11_Non supervised learning I .ipynb

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    "colab": {
      "name": "11. Non supervised learning I.ipynb",
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      "collapsed_sections": []
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      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
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    "accelerator": "GPU"
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  "cells": [
    {
      "metadata": {
        "id": "bPkGOYbK8hoh",
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      "cell_type": "markdown",
      "source": [
        "# Non supervised learning\n",
        "\n",
        "> Reminder: *In general Learning from Data is a scientific discipline that is concerned with the design and development of algorithms that allow computers to infer (from data) a model that allows compact representation (unsupervised learning) and/or good generalization (supervised learning).*\n",
        "\n",
        "## Autoencoders\n",
        "\n",
        "Suppose we have only a set of unlabeled training examples $x_1,x_2,x_3, \\dots $, where $x_i \\in \\mathbb{R}^n$. \n",
        "\n",
        "An autoencoder neural network is an *unsupervised learning* algorithm that applies backpropagation and uses a loss function that is optimal when setting the target values to be equal to the inputs, $y_i=x_i$.\n",
        "\n",
        "Specifically, we'll design a neural network architecture such that we impose a bottleneck in the network which forces a compressed knowledge representation of the original input. \n",
        "\n",
        "To build an autoencoder, you need three things: an **encoding function**, a **decoding function**, and a **distance function** to measure the amount of information loss between your data and the decompressed representation.\n",
        "\n",
        "<center>\n",
        "<img src=\"images/autoencoder.jpg\" alt=\"\" style=\"width: 700px;\"/>\n",
        "Source: https://blog.keras.io/building-autoencoders-in-keras.html\n",
        "</center>\n",
        "\n",
        "The ideal autoencoder model balances the following:\n",
        "\n",
        "+ Sensitive to the inputs enough to accurately build a reconstruction.\n",
        "+ Insensitive enough to the inputs that the model doesn't simply memorize or overfit the training data.\n",
        "\n",
        "Two practical applications of autoencoders are **data denoising**, and **dimensionality reduction** for data visualization. \n",
        "\n",
        "With appropriate dimensionality and sparsity constraints, autoencoders can learn data projections that are more interesting than PCA or other linear techniques.\n",
        "\n",
        "We'll start simple, with a single fully-connected neural layer as encoder and as decoder:"
      ]
    },
    {
      "metadata": {
        "id": "fMIfNQNu8hok",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "8c7cddde-3ef5-4e84-8fa5-438504d79c94",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1526289568112,
          "user_tz": -120,
          "elapsed": 8154,
          "user": {
            "displayName": "Jordi Vitrià",
            "photoUrl": "//lh6.googleusercontent.com/-Gjm4qgDBAbI/AAAAAAAAAAI/AAAAAAAAMMU/-Sb9eg_mX-I/s50-c-k-no/photo.jpg",
            "userId": "109730415698462856688"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "# Source: Adapted from https://blog.keras.io/building-autoencoders-in-keras.html\n",
        "\n",
        "from keras.layers import Input, Dense\n",
        "from keras.models import Model\n",
        "\n",
        "# this is the size of our encoded representations       \n",
        "encoding_dim = 32  # 32 floats -> compression of factor 24.5, \n",
        "                   # assuming the input is 784 floats\n",
        "\n",
        "input_img = Input(shape=(784,))\n",
        "\n",
        "# encoded representation of the input\n",
        "encoding_layer = Dense(encoding_dim, \n",
        "                       activation='relu')\n",
        "encoded = encoding_layer(input_img)\n",
        "\n",
        "# lossy reconstruction of the input\n",
        "decoding_layer = Dense(784, \n",
        "                       activation='sigmoid')\n",
        "decoded = decoding_layer(encoded)\n",
        "\n",
        "# this model maps an input to its reconstruction\n",
        "autoencoder = Model(input_img, decoded)"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Using TensorFlow backend.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "metadata": {
        "id": "mBXCAgAr8hom",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Let's also create a separate encoder model and a separate decoder model:"
      ]
    },
    {
      "metadata": {
        "id": "rtBE-f-58hoo",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "cell_type": "code",
      "source": [
        "# this model maps an input to its encoded representation\n",
        "encoding_model = Model(input_img, encoded)\n",
        "\n",
        "# create a placeholder for an encoded input\n",
        "# and create the decoder model\n",
        "encoded_input = Input(shape=(encoding_dim,))\n",
        "decoding_model = Model(encoded_input, decoding_layer(encoded_input))\n",
        "\n",
        "autoencoder.compile(optimizer='adam', loss='mse')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "S3yWCITp8hor",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Let's prepare our input data. "
      ]
    },
    {
      "metadata": {
        "id": "xX7q-eHW8hos",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 659
        },
        "outputId": "c8549bce-497e-4bcf-9510-9ae6913cec99",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1526289601475,
          "user_tz": -120,
          "elapsed": 26614,
          "user": {
            "displayName": "Jordi Vitrià",
            "photoUrl": "//lh6.googleusercontent.com/-Gjm4qgDBAbI/AAAAAAAAAAI/AAAAAAAAMMU/-Sb9eg_mX-I/s50-c-k-no/photo.jpg",
            "userId": "109730415698462856688"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "from keras.datasets import mnist\n",
        "import numpy as np\n",
        "(x_train, _), (x_test, _) = mnist.load_data()\n",
        "\n",
        "x_train = x_train.astype('float32') / 255.\n",
        "x_test = x_test.astype('float32') / 255.\n",
        "x_train = x_train.reshape((len(x_train), np.prod(x_train.shape[1:])))\n",
        "x_test = x_test.reshape((len(x_test), np.prod(x_test.shape[1:])))\n",
        "print(x_train.shape)\n",
        "print(x_test.shape)\n",
        "\n",
        "autoencoder.fit(x_train, \n",
        "                x_train,\n",
        "                epochs=15,\n",
        "                batch_size=256,\n",
        "                shuffle=True,\n",
        "                validation_data=(x_test, x_test))"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Downloading data from https://s3.amazonaws.com/img-datasets/mnist.npz\n",
            "11493376/11490434 [==============================] - 3s 0us/step\n",
            "(60000, 784)\n",
            "(10000, 784)\n",
            "Train on 60000 samples, validate on 10000 samples\n",
            "Epoch 1/15\n",
            "60000/60000 [==============================] - 2s 39us/step - loss: 0.0706 - val_loss: 0.0414\n",
            "Epoch 2/15\n",
            "60000/60000 [==============================] - 1s 24us/step - loss: 0.0350 - val_loss: 0.0293\n",
            "Epoch 3/15\n",
            "60000/60000 [==============================] - 1s 24us/step - loss: 0.0264 - val_loss: 0.0232\n",
            "Epoch 4/15\n",
            "60000/60000 [==============================] - 1s 23us/step - loss: 0.0217 - val_loss: 0.0195\n",
            "Epoch 5/15\n",
            "60000/60000 [==============================] - 1s 23us/step - loss: 0.0185 - val_loss: 0.0168\n",
            "Epoch 6/15\n",
            "60000/60000 [==============================] - 1s 23us/step - loss: 0.0162 - val_loss: 0.0149\n",
            "Epoch 7/15\n",
            "14848/60000 [======>.......................] - ETA: 0s - loss: 0.0151"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 1s 23us/step - loss: 0.0145 - val_loss: 0.0135\n",
            "Epoch 8/15\n",
            "60000/60000 [==============================] - 1s 23us/step - loss: 0.0133 - val_loss: 0.0126\n",
            "Epoch 9/15\n",
            "60000/60000 [==============================] - 1s 23us/step - loss: 0.0124 - val_loss: 0.0117\n",
            "Epoch 10/15\n",
            "60000/60000 [==============================] - 1s 23us/step - loss: 0.0118 - val_loss: 0.0112\n",
            "Epoch 11/15\n",
            "60000/60000 [==============================] - 1s 23us/step - loss: 0.0114 - val_loss: 0.0108\n",
            "Epoch 12/15\n",
            "60000/60000 [==============================] - 1s 23us/step - loss: 0.0111 - val_loss: 0.0106\n",
            "Epoch 13/15\n",
            "60000/60000 [==============================] - 1s 24us/step - loss: 0.0109 - val_loss: 0.0104\n",
            "Epoch 14/15\n",
            "60000/60000 [==============================] - 1s 23us/step - loss: 0.0108 - val_loss: 0.0103\n",
            "Epoch 15/15\n",
            "19968/60000 [========>.....................] - ETA: 0s - loss: 0.0107"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 1s 23us/step - loss: 0.0107 - val_loss: 0.0103\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7fa72a53e860>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
    {
      "metadata": {
        "id": "WKU0Sz-m8how",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 197
        },
        "outputId": "142e970b-ee75-4f52-c8b5-a4fc72b9c7f3",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1526289607298,
          "user_tz": -120,
          "elapsed": 3121,
          "user": {
            "displayName": "Jordi Vitrià",
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            "userId": "109730415698462856688"
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      },
      "cell_type": "code",
      "source": [
        "# encode and decode some digits\n",
        "# note that we take them from the *test* set\n",
        "encoded_imgs = encoding_model.predict(x_test)\n",
        "decoded_imgs = decoding_model.predict(encoded_imgs)\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "\n",
        "n = 10  # how many digits we will display\n",
        "plt.figure(figsize=(10, 4))\n",
        "for i in range(n):\n",
        "    # display original\n",
        "    ax = plt.subplot(2, n, i + 1)\n",
        "    plt.imshow(x_test[i].reshape(28, 28))\n",
        "    plt.gray()\n",
        "    ax.get_xaxis().set_visible(False)\n",
        "    ax.get_yaxis().set_visible(False)\n",
        "\n",
        "    # display reconstruction\n",
        "    ax = plt.subplot(2, n, i + 1 + n)\n",
        "    plt.imshow(decoded_imgs[i].reshape(28, 28))\n",
        "    plt.gray()\n",
        "    ax.get_xaxis().set_visible(False)\n",
        "    ax.get_yaxis().set_visible(False)\n",
        "plt.show()"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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777xGr2suKieSfq4PjZ3yYKkodamxbNmyRm4p2VBEVtzgUT03Xbc777yzgTN0e+AjLWOM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\ndLtgAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fa77d2a2f60>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "OI8ByJ0w8hoz",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Adding depth and sparsity constraint on the encoded representations\n",
        "\n",
        "In the previous example, the representations were only constrained by the size of the hidden layer (32 neurons). In such a situation, what typically happens is that the hidden layer is learning an approximation of PCA (principal component analysis). \n",
        "\n",
        "Another way to constrain the representations to be compact is to add a **sparsity contraint** on the activity of the hidden representations, so fewer units would \"fire\" at a given time. \n",
        "\n",
        "For any given observation, we'll encourage our network to learn an encoding and decoding which only relies on activating a small number of neurons. It's worth noting that this is a different approach towards regularization, as we normally regularize the weights of a network, not the activations.\n",
        "\n",
        "In Keras, this can be done by adding an ``activity_regularizer`` to our Dense layer:"
      ]
    },
    {
      "metadata": {
        "id": "7usvuZHA8ho0",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 3526
        },
        "outputId": "74af39da-f28c-4329-83f7-e745c862e6a4",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1526289854333,
          "user_tz": -120,
          "elapsed": 244582,
          "user": {
            "displayName": "Jordi Vitrià",
            "photoUrl": "//lh6.googleusercontent.com/-Gjm4qgDBAbI/AAAAAAAAAAI/AAAAAAAAMMU/-Sb9eg_mX-I/s50-c-k-no/photo.jpg",
            "userId": "109730415698462856688"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "#autoencoder.reset_states()\n",
        "#encoder.reset_states()\n",
        "#decoder.reset_states()\n",
        "\n",
        "from keras import regularizers\n",
        "from keras import optimizers\n",
        "from keras.regularizers import l2, l1\n",
        "from keras.layers import Input, Dense\n",
        "from keras.models import Model\n",
        "\n",
        "input_img = Input(shape=(784,))\n",
        "encoded = Dense(128, activation='relu')(input_img)\n",
        "encoded = Dense(64, activation='relu')(encoded)\n",
        "encoded = Dense(32, activation='relu',activity_regularizer=l1(10e-5))(encoded)\n",
        "decoded = Dense(64, activation='relu')(encoded)\n",
        "decoded = Dense(128, activation='relu')(decoded)\n",
        "decoded = Dense(784, activation='sigmoid')(decoded)\n",
        "\n",
        "autoencoder = Model(input_img, decoded)\n",
        "\n",
        "autoencoder.compile(optimizer='adadelta', \n",
        "                    loss='binary_crossentropy',\n",
        "                    )\n",
        "\n",
        "autoencoder.fit(x_train, x_train,\n",
        "                epochs=100,\n",
        "                batch_size=256,\n",
        "                shuffle=True,\n",
        "                validation_data=(x_test, x_test))"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Train on 60000 samples, validate on 10000 samples\n",
            "Epoch 1/100\n",
            "60000/60000 [==============================] - 3s 45us/step - loss: 0.5734 - val_loss: 0.2777\n",
            "Epoch 2/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2666 - val_loss: 0.2637\n",
            "Epoch 3/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2636 - val_loss: 0.2631\n",
            "Epoch 4/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2632 - val_loss: 0.2629\n",
            "Epoch 5/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2631 - val_loss: 0.2627\n",
            "Epoch 6/100\n",
            "50688/60000 [========================>.....] - ETA: 0s - loss: 0.2629"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2630 - val_loss: 0.2627\n",
            "Epoch 7/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2630 - val_loss: 0.2627\n",
            "Epoch 8/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2630 - val_loss: 0.2627\n",
            "Epoch 9/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2627\n",
            "Epoch 10/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 11/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2627\n",
            "Epoch 12/100\n",
            "31232/60000 [==============>...............] - ETA: 1s - loss: 0.2626"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2627\n",
            "Epoch 13/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2627\n",
            "Epoch 14/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2627\n",
            "Epoch 15/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2627\n",
            "Epoch 16/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2627\n",
            "Epoch 17/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 18/100\n",
            "30208/60000 [==============>...............] - ETA: 1s - loss: 0.2626"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 19/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 20/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 21/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2627\n",
            "Epoch 22/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 23/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 24/100\n",
            "26624/60000 [============>.................] - ETA: 1s - loss: 0.2628"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 25/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 26/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 27/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 28/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 29/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 30/100\n",
            "30208/60000 [==============>...............] - ETA: 1s - loss: 0.2626"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2627\n",
            "Epoch 31/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 32/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 33/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 34/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 35/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 36/100\n",
            "28160/60000 [=============>................] - ETA: 1s - loss: 0.2631"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2627\n",
            "Epoch 37/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 38/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2627\n",
            "Epoch 39/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 40/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 41/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 42/100\n",
            "28928/60000 [=============>................] - ETA: 1s - loss: 0.2628"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 43/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 44/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 45/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 46/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 47/100\n",
            "60000/60000 [==============================] - 2s 37us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 48/100\n",
            "29952/60000 [=============>................] - ETA: 1s - loss: 0.2630"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 49/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 50/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 51/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 52/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2627\n",
            "Epoch 53/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 54/100\n",
            "25856/60000 [===========>..................] - ETA: 1s - loss: 0.2631"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 55/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 56/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 57/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 58/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2627\n",
            "Epoch 59/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 60/100\n",
            "24320/60000 [===========>..................] - ETA: 1s - loss: 0.2631"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 61/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 62/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 63/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 64/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 65/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 66/100\n",
            "22784/60000 [==========>...................] - ETA: 1s - loss: 0.2626"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 67/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2627\n",
            "Epoch 68/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 69/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 70/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 71/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 72/100\n",
            "25344/60000 [===========>..................] - ETA: 1s - loss: 0.2631"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 73/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 74/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 75/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 76/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 77/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2627\n",
            "Epoch 78/100\n",
            "28416/60000 [=============>................] - ETA: 1s - loss: 0.2631"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2627\n",
            "Epoch 79/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 80/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2627\n",
            "Epoch 81/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2627\n",
            "Epoch 82/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 83/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 84/100\n",
            "24064/60000 [===========>..................] - ETA: 1s - loss: 0.2630"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 85/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 86/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 87/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 88/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2625\n",
            "Epoch 89/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 90/100\n",
            "27904/60000 [============>.................] - ETA: 1s - loss: 0.2630"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 91/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 92/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 93/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 94/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2628 - val_loss: 0.2626\n",
            "Epoch 95/100\n",
            "60000/60000 [==============================] - 3s 42us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 96/100\n",
            "25600/60000 [===========>..................] - ETA: 1s - loss: 0.2625"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 97/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 98/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 99/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.2629 - val_loss: 0.2626\n",
            "Epoch 100/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.2629 - val_loss: 0.2626\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7fa7091d38d0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "metadata": {
        "id": "9_piKaQZ8ho6",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Convolutional Autoencoders\n",
        "\n",
        "Since our inputs are images, it makes sense to use convolutional neural networks (convnets) as encoders and decoders. "
      ]
    },
    {
      "metadata": {
        "id": "rp7HZkc38ho6",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "cell_type": "code",
      "source": [
        "from keras.layers import Input, Dense, Conv2D, MaxPooling2D, UpSampling2D\n",
        "from keras.models import Model\n",
        "from keras import backend as K\n",
        "\n",
        "input_img = Input(shape=(28, 28, 1))  \n",
        "\n",
        "x = Conv2D(16, (3, 3), padding=\"same\", activation=\"relu\")(input_img)\n",
        "x = MaxPooling2D((2, 2), padding=\"same\")(x)\n",
        "x = Conv2D(8, (3, 3), padding=\"same\", activation=\"relu\")(x)\n",
        "x = MaxPooling2D((2, 2), padding=\"same\")(x)\n",
        "x = Conv2D(8, (3, 3), padding=\"same\", activation=\"relu\")(x)\n",
        "encoded = MaxPooling2D((2, 2), padding=\"same\")(x)\n",
        "\n",
        "# at this point the representation is (4, 4, 8) i.e. 128-dimensional\n",
        "\n",
        "x = Conv2D(8, (3, 3), padding=\"same\", activation=\"relu\")(encoded)\n",
        "x = UpSampling2D((2, 2))(x)\n",
        "x = Conv2D(8, (3, 3), padding=\"same\", activation=\"relu\")(x)\n",
        "x = UpSampling2D((2, 2))(x)\n",
        "x = Conv2D(16, (3, 3), activation=\"relu\")(x)\n",
        "x = UpSampling2D((2, 2))(x)\n",
        "decoded = Conv2D(1, (3, 3), padding=\"same\", activation=\"sigmoid\")(x)\n",
        "\n",
        "# at this point the representation is (28, 28, 1) i.e. 784-dimensional\n",
        "\n",
        "autoencoder = Model(input_img, decoded)\n",
        "autoencoder.compile(optimizer='adadelta', loss='binary_crossentropy')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "yZb8UQcz8ho8",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "cell_type": "code",
      "source": [
        "from keras.datasets import mnist\n",
        "import numpy as np\n",
        "\n",
        "(x_train, _), (x_test, _) = mnist.load_data()\n",
        "\n",
        "x_train = x_train.astype('float32') / 255.\n",
        "x_test = x_test.astype('float32') / 255.\n",
        "x_train = np.reshape(x_train, (len(x_train), 28, 28, 1))  \n",
        "x_test = np.reshape(x_test, (len(x_test), 28, 28, 1))  "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "4pgviNIE8ho_",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 1799
        },
        "outputId": "d64cd1d4-d1f3-4636-ae31-f4b6f76e7c26",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1526290372359,
          "user_tz": -120,
          "elapsed": 505690,
          "user": {
            "displayName": "Jordi Vitrià",
            "photoUrl": "//lh6.googleusercontent.com/-Gjm4qgDBAbI/AAAAAAAAAAI/AAAAAAAAMMU/-Sb9eg_mX-I/s50-c-k-no/photo.jpg",
            "userId": "109730415698462856688"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "from keras.callbacks import TensorBoard\n",
        "\n",
        "autoencoder.fit(x_train, x_train,\n",
        "                epochs=50,\n",
        "                batch_size=128,\n",
        "                shuffle=True,\n",
        "                validation_data=(x_test, x_test),\n",
        "                callbacks=[TensorBoard(log_dir='/tmp/autoencoder')])"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Train on 60000 samples, validate on 10000 samples\n",
            "Epoch 1/50\n",
            "60000/60000 [==============================] - 11s 184us/step - loss: 0.2137 - val_loss: 0.1599\n",
            "Epoch 2/50\n",
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1546 - val_loss: 0.1444\n",
            "Epoch 3/50\n",
            "46336/60000 [======================>.......] - ETA: 2s - loss: 0.1415"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 10s 165us/step - loss: 0.1405 - val_loss: 0.1365\n",
            "Epoch 4/50\n",
            "60000/60000 [==============================] - 10s 165us/step - loss: 0.1328 - val_loss: 0.1276\n",
            "Epoch 5/50\n",
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1283 - val_loss: 0.1247\n",
            "Epoch 6/50\n",
            "23808/60000 [==========>...................] - ETA: 5s - loss: 0.1262"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 10s 167us/step - loss: 0.1249 - val_loss: 0.1278\n",
            "Epoch 7/50\n",
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1224 - val_loss: 0.1217\n",
            "Epoch 8/50\n",
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1205 - val_loss: 0.1229\n",
            "Epoch 9/50\n",
            "19968/60000 [========>.....................] - ETA: 6s - loss: 0.1192"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1187 - val_loss: 0.1129\n",
            "Epoch 10/50\n",
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1169 - val_loss: 0.1154\n",
            "Epoch 11/50\n",
            "60000/60000 [==============================] - 10s 165us/step - loss: 0.1156 - val_loss: 0.1126\n",
            "Epoch 12/50\n",
            "18176/60000 [========>.....................] - ETA: 6s - loss: 0.1146"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 10s 164us/step - loss: 0.1145 - val_loss: 0.1119\n",
            "Epoch 13/50\n",
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1132 - val_loss: 0.1117\n",
            "Epoch 14/50\n",
            "60000/60000 [==============================] - 10s 165us/step - loss: 0.1122 - val_loss: 0.1081\n",
            "Epoch 15/50\n",
            "18432/60000 [========>.....................] - ETA: 6s - loss: 0.1116"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 10s 165us/step - loss: 0.1115 - val_loss: 0.1093\n",
            "Epoch 16/50\n",
            "60000/60000 [==============================] - 10s 167us/step - loss: 0.1106 - val_loss: 0.1114\n",
            "Epoch 17/50\n",
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1098 - val_loss: 0.1094\n",
            "Epoch 18/50\n",
            "18432/60000 [========>.....................] - ETA: 6s - loss: 0.1097"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 10s 168us/step - loss: 0.1095 - val_loss: 0.1094\n",
            "Epoch 19/50\n",
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1090 - val_loss: 0.1068\n",
            "Epoch 20/50\n",
            "60000/60000 [==============================] - 10s 167us/step - loss: 0.1083 - val_loss: 0.1073\n",
            "Epoch 21/50\n",
            "18432/60000 [========>.....................] - ETA: 6s - loss: 0.1084"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1083 - val_loss: 0.1068\n",
            "Epoch 22/50\n",
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1078 - val_loss: 0.1099\n",
            "Epoch 23/50\n",
            "60000/60000 [==============================] - 10s 168us/step - loss: 0.1071 - val_loss: 0.1083\n",
            "Epoch 24/50\n",
            "18432/60000 [========>.....................] - ETA: 6s - loss: 0.1070"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1066 - val_loss: 0.1084\n",
            "Epoch 25/50\n",
            "60000/60000 [==============================] - 10s 167us/step - loss: 0.1062 - val_loss: 0.1044\n",
            "Epoch 26/50\n",
            "60000/60000 [==============================] - 10s 167us/step - loss: 0.1056 - val_loss: 0.1026\n",
            "Epoch 27/50\n",
            "18176/60000 [========>.....................] - ETA: 6s - loss: 0.1053"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1053 - val_loss: 0.1054\n",
            "Epoch 28/50\n",
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1052 - val_loss: 0.1057\n",
            "Epoch 29/50\n",
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1049 - val_loss: 0.1051\n",
            "Epoch 30/50\n",
            "17792/60000 [=======>......................] - ETA: 6s - loss: 0.1051"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 10s 165us/step - loss: 0.1045 - val_loss: 0.1023\n",
            "Epoch 31/50\n",
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1041 - val_loss: 0.1030\n",
            "Epoch 32/50\n",
            "60000/60000 [==============================] - 10s 165us/step - loss: 0.1040 - val_loss: 0.1018\n",
            "Epoch 33/50\n",
            "18432/60000 [========>.....................] - ETA: 6s - loss: 0.1039"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1038 - val_loss: 0.1031\n",
            "Epoch 34/50\n",
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1037 - val_loss: 0.1008\n",
            "Epoch 35/50\n",
            "60000/60000 [==============================] - 10s 167us/step - loss: 0.1033 - val_loss: 0.1019\n",
            "Epoch 36/50\n",
            "17920/60000 [=======>......................] - ETA: 6s - loss: 0.1029"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1031 - val_loss: 0.1048\n",
            "Epoch 37/50\n",
            "60000/60000 [==============================] - 10s 165us/step - loss: 0.1029 - val_loss: 0.1008\n",
            "Epoch 38/50\n",
            "60000/60000 [==============================] - 10s 167us/step - loss: 0.1025 - val_loss: 0.1007\n",
            "Epoch 39/50\n",
            "18560/60000 [========>.....................] - ETA: 6s - loss: 0.1032"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 10s 167us/step - loss: 0.1024 - val_loss: 0.1015\n",
            "Epoch 40/50\n",
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1023 - val_loss: 0.1039\n",
            "Epoch 41/50\n",
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1022 - val_loss: 0.1019\n",
            "Epoch 42/50\n",
            "18432/60000 [========>.....................] - ETA: 6s - loss: 0.1014"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1018 - val_loss: 0.1021\n",
            "Epoch 43/50\n",
            "60000/60000 [==============================] - 10s 165us/step - loss: 0.1018 - val_loss: 0.1009\n",
            "Epoch 44/50\n",
            "60000/60000 [==============================] - 10s 167us/step - loss: 0.1017 - val_loss: 0.1021\n",
            "Epoch 45/50\n",
            "18560/60000 [========>.....................] - ETA: 6s - loss: 0.1014"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1012 - val_loss: 0.1018\n",
            "Epoch 46/50\n",
            "60000/60000 [==============================] - 10s 165us/step - loss: 0.1014 - val_loss: 0.1002\n",
            "Epoch 47/50\n",
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1011 - val_loss: 0.1017\n",
            "Epoch 48/50\n",
            "18560/60000 [========>.....................] - ETA: 6s - loss: 0.1014"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1012 - val_loss: 0.1024\n",
            "Epoch 49/50\n",
            "60000/60000 [==============================] - 10s 165us/step - loss: 0.1008 - val_loss: 0.0989\n",
            "Epoch 50/50\n",
            "60000/60000 [==============================] - 10s 166us/step - loss: 0.1006 - val_loss: 0.0990\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7fa71131ea90>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "metadata": {
        "id": "10QtRdjO8hpC",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 137
        },
        "outputId": "78c82d61-6b89-406d-b871-e4e4a27dba3d",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1526290388920,
          "user_tz": -120,
          "elapsed": 2498,
          "user": {
            "displayName": "Jordi Vitrià",
            "photoUrl": "//lh6.googleusercontent.com/-Gjm4qgDBAbI/AAAAAAAAAAI/AAAAAAAAMMU/-Sb9eg_mX-I/s50-c-k-no/photo.jpg",
            "userId": "109730415698462856688"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "decoded_imgs = autoencoder.predict(x_test)\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "n = 10\n",
        "plt.figure(figsize=(10, 2))\n",
        "for i in range(1,n):\n",
        "    # display original\n",
        "    ax = plt.subplot(2, n, i)\n",
        "    plt.imshow(x_test[i].reshape(28, 28))\n",
        "    plt.gray()\n",
        "    ax.get_xaxis().set_visible(False)\n",
        "    ax.get_yaxis().set_visible(False)\n",
        "\n",
        "    # display reconstruction\n",
        "    ax = plt.subplot(2, n, i + n)\n",
        "    plt.imshow(decoded_imgs[i].reshape(28, 28))\n",
        "    plt.gray()\n",
        "    ax.get_xaxis().set_visible(False)\n",
        "    ax.get_yaxis().set_visible(False)\n",
        "plt.show()"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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MYcOG8b3vfQ8IqmDm+n26NyQSCR555BEgODK6+uqrLehbue3yxrNN\nMpk0Be6jjz4CUsqj9qZcWbuCggJTWpUqKT777DNL6c6WsuHKgOM4juPkObGqPLlYLJbTbl4ymdxj\njmFdzjEcUJcp6y7Tc8wGe5pjpuZXXFxswWi9evUCggBJBbLWhEyvYbimu7y/dHtXUbpOY7FYWhSs\nKM2xuuhaGDlypPWqePbZZwF44403gLKqV1TuxXSRzjVs0aKFBeoqEFtxZiNHjrS4unSzuzm6MuA4\njuM4eY4rAz7HyBMlb0TRv4q+D2ca1BRfwxQ+x+wRi8Us7U3F4OTFhlPconQvpoN0rmFxcbGlxHfs\n2BHAUrdnzpxZk4+sEbubY8YCCB2nPhAOhHWc+kIymSzTbhyCgFMIWnw7NWf79u3WLEppvlEKPPZj\nAsdxHMfJc6o8JnAcx3Ecp/7jyoDjOI7j5DluDDiO4zhOnuPGgOM4juPkOW4MOI7jOE6e48aA4ziO\n4+Q5bgw4juM4Tp7z//MIaSPWacXfAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fa6fc8a8cf8>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "v1x9ZS2j8hpF",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Denoising autoencoders\n",
        "\n",
        "Another approach towards developing a generalizable model is to slightly corrupt the input data but still maintain the uncorrupted data as our target output.\n",
        "\n",
        "With this approach, our model isn't able to simply develop a mapping which memorizes the training data because our input and target output are no longer the same.\n",
        "\n",
        "<center>\n",
        "<img src=\"images/denoised_digits.png\" alt=\"\" style=\"width: 700px;\"/> \n",
        "(Source: https://blog.keras.io/building-autoencoders-in-keras.html)\n",
        "</center>"
      ]
    },
    {
      "metadata": {
        "id": "myqiSgdb8hpG",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 78
        },
        "outputId": "f056e0a0-74c7-4b41-d81f-f25bb5f12751",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1526290717475,
          "user_tz": -120,
          "elapsed": 5473,
          "user": {
            "displayName": "Jordi Vitrià",
            "photoUrl": "//lh6.googleusercontent.com/-Gjm4qgDBAbI/AAAAAAAAAAI/AAAAAAAAMMU/-Sb9eg_mX-I/s50-c-k-no/photo.jpg",
            "userId": "109730415698462856688"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from keras.datasets import mnist\n",
        "from keras.layers import Dense\n",
        "from keras.models import Sequential\n",
        "\n",
        "(x_train, _), (x_test, _) = mnist.load_data()\n",
        "\n",
        "x_train = x_train.astype('float32') / 255.\n",
        "x_test = x_test.astype('float32') / 255.\n",
        "x_train = np.reshape(x_train, (len(x_train), 784))\n",
        "x_test = np.reshape(x_test, (len(x_test), 784))\n",
        "\n",
        "noise_factor = 0.5\n",
        "x_train_noisy = x_train + noise_factor * np.random.normal(loc=0.0, scale=1.0, size=x_train.shape) \n",
        "x_test_noisy = x_test + noise_factor * np.random.normal(loc=0.0, scale=1.0, size=x_test.shape) \n",
        "x_train_noisy = np.clip(x_train_noisy, 0., 1.)\n",
        "x_test_noisy = np.clip(x_test_noisy, 0., 1.)\n",
        "\n",
        "n = 10\n",
        "plt.figure(figsize=(10, 2))\n",
        "for i in range(n):\n",
        "    ax = plt.subplot(1, n, i+1)\n",
        "    plt.imshow(x_test_noisy[i].reshape(28, 28))\n",
        "    plt.gray()\n",
        "    ax.get_xaxis().set_visible(False)\n",
        "    ax.get_yaxis().set_visible(False)\n",
        "plt.show()"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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pBT+zk5GRYak0UiBvvvlmlvvg5ZdfjrN3uXLlsjGTRksEd95I3ZN6TvV+JuAy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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fa709774c18>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "wr0836wg8hpM",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 3526
        },
        "outputId": "ac6e6e04-49ce-4eb4-a599-35e5fd24403f",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1526290654085,
          "user_tz": -120,
          "elapsed": 242736,
          "user": {
            "displayName": "Jordi Vitrià",
            "photoUrl": "//lh6.googleusercontent.com/-Gjm4qgDBAbI/AAAAAAAAAAI/AAAAAAAAMMU/-Sb9eg_mX-I/s50-c-k-no/photo.jpg",
            "userId": "109730415698462856688"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "model = Sequential()\n",
        "model.add(Dense(128, activation='relu', input_dim=784))\n",
        "model.add(Dense(64, activation='relu'))\n",
        "model.add(Dense(32, activation='relu'))\n",
        "model.add(Dense(64, activation='relu'))\n",
        "model.add(Dense(128, activation='relu'))\n",
        "model.add(Dense(784, activation='sigmoid'))\n",
        "model.compile(optimizer='adam', loss='binary_crossentropy')\n",
        "\n",
        "model.fit(x_train_noisy, x_train, \n",
        "          epochs=100,\n",
        "          batch_size=256,\n",
        "          shuffle=True,\n",
        "          validation_data=(x_test_noisy, x_test))"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Train on 60000 samples, validate on 10000 samples\n",
            "Epoch 1/100\n",
            "60000/60000 [==============================] - 3s 47us/step - loss: 0.2645 - val_loss: 0.1968\n",
            "Epoch 2/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1776 - val_loss: 0.1653\n",
            "Epoch 3/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1606 - val_loss: 0.1555\n",
            "Epoch 4/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1531 - val_loss: 0.1492\n",
            "Epoch 5/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1481 - val_loss: 0.1453\n",
            "Epoch 6/100\n",
            "58624/60000 [============================>.] - ETA: 0s - loss: 0.1436"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1436 - val_loss: 0.1411\n",
            "Epoch 7/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1399 - val_loss: 0.1376\n",
            "Epoch 8/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1370 - val_loss: 0.1351\n",
            "Epoch 9/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1349 - val_loss: 0.1341\n",
            "Epoch 10/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1331 - val_loss: 0.1315\n",
            "Epoch 11/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1315 - val_loss: 0.1309\n",
            "Epoch 12/100\n",
            "38400/60000 [==================>...........] - ETA: 0s - loss: 0.1302"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1302 - val_loss: 0.1294\n",
            "Epoch 13/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1290 - val_loss: 0.1282\n",
            "Epoch 14/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1280 - val_loss: 0.1282\n",
            "Epoch 15/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.1271 - val_loss: 0.1267\n",
            "Epoch 16/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.1262 - val_loss: 0.1270\n",
            "Epoch 17/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1255 - val_loss: 0.1258\n",
            "Epoch 18/100\n",
            "32768/60000 [===============>..............] - ETA: 1s - loss: 0.1245"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1247 - val_loss: 0.1250\n",
            "Epoch 19/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1239 - val_loss: 0.1241\n",
            "Epoch 20/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1233 - val_loss: 0.1236\n",
            "Epoch 21/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1228 - val_loss: 0.1230\n",
            "Epoch 22/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1221 - val_loss: 0.1230\n",
            "Epoch 23/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1215 - val_loss: 0.1223\n",
            "Epoch 24/100\n",
            "26368/60000 [============>.................] - ETA: 1s - loss: 0.1208"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.1210 - val_loss: 0.1221\n",
            "Epoch 25/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.1205 - val_loss: 0.1220\n",
            "Epoch 26/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1202 - val_loss: 0.1210\n",
            "Epoch 27/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1198 - val_loss: 0.1205\n",
            "Epoch 28/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1195 - val_loss: 0.1209\n",
            "Epoch 29/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.1191 - val_loss: 0.1200\n",
            "Epoch 30/100\n",
            "30976/60000 [==============>...............] - ETA: 1s - loss: 0.1182"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1188 - val_loss: 0.1202\n",
            "Epoch 31/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1186 - val_loss: 0.1198\n",
            "Epoch 32/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1183 - val_loss: 0.1196\n",
            "Epoch 33/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.1181 - val_loss: 0.1192\n",
            "Epoch 34/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1177 - val_loss: 0.1188\n",
            "Epoch 35/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1175 - val_loss: 0.1194\n",
            "Epoch 36/100\n",
            "32768/60000 [===============>..............] - ETA: 1s - loss: 0.1171"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1172 - val_loss: 0.1191\n",
            "Epoch 37/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1170 - val_loss: 0.1181\n",
            "Epoch 38/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1167 - val_loss: 0.1180\n",
            "Epoch 39/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1166 - val_loss: 0.1180\n",
            "Epoch 40/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1164 - val_loss: 0.1180\n",
            "Epoch 41/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1161 - val_loss: 0.1180\n",
            "Epoch 42/100\n",
            "31488/60000 [==============>...............] - ETA: 1s - loss: 0.1157"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1160 - val_loss: 0.1178\n",
            "Epoch 43/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1157 - val_loss: 0.1178\n",
            "Epoch 44/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1156 - val_loss: 0.1176\n",
            "Epoch 45/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1154 - val_loss: 0.1171\n",
            "Epoch 46/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1152 - val_loss: 0.1169\n",
            "Epoch 47/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1151 - val_loss: 0.1172\n",
            "Epoch 48/100\n",
            "28160/60000 [=============>................] - ETA: 1s - loss: 0.1149"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1149 - val_loss: 0.1167\n",
            "Epoch 49/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1147 - val_loss: 0.1168\n",
            "Epoch 50/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1147 - val_loss: 0.1166\n",
            "Epoch 51/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1145 - val_loss: 0.1167\n",
            "Epoch 52/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1143 - val_loss: 0.1165\n",
            "Epoch 53/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1142 - val_loss: 0.1162\n",
            "Epoch 54/100\n",
            "32768/60000 [===============>..............] - ETA: 1s - loss: 0.1140"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1140 - val_loss: 0.1164\n",
            "Epoch 55/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1140 - val_loss: 0.1166\n",
            "Epoch 56/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1139 - val_loss: 0.1158\n",
            "Epoch 57/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1138 - val_loss: 0.1160\n",
            "Epoch 58/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.1137 - val_loss: 0.1160\n",
            "Epoch 59/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1136 - val_loss: 0.1158\n",
            "Epoch 60/100\n",
            "29696/60000 [=============>................] - ETA: 1s - loss: 0.1132"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.1134 - val_loss: 0.1162\n",
            "Epoch 61/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.1134 - val_loss: 0.1159\n",
            "Epoch 62/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.1133 - val_loss: 0.1158\n",
            "Epoch 63/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1132 - val_loss: 0.1156\n",
            "Epoch 64/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1131 - val_loss: 0.1157\n",
            "Epoch 65/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1129 - val_loss: 0.1156\n",
            "Epoch 66/100\n",
            "32512/60000 [===============>..............] - ETA: 1s - loss: 0.1128"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1129 - val_loss: 0.1159\n",
            "Epoch 67/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1129 - val_loss: 0.1155\n",
            "Epoch 68/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1128 - val_loss: 0.1152\n",
            "Epoch 69/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1128 - val_loss: 0.1151\n",
            "Epoch 70/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1126 - val_loss: 0.1160\n",
            "Epoch 71/100\n",
            "60000/60000 [==============================] - 2s 41us/step - loss: 0.1125 - val_loss: 0.1155\n",
            "Epoch 72/100\n",
            "32000/60000 [===============>..............] - ETA: 1s - loss: 0.1124"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1125 - val_loss: 0.1153\n",
            "Epoch 73/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1124 - val_loss: 0.1153\n",
            "Epoch 74/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1124 - val_loss: 0.1151\n",
            "Epoch 75/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1124 - val_loss: 0.1155\n",
            "Epoch 76/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1122 - val_loss: 0.1150\n",
            "Epoch 77/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1122 - val_loss: 0.1152\n",
            "Epoch 78/100\n",
            "32512/60000 [===============>..............] - ETA: 1s - loss: 0.1121"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1121 - val_loss: 0.1151\n",
            "Epoch 79/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1121 - val_loss: 0.1156\n",
            "Epoch 80/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1121 - val_loss: 0.1149\n",
            "Epoch 81/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1119 - val_loss: 0.1148\n",
            "Epoch 82/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1119 - val_loss: 0.1147\n",
            "Epoch 83/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1118 - val_loss: 0.1146\n",
            "Epoch 84/100\n",
            "30976/60000 [==============>...............] - ETA: 1s - loss: 0.1117"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1118 - val_loss: 0.1145\n",
            "Epoch 85/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1117 - val_loss: 0.1143\n",
            "Epoch 86/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1116 - val_loss: 0.1146\n",
            "Epoch 87/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1116 - val_loss: 0.1145\n",
            "Epoch 88/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1115 - val_loss: 0.1148\n",
            "Epoch 89/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1115 - val_loss: 0.1143\n",
            "Epoch 90/100\n",
            "31488/60000 [==============>...............] - ETA: 1s - loss: 0.1114"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1114 - val_loss: 0.1145\n",
            "Epoch 91/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1115 - val_loss: 0.1143\n",
            "Epoch 92/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1114 - val_loss: 0.1142\n",
            "Epoch 93/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1112 - val_loss: 0.1144\n",
            "Epoch 94/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1113 - val_loss: 0.1143\n",
            "Epoch 95/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1111 - val_loss: 0.1146\n",
            "Epoch 96/100\n",
            "32000/60000 [===============>..............] - ETA: 1s - loss: 0.1111"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1112 - val_loss: 0.1142\n",
            "Epoch 97/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1112 - val_loss: 0.1145\n",
            "Epoch 98/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1110 - val_loss: 0.1144\n",
            "Epoch 99/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1110 - val_loss: 0.1146\n",
            "Epoch 100/100\n",
            "60000/60000 [==============================] - 2s 40us/step - loss: 0.1110 - val_loss: 0.1142\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<keras.callbacks.History at 0x7fa6b7b49978>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "metadata": {
        "id": "RdU08UVm8hpP",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 333
        },
        "outputId": "de61fa5a-ac4c-46fd-b03b-63ae5b7a962b",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1526290747085,
          "user_tz": -120,
          "elapsed": 3009,
          "user": {
            "displayName": "Jordi Vitrià",
            "photoUrl": "//lh6.googleusercontent.com/-Gjm4qgDBAbI/AAAAAAAAAAI/AAAAAAAAMMU/-Sb9eg_mX-I/s50-c-k-no/photo.jpg",
            "userId": "109730415698462856688"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "decoded_imgs = model.predict(x_test)\n",
        "n = 10\n",
        "plt.figure(figsize=(15, 6))\n",
        "for i in range(1, n):\n",
        "    # display original\n",
        "    ax = plt.subplot(3, n, i)\n",
        "    plt.imshow(x_test[i].reshape(28, 28))\n",
        "    plt.gray()\n",
        "    ax.get_xaxis().set_visible(False)\n",
        "    ax.get_yaxis().set_visible(False)\n",
        "\n",
        "    # display noisy\n",
        "    ax = plt.subplot(3, n, i + n)\n",
        "    plt.imshow(x_test_noisy[i].reshape(28, 28))\n",
        "    plt.gray()\n",
        "    ax.get_xaxis().set_visible(False)\n",
        "    ax.get_yaxis().set_visible(False)\n",
        "\n",
        "    # display reconstruction\n",
        "    ax = plt.subplot(3, n, i + 2*n)\n",
        "    plt.imshow(decoded_imgs[i].reshape(28, 28))\n",
        "    plt.gray()\n",
        "    ax.get_xaxis().set_visible(False)\n",
        "    ax.get_yaxis().set_visible(False)\n",
        "plt.show()"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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qvv7xxx8BAE8++WRoo0uFIQsAsMMOOwAAtt5669D2ww8/lOWamnfeeUOf0q3L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\nfcqCCy4Y2qZOnVor3j6utypgjlWHpnVa50smI6E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UJeaCjoW4FEPrYDDXvV5Xhlzp+ceq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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7fa707db7f98>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "RImSsDWw8hpS",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Variational Autoencoders\n",
        "\n",
        "A variational autoencoder is an autoencoder that adds probabilistic constraints on the representations being learned. \n",
        "\n",
        "> When using probabilistic models, **compressed representation** is called **latent variable model**. \n",
        "\n",
        "So, instead of learning a function this model is learning a probabilistic distribution function that models your data.\n",
        "\n",
        "> Why? Standard autoencoders are not suited to work as a generative model. If you pick a random value for your decoder you won't get necessarily a good reconstruction: the value can far away from any previous value the network has seen before! That's why attaching a probabilistic model to the compressed representation is a good idea! \n",
        "\n",
        "For sake of simplicity, let's use a standard normal distribution to define the distribution of inputs ($\\mathbf V$) the decoder will receive. \n",
        "\n",
        "The architecture of a variational autoencoder (VAE) is thus:"
      ]
    },
    {
      "metadata": {
        "id": "uvVQIGE08hpS",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "<center>\n",
        "<img src=\"images/vae1.png\" alt=\"\" style=\"width: 300px;\"/> \n",
        "(Source: http://ijdykeman.github.io/ml/2016/12/21/cvae.html)\n",
        "</center>"
      ]
    },
    {
      "metadata": {
        "id": "uPefv7SY8hpT",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "We want the decoder to take any point taken from a standard normal distribution to return a reasonable element of our dataset:\n",
        "\n",
        "<center>\n",
        "<img src=\"images/vae2.png\" alt=\"\" style=\"width: 500px;\"/> \n",
        "(Source: http://ijdykeman.github.io/ml/2016/12/21/cvae.html)\n",
        "</center>"
      ]
    },
    {
      "metadata": {
        "id": "fQKKsV2g8hpU",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Let's consider the encoder role in this architecture. \n",
        "\n",
        "In a traditional autoencoder, the encoder model takes a sample from data and returns a single point in the latent space, which is then passed to the decoder.\n",
        "\n",
        "In VAE the encoder instead produces (the parameters of) a probability distribution in the latent space:\n",
        "\n",
        "<center>\n",
        "<img src=\"images/vae3.png\" alt=\"\" style=\"width: 500px;\"/> \n",
        "(Source: http://ijdykeman.github.io/ml/2016/12/21/cvae.html)\n",
        "</center>\n",
        "\n",
        "These distributions are (non standard) Gaussians of the same dimensionality as the latent space. "
      ]
    },
    {
      "metadata": {
        "id": "S9UfZpYt8hpV",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Implementation\n",
        "\n",
        "First, let’s implement the encoder net, which takes input $X$ and outputs two things: $\\mu(X)$ and $\\Sigma(X)$, the parameters of the Gaussian. Our encoder will be based in a convolutional neural net. \n",
        "\n",
        "Our latent variable is two dimensional, so that we could easily visualize it."
      ]
    },
    {
      "metadata": {
        "id": "qcJ-KaseMpah",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "4afaa1f5-7a7a-4df0-c2a9-fccae5a03304",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1526322671531,
          "user_tz": -120,
          "elapsed": 2217,
          "user": {
            "displayName": "Jordi Vitrià",
            "photoUrl": "//lh6.googleusercontent.com/-Gjm4qgDBAbI/AAAAAAAAAAI/AAAAAAAAMMU/-Sb9eg_mX-I/s50-c-k-no/photo.jpg",
            "userId": "109730415698462856688"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "import keras\n",
        "from keras import layers\n",
        "from keras import backend as K\n",
        "from keras.models import Model\n",
        "import numpy as np\n",
        "\n",
        "img_shape = (28, 28, 1)\n",
        "batch_size = 16\n",
        "latent_dim = 2  # Dimensionality of the latent space: a plane\n",
        "\n",
        "input_img = keras.Input(shape=img_shape)\n",
        "\n",
        "# encoder\n",
        "\n",
        "x = layers.Conv2D(32, 3,\n",
        "                  padding='same', activation='relu')(input_img)\n",
        "x = layers.Conv2D(64, 3,\n",
        "                  padding='same', activation='relu',\n",
        "                  strides=(2, 2))(x)\n",
        "x = layers.Conv2D(64, 3,\n",
        "                  padding='same', activation='relu')(x)\n",
        "x = layers.Conv2D(64, 3,\n",
        "                  padding='same', activation='relu')(x)\n",
        "\n",
        "shape_before_flattening = K.int_shape(x)\n",
        "\n",
        "x = layers.Flatten()(x)\n",
        "x = layers.Dense(32, activation='relu')(x)\n",
        "\n",
        "z_mean = layers.Dense(latent_dim)(x)\n",
        "z_log_var = layers.Dense(latent_dim)(x)"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Using TensorFlow backend.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "metadata": {
        "id": "0YiElDut8hpX",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Up to now we have an encoder that takes images and produce (the parameters of) a pdf in the latent space.  \n",
        "\n",
        "The decoder takes points in the latent space and return reconstructions.\n",
        "\n",
        "How do we connect both models? By sampling from the produced distribution!\n",
        "\n",
        "\n",
        "<center>\n",
        "<img src=\"images/vae4.png\" alt=\"\" style=\"width: 400px;\"/> \n",
        "(Source: http://ijdykeman.github.io/ml/2016/12/21/cvae.html)\n",
        "</center>"
      ]
    },
    {
      "metadata": {
        "id": "ttMkBRov8hpY",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "To this end we will implement a *random variate reparameterisation*: the substitution of a random variable by a deterministic transformation of a simpler random variable.\n",
        "\n",
        "There are several methods by which non-uniform random numbers, or random variates, can be generated. The most popular methods are the **one-liners**, which give us the simple tools to generate random variates in one line of code, following the classic paper by Luc Devroye (Luc Devroye, Random variate generation in one line of code, Proceedings of the 28th conference on Winter simulation, 1996).\n",
        "\n",
        "In the case of a Gaussian, we can use the following algorithm:\n",
        "+ Generate $\\epsilon \\sim \\mathcal{N}(0;1)$.\n",
        "+ Compute a sample from $\\mathcal{N}(\\mu; RR^T)$ as $\\mu + R \\epsilon$."
      ]
    },
    {
      "metadata": {
        "id": "0O7QBAkl8hpZ",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "cell_type": "code",
      "source": [
        "def sampling(args):\n",
        "    z_mean, z_log_var = args\n",
        "    epsilon = K.random_normal(shape=(K.shape(z_mean)[0], latent_dim),\n",
        "                              mean=0., stddev=1.)\n",
        "    return z_mean + K.exp(z_log_var) * epsilon\n",
        "\n",
        "z = layers.Lambda(sampling)([z_mean, z_log_var])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "ufTMs1_r8hpb",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Now we can create the decoder net. In order to be coherent with our previous definitions, we must assure that points sampled fron the latent space fit a standard normal distribition, but the encoder is producing non standard normal distributions. So, we must add a constraint for getting something like this:\n",
        "\n",
        "<center>\n",
        "<img src=\"images/vae5.png\" alt=\"\" style=\"width: 700px;\"/> \n",
        "(Source: http://ijdykeman.github.io/ml/2016/12/21/cvae.html)\n",
        "</center>\n",
        "\n",
        "In order to impose this constraint in the loss function by using the Kullback-Leibler divergence.\n",
        "\n",
        "> The Kullback–Leibler divergence is a measure of how one probability distribution diverges from a second expected probability distribution. \n",
        "For discrete probability distributions $P$ and $Q$, the Kullback–Leibler divergence from $Q$ to $P$ is defined to be\n",
        "$$ D_{\\mathrm {KL} }(P\\|Q)=\\sum _{i}P(i)\\,\\log {\\frac {P(i)}{Q(i)}}. $$\n",
        "\n",
        "The rest of the loss function must take into account the \"reconstruction\" error.\n"
      ]
    },
    {
      "metadata": {
        "id": "JxwzwxJs8hpc",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 608
        },
        "outputId": "fc99196c-f232-4385-c665-73b8e2a07be0",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1526322953589,
          "user_tz": -120,
          "elapsed": 700,
          "user": {
            "displayName": "Jordi Vitrià",
            "photoUrl": "//lh6.googleusercontent.com/-Gjm4qgDBAbI/AAAAAAAAAAI/AAAAAAAAMMU/-Sb9eg_mX-I/s50-c-k-no/photo.jpg",
            "userId": "109730415698462856688"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "# This is the input where we will feed `z`.\n",
        "decoder_input = layers.Input(K.int_shape(z)[1:])\n",
        "\n",
        "# Upsample to the correct number of units\n",
        "x = layers.Dense(np.prod(shape_before_flattening[1:]),\n",
        "                 activation='relu')(decoder_input)\n",
        "\n",
        "# Reshape into an image of the same shape as before our last `Flatten` layer\n",
        "x = layers.Reshape(shape_before_flattening[1:])(x)\n",
        "\n",
        "# We then apply then reverse operation to the initial\n",
        "# stack of convolution layers: a `Conv2DTranspose` layers\n",
        "# with corresponding parameters.\n",
        "x = layers.Conv2DTranspose(32, 3,\n",
        "                           padding='same', activation='relu',\n",
        "                           strides=(2, 2))(x)\n",
        "x = layers.Conv2D(1, 3,\n",
        "                  padding='same', activation='sigmoid')(x)\n",
        "# We end up with a feature map of the same size as the original input.\n",
        "\n",
        "# This is our decoder model.\n",
        "decoder = Model(decoder_input, x)\n",
        "\n",
        "# We then apply it to `z` to recover the decoded `z`.\n",
        "z_decoded = decoder(z)\n",
        "\n",
        "class CustomVariationalLayer(keras.layers.Layer):\n",
        "\n",
        "    def vae_loss(self, x, z_decoded):\n",
        "        x = K.flatten(x)\n",
        "        z_decoded = K.flatten(z_decoded)\n",
        "        xent_loss = keras.metrics.binary_crossentropy(x, z_decoded)\n",
        "        kl_loss = -5e-4 * K.mean(\n",
        "            1 + z_log_var - K.square(z_mean) - K.exp(z_log_var), axis=-1)\n",
        "        return K.mean(xent_loss + kl_loss)\n",
        "\n",
        "    def call(self, inputs):\n",
        "        x = inputs[0]\n",
        "        z_decoded = inputs[1]\n",
        "        loss = self.vae_loss(x, z_decoded)\n",
        "        self.add_loss(loss, inputs=inputs)\n",
        "        # We don't use this output.\n",
        "        return x\n",
        "\n",
        "# We call our custom layer on the input and the decoded output,\n",
        "# to obtain the final model output.\n",
        "y = CustomVariationalLayer()([input_img, z_decoded])\n",
        "\n",
        "from keras.datasets import mnist\n",
        "\n",
        "vae = Model(input_img, y)\n",
        "vae.compile(optimizer='rmsprop', loss=None)\n",
        "vae.summary()"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "__________________________________________________________________________________________________\n",
            "Layer (type)                    Output Shape         Param #     Connected to                     \n",
            "==================================================================================================\n",
            "input_1 (InputLayer)            (None, 28, 28, 1)    0                                            \n",
            "__________________________________________________________________________________________________\n",
            "conv2d_1 (Conv2D)               (None, 28, 28, 32)   320         input_1[0][0]                    \n",
            "__________________________________________________________________________________________________\n",
            "conv2d_2 (Conv2D)               (None, 14, 14, 64)   18496       conv2d_1[0][0]                   \n",
            "__________________________________________________________________________________________________\n",
            "conv2d_3 (Conv2D)               (None, 14, 14, 64)   36928       conv2d_2[0][0]                   \n",
            "__________________________________________________________________________________________________\n",
            "conv2d_4 (Conv2D)               (None, 14, 14, 64)   36928       conv2d_3[0][0]                   \n",
            "__________________________________________________________________________________________________\n",
            "flatten_1 (Flatten)             (None, 12544)        0           conv2d_4[0][0]                   \n",
            "__________________________________________________________________________________________________\n",
            "dense_1 (Dense)                 (None, 32)           401440      flatten_1[0][0]                  \n",
            "__________________________________________________________________________________________________\n",
            "dense_2 (Dense)                 (None, 2)            66          dense_1[0][0]                    \n",
            "__________________________________________________________________________________________________\n",
            "dense_3 (Dense)                 (None, 2)            66          dense_1[0][0]                    \n",
            "__________________________________________________________________________________________________\n",
            "lambda_1 (Lambda)               (None, 2)            0           dense_2[0][0]                    \n",
            "                                                                 dense_3[0][0]                    \n",
            "__________________________________________________________________________________________________\n",
            "model_1 (Model)                 (None, 28, 28, 1)    56385       lambda_1[0][0]                   \n",
            "__________________________________________________________________________________________________\n",
            "custom_variational_layer_1 (Cus [(None, 28, 28, 1),  0           input_1[0][0]                    \n",
            "                                                                 model_1[1][0]                    \n",
            "==================================================================================================\n",
            "Total params: 550,629\n",
            "Trainable params: 550,629\n",
            "Non-trainable params: 0\n",
            "__________________________________________________________________________________________________\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:51: UserWarning: Output \"custom_variational_layer_1\" missing from loss dictionary. We assume this was done on purpose, and we will not be expecting any data to be passed to \"custom_variational_layer_1\" during training.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "metadata": {
        "id": "9Xd3P7q-8hpj",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Training a VAE\n",
        "\n",
        "How do we train a model that have a sampling step? \n",
        "\n",
        "<center>\n",
        "<img src=\"images/vae_sampling.png\" alt=\"\" style=\"width: 800px;\"/> \n",
        "</center>\n",
        "\n",
        "In fact this is not a problem! By using the *one-liner* method for sampling we have expressed the latent distribution in a way that its parameters are factored out of the parameters of the random variable so that backpropagation can be used to find the optimal parameters of the latent distribution. For this reason this method is called *reparametrization trick*.\n",
        "\n",
        "By using this trick we can train end-to-end a VAE with backpropagation."
      ]
    },
    {
      "metadata": {
        "id": "uj92vRKz8hpk",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "base_uri": "https://localhost:8080/",
          "height": 968
        },
        "outputId": "e429f80b-6ffd-430f-99eb-d6ce453ce992",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1526336089427,
          "user_tz": -120,
          "elapsed": 4605673,
          "user": {
            "displayName": "Jordi Vitrià",
            "photoUrl": "//lh6.googleusercontent.com/-Gjm4qgDBAbI/AAAAAAAAAAI/AAAAAAAAMMU/-Sb9eg_mX-I/s50-c-k-no/photo.jpg",
            "userId": "109730415698462856688"
          }
        }
      },
      "cell_type": "code",
      "source": [
        "# Train the VAE on MNIST digits\n",
        "(x_train, _), (x_test, y_test) = mnist.load_data()\n",
        "\n",
        "x_train = x_train.astype('float32') / 255.\n",
        "x_train = x_train.reshape(x_train.shape + (1,))\n",
        "x_test = x_test.astype('float32') / 255.\n",
        "x_test = x_test.reshape(x_test.shape + (1,))\n",
        "\n",
        "vae.fit(x=x_train, y=None,\n",
        "        shuffle=True,\n",
        "        epochs=10,\n",
        "        batch_size=batch_size,\n",
        "        validation_data=(x_test, None))\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm\n",
        "\n",
        "# Display a 2D manifold of the digits\n",
        "n = 15  # figure with 15x15 digits\n",
        "digit_size = 28\n",
        "figure = np.zeros((digit_size * n, digit_size * n))\n",
        "# Linearly spaced coordinates on the unit square were transformed\n",
        "# through the inverse CDF (ppf) of the Gaussian\n",
        "# to produce values of the latent variables z,\n",
        "# since the prior of the latent space is Gaussian\n",
        "grid_x = norm.ppf(np.linspace(0.05, 0.95, n))\n",
        "grid_y = norm.ppf(np.linspace(0.05, 0.95, n))\n",
        "\n",
        "for i, yi in enumerate(grid_x):\n",
        "    for j, xi in enumerate(grid_y):\n",
        "        z_sample = np.array([[xi, yi]])\n",
        "        z_sample = np.tile(z_sample, batch_size).reshape(batch_size, 2)\n",
        "        x_decoded = decoder.predict(z_sample, batch_size=batch_size)\n",
        "        digit = x_decoded[0].reshape(digit_size, digit_size)\n",
        "        figure[i * digit_size: (i + 1) * digit_size,\n",
        "               j * digit_size: (j + 1) * digit_size] = digit\n",
        "\n",
        "plt.figure(figsize=(10, 10))\n",
        "plt.imshow(figure, cmap='Greys_r')\n",
        "plt.show()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Train on 60000 samples, validate on 10000 samples\n",
            "Epoch 1/10\n",
            "12112/60000 [=====>........................] - ETA: 5:41 - loss: 0.1852"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 451s 8ms/step - loss: 0.1857 - val_loss: 0.1857\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "Epoch 2/10\n",
            "59984/60000 [============================>.] - ETA: 0s - loss: 0.1855"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 450s 7ms/step - loss: 0.1855 - val_loss: 0.1874\n",
            "Epoch 3/10\n",
            " 9024/60000 [===>..........................] - ETA: 6:20 - loss: 0.1847"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 471s 8ms/step - loss: 0.1854 - val_loss: 0.1861\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "Epoch 4/10\n",
            "59984/60000 [============================>.] - ETA: 0s - loss: 0.1854"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 473s 8ms/step - loss: 0.1854 - val_loss: 0.1887\n",
            "Epoch 5/10\n",
            " 9024/60000 [===>..........................] - ETA: 6:23 - loss: 0.1854"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 470s 8ms/step - loss: 0.1853 - val_loss: 0.1859\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "Epoch 6/10\n",
            "59984/60000 [============================>.] - ETA: 0s - loss: 0.1851"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 467s 8ms/step - loss: 0.1851 - val_loss: 0.1851\n",
            "Epoch 7/10\n",
            " 9024/60000 [===>..........................] - ETA: 6:14 - loss: 0.1846"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 451s 8ms/step - loss: 0.1851 - val_loss: 0.1876\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "Epoch 8/10\n",
            "59984/60000 [============================>.] - ETA: 0s - loss: 0.1851"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 449s 7ms/step - loss: 0.1851 - val_loss: 0.1867\n",
            "Epoch 9/10\n",
            " 9024/60000 [===>..........................] - ETA: 6:09 - loss: 0.1848"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "60000/60000 [==============================] - 450s 8ms/step - loss: 0.1849 - val_loss: 0.1846\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "Epoch 10/10\n",
            "59984/60000 [============================>.] - ETA: 0s - loss: 0.1850"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r60000/60000 [==============================] - 470s 8ms/step - loss: 0.1850 - val_loss: 0.1845\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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S1+rKygpCoRDvrXK5DK/XyyVTFhcXkUwmeZy0ZKrFcaH1IWYiJxIJ5PN5XkNra2u4deuW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HL37xC+zu7rJxVSwWOdLWqdBBTYbr+Pg45ufnMTs7i/n5eQCtTvUUXSRdisUiEokEXxoejwdX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\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m9d4r41El+QEa4fPRRx/VXa7Xr1/f1fBiO7o5nU6cPn1aMitYJJAIwW6tKSNqtRm6R2OW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\nRprqAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f46896d4470>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "O0qJFe0i8hp0",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Conditional VAE\n",
        "\n",
        "What about producing specific number instances on demand?\n",
        "\n",
        "We can do this by adding an extra input (as a one-hot encoding) to both the encoder and the decoder:\n",
        "\n",
        "<center>\n",
        "<img src=\"images/vae6.png\" alt=\"\" style=\"width: 400px;\"/> \n",
        "(Source: http://ijdykeman.github.io/ml/2016/12/21/cvae.html)\n",
        "</center>"
      ]
    },
    {
      "metadata": {
        "id": "EOGVRt7M8hp1",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "To generate an image of a particular number just feed that number in the decoder along with a random point in the latent space.\n",
        "\n",
        "<center>\n",
        "<img src=\"images/vae7.png\" alt=\"\" style=\"width: 600px;\"/> \n",
        "(Source: http://ijdykeman.github.io/ml/2016/12/21/cvae.html)\n",
        "</center>\n",
        "\n",
        "The latent space is no longer encoding what number are you dealing with (because this is already encoded in the extra input!). Instead, it is encoding information such as stroke width, angle, etc."
      ]
    },
    {
      "metadata": {
        "id": "hJ2wrlEG8hp2",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Bibliography"
      ]
    },
    {
      "metadata": {
        "id": "NELXnqW-8hp4",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "+ Doersch, Carl. “Tutorial on variational autoencoders.” arXiv preprint arXiv:1606.05908 (2016).\n",
        "+ Kingma, Diederik P., and Max Welling. “Auto-encoding variational bayes.” arXiv preprint arXiv:1312.6114 (2013)."
      ]
    }
  ]
}