXJO6rOjPow0x3apr295xuAoHLPorAM+7Ie1Y\nRyrrMX9NMXYdrUbBo596PbfenE92eb3j6KhWKeEQwHM3KP1JsZFO1wX67re3AgCadImzrQQAoM3Z\n0NodYlay9wWCuhuTAIW8q0dnuzo7pz/jrt//5oZDqKhthGgnC6yefTEW33mB69N2R41W2/PHPvaZ\nq0nK2Q1JIDbK6dFxq6eN9tFmMJeU13oMqdSK02ny0uMR4fR+TP35tFpNvaLdDQxbSipwmzrO/prR\nxjkO5h+n1j+w91i1oeZRZW2T5ciuKtOqceb+ks6u/9wqlaaZqcP74uCcaTjvjDTXBXq/LqFpx7eq\npKovFT5/bXG7RQyzUmLbHWrbXZgEKCw8p9YRApT/vIcr6nDPu9tR09jSbtNMeq9ow4zgjtJX8ly9\nX5n5G4zm35hIJzISonH4VB1aWyUmPrkct88vdCWBT399AXon+Das1JudR6q8jtOfNDgDv5vmHm5q\nbgPX+iBmvbYJ9/3P3aY/4uEleHKxZ+evVqzP/Fwrn+1LH44Vqd4JaDFmp8Sh9FQdpJSGO4BT6iik\nqWdnGt6/9YHJeOQqYy2pFXs85x7oC/plp8Siur7Zp6Go/sYkQGFBPxTxZE2j4bP/vuPWzRX+0lc3\n8exetcOyO5qDfNEvORZvbizBF2rTzed7Tvg0Yqktd0xyjxq69V8bcfnTKy33EwIY0td7Ms20mKCn\n8XWFOMA9EMA8dNRXSnOQ+2eRnRKL0w3NHkNPRz+yFLuPVns0QyXFRSLXtMzpG+tLPM7zx8V7XI+z\n1Nnnne0Y74qAJQEhxLeFEC8KId4UQkwO1HmJAOMi9YdP1Rmqa5r7CfzNqtPZl8qm3SErWbnQ3vSK\ne3SLlgQiHJ27HNwzZQgOPD4NgLEJxtz8A3gu/6nXVud8R2YBa0nAXPzOV63SmBC1iYMPf+y5pvJ/\n1hUbRhPNnKjM4zA3ES35+phHbaQy3dwKbZTV4Yo6XD9vrc99If7g029dCPGKEOK4EGKHafsUIcRu\nIcQ+IcTsto4hpXxfSjkTwCwA3+98yESd8/HPzwegLJ/Y3Or+D9nU4q8uRd8FKQegX5Jn+7X2s+hk\nDlDfK5CfHo9G3c9y9lTj3AUBYdlhrWeePGZ2sKzGY57DF6ahvTkp7mPo11jwVauUhuY6rXnpf2oH\n8Ng8dzmNf68phpRKP8hj3zkbd6lF9bS+koQY94cP83rKGQnuUU9aH8K/VhdhzYGTKDvdYEgS3cnX\nX/s/ARjGpwkhnACeBTAVwFAA1wshhgohhgshPjZ99da99X71fUQBpXUO//KNza7/0MFSVR+cgmG9\nEz2HW85R10vo7J2AJisl1nDh0l/kAKU5qL07IG+F6wDlgn7RH1fgl69vAaCU8v6/SQORkxqHJ65x\nV35N1XVun/XAIlTUdmy9A2m6EygYYKyhtN6iKq1DADecO8BwN7Pi7kn47K4LXc8v/fNKwzKgWn2q\n9/5vgmvm8Jf7ylyJw5ehsf7g029dSrkSgPk7Hwtgn5TygJSyEcAbAK6SUm6XUl5h+jouFE8A+ERK\nucnbuYQQtwkhNgohNp44wUWoyX/i1VErrVIp6QAAF56ZgY9+dn63n/uBK4a6Zi4DQPHJ4CyiYr4w\nA+4yC13MAZajZM4/I91j27K7LnSt4GaWrotv3o1jsPH+S13PH1uoNMcsUks7K6N4lNf0lUwdQuDV\nm93HL2pjspZeVX0Tzpu7DBuKyg13arFRTlxwprFSqr4z+J+riyyTem56PHonxOChK91DlJftcq/E\n9oz6Nzi6fwqEEBiRnYQROckY3T/FMEmxu3Xl154FQN/bUapu8+bnAC4FcK0QYpa3naSU86SUBVLK\ngoyMtkvUEnXVjeMGGBaI7y63nJ+Hz+6ahHfvGA8ArlmigZbRy3vnq77fpDP0SUBbk+G1W8/FOerP\nV7uu5mf0wkVDepvfDgAYl+cuiT15WCbSe0XjfbV0x/82Ge/epJSu4b39kmMNF848Xd9De4v6aHYd\nqcbhijqUnqrzLJSn+95evflb+McNo3GlruRDW7490n1Z/MNHX3tdTvPMPgnYWlKBz/ecQEMn1m7u\nrIB1DEspn5FSjpFSzpJSPh+o8xLppZkqdzqdgW2cHzMgFS/cOAa/taj1EwhD+ymzf388IRdnZxln\nAuvH93eGvoREf10Bvng1uZT4MBkqNsozOY7MSUZmYgxqTO37EsahttpY/C/3lWFAWhyuH6usfXDP\nO9t8ij9Od27zQCn9uP/UuCgIIfDod7wvKaqXGGv8uWolNSYNznAlSMBYptuqkml36UoSOAwgR/c8\nW91GZFvv3mFcvSsiCD20lw/LdDVNBVpqfBQOzpmGP1w5DB//fKIrETyim1XdWfpPy/oJeCPVdZmT\nYz1LZ/sq37ReQnNLK6Q0TvZuVMt6FJ+shRACc9S7kWofFmz5/fs7cMXf3BMJ27oTiFA/OOgL9LXF\nPB9CmxRmjt+qOS0QupIENgAYJITIE0JEAbgOwIf+CEoIMUMIMa+yMjilVSl05abHI1lX97+rnaE9\nkf6iVKt+uu7qQiyA8U5An1t/e/lgLLpzIr73rRyLd3kamZOMXFMpb62+kOaIVtRO973ERyuf5GdY\nNNOcbmg21ALStLZKvFNYivlriw3brdZN0ES2MYPamwRd0teap6QpfqvCdYHg6xDR1wGsATBYCFEq\nhPiJlLIZwM8ALAawE8BbUsqv/BGUlPIjKeVtSUnd31ZL4WfLA+5pKsEar28XWu2azzq5mpaevhS3\nvsSGEAJDMr0XoTN7/6fnYYVp/QPznZM2QufdQvf6xm/dPh53TBqIOy8Z5Nqmlc++551tGP3IUmw6\nZCwmuHTnMVc9ID1zc5B+fQmrYaf/nXluW98SNtx/KbY+qPzduZKAlIY7gSvO8a2Pwd98HR10vZSy\nr5QyUkqZLaV8Wd2+UEp5ppRyoJTyse4Nlcj/grm2qx28PnMcAOuFVDpKX2PI37nVvD5AoXox19fb\niXA6cM+UIYYENEldk0FbN3iWab1gb7WWzG3y+nIa+qU8H/220i8wun9Km/HHRDqRFBuJtPgoHNYV\n8BOmUUiaX+gSWXdjKWkKS3/5/gj86s2thg7McDR+YBoOPD6t08XxvPPv8c7OMrYKfLFXGT5unpBm\nZm5n10pcFxaXIybS2anlLPV9AT8cNwA/HDfA5/f2S471abTSry4NXBIIvwZRIgDfGZWNPY9O9Whr\nDkf+TAATBynzAswVPrvKXIJCW3+5vRnIVvMiispqcM1zawwVZQFgwsC0dmcsd1W/5Bhdc5Bnqnzg\niqFIiIkI6AIztkwC7BimQGir7DJ1zrh8ZZx/pJ873L313Xzgw8zv53UVZAFg1muFlvsNyUzE57+Z\n5PU4+j6PztLuBKSUkJAeF/tbzs/D9j9c3uXzdIQtm4OklB8B+KigoGBmsGMhIt/dceFAjMxJxoSB\nae3v3EERDoFm0yimn5yf1+77ppzd1/C8IDfFchx+8cmaNj+BL/zlRBxqY5UwX2Qlx6KmsQVVdc2W\ndwLBYMskQEQ9k8MhcJ5FqQh/6Jscg5LyOlw9Ksu1mtcEH88178YxOFRei3krD6C2wXo2rtbJfPN5\nuZZLYqbGRyE1vvNzHQB385V2riBVFDdgEiCiHuH+6UNx+/xCzJ46pN0lHc0mD1Nq/Xy87YjlWr43\njhuAG8YpM4wfnNH1iXPeuJf4rENzq4Qfpmd0GZMAEfUIlw/LRNHc6V06Rr/kGGwtMfY1rr33kjYX\ntPGnfup6Drf+e2NAzucLJgEi6nHevG0c0np1vGlm19Fqj7V8A5UAACA9PhpRTgcaTQvMBJMtk4AQ\nYgaAGWec4b22OBGFr3PzO9fxrM2QDhaHQxgSwLThmW3sHRi2HCPHshFE1B3aGgIaDNVBWlxIz5ZJ\ngIioOwzQrTNwbl5ql/sYOiNeVx7CqpM60JgEiCisaCu8/e0Ho4Jy/rdmjXc9PmyDJGDLPgEiou7y\n2V2Tgnr+7GR3aYr2ah8FAu8EiIgCSL/S2C0+zHjubrZMAqwdREShKpDF4Xxhy+Yg1g4iolD2jxtG\nI9omBQxtmQSIiELZtOF9298pQOyRioiIKCiYBIiIwhiTABFRGGMSICIKY0wCRERhzJZJgPMEiIgC\nw5ZJgFVEiYgCw5ZJgIiIAkNIqxWVbUIIcQJAcSffng6gzI/hdLeeFi/Q82LuafECPS/mnhYv0PNi\nbi/eAVLKDF8PZusk0BVCiI1SyoJgx+GrnhYv0PNi7mnxAj0v5p4WL9DzYvZ3vGwOIiIKY0wCRERh\nLJSTwLxgB9BBPS1eoOfF3NPiBXpezD0tXqDnxezXeEO2T4CIiNoXyncCRETUDiYBIqIwFnJJQAgx\nRQixWwixTwgxO8ixvCKEOC6E2KHbliqEWCqE2Kv+m6JuF0KIZ9S4twkhRuvec5O6/14hxE3dGG+O\nEGK5EOJrIcRXQohf9oCYY4QQ64UQW9WYH1K35wkh1qmxvSmEiFK3R6vP96mv5+qOda+6fbcQ4vLu\nilk9l1MIsVkI8XEPibdICLFdCLFFCLFR3Wbnv4tkIcQ7QohdQoidQojxNo93sPqz1b6qhBB3BiRm\nKWXIfAFwAtgPIB9AFICtAIYGMZ4LAIwGsEO37UkAs9XHswE8oT6eBuATAALAOADr1O2pAA6o/6ao\nj1O6Kd6+AEarjxMA7AEw1OYxCwC91MeRANapsbwF4Dp1+/MA7lAf/x+A59XH1wF4U308VP17iQaQ\np/4dObvxb+PXAP4L4GP1ud3jLQKQbtpm57+LfwG4VX0cBSDZzvGaYncCOApgQCBi7tZvJtBfAMYD\nWKx7fi+Ae4McUy6MSWA3gL7q474AdquPXwBwvXk/ANcDeEG33bBfN8f+AYDLekrMAOIAbAJwLpQZ\nlRHmvwsAiwGMVx9HqPsJ89+Kfr9uiDMbwGcALgbwsXp+28arHr8InknAln8XAJIAHIQ68MXu8VrE\nPxnAqkDFHGrNQVkASnTPS9VtdtJHSnlEfXwUQB/1sbfYg/I9qc0Oo6B8srZ1zGrTyhYAxwEshfKp\nuEJK2Wxxflds6uuVANICHPPTAH4LoFV9nmbzeAFAAlgihCgUQtymbrPr30UegBMAXlWb3F4SQsTb\nOF6z6wC8rj7u9phDLQn0KFJJ1bYboyuE6AXgXQB3Simr9K/ZMWYpZYuUciSUT9hjAQwJckheCSGu\nAHBcSlkY7Fg66Hwp5WgAUwH8VAhxgf5Fm/1dREBphn1OSjkKQA2UphQXm8XrovYFXQngbfNr3RVz\nqCWBwwBydM+z1W12ckwI0RcA1H+Pq9u9xR7Q70kIEQklAfxHSvleT4hZI6WsALAcSnNKshAiwuL8\nrtjU15MAnAxgzOcBuFIIUQTgDShNQn+1cbwAACnlYfXf4wD+ByXZ2vXvohRAqZRynfr8HShJwa7x\n6k0FsElKeUx93u0xh1oS2ABgkDrSIgrKbdWHQY7J7EMAWo/9TVDa3bXtP1J7/ccBqFRvAxcDmCyE\nSFFHBkxWt/mdEEIAeBnATinln3tIzBlCiGT1cSyUPoydUJLBtV5i1r6XawEsUz9hfQjgOnU0Th6A\nQQDW+zteKeW9UspsKWUulL/PZVLKG+waLwAIIeKFEAnaYyi/zx2w6d+FlPIogBIhxGB10yUAvrZr\nvCbXw90UpMXWvTF3dydHoL+g9JrvgdIu/Lsgx/I6gCMAmqB8OvkJlPbczwDsBfApgFR1XwHgWTXu\n7QAKdMe5BcA+9evmboz3fCi3m9sAbFG/ptk85nMAbFZj3gHgAXV7PpSL4j4ot9bR6vYY9fk+9fV8\n3bF+p34vuwFMDcDfxyS4RwfZNl41tq3q11fa/yub/12MBLBR/bt4H8pIGdvGq54rHspdXpJuW7fH\nzLIRRERhLNSag4iIqAOYBIiIwhiTABFRGGMSICIKY0wCRERhjEmAiCiMMQkQEYWx/wf8cq56X8Uv\nbwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 3434/3434 [00:31<00:00, 108.25it/s]\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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/N+L2+YXtvEOhjZT6pkLp83insBSLdrSdQOqbWjDnk51BvXtgEqCw8OW+jo1H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\nbwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AKMdWVHeCxj8",
        "colab_type": "text"
      },
      "source": [
        "### Evaluate performance of the standard CNN\n",
        "\n",
        "Next, let's evaluate the classification performance of our CelebA-trained standard CNN on the training dataset.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "35-PDgjdWk6_",
        "outputId": "4d9775f6-c410-4077-fab8-a697552ca9a9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "### Evaluation of standard CNN ###\n",
        "\n",
        "# TRAINING DATA\n",
        "# Evaluate on a subset of CelebA+Imagenet\n",
        "(batch_x, batch_y) = loader.get_batch(5000)\n",
        "y_pred_standard = tf.round(tf.nn.sigmoid(standard_classifier.predict(batch_x)))\n",
        "acc_standard = tf.reduce_mean(tf.cast(tf.equal(batch_y, y_pred_standard), tf.float32))\n",
        "\n",
        "print(\"Standard CNN accuracy on (potentially biased) training set: {:.4f}\".format(acc_standard.numpy()))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Standard CNN accuracy on (potentially biased) training set: 0.9980\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qu7R14KaEEvU",
        "colab_type": "text"
      },
      "source": [
        "We will also evaluate our networks on an independent test dataset containing faces that were not seen during training. For the test data, we'll look at the classification accuracy across four different demographics, based on the Fitzpatrick skin scale and sex-based labels: dark-skinned male, dark-skinned female, light-skinned male, and light-skinned female. \n",
        "\n",
        "Let's take a look at some sample faces in the test set. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "vfDD8ztGWk6x",
        "outputId": "7e6d7fe6-44f9-4317-b543-7540462268b7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        }
      },
      "source": [
        "### Load test dataset and plot examples ###\n",
        "\n",
        "test_faces = mdl.lab2.get_test_faces()\n",
        "keys = [\"Light Female\", \"Light Male\", \"Dark Female\", \"Dark Male\"]\n",
        "for group, key in zip(test_faces,keys): \n",
        "  plt.figure(figsize=(5,5))\n",
        "  plt.imshow(np.hstack(group))\n",
        "  plt.title(key, fontsize=15)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Gcnx2m2YxJ4WA0jovGinSHJ1QzeaI0tgmYtuWlCLWD0QSQ7dnsZyxWq0Ybc4w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\n",
            "text/plain": [
              "<Figure size 360x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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1wwFgiVFJy9657pHhbHnE8vQmzXSKq6p/sQ5nXOVQU5VD6ECXGqaopMJgctas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\nnX2i7f8Dd1aRmpWROwsAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 360x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AnQfHPP/iLRbLOcVkg3e/7WnGswnH8yOuPfNbfOrTn0YXR2zWNU0IzHePEFOw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8kQI3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\nAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 360x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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l4l2bxm4zFk3LonMs2oRTRQGTaXIRohJ8azG9RQyiCD4SYl9tEANFntFZs4IC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\nkDu2Yzu2t7UdB7ljO7Zje1vb/wfKUNnUSB2jiAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 360x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uo1z3cdbEUMM",
        "colab_type": "text"
      },
      "source": [
        "Now, let's evaluated the probability of each of these face demographics being classified as a face using the standard CNN classifier we've just trained. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GI4O0Y1GAot9",
        "colab_type": "code",
        "outputId": "322ab4ca-2a8a-4322-ca96-376c1953471e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "### Evaluate the standard CNN on the test data ### \n",
        "\n",
        "standard_classifier_logits = [standard_classifier(np.array(x, dtype=np.float32)) for x in test_faces]\n",
        "standard_classifier_probs = tf.squeeze(tf.sigmoid(standard_classifier_logits))\n",
        "\n",
        "# Plot the prediction accuracies per demographic\n",
        "xx = range(len(keys))\n",
        "yy = standard_classifier_probs.numpy().mean(1)\n",
        "plt.bar(xx, yy)\n",
        "plt.xticks(xx, keys)\n",
        "plt.ylim(max(0,yy.min()-yy.ptp()/2.), yy.max()+yy.ptp()/2.)\n",
        "plt.title(\"Standard classifier predictions\");"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j0Cvvt90DoAm",
        "colab_type": "text"
      },
      "source": [
        "Take a look at the accuracies for this first model across these four groups. What do you observe? Would you consider this model biased or unbiased? What are some reasons why a trained model may have biased accuracies? "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0AKcHnXVtgqJ",
        "colab_type": "text"
      },
      "source": [
        "## 2.3 Mitigating algorithmic bias\n",
        "\n",
        "Imbalances in the training data can result in unwanted algorithmic bias. For example, the majority of faces in CelebA (our training set) are those of light-skinned females. As a result, a classifier trained on CelebA will be better suited at recognizing and classifying faces with features similar to these, and will thus be biased.\n",
        "\n",
        "How could we overcome this? A naive solution -- and on that is being adopted by many companies and organizations -- would be to annotate different subclasses (i.e., light-skinned females, males with hats, etc.) within the training data, and then manually even out the data with respect to these groups.\n",
        "\n",
        "But this approach has two major disadvantages. First, it requires annotating massive amounts of data, which is not scalable. Second, it requires that we know what potential biases (e.g., race, gender, pose, occlusion, hats, glasses, etc.) to look for in the data. As a result, manual annotation may not capture all the different features that are imbalanced within the training data.\n",
        "\n",
        "Instead, let's actually **learn** these features in an unbiased, unsupervised manner, without the need for any annotation, and then train a classifier fairly with respect to these features. In the rest of this lab, we'll do exactly that."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nLemS7dqECsI",
        "colab_type": "text"
      },
      "source": [
        "## 2.4 Variational autoencoder (VAE) for learning latent structure\n",
        "\n",
        "As you saw, the accuracy of the CNN varies across the four demographics we looked at. To think about why this may be, consider the dataset the model was trained on, CelebA. If certain features, such as dark skin or hats, are *rare* in CelebA, the model may end up biased against these as a result of training with a biased dataset. That is to say, its classification accuracy will be worse on faces that have under-represented features, such as dark-skinned faces or faces with hats, relevative to faces with features well-represented in the training data! This is a problem. \n",
        "\n",
        "Our goal is to train a *debiased* version of this classifier -- one that accounts for potential disparities in feature representation within the training data. Specifically, to build a debiased facial classifier, we'll train a model that **learns a representation of the underlying latent space** to the face training data. The model then uses this information to mitigate unwanted biases by sampling faces with rare features, like dark skin or hats, *more frequently* during training. The key design requirement for our model is that it can learn an *encoding* of the latent features in the face data in an entirely *unsupervised* way. To achieve this, we'll turn to variational autoencoders (VAEs).\n",
        "\n",
        "![The concept of a VAE](http://kvfrans.com/content/images/2016/08/vae.jpg)\n",
        "\n",
        "As shown in the schematic above and in Lecture 4, VAEs rely on an encoder-decoder structure to learn a latent representation of the input data. In the context of computer vision, the encoder network takes in input images, encodes them into a series of variables defined by a mean and standard deviation, and then draws from the distributions defined by these parameters to generate a set of sampled latent variables. The decoder network then \"decodes\" these variables to generate a reconstruction of the original image, which is used during training to help the model identify which latent variables are important to learn. \n",
        "\n",
        "Let's formalize two key aspects of the VAE model and define relevant functions for each.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KmbXKtcPkTXA",
        "colab_type": "text"
      },
      "source": [
        "### Understanding VAEs: loss function\n",
        "\n",
        "In practice, how can we train a VAE? In learning the latent space, we constrain the means and standard deviations to approximately follow a unit Gaussian. Recall that these are learned parameters, and therefore must factor into the loss computation, and that the decoder portion of the VAE is using these parameters to output a reconstruction that should closely match the input image, which also must factor into the loss. What this means is that we'll have two terms in our VAE loss function:\n",
        "\n",
        "1.  **Latent loss ($L_{KL}$)**: measures how closely the learned latent variables match a unit Gaussian and is defined by the Kullback-Leibler (KL) divergence.\n",
        "2.   **Reconstruction loss ($L_{x}{(x,\\hat{x})}$)**: measures how accurately the reconstructed outputs match the input and is given by the $L^1$ norm of the input image and its reconstructed output.  \n",
        "\n",
        "The equations for both of these losses are provided below:\n",
        "\n",
        "$$ L_{KL}(\\mu, \\sigma) = \\frac{1}{2}\\sum\\limits_{j=0}^{k-1}\\small{(\\sigma_j + \\mu_j^2 - 1 - \\log{\\sigma_j})} $$\n",
        "\n",
        "$$ L_{x}{(x,\\hat{x})} = ||x-\\hat{x}||_1 $$ \n",
        "\n",
        "Thus for the VAE loss we have: \n",
        "\n",
        "$$ L_{VAE} = c\\cdot L_{KL} + L_{x}{(x,\\hat{x})} $$\n",
        "\n",
        "where $c$ is a weighting coefficient used for regularization. \n",
        "\n",
        "Now we're ready to define our VAE loss function:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S00ASo1ImSuh",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "### Defining the VAE loss function ###\n",
        "\n",
        "''' Function to calculate VAE loss given:\n",
        "      an input x, \n",
        "      reconstructed output x_recon, \n",
        "      encoded means mu, \n",
        "      encoded log of standard deviation logsigma, \n",
        "      weight parameter for the latent loss kl_weight\n",
        "'''\n",
        "def vae_loss_function(x, x_recon, mu, logsigma, kl_weight=0.0005):\n",
        "  # TODO: Define the latent loss. Note this is given in the equation for L_{KL}\n",
        "  # in the text block directly above\n",
        "  latent_loss = 0.5*tf.reduce_sum(tf.exp(logsigma)+tf.square(mu)-1-logsigma)\n",
        "\n",
        "  # TODO: Define the reconstruction loss as the mean absolute pixel-wise \n",
        "  # difference between the input and reconstruction. Hint: you'll need to \n",
        "  # use tf.reduce_mean, and supply an axis argument which specifies which \n",
        "  # dimensions to reduce over. For example, reconstruction loss needs to average \n",
        "  # over the height, width, and channel image dimensions.\n",
        "  # https://www.tensorflow.org/api_docs/python/tf/math/reduce_mean\n",
        "  reconstruction_loss = tf.reduce_mean(tf.abs(x-x_recon),axis=(0,1,2))\n",
        "\n",
        "  # TODO: Define the VAE loss. Note this is given in the equation for L_{VAE}\n",
        "  # in the text block directly above\n",
        "  vae_loss = kl_weight*latent_loss + reconstruction_loss\n",
        "  \n",
        "  return vae_loss"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E8mpb3pJorpu",
        "colab_type": "text"
      },
      "source": [
        "Great! Now that we have a more concrete sense of how VAEs work, let's explore how we can leverage this network structure to train a *debiased* facial classifier."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DqtQH4S5fO8F",
        "colab_type": "text"
      },
      "source": [
        "### Understanding VAEs: reparameterization \n",
        "\n",
        "As you may recall from lecture, VAEs use a \"reparameterization  trick\" for sampling learned latent variables. Instead of the VAE encoder generating a single vector of real numbers for each latent variable, it generates a vector of means and a vector of standard deviations that are constrained to roughly follow Gaussian distributions. We then sample from the standard deviations and add back the mean to output this as our sampled latent vector. Formalizing this for a latent variable $z$ where we sample $\\epsilon \\sim \\mathcal{N}(0,(I))$ we have: \n",
        "\n",
        "$$ z = \\mathbb{\\mu} + e^{\\left(\\frac{1}{2} \\cdot \\log{\\Sigma}\\right)}\\circ \\epsilon $$\n",
        "\n",
        "where $\\mu$ is the mean and $\\Sigma$ is the covariance matrix. This is useful because it will let us neatly define the loss function for the VAE, generate randomly sampled latent variables, achieve improved network generalization, **and** make our complete VAE network differentiable so that it can be trained via backpropagation. Quite powerful!\n",
        "\n",
        "Let's define a function to implement the VAE sampling operation:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cT6PGdNajl3K",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "### VAE Reparameterization ###\n",
        "\n",
        "\"\"\"Reparameterization trick by sampling from an isotropic unit Gaussian.\n",
        "# Arguments\n",
        "    z_mean, z_logsigma (tensor): mean and log of standard deviation of latent distribution (Q(z|X))\n",
        "# Returns\n",
        "    z (tensor): sampled latent vector\n",
        "\"\"\"\n",
        "def sampling(z_mean, z_logsigma):\n",
        "  # By default, random.normal is \"standard\" (ie. mean=0 and std=1.0)\n",
        "  batch, latent_dim = z_mean.shape\n",
        "  epsilon = tf.random.normal(shape=(batch, latent_dim))\n",
        "\n",
        "  # TODO: Define the reparameterization computation!\n",
        "  # Note the equation is given in the text block immediately above.\n",
        "  z = z_mean +tf.exp(z_logsigma)*epsilon \n",
        "  return z"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qtHEYI9KNn0A",
        "colab_type": "text"
      },
      "source": [
        "## 2.5 Debiasing variational autoencoder (DB-VAE)\n",
        "\n",
        "Now, we'll use the general idea behind the VAE architecture to build a model, termed a [*debiasing variational autoencoder*](https://lmrt.mit.edu/sites/default/files/AIES-19_paper_220.pdf) or DB-VAE, to mitigate (potentially) unknown biases present within the training idea. We'll train our DB-VAE model on the facial detection task, run the debiasing operation during training, evaluate on the PPB dataset, and compare its accuracy to our original, biased CNN model.    \n",
        "\n",
        "### The DB-VAE model\n",
        "\n",
        "The key idea behind this debiasing approach is to use the latent variables learned via a VAE to adaptively re-sample the CelebA data during training. Specifically, we will alter the probability that a given image is used during training based on how often its latent features appear in the dataset. So, faces with rarer features (like dark skin, sunglasses, or hats) should become more likely to be sampled during training, while the sampling probability for faces with features that are over-represented in the training dataset should decrease (relative to uniform random sampling across the training data). \n",
        "\n",
        "A general schematic of the DB-VAE approach is shown here:\n",
        "\n",
        "![DB-VAE](https://raw.githubusercontent.com/aamini/introtodeeplearning/2019/lab2/img/DB-VAE.png)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ziA75SN-UxxO",
        "colab_type": "text"
      },
      "source": [
        "Recall that we want to apply our DB-VAE to a *supervised classification* problem -- the facial detection task. Importantly, note how the encoder portion in the DB-VAE architecture also outputs a single supervised variable, $z_o$, corresponding to the class prediction -- face or not face. Usually, VAEs are not trained to output any supervised variables (such as a class prediction)! This is another key distinction between the DB-VAE and a traditional VAE. \n",
        "\n",
        "Keep in mind that we only want to learn the latent representation of *faces*, as that's what we're ultimately debiasing against, even though we are training a model on a binary classification problem. We'll need to ensure that, **for faces**, our DB-VAE model both learns a representation of the unsupervised latent variables, captured by the distribution $q_\\phi(z|x)$, **and** outputs a supervised class prediction $z_o$, but that, **for negative examples**, it only outputs a class prediction $z_o$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XggIKYPRtOZR",
        "colab_type": "text"
      },
      "source": [
        "### Defining the DB-VAE loss function\n",
        "\n",
        "This means we'll need to be a bit clever about the loss function for the DB-VAE. The form of the loss will depend on whether it's a face image or a non-face image that's being considered. \n",
        "\n",
        "For **face images**, our loss function will have two components:\n",
        "\n",
        "\n",
        "1.   **VAE loss ($L_{VAE}$)**: consists of the latent loss and the reconstruction loss.\n",
        "2.   **Classification loss ($L_y(y,\\hat{y})$)**: standard cross-entropy loss for a binary classification problem. \n",
        "\n",
        "In contrast, for images of **non-faces**, our loss function is solely the classification loss. \n",
        "\n",
        "We can write a single expression for the loss by defining an indicator variable $\\mathcal{I}_f$which reflects which training data are images of faces ($\\mathcal{I}_f(y) = 1$ ) and which are images of non-faces ($\\mathcal{I}_f(y) = 0$). Using this, we obtain:\n",
        "\n",
        "$$L_{total} = L_y(y,\\hat{y}) + \\mathcal{I}_f(y)\\Big[L_{VAE}\\Big]$$\n",
        "\n",
        "Let's write a function to define the DB-VAE loss function:\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VjieDs8Ovcqs",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "### Loss function for DB-VAE ###\n",
        "\n",
        "\"\"\"Loss function for DB-VAE.\n",
        "# Arguments\n",
        "    x: true input x\n",
        "    x_pred: reconstructed x\n",
        "    y: true label (face or not face)\n",
        "    y_logit: predicted labels\n",
        "    mu: mean of latent distribution (Q(z|X))\n",
        "    logsigma: log of standard deviation of latent distribution (Q(z|X))\n",
        "# Returns\n",
        "    total_loss: DB-VAE total loss\n",
        "    classification_loss = DB-VAE classification loss\n",
        "\"\"\"\n",
        "def debiasing_loss_function(x, x_pred, y, y_logit, mu, logsigma):\n",
        "\n",
        "  # TODO: call the relevant function to obtain VAE loss\n",
        "  vae_loss = vae_loss_function(x,x_pred,mu,logsigma) # TODO\n",
        "\n",
        "  # TODO: define the classification loss using sigmoid_cross_entropy\n",
        "  # https://www.tensorflow.org/api_docs/python/tf/nn/sigmoid_cross_entropy_with_logits\n",
        "  classification_loss = tf.nn.sigmoid_cross_entropy_with_logits(y,y_logit)\n",
        "\n",
        "  # Use the training data labels to create variable face_indicator:\n",
        "  #   indicator that reflects which training data are images of faces\n",
        "  face_indicator = tf.cast(tf.equal(y, 1), tf.float32)\n",
        "\n",
        "  # TODO: define the DB-VAE total loss! Use tf.reduce_mean to average over all\n",
        "  # samples\n",
        "  total_loss = tf.reduce_mean(vae_loss*face_indicator + classification_loss)\n",
        "\n",
        "  return total_loss, classification_loss"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YIu_2LzNWwWY",
        "colab_type": "text"
      },
      "source": [
        "### DB-VAE architecture\n",
        "\n",
        "Now we're ready to define the DB-VAE architecture. To build the DB-VAE, we will use the standard CNN classifier from above as our encoder, and then define a decoder network. We will create and initialize the two models, and then construct the end-to-end VAE. We will use a latent space with 100 latent variables.\n",
        "\n",
        "The decoder network will take as input the sampled latent variables, run them through a series of deconvolutional layers, and output a reconstruction of the original input image."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JfWPHGrmyE7R",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "### Define the decoder portion of the DB-VAE ###\n",
        "\n",
        "n_filters = 12 # base number of convolutional filters, same as standard CNN\n",
        "latent_dim = 100 # number of latent variables\n",
        "\n",
        "def make_face_decoder_network():\n",
        "  # Functionally define the different layer types we will use\n",
        "  Conv2DTranspose = functools.partial(tf.keras.layers.Conv2DTranspose, padding='same', activation='relu')\n",
        "  BatchNormalization = tf.keras.layers.BatchNormalization\n",
        "  Flatten = tf.keras.layers.Flatten\n",
        "  Dense = functools.partial(tf.keras.layers.Dense, activation='relu')\n",
        "  Reshape = tf.keras.layers.Reshape\n",
        "\n",
        "  # Build the decoder network using the Sequential API\n",
        "  decoder = tf.keras.Sequential([\n",
        "    # Transform to pre-convolutional generation\n",
        "    Dense(units=4*4*6*n_filters),  # 4x4 feature maps (with 6N occurances)\n",
        "    Reshape(target_shape=(4, 4, 6*n_filters)),\n",
        "\n",
        "    # Upscaling convolutions (inverse of encoder)\n",
        "    Conv2DTranspose(filters=4*n_filters, kernel_size=3,  strides=2),\n",
        "    Conv2DTranspose(filters=2*n_filters, kernel_size=3,  strides=2),\n",
        "    Conv2DTranspose(filters=1*n_filters, kernel_size=5,  strides=2),\n",
        "    Conv2DTranspose(filters=3, kernel_size=5,  strides=2),\n",
        "  ])\n",
        "\n",
        "  return decoder"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yWCMu12w1BuD",
        "colab_type": "text"
      },
      "source": [
        "Now, we will put this decoder together with the standard CNN classifier as our encoder to define the DB-VAE. Note that at this point, there is nothing special about how we put the model together that makes it a \"debiasing\" model -- that will come when we define the training operation. Here, we will define the core VAE architecture by sublassing the `Model` class; defining encoding, reparameterization, and decoding operations; and calling the network end-to-end."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dSFDcFBL13c3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "### Defining and creating the DB-VAE ###\n",
        "\n",
        "class DB_VAE(tf.keras.Model):\n",
        "  def __init__(self, latent_dim):\n",
        "    super(DB_VAE, self).__init__()\n",
        "    self.latent_dim = latent_dim\n",
        "\n",
        "    # Define the number of outputs for the encoder. Recall that we have \n",
        "    # `latent_dim` latent variables, as well as a supervised output for the \n",
        "    # classification.\n",
        "    num_encoder_dims = 2*self.latent_dim + 1\n",
        "\n",
        "    self.encoder = make_standard_classifier(num_encoder_dims)\n",
        "    self.decoder = make_face_decoder_network()\n",
        "\n",
        "  # function to feed images into encoder, encode the latent space, and output\n",
        "  #   classification probability \n",
        "  def encode(self, x):\n",
        "    # encoder output\n",
        "    encoder_output = self.encoder(x)\n",
        "\n",
        "    # classification prediction\n",
        "    y_logit = tf.expand_dims(encoder_output[:, 0], -1)\n",
        "    # latent variable distribution parameters\n",
        "    z_mean = encoder_output[:, 1:self.latent_dim+1] \n",
        "    z_logsigma = encoder_output[:, self.latent_dim+1:]\n",
        "\n",
        "    return y_logit, z_mean, z_logsigma\n",
        "\n",
        "  # VAE reparameterization: given a mean and logsigma, sample latent variables\n",
        "  def reparameterize(self, z_mean, z_logsigma):\n",
        "    # TODO: call the sampling function defined above\n",
        "    z = sampling(z_mean,z_logsigma)\n",
        "    return z\n",
        "\n",
        "  # Decode the latent space and output reconstruction\n",
        "  def decode(self, z):\n",
        "    # TODO: use the decoder to output the reconstruction\n",
        "    reconstruction = self.decoder(z)\n",
        "    return reconstruction\n",
        "\n",
        "  # The call function will be used to pass inputs x through the core VAE\n",
        "  def call(self, x): \n",
        "    # Encode input to a prediction and latent space\n",
        "    y_logit, z_mean, z_logsigma = self.encode(x)\n",
        "\n",
        "    # TODO: reparameterization\n",
        "    z = self.reparameterize(z_mean,z_logsigma)\n",
        "\n",
        "    # TODO: reconstruction\n",
        "    recon = self.decode(z)\n",
        "    return y_logit, z_mean, z_logsigma, recon\n",
        "\n",
        "  # Predict face or not face logit for given input x\n",
        "  def predict(self, x):\n",
        "    y_logit, z_mean, z_logsigma = self.encode(x)\n",
        "    return y_logit\n",
        "\n",
        "dbvae = DB_VAE(latent_dim)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M-clbYAj2waY",
        "colab_type": "text"
      },
      "source": [
        "As stated, the encoder architecture is identical to the CNN from earlier in this lab. Note the outputs of our constructed DB_VAE model in the `call` function: `y_logit, z_mean, z_logsigma, z`. Think carefully about why each of these are outputted and their significance to the problem at hand.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nbDNlslgQc5A",
        "colab_type": "text"
      },
      "source": [
        "### Adaptive resampling for automated debiasing with DB-VAE\n",
        "\n",
        "So, how can we actually use DB-VAE to train a debiased facial detection classifier?\n",
        "\n",
        "Recall the DB-VAE architecture: as input images are fed through the network, the encoder learns an estimate $\\mathcal{Q}(z|X)$ of the latent space. We want to increase the relative frequency of rare data by increased sampling of under-represented regions of the latent space. We can approximate $\\mathcal{Q}(z|X)$ using the frequency distributions of each of the learned latent variables, and then define the probability distribution of selecting a given datapoint $x$ based on this approximation. These probability distributions will be used during training to re-sample the data.\n",
        "\n",
        "You'll write a function to execute this update of the sampling probabilities, and then call this function within the DB-VAE training loop to actually debias the model. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Fej5FDu37cf7",
        "colab_type": "text"
      },
      "source": [
        "First, we've defined a short helper function `get_latent_mu` that returns the latent variable means returned by the encoder after a batch of images is inputted to the network:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ewWbf7TE7wVc",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Function to return the means for an input image batch\n",
        "def get_latent_mu(images, dbvae, batch_size=1024):\n",
        "  N = images.shape[0]\n",
        "  mu = np.zeros((N, latent_dim))\n",
        "  for start_ind in range(0, N, batch_size):\n",
        "    end_ind = min(start_ind+batch_size, N+1)\n",
        "    batch = (images[start_ind:end_ind]).astype(np.float32)/255.\n",
        "    _, batch_mu, _ = dbvae.encode(batch)\n",
        "    mu[start_ind:end_ind] = batch_mu\n",
        "  return mu"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wn4yK3SC72bo",
        "colab_type": "text"
      },
      "source": [
        "Now, let's define the actual resampling algorithm `get_training_sample_probabilities`. Importantly note the argument `smoothing_fac`. This parameter tunes the degree of debiasing: for `smoothing_fac=0`, the re-sampled training set will tend towards falling uniformly over the latent space, i.e., the most extreme debiasing."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HiX9pmmC7_wn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "### Resampling algorithm for DB-VAE ###\n",
        "\n",
        "'''Function that recomputes the sampling probabilities for images within a batch\n",
        "      based on how they distribute across the training data'''\n",
        "def get_training_sample_probabilities(images, dbvae, bins=10, smoothing_fac=0.001): \n",
        "    print(\"Recomputing the sampling probabilities\")\n",
        "    \n",
        "    # TODO: run the input batch and get the latent variable means\n",
        "    mu = get_latent_mu(images, dbvae) # TODO\n",
        "\n",
        "    # sampling probabilities for the images\n",
        "    training_sample_p = np.zeros(mu.shape[0])\n",
        "    \n",
        "    # consider the distribution for each latent variable \n",
        "    for i in range(latent_dim):\n",
        "      \n",
        "        latent_distribution = mu[:,i]\n",
        "        # generate a histogram of the latent distribution\n",
        "        hist_density, bin_edges =  np.histogram(latent_distribution, density=True, bins=bins)\n",
        "\n",
        "        # find which latent bin every data sample falls in \n",
        "        bin_edges[0] = -float('inf')\n",
        "        bin_edges[-1] = float('inf')\n",
        "        \n",
        "        # TODO: call the digitize function to find which bins in the latent distribution \n",
        "        #    every data sample falls in to\n",
        "        # https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.digitize.html\n",
        "        bin_idx = np.digitize(latent_distribution, bin_edges) # TODO\n",
        "\n",
        "        # smooth the density function\n",
        "        hist_smoothed_density = hist_density + smoothing_fac\n",
        "        hist_smoothed_density = hist_smoothed_density / np.sum(hist_smoothed_density)\n",
        "\n",
        "        # invert the density function \n",
        "        p = 1.0/(hist_smoothed_density[bin_idx-1])\n",
        "        \n",
        "        # TODO: normalize all probabilities\n",
        "        p = p/np.sum(p)\n",
        "        \n",
        "        # TODO: update sampling probabilities by considering whether the newly\n",
        "        #     computed p is greater than the existing sampling probabilities.\n",
        "        training_sample_p = np.maximum(p,training_sample_p)\n",
        "        \n",
        "    # final normalization\n",
        "    training_sample_p /= np.sum(training_sample_p)\n",
        "\n",
        "    return training_sample_p"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pF14fQkVUs-a",
        "colab_type": "text"
      },
      "source": [
        "Now that we've defined the resampling update, we can train our DB-VAE model on the CelebA/ImageNet training data, and run the above operation to re-weight the importance of particular data points as we train the model. Remember again that we only want to debias for features relevant to *faces*, not the set of negative examples. Complete the code block below to execute the training loop!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xwQs-Gu5bKEK",
        "colab_type": "code",
        "outputId": "d408232d-5b17-4bb7-ca55-2de3fecb2769",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 780
        }
      },
      "source": [
        "### Training the DB-VAE ###\n",
        "\n",
        "# Hyperparameters\n",
        "batch_size = 32\n",
        "learning_rate = 5e-4\n",
        "latent_dim = 100\n",
        "\n",
        "# DB-VAE needs slightly more epochs to train since its more complex than \n",
        "# the standard classifier so we use 6 instead of 2\n",
        "num_epochs = 6  \n",
        "\n",
        "# instantiate a new DB-VAE model and optimizer\n",
        "dbvae = DB_VAE(100)\n",
        "optimizer = tf.keras.optimizers.Adam(learning_rate)\n",
        "\n",
        "# To define the training operation, we will use tf.function which is a powerful tool \n",
        "#   that lets us turn a Python function into a TensorFlow computation graph.\n",
        "@tf.function\n",
        "def debiasing_train_step(x, y):\n",
        "\n",
        "  with tf.GradientTape() as tape:\n",
        "    # Feed input x into dbvae. Note that this is using the DB_VAE call function!\n",
        "    y_logit, z_mean, z_logsigma, x_recon = dbvae(x)\n",
        "\n",
        "    '''TODO: call the DB_VAE loss function to compute the loss'''\n",
        "    loss, class_loss = debiasing_loss_function(x, x_recon, y, y_logit, z_mean, z_logsigma) # TODO\n",
        "  \n",
        "  '''TODO: use the GradientTape.gradient method to compute the gradients.\n",
        "     Hint: this is with respect to the trainable_variables of the dbvae.'''\n",
        "  grads = tape.gradient(loss, dbvae.trainable_variables) # TODO\n",
        "\n",
        "  # apply gradients to variables\n",
        "  optimizer.apply_gradients(zip(grads, dbvae.trainable_variables))\n",
        "  return loss\n",
        "\n",
        "# get training faces from data loader\n",
        "all_faces = loader.get_all_train_faces()\n",
        "\n",
        "if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists\n",
        "\n",
        "# The training loop -- outer loop iterates over the number of epochs\n",
        "for i in range(num_epochs):\n",
        "\n",
        "  IPython.display.clear_output(wait=True)\n",
        "  print(\"Starting epoch {}/{}\".format(i+1, num_epochs))\n",
        "\n",
        "  # Recompute data sampling proabilities\n",
        "  '''TODO: recompute the sampling probabilities for debiasing'''\n",
        "  p_faces = get_training_sample_probabilities(all_faces,dbvae) # TODO\n",
        "  \n",
        "  # get a batch of training data and compute the training step\n",
        "  for j in tqdm(range(loader.get_train_size() // batch_size)):\n",
        "    # load a batch of data\n",
        "    (x, y) = loader.get_batch(batch_size, p_pos=p_faces)\n",
        "    # loss optimization\n",
        "    loss = debiasing_train_step(x, y)\n",
        "    \n",
        "    # plot the progress every 200 steps\n",
        "    if j % 500 == 0: \n",
        "      mdl.util.plot_sample(x, y, dbvae)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Starting epoch 6/6\n",
            "Recomputing the sampling probabilities\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "\r  0%|          | 0/3434 [00:00<?, ?it/s]"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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c1pNLPalnZ+d85Stf5Xi5IDhluVyA3ObrX/8axYyh8xz3sWJCKrW+M01MU0ZUiTHifcSA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\nSnQtzyzXSnQtzyzXSnQtzyz/PwNWc/2zEBXFAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 144x72 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            " 14%|█▍        | 492/3434 [00:03<00:22, 131.60it/s]"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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cwSMGK4BrD7i9dQ60Ys2oUsJyiPZROK0zIYPMn1Basz4oLLPLyNxaV8jQzFk0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\nYII=\n",
            "text/plain": [
              "<Figure size 144x72 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            " 29%|██▉       | 993/3434 [00:08<00:18, 129.34it/s]"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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8fq5om7S2JqvVOD4+tmKyTqdjbkZEuHXrlpWQaFPjcDg0qzIej0nTlF/5lV+h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\nBoJFE8QAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 144x72 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            " 43%|████▎     | 1492/3434 [00:12<00:15, 128.39it/s]"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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uu59289IQEltMe+Mp+dznPscnP/nJ+vS12xqzCI3zNZYg9Xs3SbZPI6ShRMNR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\nczm1nCvRuZxazpXoXE4t/x+6/dYYoQGsXAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 144x72 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            " 58%|█████▊    | 1990/3434 [00:16<00:11, 128.01it/s]"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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LNMdqc0XGZxDJeder9mFXTfdFZJ2fN8deD79YT4Aan84S/admdvvC798C/pGZ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\neWa5UqIreWb5t1GeVYuNVeM/AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 144x72 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            " 73%|███████▎  | 2492/3434 [00:20<00:07, 124.60it/s]"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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BqRNmzrHuPJILi+UR/X1kZyrW/lOcXXQL1zOIuSbU2oG8Kl6KQR0ilq0KiGSE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\n1EkBPEtnt5SYCUzuUku6XY4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            "text/plain": [
              "<Figure size 144x72 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            " 87%|████████▋ | 2993/3434 [00:24<00:03, 128.53it/s]"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ZLSyUyxVin3qsptJdpHYIIuVeP6NDT9pxpvde33MPrDUJ45iwtuNoM3EwjUyDsFpNAS7v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\nST0GKBdXNgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 144x72 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "100%|██████████| 3434/3434 [00:27<00:00, 123.33it/s]\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uZBlWDPOVcHg",
        "colab_type": "text"
      },
      "source": [
        "Wonderful! Now we should have a trained and (hopefully!) debiased facial classification model, ready for evaluation!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Eo34xC7MbaiQ",
        "colab_type": "text"
      },
      "source": [
        "## 2.6 Evaluation of DB-VAE on Test Dataset\n",
        "\n",
        "Finally let's test our DB-VAE model on the test dataset, looking specifically at its accuracy on each the \"Dark Male\", \"Dark Female\", \"Light Male\", and \"Light Female\" demographics. We will compare the performance of this debiased model against the (potentially biased) standard CNN from earlier in the lab."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bgK77aB9oDtX",
        "colab_type": "code",
        "outputId": "41b77fbd-ad35-42d3-a57b-d16dfb73cd54",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "dbvae_logits = [dbvae.predict(np.array(x, dtype=np.float32)) for x in test_faces]\n",
        "dbvae_probs = tf.squeeze(tf.sigmoid(dbvae_logits))\n",
        "\n",
        "xx = np.arange(len(keys))\n",
        "plt.bar(xx, standard_classifier_probs.numpy().mean(1), width=0.2, label=\"Standard CNN\")\n",
        "plt.bar(xx+0.2, dbvae_probs.numpy().mean(1), width=0.2, label=\"DB-VAE\")\n",
        "plt.xticks(xx, keys); \n",
        "plt.title(\"Network predictions on test dataset\")\n",
        "plt.ylabel(\"Probability\"); plt.legend(bbox_to_anchor=(1.04,1), loc=\"upper left\");\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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JP2e/AR5JL2vVkHymC7fxZyW/xPhb+r6tBc4hOave0Vr82EfEHIqP\n5r+G5PLhKuApYN8idS4BbpH0Msnf52eBbza+i2bbplXesjf/mpekMUCPiPiPHRxW2fDxNzNrvXbW\nM/6mfEXSlSTxv8nW14QtWz7+ZmatVKs84zczM7Pt0+oG95mZmdn2c+I3MzMrI078ZmZmZcSJ38zM\nrIw48ZuZmZWR/w+D/EuEwWy2JwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rESoXRPQo_mq",
        "colab_type": "text"
      },
      "source": [
        "## 2.7 Conclusion \n",
        "\n",
        "We encourage you to think about and maybe even address some questions raised by the approach and results outlined here:\n",
        "\n",
        "*  How does the accuracy of the DB-VAE across the four demographics compare to that of the standard CNN? Do you find this result surprising in any way?\n",
        "*  How can the performance of the DB-VAE classifier be improved even further? We purposely did not optimize hyperparameters to leave this up to you! If you want to go further, try to optimize your model to achieve the best performance. **[Email us](mailto:introtodeeplearning-staff@mit.edu) a copy of your notebook with the 2.6 bar plot executed, and we'll give out prizes to the best performers!** \n",
        "*  In which applications (either related to facial detection or not!) would debiasing in this way be desired? Are there applications where you may not want to debias your model? \n",
        "* Do you think it should be necessary for companies to demonstrate that their models, particularly in the context of tasks like facial detection, are not biased? If so, do you have thoughts on how this could be standardized and implemented?\n",
        "* Do you have ideas for other ways to address issues of bias, particularly in terms of the training data?\n",
        "\n",
        "Hopefully this lab has shed some light on a few concepts, from vision based tasks, to VAEs, to algorithmic bias. We like to think it has, but we're biased ;). \n",
        "\n",
        "![Faces](https://media1.tenor.com/images/44e1f590924eca94fe86067a4cf44c72/tenor.gif?itemid=3394328)"
      ]
    }
  ]
}