code-questions/Case_Study_Debugging_in_Classification.ipynb

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      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "#### Copyright 2018 Google LLC."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "both",
        "id": "36xim66b_oeE"
      },
      "source": [
        "# Licensed under the Apache License, Version 2.0 (the \"License\");\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MvIx0zxzE93Y"
      },
      "source": [
        "# Case Study: Debugging in Classification"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9tNgLQzd1QHX"
      },
      "source": [
        "This Colab quickly demonstrates a few concepts related to debugging classification models. You will explore potential problems in implementing these tasks:\n",
        "\n",
        "* Calculating loss for classification problems.\n",
        "* Optimizing your model\n",
        "* Applying regularization.\n",
        "* Following best practices in development and debugging.\n",
        "\n",
        "Please **make a copy** of this Colab before running it. Click on *File*, and then click on *Save a copy in Drive*."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0X7dDkLFFCYT"
      },
      "source": [
        "## Load MNIST Data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vmtkGlmC0a0O"
      },
      "source": [
        "MNIST is a dataset of images of the numbers 0 to 9. The problem is to classify the images as numbers. Setup libraries and load the MNIST dataset. Display the first few rows to verify that the data loaded. You'll explore the data format after the data loads."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RNYSqbAcFOIs",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 233
        },
        "outputId": "fe5693b8-f8d9-4910-8269-a991f788c3e1"
      },
      "source": [
        "# Reset environment for a new run\n",
        "% reset -f\n",
        "\n",
        "# Load Libraries\n",
        "from os.path import join # for joining file pathnames\n",
        "import pandas as pd\n",
        "import tensorflow as tf\n",
        "from tensorflow import keras\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import unittest\n",
        "import sys\n",
        "\n",
        "# Set Pandas display options\n",
        "pd.options.display.max_rows = 10\n",
        "pd.options.display.float_format = '{:.1f}'.format\n",
        "\n",
        "# Load data\n",
        "mnistDf_backup = pd.read_csv(\n",
        "  \"https://download.mlcc.google.com/mledu-datasets/mnist_train_small.csv\",\n",
        "  sep=\",\",\n",
        "  header=None)\n",
        "# Shuffle data\n",
        "mnistDf_backup.sample(frac=1).reset_index(drop=True)\n",
        "# Use the first 5000 examples for faster prototyping\n",
        "mnistDf = mnistDf_backup[0:5000]\n",
        "\n",
        "mnistDf.head()"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "   0    1    2    3    4    5    6    7    8    9    ...  775  776  777  778  \\\n",
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          "metadata": {},
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        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z70hEJlEGyMJ"
      },
      "source": [
        "## Understanding the Data Format"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kg0-25p2mOi0"
      },
      "source": [
        "Each row represents one labeled example. Column 0 represents the label that a human rater has assigned for one handwritten digit. For example, if Column 0 contains '6', then a human rater interpreted the handwritten character as the digit '6'.  The ten digits 0-9 are each represented, with a unique class label for each possible digit. Thus, this is a multi-class classification problem with 10 classes."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PQ7vuOwRCsZ1"
      },
      "source": [
        "![img](https://www.tensorflow.org/versions/r0.11/images/MNIST-Matrix.png)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dghlqJPIu8UM"
      },
      "source": [
        "Columns 1 through 784 contain the feature values, one per pixel for the 28×28=784 pixel values. The pixel values are on a gray scale in which 0 represents white, 255 represents black, and values between 0 and 255 represent shades of gray. Most of the pixel values are 0; you may want to take a minute to confirm that they aren't all 0.  Modify the form below and run the code to view data for a given example."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2ZkrL5MCqiJI",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 476
        },
        "outputId": "3833f265-6f9e-45f9-a1e8-cb2122e90f98"
      },
      "source": [
        "showExample = 0 # @param\n",
        "digitData = np.reshape(mnistDf.iloc[showExample,0:-1],[28,28])\n",
        "print digitData"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "error",
          "ename": "KeyError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m\u001b[0m",
            "\u001b[0;31mKeyError\u001b[0mTraceback (most recent call last)",
            "\u001b[0;32m<ipython-input-6-e65fe620e59c>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mshowExample\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0\u001b[0m \u001b[0;31m# @param\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mdigitData\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmnistDf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0miloc\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mshowExample\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m28\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m28\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0;32mprint\u001b[0m \u001b[0mdigitData\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python2.7/dist-packages/pandas/core/series.pyc\u001b[0m in \u001b[0;36m__getitem__\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m    866\u001b[0m         \u001b[0mkey\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcom\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mapply_if_callable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    867\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 868\u001b[0;31m             \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_value\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    869\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    870\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mis_scalar\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python2.7/dist-packages/pandas/core/indexes/base.pyc\u001b[0m in \u001b[0;36mget_value\u001b[0;34m(self, series, key)\u001b[0m\n\u001b[1;32m   4373\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   4374\u001b[0m             return self._engine.get_value(s, k,\n\u001b[0;32m-> 4375\u001b[0;31m                                           tz=getattr(series.dtype, 'tz', None))\n\u001b[0m\u001b[1;32m   4376\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   4377\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m0\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mholds_integer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mis_boolean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32mpandas/_libs/index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_value\u001b[0;34m()\u001b[0m\n",
            "\u001b[0;32mpandas/_libs/index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_value\u001b[0;34m()\u001b[0m\n",
            "\u001b[0;32mpandas/_libs/index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[0;34m()\u001b[0m\n",
            "\u001b[0;32mpandas/_libs/index_class_helper.pxi\u001b[0m in \u001b[0;36mpandas._libs.index.Int64Engine._check_type\u001b[0;34m()\u001b[0m\n",
            "\u001b[0;31mKeyError\u001b[0m: (28, 28)"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NdGR7XJFG3SC"
      },
      "source": [
        "## Do you have Imbalanced Classes?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iaCeo87dGq6F"
      },
      "source": [
        "As we read in the course, imbalanced classes make classification harder. Let's look at the distribution of classes. Do you have imbalanced classes?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ovuBykz5GCHl",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 474
        },
        "outputId": "51ed912c-ab07-409d-db1a-54135c090273"
      },
      "source": [
        "#%hide_result # hides result of cell computation\n",
        "# Calculate the number of classes\n",
        "numClasses = mnistDf.iloc[:,0].unique().shape[0]\n",
        "# Plot histogram of class distribution\n",
        "plt.hist(mnistDf.iloc[:,0], bins=range(numClasses+1))\n",
        "plt.xticks(range(numClasses+1))"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([<matplotlib.axis.XTick at 0x7fb202dd1f90>,\n",
              "  <matplotlib.axis.XTick at 0x7fb202dd1a50>,\n",
              "  <matplotlib.axis.XTick at 0x7fb202dd13d0>,\n",
              "  <matplotlib.axis.XTick at 0x7fb202caaf50>,\n",
              "  <matplotlib.axis.XTick at 0x7fb202cc1350>,\n",
              "  <matplotlib.axis.XTick at 0x7fb202cc1890>,\n",
              "  <matplotlib.axis.XTick at 0x7fb202cc1e10>,\n",
              "  <matplotlib.axis.XTick at 0x7fb202d443d0>,\n",
              "  <matplotlib.axis.XTick at 0x7fb202d44950>,\n",
              "  <matplotlib.axis.XTick at 0x7fb202d44ed0>,\n",
              "  <matplotlib.axis.XTick at 0x7fb202d4c490>],\n",
              " <a list of 11 Text xticklabel objects>)"
            ]
          },
          "metadata": {},
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a7b5jJzMFd9f"
      },
      "source": [
        "The preceding graph shows that the 10 classes are roughly equally represented."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z9gUThwlOjRu"
      },
      "source": [
        "## Shuffle and Split Dataset"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yPd1qfBGOmot"
      },
      "source": [
        "As part of [Data Debugging](https://developers.google.com/machine-learning/testing-debugging/common/data-errors) best practices, ensure your splits are statistically equivalent by shuffling your data to remove any pre-existing order."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9dKZM0l8Om_Q"
      },
      "source": [
        "# Shuffle data\n",
        "mnistDf = mnistDf.sample(frac=1).reset_index(drop=True)\n",
        "\n",
        "# Split dataset into data and labels\n",
        "mnistData = mnistDf.iloc[:,1:-1].copy(deep=True)\n",
        "mnistLabels = mnistDf.iloc[:,0].copy(deep=True)"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "i7cOxjDqJW1r"
      },
      "source": [
        "## Process Data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T8Hsfx4OJh4J"
      },
      "source": [
        "Scale the data values to `[0,1]` since the values are bounded to `[0,255]` and do not contain outliers. Then check that the scaled data values are as expected by generating summary statistics using the `DataFrame.describe()` function.\n",
        "\n",
        "Run the following cell to scale data and generate statistics. This cell takes a few minutes to run."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xz6glQVeJhGa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 326
        },
        "outputId": "37bf3331-9b26-45fc-8a3c-59c06a26de86"
      },
      "source": [
        "def minMaxScaler(arr):\n",
        "  min = np.min(arr)\n",
        "  max = np.max(arr)\n",
        "  arr = (arr-min)/max\n",
        "  return arr\n",
        "\n",
        "for featureIdx in range(mnistData.shape[1]):\n",
        "  mnistData.iloc[:,featureIdx] = minMaxScaler(mnistData.iloc[:,featureIdx])\n",
        "\n",
        "mnistData.describe()"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       1    2    3    4    5    6    7    8    9    10   ...    774    775  \\\n",
              "count  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  ... 5000.0 5000.0   \n",
              "mean   nan  nan  nan  nan  nan  nan  nan  nan  nan  nan  ...    0.0    0.0   \n",
              "std    nan  nan  nan  nan  nan  nan  nan  nan  nan  nan  ...    0.0    0.0   \n",
              "min    nan  nan  nan  nan  nan  nan  nan  nan  nan  nan  ...    0.0    0.0   \n",
              "25%    nan  nan  nan  nan  nan  nan  nan  nan  nan  nan  ...    0.0    0.0   \n",
              "50%    nan  nan  nan  nan  nan  nan  nan  nan  nan  nan  ...    0.0    0.0   \n",
              "75%    nan  nan  nan  nan  nan  nan  nan  nan  nan  nan  ...    0.0    0.0   \n",
              "max    nan  nan  nan  nan  nan  nan  nan  nan  nan  nan  ...    1.0    1.0   \n",
              "\n",
              "         776    777    778    779    780  781  782  783  \n",
              "count 5000.0 5000.0 5000.0 5000.0 5000.0  0.0  0.0  0.0  \n",
              "mean     0.0    0.0    0.0    0.0    0.0  nan  nan  nan  \n",
              "std      0.0    0.0    0.0    0.0    0.0  nan  nan  nan  \n",
              "min      0.0    0.0    0.0    0.0    0.0  nan  nan  nan  \n",
              "25%      0.0    0.0    0.0    0.0    0.0  nan  nan  nan  \n",
              "50%      0.0    0.0    0.0    0.0    0.0  nan  nan  nan  \n",
              "75%      0.0    0.0    0.0    0.0    0.0  nan  nan  nan  \n",
              "max      1.0    1.0    1.0    1.0    1.0  nan  nan  nan  \n",
              "\n",
              "[8 rows x 783 columns]"
            ],
            "text/html": [
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>1</th>\n",
              "      <th>2</th>\n",
              "      <th>3</th>\n",
              "      <th>4</th>\n",
              "      <th>5</th>\n",
              "      <th>6</th>\n",
              "      <th>7</th>\n",
              "      <th>8</th>\n",
              "      <th>9</th>\n",
              "      <th>10</th>\n",
              "      <th>...</th>\n",
              "      <th>774</th>\n",
              "      <th>775</th>\n",
              "      <th>776</th>\n",
              "      <th>777</th>\n",
              "      <th>778</th>\n",
              "      <th>779</th>\n",
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              "      <th>782</th>\n",
              "      <th>783</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
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              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>...</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
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              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>...</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>...</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>...</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>...</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>...</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>...</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>...</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "      <td>nan</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>8 rows × 783 columns</p>\n",
              "</div>"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ja7-yiPaNSqQ"
      },
      "source": [
        "Oh no! Some of your features are all `NaN`. What do you think the cause is? Hint: While NaNs have many causes, in this case, the NaN values are caused by the properties of your data. Use the next code cell to explore your data. Then check the next cell for the solution. Try to find the solution yourself. Debugging `NaN`s and exploring your data are important skills."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MDcTFax_FaAh"
      },
      "source": [
        "# First reload your data\n",
        "mnistData = mnistDf.iloc[:,1:-1].copy(deep=True)"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lPRf41XwNlSJ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 326
        },
        "outputId": "0fe12561-8c4b-44af-d59e-bc986ec246fd"
      },
      "source": [
        "# Explore your data\n",
        "mnistData.describe()"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "         1      2      3      4      5      6      7      8      9      10   \\\n",
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              "\n",
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              "max    ...  254.0  253.0  254.0   68.0   43.0  244.0   62.0    0.0    0.0   \n",
              "\n",
              "         783  \n",
              "count 5000.0  \n",
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              "[8 rows x 783 columns]"
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              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>...</td>\n",
              "      <td>254.0</td>\n",
              "      <td>253.0</td>\n",
              "      <td>254.0</td>\n",
              "      <td>68.0</td>\n",
              "      <td>43.0</td>\n",
              "      <td>244.0</td>\n",
              "      <td>62.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>8 rows × 783 columns</p>\n",
              "</div>"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nKdUi_QENxXp"
      },
      "source": [
        "### Solution"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OCYR63qR249Y"
      },
      "source": [
        "Start exploring your data by generating a high-level summary using `Dataframe.describe()`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KrZUagAw24oS",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 326
        },
        "outputId": "5f74e699-bb5f-426c-b124-a833414f5be8"
      },
      "source": [
        "mnistData.describe()"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "         1      2      3      4      5      6      7      8      9      10   \\\n",
              "count 5000.0 5000.0 5000.0 5000.0 5000.0 5000.0 5000.0 5000.0 5000.0 5000.0   \n",
              "mean     0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0   \n",
              "std      0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0   \n",
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              "max      0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0   \n",
              "\n",
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              "mean   ...    0.5    0.3    0.1    0.0    0.0    0.0    0.0    0.0    0.0   \n",
              "std    ...    9.4    7.7    5.2    1.0    0.6    3.5    0.9    0.0    0.0   \n",
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              "75%    ...    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0    0.0   \n",
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              "\n",
              "         783  \n",
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              "[8 rows x 783 columns]"
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              "      <th>4</th>\n",
              "      <th>5</th>\n",
              "      <th>6</th>\n",
              "      <th>7</th>\n",
              "      <th>8</th>\n",
              "      <th>9</th>\n",
              "      <th>10</th>\n",
              "      <th>...</th>\n",
              "      <th>774</th>\n",
              "      <th>775</th>\n",
              "      <th>776</th>\n",
              "      <th>777</th>\n",
              "      <th>778</th>\n",
              "      <th>779</th>\n",
              "      <th>780</th>\n",
              "      <th>781</th>\n",
              "      <th>782</th>\n",
              "      <th>783</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>...</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>...</td>\n",
              "      <td>0.5</td>\n",
              "      <td>0.3</td>\n",
              "      <td>0.1</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>...</td>\n",
              "      <td>9.4</td>\n",
              "      <td>7.7</td>\n",
              "      <td>5.2</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.6</td>\n",
              "      <td>3.5</td>\n",
              "      <td>0.9</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>...</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>...</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>...</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>...</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>...</td>\n",
              "      <td>254.0</td>\n",
              "      <td>253.0</td>\n",
              "      <td>254.0</td>\n",
              "      <td>68.0</td>\n",
              "      <td>43.0</td>\n",
              "      <td>244.0</td>\n",
              "      <td>62.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>8 rows × 783 columns</p>\n",
              "</div>"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bTnxgrt49tJe",
        "outputId": "d0a91dfb-0df6-4e93-b557-c25ff9d0fd3d"
      },
      "source": [
        "mnistData.isnull().any()"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1      False\n",
              "2      False\n",
              "3      False\n",
              "4      False\n",
              "5      False\n",
              "       ...  \n",
              "779    False\n",
              "780    False\n",
              "781    False\n",
              "782    False\n",
              "783    False\n",
              "Length: 783, dtype: bool"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cp3rP2saNyup"
      },
      "source": [
        "Because some of the feature columns are all zeros, the scaling function divided by 0 (because `np.max` returns 0). The division by 0 resulted in NaN values. This result shows you how easily NaNs can arise in engineered data. The `describe` function will not detect every occurrence of NaN (or None). Instead,  use the command `DataFrame.isnull().any()`.\n",
        "\n",
        "*Note*: Given the maximum value of the feature data is 255, you could simply divide the input by 255 instead of using min-max scaling, and avoid introducing NaNs. However, this example purposely uses min-max scaling to show how NaNs can appear in engineered data.\n",
        "\n",
        "Now let's try scaling the data again."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YSV3SNG2LNp2"
      },
      "source": [
        "# Redefine the scaling function to check for zeros\n",
        "def minMaxScaler(arr):\n",
        "  max = np.max(arr)\n",
        "  if(max!=0):  # avoid /0\n",
        "    min = np.min(arr)\n",
        "    arr = (arr-min)/max\n",
        "  return arr\n",
        "\n",
        "# Reload data\n",
        "mnistData = mnistDf.iloc[:,1:-1].copy(deep=True)\n",
        "\n",
        "# Scale data\n",
        "for featureIdx in range(mnistData.shape[1]):\n",
        "  mnistData.iloc[:,featureIdx] = minMaxScaler(mnistData.iloc[:,featureIdx])"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_xXmVNVJXrG1"
      },
      "source": [
        "You should follow best practice and prevent this bug from recurring by writing a unit test to check for not having `NaN` values in your engineered data."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RpsG2yzsBBE3"
      },
      "source": [
        "#@title Define function to validate data\n",
        "\n",
        "def test_data_schema(input_data, schema):\n",
        "  \"\"\"Tests that the datatypes and ranges of values in the dataset\n",
        "    adhere to expectations.\n",
        "\n",
        "    Args:\n",
        "      input_function: Dataframe containing data to test\n",
        "      schema: Schema which describes the properties of the data.\n",
        "  \"\"\"\n",
        "\n",
        "  def test_dtypes():\n",
        "    for column in schema.keys():\n",
        "      assert input_data[column].map(type).eq(\n",
        "          schema[column]['dtype']).all(), (\n",
        "          \"Incorrect dtype in column '%s'.\" % column\n",
        "      )\n",
        "    print('Input dtypes are correct.')\n",
        "\n",
        "  def test_ranges():\n",
        "    for column in schema.keys():\n",
        "      schema_max = schema[column]['range']['max']\n",
        "      schema_min = schema[column]['range']['min']\n",
        "      # Assert that data falls between schema min and max.\n",
        "      assert input_data[column].max() <= schema_max, (\n",
        "          \"Maximum value of column '%s' is too low.\" % column\n",
        "      )\n",
        "      assert input_data[column].min() >= schema_min, (\n",
        "          \"Minimum value of column '%s' is too high.\" % column\n",
        "      )\n",
        "    print('Data falls within specified ranges.')\n",
        "\n",
        "  test_dtypes()\n",
        "  test_ranges()"
      ],
      "execution_count": 47,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "i3-uFNHbBTZ8",
        "outputId": "9a5ee1af-0ccc-4ddf-f46d-8131cfb819da"
      },
      "source": [
        "mnist_schema = dict((col_name, {'range': {'min': 0,'max': 255},'dtype': int}) for col_name in range(1, mnistDf.shape[1]))\n",
        "mnist_schema[0] = {'range': {'min': 0,'max': 9},'dtype': int}\n",
        "\n",
        "print('Validating mnist data against data schema...')\n",
        "test_data_schema(mnistDf, mnist_schema)"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Validating mnist data against data schema...\n",
            "Input dtypes are correct.\n",
            "Data falls within specified ranges.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9IBsKY3i6itJ"
      },
      "source": [
        "## Remove All-Zero Features?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o7BIOScX6kp5"
      },
      "source": [
        "You might think that getting NaNs and discovering that some features were all-zero is good luck because those features can be discarded. However, your training data and validation data might have different all-zero features. Since you should not use validation data to make modeling decisions, you cannot remove only those features that are all-zero in both. Furthermore, data in the future might have different characteristics. There are pros and cons in either case. This Colab keeps the features since reducing the feature set is not a concern."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HE0WOm7O3TGl"
      },
      "source": [
        "## Establish Baseline"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PAWzL8sW3U9V"
      },
      "source": [
        "Following development best practices, you should establish a baseline. The simplest baseline is predicting the most common class. You saw that the most common class is 1. Let's check the accuracy when always predicting 1."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PhT7hh6j5HmA",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e7d6b8c0-7531-4994-fce1-9b42a169d1f3"
      },
      "source": [
        "np.sum(mnistLabels==1)*1.0/mnistLabels.shape[0]*100"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "11.42"
            ]
          },
          "metadata": {},
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VOE2yBOK5fQw"
      },
      "source": [
        "Your baseline accuracy is about 11%. Should be easy to beat, right?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B6AOgLcC5nwp"
      },
      "source": [
        "## Train a Linear Model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2hH-T1mn5pao"
      },
      "source": [
        "Let's start nice and easy with a linear model. All we need is an accuracy > 11%.\n",
        "\n",
        "First, let's define a function to plot our loss and accuracy curves. The function will also print the final loss and accuracy. Instead of using `verbose=1`, you can call the function."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P68UKi78a0T-"
      },
      "source": [
        "def showClassificationResults(trainHistory):\n",
        "  \"\"\"Function to:\n",
        "   * Print final loss & accuracy.\n",
        "   * Plot loss & accuracy curves.\n",
        "\n",
        "  Args:\n",
        "    trainHistory: object returned by model.fit\n",
        "  \"\"\"\n",
        "\n",
        "  # Print final loss and accuracy\n",
        "  print(\"Final training loss: \" + str(trainHistory.history['loss'][-1]))\n",
        "  print(\"Final validation loss: \" + str(trainHistory.history['val_loss'][-1]))\n",
        "  print(\"Final training accuracy: \" + str(trainHistory.history['accuracy'][-1]))\n",
        "  print(\"Final validation accuracy: \" + str(trainHistory.history['val_accuracy'][-1]))\n",
        "\n",
        "  # Plot loss and accuracy curves\n",
        "  f = plt.figure(figsize=(10,4))\n",
        "  axLoss = f.add_subplot(121)\n",
        "  axAcc = f.add_subplot(122)\n",
        "  axLoss.plot(trainHistory.history['loss'])\n",
        "  axLoss.plot(trainHistory.history['val_loss'])\n",
        "  axLoss.legend(['Training loss', 'Validation loss'], loc='best')\n",
        "  axLoss.set_xlabel('Training epochs')\n",
        "  axLoss.set_ylabel('Loss')\n",
        "  axAcc.plot(trainHistory.history['accuracy'])\n",
        "  axAcc.plot(trainHistory.history['val_accuracy'])\n",
        "  axAcc.legend(['Training accuracy', 'Validation accuracy'], loc='best')\n",
        "  axAcc.set_xlabel('Training epochs')\n",
        "  axAcc.set_ylabel('Accuracy')"
      ],
      "execution_count": 43,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dU4bG_nYcTeR"
      },
      "source": [
        "Now train a linear model with an output layer and a hidden layer."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5_gWbZxS5mFg",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351
        },
        "outputId": "85dba69b-dd50-4ccb-987b-7b0be82f41c3"
      },
      "source": [
        "model = None\n",
        "# Define\n",
        "model = keras.Sequential()\n",
        "model.add(keras.layers.Dense(mnistData.shape[1],\n",
        "                             activation='linear',\n",
        "                             input_dim=mnistData.shape[1]))\n",
        "model.add(keras.layers.Dense(10, activation='softmax'))\n",
        "# Compile\n",
        "model.compile(optimizer=\"adam\", loss='mse', metrics=['accuracy'])\n",
        "# Train\n",
        "trainHistory = model.fit(mnistData, mnistLabels, epochs=100, batch_size=100,\n",
        "                         validation_split=0.2, verbose=0)\n",
        "# Plot\n",
        "showClassificationResults(trainHistory)"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Final training loss: 3.024850457906723\n",
            "Final validation loss: 3.8349536418914796\n",
            "Final training accuracy: 0.1455\n",
            "Final validation accuracy: 0.143\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f8nF3XAnAres"
      },
      "source": [
        "Wow, that accuracy is terrible! What could the cause be?\n",
        "\n",
        "Hint: You followed the same procedure as for the previous regression problem. Do you need an adaptation for a classification problem? Experiment with the code above or skip to the solution below."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dqnRGq2UCEYP"
      },
      "source": [
        "### Solution"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DmvvQeJfCFc9"
      },
      "source": [
        "In regression, the last layer uses a linear activation function. In classification, the last layer cannot use a linear transform. Instead, one option is a softmax transform. Furthermore, in regression, the loss is calculated using MSE while in classification, loss is calculated using crossentropy. Before running your model, if you wrote a test to validate the output values, your test would detect the anomalous output. You'll look at such a test later. Move onto the next section to fix the loss calculation."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "296GJgdPkWDE"
      },
      "source": [
        "## Fixing Loss Calculation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A-mGfHlpDITS"
      },
      "source": [
        "Since your labels are integers instead of one-hot encodings, use `sparse_categorical_crossentropy` instead of `categorical_crossentropy` so that you avoid converting the integers to one-hot encoding."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HFxuJSj2JhIZ"
      },
      "source": [
        "Retrain the model with the new loss calculation by running the following cell. Look through the code to note the changes. What do you think of the result?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vhfoEAR_gwFW",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351
        },
        "outputId": "8e1faac3-f8fa-4e3f-bb64-adf58cb2bac9"
      },
      "source": [
        "model = None\n",
        "# Define\n",
        "model = keras.Sequential()\n",
        "model.add(keras.layers.Dense(mnistData.shape[1], activation='linear',\n",
        "                             input_dim = mnistData.shape[1]))\n",
        "model.add(keras.layers.Dense(10, activation='softmax'))\n",
        "# Compile\n",
        "model.compile(optimizer=\"adam\",\n",
        "              loss='sparse_categorical_crossentropy',\n",
        "              metrics=['accuracy'])\n",
        "# Train\n",
        "trainHistory = model.fit(mnistData, mnistLabels, epochs=10, batch_size=100,\n",
        "                         validation_split=0.1, verbose=0)\n",
        "# Plot\n",
        "showClassificationResults(trainHistory)"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Final training loss: 0.17480523727006383\n",
            "Final validation loss: 0.3656942665576935\n",
            "Final training accuracy: 0.9482222\n",
            "Final validation accuracy: 0.888\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gr2QBQEvEN3D"
      },
      "source": [
        "Your loss curves are much better. Your accuracy has improved too. You're on the right track."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-hNND_KIFyf7"
      },
      "source": [
        "## Train a Nonlinear Model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v_o9SEa3F0xy"
      },
      "source": [
        "Switch to a nonlinear model by modifying the code below to use relu activation functions instead of linear activation functions. Run the code. What do you observe?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bprM8t-ti-KQ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351
        },
        "outputId": "8c97656e-5f67-4fd6-f183-43cd02d2350b"
      },
      "source": [
        "model = None\n",
        "# Define\n",
        "model = keras.Sequential()\n",
        "model.add(keras.layers.Dense(mnistData.shape[1], activation='relu', # use 'relu'\n",
        "                             input_dim=mnistData.shape[1]))\n",
        "model.add(keras.layers.Dense(10, activation='softmax'))\n",
        "# Compile\n",
        "model.compile(optimizer=\"adam\", loss='sparse_categorical_crossentropy',\n",
        "              metrics=['accuracy'])\n",
        "# Train\n",
        "trainHistory = model.fit(mnistData, mnistLabels, epochs=20, batch_size=100,\n",
        "                        validation_split=0.1, verbose=0)\n",
        "# Plot\n",
        "showClassificationResults(trainHistory)"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Final training loss: 0.0045535347734888395\n",
            "Final validation loss: 0.15824018120765687\n",
            "Final training accuracy: 1.0\n",
            "Final validation accuracy: 0.948\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LodYblJbF673"
      },
      "source": [
        "The quality of the nonlinear model is significantly better than of the linear model. Progress! Move onto the next section."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1u9z5zSIGF4H"
      },
      "source": [
        "## Adding a Second Layer"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Xa_gtVEHJCON"
      },
      "source": [
        "Increasing the model's capacity significantly improved your results. Perhaps you can continue this strategy by adding a second relu layer. Run the following code cell to train the model with another relu layer."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HgY8AFlWGHd2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351
        },
        "outputId": "6e32a80b-7542-46ac-a18c-f74a3437aa90"
      },
      "source": [
        "model = None\n",
        "# Define\n",
        "model = keras.Sequential()\n",
        "model.add(keras.layers.Dense(mnistData.shape[1], activation='relu',\n",
        "                             input_dim = mnistData.shape[1]))\n",
        "model.add(keras.layers.Dense(mnistData.shape[1], activation='relu'))\n",
        "model.add(keras.layers.Dense(10,activation='softmax'))\n",
        "# Compile\n",
        "model.compile(optimizer=\"adam\", loss='sparse_categorical_crossentropy',\n",
        "              metrics=['accuracy'])\n",
        "# Train\n",
        "trainHistory = model.fit(mnistData, mnistLabels, epochs=10, batch_size=100,\n",
        "                        validation_split=0.1, verbose=0)\n",
        "# Plot\n",
        "showClassificationResults(trainHistory)"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Final training loss: 0.001780000555380765\n",
            "Final validation loss: 0.15322310328483582\n",
            "Final training accuracy: 1.0\n",
            "Final validation accuracy: 0.956\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2lcvRLzjJS6L"
      },
      "source": [
        "Guess what. Your previous model had training and validation accuracies of 100% and 95%. You can't do much better than that! So your new accuracy is about the same. How high can you push your accuracy? With this configuration the highest training and validation accuracies appear to be 100% and 96% respectively. Since the neural net returns similar accuracy with 1 or 2 layers, let's use the simpler model with 1 layer.\n",
        "\n",
        "Does your model begin to overfit the training data if you train for long enough? (Your model starts overfitting training data at the point when your validation loss starts increasing.)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tDdWPO1AKsXx"
      },
      "source": [
        "## Check for Training/Validation Data Skew"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UTGSClhnKutt"
      },
      "source": [
        "Our validation accuracy is a little worse than our training accuracy. While this result is always expected, you should check for typical errors. The commonest cause is having different distributions of data and labels in training and validation. Confirm that the distribution of classes in training and validation data is similar."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5-8aUQ7eg2Z1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 418
        },
        "outputId": "f5bd1730-70a8-4444-c627-22a8c0044f75"
      },
      "source": [
        "#%hide_result # hides result of cell computation\n",
        "\n",
        "f = plt.figure(figsize=(10,3))\n",
        "ax = f.add_subplot(1,2,1)\n",
        "plt.hist(mnistLabels[0:len(mnistLabels)*8/10], bins=range(numClasses+1))\n",
        "plt.xticks(range(numClasses+1))\n",
        "ax2 = f.add_subplot(1,2,2,)\n",
        "plt.hist(mnistLabels[len(mnistLabels)*8/10:-1], bins=range(numClasses+1))\n",
        "plt.xticks(range(numClasses+1))"
      ],
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([<matplotlib.axis.XTick at 0x7fb1ed6af190>,\n",
              "  <matplotlib.axis.XTick at 0x7fb1ed6a6c10>,\n",
              "  <matplotlib.axis.XTick at 0x7fb1ed6a6510>,\n",
              "  <matplotlib.axis.XTick at 0x7fb1ed66be50>,\n",
              "  <matplotlib.axis.XTick at 0x7fb1ed67b3d0>,\n",
              "  <matplotlib.axis.XTick at 0x7fb1ed66bd90>,\n",
              "  <matplotlib.axis.XTick at 0x7fb1ed67bad0>,\n",
              "  <matplotlib.axis.XTick at 0x7fb1ed604050>,\n",
              "  <matplotlib.axis.XTick at 0x7fb1ed604590>,\n",
              "  <matplotlib.axis.XTick at 0x7fb1ed604ad0>,\n",
              "  <matplotlib.axis.XTick at 0x7fb1ed60e050>],\n",
              " <a list of 11 Text xticklabel objects>)"
            ]
          },
          "metadata": {},
          "execution_count": 55
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlkAAADFCAYAAABnw+dWAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi40LCBodHRwOi8vbWF0cGxvdGxpYi5vcmcv7US4rQAAFFBJREFUeJzt3X+sX/V93/Hnqza/k2J+eIjYpHYFS4vQGqhFyOhQhJMOCMJoSlNolzotkzWNbqSpFEwrLYvUSLBV+VG1ovJiWpNRCCN0oCzrQoEsq1RIr/kVg5PiEAj2DL5JgCSN2sTJe3+c4+Zi34vvtc/nXn/v9/mQvvqe8znn+/6+/eN+7vt8zueck6pCkiRJw/qJhU5AkiRpMbLIkiRJasAiS5IkqQGLLEmSpAYssiRJkhqwyJIkSWrAIkuSJKkBiyxJkqQGLLIkLWpJbkmyJ8m2KW3/JcmXkzyR5M+TLJuy7YYkO5J8Jcm/XJisJS0GORLu+H7qqafWqlWrFjoNSfNo69at36iq5a2/J8lFwHeBW6vqnL7tF4EHqmpvkpsAqur6JGcDtwPnA28A/hL4p1X1w5ni239J42e2/dfS+UjmYFatWsXExMRCpyFpHiV5bj6+p6q+kGTVfm2fm7L6EPCufnkdcEdV/QPwtSQ76Aquv54pvv2XNH5m2395ulDSuPsN4H/1yyuA56ds29m3vUqSDUkmkkxMTk7OQ4qSRpFFlqSxleR3gb3AbXP5XFVtqqo1VbVm+fLmZzwljagj4nShJM23JO8FLgfW1o8np+4Czpiy28q+TZLmzJEsSWMnySXAB4Arqup7UzbdC1yV5Jgkq4GzgC8uRI6SRp8jWZIWtSS3A28DTk2yE/ggcANwDHBfEoCHqurfVtWTSe4EnqI7jXjta11ZKEmvxSJrP6s2/s9msZ+98Z3NYkuaXlVdPU3z5tfY/8PAh9tlJC0sf8/NH08XSpIkNWCRJUmS1IBFliRJUgMWWZIkSQ1YZEmSJDVgkSVJktSAt3CQpEXCS/OlI4sjWZIkSQ04kiUdAkcMJEkH40iWJElSAxZZkiRJDVhkSZIkNWCRJUmS1IAT3yVJ0hGv5QVH0OaiI0eyJEmSGrDIkiRJasDThZKkBeV957RYzbrISrIEmAB2VdXlSVYDdwCnAFuB91TV95McA9wK/DzwTeCXq+rZwTOXNGf+MpOk+TOXkazrgO3AT/brNwEfrao7kvwxcA1wc//+UlWdmeSqfr9fHjDnkeUvOGn+JbkFuBzYU1Xn9G0nA58CVgHPAu+uqpeSBPg4cBnwPeC9VfXIQuQtafTNqshKshJ4J/Bh4P19R3Qx8Cv9LluA/0RXZK3rlwHuAv4wSaqqhkq69RUGkhaVPwX+kG6EfZ+NwP1VdWOSjf369cClwFn96y10fdpb5jVbSYvGbCe+fwz4APCjfv0U4OWq2tuv7wRW9MsrgOcB+u2v9Pu/SpINSSaSTExOTh5i+pL02qrqC8C39mteR3dwSP9+5ZT2W6vzELAsyenzk6mkxeagI1lJ9g2zb03ytqG+uKo2AZsA1qxZM9golzTqHKmdF6dV1e5++QXgtH75Hw8Se/sOIHdPaSPJBmADwBvf+Ma2mUoaWbM5XXghcEWSy4Bj6eZkfZzuCG9pP1q1EtjV778LOAPYmWQpcCLdBHhpXlmsaDaqqpLM6UDPg0S1Zv+1OBz0dGFV3VBVK6tqFXAV8EBV/SrwIPCufrf1wD398r39Ov32B4acjyVJA3hx32nA/n1P377vIHGfqQeQkjQnh3OfrOuBO5L8HvAosLlv3wx8MskOunkQVx1eipI0uH0Hgzdy4EHibya5g27C+ytTTiuOtVEdWfGqbi2kORVZVfV54PP98jPA+dPs8/fALw2Qm+bAjkSaXpLbgbcBpybZCXyQrri6M8k1wHPAu/vdP0t3+4YddLdw+PV5T1jSouEd3yUtalV19Qyb1k6zbwHXts1I0rjw2YWSJEkNOJIlSfNoVOc2SZo7R7IkSZIasMiSJElqwNOFOiivXJQkae4cyZIkSWrAIkuSJKkBiyxJkqQGLLIkSZIasMiSJElqwKsLtaC8MaMkLR726a/mSJYkSVIDFlmSJEkNWGRJkiQ1YJElSZLUgBPfJUk6BE7y1sE4kiVJktSARZYkSVIDFlmSxlaS30ryZJJtSW5PcmyS1UkeTrIjyaeSHL3QeUoaTRZZksZSkhXAfwDWVNU5wBLgKuAm4KNVdSbwEnDNwmUpaZRZZEkaZ0uB45IsBY4HdgMXA3f127cAVy5QbpJGnEWWpLFUVbuA3we+TldcvQJsBV6uqr39bjuBFft/NsmGJBNJJiYnJ+crZUkjxiJL0lhKchKwDlgNvAE4AbhkNp+tqk1Vtaaq1ixfvrxhlpJG2UGLrH4i6BeTPN5PEP1Q3z7t5NAkx/TrO/rtq9r+ESTpkLwd+FpVTVbVD4C7gQuBZf3pQ4CVwK6FSlDSaJvNSNY/ABdX1c8BbwYuSXIBM08OvQZ4qW//aL+fJB1pvg5ckOT4JAHWAk8BDwLv6vdZD9yzQPlJGnEHLbKq891+9aj+Vcw8OXRdv06/fW3fgUnSEaOqHqbrox4BvkTXH24Crgfen2QHcAqwecGSlDTSZvVYnSRL6CaEngn8EfBVZp4cugJ4HqCq9iZ5ha6j+saAeUvSYauqDwIf3K/5GeD8BUhH0iIzq4nvVfXDqnoz3fyE84GfOdwv9uocSZK0mM3p6sKqepluvsJbmXly6C7gDIB++4nAN6eJ5dU5kiRp0ZrN1YXLkyzrl48D3gFsZ+bJoff26/TbH6iqGjJpSZKkI91s5mSdDmzp52X9BHBnVX0myVPAHUl+D3iUH08O3Qx8sp80+i26x1RIkiSNlYMWWVX1BHDuNO3TTg6tqr8HfmmQ7CRJkkaUd3yXJElqwCJLkiSpAYssSZKkBiyyJEmSGrDIkiRJasAiS5IkqQGLLEmSpAYssiRJkhqwyJIkSWrAIkuSJKkBiyxJkqQGLLIkSZIasMiSNLaSLEtyV5IvJ9me5K1JTk5yX5Kn+/eTFjpPSaPJIkvSOPs48BdV9TPAzwHbgY3A/VV1FnB/vy5Jc2aRJWksJTkRuAjYDFBV36+ql4F1wJZ+ty3AlQuToaRRZ5ElaVytBiaBP0nyaJJPJDkBOK2qdvf7vACctv8Hk2xIMpFkYnJych5TljRKLLIkjaulwHnAzVV1LvB37HdqsKoKqP0/WFWbqmpNVa1Zvnz5vCQrafRYZEkaVzuBnVX1cL9+F13R9WKS0wH69z0LlJ+kEWeRJWksVdULwPNJ3tQ3rQWeAu4F1vdt64F7FiA9SYvA0oVOQJIW0L8HbktyNPAM8Ot0B593JrkGeA549wLmJ2mEWWRJGltV9RiwZppNa+c7F0mLj6cLJUmSGrDIkiRJasAiS5IkqQGLLEmSpAYOWmQlOSPJg0meSvJkkuv69mkfoprOHyTZkeSJJOe1/kNIkiQdaWYzkrUX+O2qOhu4ALg2ydnM/BDVS4Gz+tcG4ObBs5YkSTrCHbTIqqrdVfVIv/wduqfUr2Dmh6iuA26tzkPAsn13T5YkSRoXc5qTlWQVcC7wMDM/RHUF8PyUj+3s2/aP5QNWJUnSojXrIivJ64BPA++rqm9P3TbTQ1Rfiw9YlSRJi9msiqwkR9EVWLdV1d1980wPUd0FnDHl4yv7NkmSpLExm6sLA2wGtlfVR6ZsmukhqvcCv9ZfZXgB8MqU04qSJEljYTbPLrwQeA/wpSSP9W2/A9zI9A9R/SxwGbAD+B7dA1clSZLGykGLrKr6KyAzbD7gIar9/KxrDzMvSZKkkeYd3yVJkhqwyJIkSWrAIkuSJKkBiyxJkqQGLLIkSZIasMiSNLaSLEnyaJLP9OurkzycZEeSTyU5eqFzlDS6LLIkjbPr6B56v89NwEer6kzgJeCaBclK0qJgkSVpLCVZCbwT+ES/HuBi4K5+ly3AlQuTnaTFwCJL0rj6GPAB4Ef9+inAy1W1t1/fCayY7oNJNiSZSDIxOTnZPlNJI8kiS9LYSXI5sKeqth7K56tqU1Wtqao1y5cvHzg7SYvFbJ5dKEmLzYXAFUkuA44FfhL4OLAsydJ+NGslsGsBc5Q04hzJkjR2quqGqlpZVauAq4AHqupXgQeBd/W7rQfuWaAUJS0CFlmS9GPXA+9PsoNujtbmBc5H0gjzdKGksVZVnwc+3y8/A5y/kPlIWjwcyZIkSWrAIkuSJKkBiyxJkqQGLLIkSZIasMiSJElqwCJLkiSpAYssSZKkBiyyJEmSGrDIkiRJasAiS5IkqQGLLEmSpAYOWmQluSXJniTbprSdnOS+JE/37yf17UnyB0l2JHkiyXktk5ckSTpSzWYk60+BS/Zr2wjcX1VnAff36wCXAmf1rw3AzcOkKUmSNFoOWmRV1ReAb+3XvA7Y0i9vAa6c0n5rdR4CliU5fahkJUmSRsWhzsk6rap298svAKf1yyuA56fst7NvO0CSDUkmkkxMTk4eYhqSJElHpsOe+F5VBdQhfG5TVa2pqjXLly8/3DQkSZKOKIdaZL247zRg/76nb98FnDFlv5V9myRJ0lg51CLrXmB9v7weuGdK+6/1VxleALwy5bSiJEnS2JjNLRxuB/4aeFOSnUmuAW4E3pHkaeDt/TrAZ4FngB3AfwX+XZOsJekwJTkjyYNJnkryZJLr+vZpb1EjSXO19GA7VNXVM2xaO82+BVx7uElJ0jzYC/x2VT2S5PXA1iT3Ae+lu0XNjUk20t2i5voFzFPSiPKO75LGUlXtrqpH+uXvANvproae6RY1kjQnFlmSxl6SVcC5wMPMfIuaqft7CxpJB2WRJWmsJXkd8GngfVX17anbZrpFjbegkTQbFlmSxlaSo+gKrNuq6u6+eaZb1EjSnFhkSRpLSQJsBrZX1UembJrpFjWSNCcHvbpQkhapC4H3AF9K8ljf9jt0t6S5s79dzXPAuxcoP0kjziJL0liqqr8CMsPmA25RI0lz5elCSZKkBiyyJEmSGrDIkiRJasAiS5IkqQGLLEmSpAYssiRJkhqwyJIkSWrAIkuSJKkBiyxJkqQGLLIkSZIasMiSJElqwCJLkiSpAYssSZKkBiyyJEmSGrDIkiRJasAiS5IkqQGLLEmSpAYssiRJkhpoUmQluSTJV5LsSLKxxXdIUiv2YZKGMHiRlWQJ8EfApcDZwNVJzh76eySpBfswSUNpMZJ1PrCjqp6pqu8DdwDrGnyPJLVgHyZpEEsbxFwBPD9lfSfwlv13SrIB2NCvfjfJV+bwHacC3zjkDI1tbGMPLjfNOfZPtchjAAftw+y/jG3sRRd7rn3YrPqvFkXWrFTVJmDToXw2yURVrRk4JWMb29hHaOwjjf2XsY29uGK3it/idOEu4Iwp6yv7NkkaBfZhkgbRosj6G+CsJKuTHA1cBdzb4HskqQX7MEmDGPx0YVXtTfKbwP8GlgC3VNWTA3/NIQ3TG9vYxh7Z2PNmHvqwUf03MLaxF3PsJvFTVUPHlCRJGnve8V2SJKkBiyxJkqQGRqrIavmoiyS3JNmTZNvAcc9I8mCSp5I8meS6AWMfm+SLSR7vY39oqNhTvmNJkkeTfKZB7GeTfCnJY0kmBo69LMldSb6cZHuStw4U9019vvte307yviFi9/F/q/+33Jbk9iTHDhj7uj7uk4eb83Q/L0lOTnJfkqf795MOP+vFYxT7rz62fdj0ce2/Doxv/7W/qhqJF90E1K8CPw0cDTwOnD1g/IuA84BtA+d9OnBev/x64G+HyhsI8Lp++SjgYeCCgfN/P/BnwGca/Js+C5za6P/LFuDf9MtHA8safMcS4AXgpwaKtwL4GnBcv34n8N6BYp8DbAOOp7vg5S+BMw8j3gE/L8B/Bjb2yxuBm1r8247ia1T7rz62fdj0ce2/Xh3P/mua1yiNZDV91EVVfQH41lDxpsTdXVWP9MvfAbbT/WccInZV1Xf71aP612BXMiRZCbwT+MRQMedDkhPpfog2A1TV96vq5QZftRb4alU9N2DMpcBxSZbSdSj/b6C4Pws8XFXfq6q9wP8B/tWhBpvh52Ud3S8H+vcrDzX+IjSS/Vcf2z5sHtl/TWtk+69RKrKme9TFID/o8yXJKuBcuqO1oWIuSfIYsAe4r6oGiw18DPgA8KMBY05VwOeSbE33mJKhrAYmgT/pTxN8IskJA8bf5yrg9qGCVdUu4PeBrwO7gVeq6nMDhd8G/IskpyQ5HriMV99wcwinVdXufvkF4LSB44+yke+/wD5sP/ZfU9h/TW+UiqyRluR1wKeB91XVt4eKW1U/rKo3092V+vwk5wwRN8nlwJ6q2jpEvBn8QlWdB1wKXJvkooHiLqUbCr65qs4F/o5u+Hcw6W5SeQXw3weMeRLd0dRq4A3ACUn+9RCxq2o7cBPwOeAvgMeAHw4Re4bvKwYckdDCsw87gP3Xq2Paf01jlIqskX3URZKj6Dqn26rq7hbf0Q8nPwhcMlDIC4ErkjxLd2rj4iT/baDYwD8e+VBVe4A/pzulMoSdwM4pR8R30XVaQ7oUeKSqXhww5tuBr1XVZFX9ALgb+OdDBa+qzVX181V1EfAS3dyaIb2Y5HSA/n3PwPFH2cj2X2AfNh37rwPYf01jlIqskXzURZLQnVvfXlUfGTj28iTL+uXjgHcAXx4idlXdUFUrq2oV3d/1A1U1yFEJQJITkrx+3zLwi3RDwoetql4Ank/ypr5pLfDUELGnuJoBh9p7XwcuSHJ8//9mLd38l0Ek+Sf9+xvp5jP82VCxe/cC6/vl9cA9A8cfZSPZf4F92HTsv6Zl/zWdIWbPz9eL7jzs39JdpfO7A8e+ne488g/ojiSuGSjuL9ANOz5BN8T5GHDZQLH/GfBoH3sb8B8b/b2/jeGvzPlpuiusHgeebPDv+WZgov+7+R/ASQPGPgH4JnBig7/rD9H9ktkGfBI4ZsDY/5eus34cWHuYsQ74eQFOAe4Hnqa7+ufkof9+Rvk1iv1XH9s+7MB49l/Tx7b/2u/lY3UkSZIaGKXThZIkSSPDIkuSJKkBiyxJkqQGLLIkSZIasMiSJElqwCJLkiSpAYssSZKkBv4/xLMI2MwjqzkAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 720x216 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JYAlIiUBqe4H"
      },
      "source": [
        "## Apply Dropout Regularization"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9UDeCe7Iqgc3"
      },
      "source": [
        "Dropout regularization is a common regularization method that removes a random selection of a fixed number of units in a network layer for a single gradient step. Typically, dropout will improve generalization at a dropout rate of between 10% and 50% of neurons. \n",
        "\n",
        "Try to reduce the divergence between training and validation loss by using dropout regularization with values between 0.1 and 0.5. Dropout does not improve the results in this case. However, at a dropout of 0.5, the difference in loss decreases, though both training and validation loss decrease in absolute terms."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "A0LNZvchsWJa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 369
        },
        "outputId": "9f4b7ac8-7d1a-4681-faf9-8549f0281de0"
      },
      "source": [
        "from keras import regularizers\n",
        "model = None\n",
        "# Define lambda\n",
        "dropoutLambda = 0.5 #@param\n",
        "# Define model\n",
        "model = keras.Sequential()\n",
        "model.add(keras.layers.Dense(mnistData.shape[1],\n",
        "                             input_dim=mnistData.shape[1],\n",
        "                             activation='relu'))\n",
        "model.add(keras.layers.Dropout(dropoutLambda,\n",
        "                               noise_shape=(1, mnistData.shape[1])))\n",
        "model.add(keras.layers.Dense(10, activation='softmax'))\n",
        "# Compile\n",
        "model.compile(optimizer = \"adam\",\n",
        "              loss = 'sparse_categorical_crossentropy',\n",
        "              metrics = ['accuracy'])\n",
        "# Train\n",
        "trainHistory = model.fit(mnistData,\n",
        "                        mnistLabels,\n",
        "                        epochs=30,\n",
        "                        batch_size=500,\n",
        "                        validation_split=0.1,\n",
        "                        verbose=0)\n",
        "# Plot\n",
        "showClassificationResults(trainHistory)"
      ],
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Using TensorFlow backend.\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Final training loss: 0.11273058421081966\n",
            "Final validation loss: 0.18276895582675934\n",
            "Final training accuracy: 0.97333336\n",
            "Final validation accuracy: 0.94\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FDP4RPSNxyHc"
      },
      "source": [
        "Sample results using dropout regularization after 30 epochs:\n",
        "\n",
        "Lambda | Training Loss | Validation Loss\n",
        "------- | ------------------------------------------------------\n",
        "0.1 | 0.99 | 0.95\n",
        "0.2 | 0.99 | 0.95\n",
        "0.3 | 0.99 | 0.95\n",
        "0.5 | 0.97 | 0.94"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "md6_n4woxgdQ"
      },
      "source": [
        "## Check Accuracy for Data Slices"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JndFQG56xhYD"
      },
      "source": [
        "For classification problems, you should always check the metrics by class to ensure your model predicts well across all classes. Check accuracy on the 10 classes by running the next cell by using the function `sklearn.metrics.classification_report` from the scikit-learn library. In the output, the rows with indices 0 to 9 correspond to the classes for the labels 0 to 9. The columns \"Precision\", \"Recall\", and \"[F1-Score](https://en.wikipedia.org/wiki/F1_score)\" correspond to the respective classification metrics for each class. \"Support\" is the number of examples for the class in question. For example, for the label \"4\", when predicting on 464 examples labelled \"4\", the model has a precision of 0.98, a recall of 0.97, and a F1 score of 0.98.\n",
        "\n",
        "The classification metrics are very uniform across all classes, which is perfect. In your classification problem, in case any metric is lower for a class, then you should investigate why the model has lower-quality predictions for that class."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YArLe5K8xjoE",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8f307736-1697-40ea-928e-fae306e1d901"
      },
      "source": [
        "from sklearn.metrics import classification_report\n",
        "mnistPred = model.predict_classes(x = mnistData)\n",
        "print(classification_report(mnistLabels, mnistPred))"
      ],
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "              precision    recall  f1-score   support\n",
            "\n",
            "           0       0.99      1.00      0.99       499\n",
            "           1       0.98      0.99      0.98       571\n",
            "           2       0.98      0.98      0.98       504\n",
            "           3       0.99      0.98      0.98       487\n",
            "           4       0.97      0.97      0.97       464\n",
            "           5       0.99      0.98      0.98       434\n",
            "           6       0.99      0.99      0.99       491\n",
            "           7       0.99      0.96      0.97       550\n",
            "           8       0.98      0.98      0.98       485\n",
            "           9       0.95      0.97      0.96       515\n",
            "\n",
            "   micro avg       0.98      0.98      0.98      5000\n",
            "   macro avg       0.98      0.98      0.98      5000\n",
            "weighted avg       0.98      0.98      0.98      5000\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XGaXjzW2ItTr"
      },
      "source": [
        "## Testing for Anomalous Values"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Rkl5SPIsI3Bb"
      },
      "source": [
        "In the section [Train a Linear Model](https://colab.corp.google.com/google_src/cloud/karangill/mlcc/google3/engedu/ml/capitalg/colab/testing_debugging_classification.ipynb#scrollTo=B6AOgLcC5nwp), you debugged an incorrect calculation of loss. Before running your model, if you wrote a test to validate the output values, your test would detect the anomalous output. For example, you could test whether the distribution of predicted labels on the training dataset is similar to the actual distribution of training labels. A simple statistical implementation of this concept is to compare the standard deviation and mean of the predicted and actual labels.\n",
        "\n",
        "First, check the standard deviation and mean of the actual labels."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "F_WjpuqmZuAr",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "70901bed-e186-484d-a3e4-a0f1cce2a051"
      },
      "source": [
        "print(\"Mean of actual labels: \" + str(np.mean(mnistLabels)))\n",
        "print(\"Standard deviation of actual labels: \" + str(np.std(mnistLabels)))"
      ],
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean of actual labels: 4.4754\n",
            "Standard deviation of actual labels: 2.9147546792140155\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W30mjNZUv8Gx"
      },
      "source": [
        "Write tests to check if the mean and standard deviation of the predicted labels falls within the expected range. The expected range defined in the tests below is somewhat arbitrary. In practice, you will tune the range thresholds to accommodate natural variation in predictions."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P-XChYMVHFhn"
      },
      "source": [
        "class mlTest(unittest.TestCase): \n",
        "  '''Class to test statistics of predicted output on training data against\n",
        "     statistics of labels to validate that model predictions are in the]\n",
        "     expected range.\n",
        "  '''\n",
        "     \n",
        "  def testStd(self):\n",
        "    y = model.predict(mnistData)\n",
        "    yStd = np.std(y)\n",
        "    yStdActual = np.std(mnistLabels)\n",
        "    deltaStd = 0.05\n",
        "    errorMsg = 'Std. dev. of predicted values ' + str(yStd) + \\\n",
        "               ' and actual values ' + str(yStdActual) + \\\n",
        "               ' differs by >' + str(deltaStd) + '.'\n",
        "    self.assertAlmostEqual(yStd, yStdActual, delta=deltaStd, msg=errorMsg)\n",
        "\n",
        "  def testMean(self):\n",
        "    y = model.predict(mnistData)\n",
        "    yMean = np.mean(y)\n",
        "    yMeanActual = np.mean(mnistLabels)\n",
        "    deltaMean = 0.05\n",
        "    errorMsg = 'Mean of predicted values ' + str(yMean) + \\\n",
        "               ' and actual values ' + str(yMeanActual) + \\\n",
        "               ' differs by >' + str(deltaMean) + '.'\n",
        "    self.assertAlmostEqual(yMean, yMeanActual, delta=deltaMean, msg=errorMsg)"
      ],
      "execution_count": 59,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Prq5XYuAKE0y"
      },
      "source": [
        "Run the following cell to train a model with the wrong loss calculation and execute the tests. The tests should fail."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_51wIJhXKF68",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c2b767f6-0608-4108-c1cb-4b482ed11cde"
      },
      "source": [
        "#@title Train model and run tests\n",
        "\n",
        "model = None\n",
        "# Define\n",
        "model = keras.Sequential()\n",
        "model.add(keras.layers.Dense(mnistData.shape[1],\n",
        "                             activation='linear',\n",
        "                             input_dim=mnistData.shape[1]))\n",
        "model.add(keras.layers.Dense(1, activation='linear'))\n",
        "# Compile\n",
        "model.compile(optimizer=\"adam\", loss='mse', metrics=['accuracy'])\n",
        "# Train\n",
        "trainHistory = model.fit(mnistData, mnistLabels, epochs=10, batch_size=100,\n",
        "                         validation_split=0.1, verbose=0)\n",
        "\n",
        "suite = unittest.TestLoader().loadTestsFromTestCase(mlTest)\n",
        "unittest.TextTestRunner(verbosity=1, stream=sys.stderr).run(suite)"
      ],
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "FF\n",
            "======================================================================\n",
            "FAIL: testMean (__main__.mlTest)\n",
            "----------------------------------------------------------------------\n",
            "Traceback (most recent call last):\n",
            "  File \"<ipython-input-59-f8aa3a0ebb02>\", line 21, in testMean\n",
            "    self.assertAlmostEqual(yMean, yMeanActual, delta=deltaMean, msg=errorMsg)\n",
            "AssertionError: Mean of predicted values 5.1531897 and actual values 4.4754 differs by >0.05.\n",
            "\n",
            "======================================================================\n",
            "FAIL: testStd (__main__.mlTest)\n",
            "----------------------------------------------------------------------\n",
            "Traceback (most recent call last):\n",
            "  File \"<ipython-input-59-f8aa3a0ebb02>\", line 13, in testStd\n",
            "    self.assertAlmostEqual(yStd, yStdActual, delta=deltaStd, msg=errorMsg)\n",
            "AssertionError: Std. dev. of predicted values 2.4419386 and actual values 2.9147546792140155 differs by >0.05.\n",
            "\n",
            "----------------------------------------------------------------------\n",
            "Ran 2 tests in 0.589s\n",
            "\n",
            "FAILED (failures=2)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<unittest.runner.TextTestResult run=2 errors=0 failures=2>"
            ]
          },
          "metadata": {},
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LalmZjs7b0M5"
      },
      "source": [
        "Since the tests fail, check the data distribution of predicted labels for anomalies."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "11S1Mh6VbtgT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 320
        },
        "outputId": "d11c13d0-0249-4f23-af5c-f622a89cb67c"
      },
      "source": [
        "yPred = model.predict(mnistData)\n",
        "plt.hist(yPred, bins=range(11))"
      ],
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([ 97., 426., 579., 622., 666., 687., 640., 547., 409., 219.]),\n",
              " array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10]),\n",
              " <a list of 10 Patch objects>)"
            ]
          },
          "metadata": {},
          "execution_count": 61
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2vLmiLOob_zY"
      },
      "source": [
        "Given equally represented classes, the predicted labels are clearly skewed. From this plot, a possible explanation is that your loss calculation does not appear to be weighting all classes equally. This anomaly is a hint that your loss calculation is incorrect."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r2dShXOwTe0B"
      },
      "source": [
        "## Optional: Pass Tests by Fixing Loss Calculation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K7UhxfMKTi_7"
      },
      "source": [
        "As an optional exercise, you can attempt to pass the tests by fixing the loss calculation. You will need to:\n",
        "1. Fix the loss calculation by setting the output layer's activation to `softmax`.\n",
        "1. Set the model's loss to `sparse_categorical_crossentropy`.\n",
        "1. Set the number of units in the output layer to 10 corresponding to the 10 classes.\n",
        "1. Adapt the tests to the modified output layer."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-Y40d127KFEN"
      },
      "source": [
        "class mlTest(unittest.TestCase): \n",
        "  '''Class to test statistics of predicted output on training data against\n",
        "     statistics of labels to validate that model predictions are in the]\n",
        "     expected range.\n",
        "  '''\n",
        "     \n",
        "  def testStd(self):\n",
        "    y = model.predict(mnistData)\n",
        "    yStd = np.std(y)\n",
        "    yStdActual = np.std(mnistLabels)\n",
        "    deltaStd = 0.05\n",
        "    errorMsg = 'Std. dev. of predicted values ' + str(yStd) + \\\n",
        "               ' and actual values ' + str(yStdActual) + \\\n",
        "               ' differs by >' + str(deltaStd) + '.'\n",
        "    self.assertAlmostEqual(yStd, yStdActual, delta=deltaStd, msg=errorMsg)\n",
        "\n",
        "  def testMean(self):\n",
        "    y = model.predict(mnistData)\n",
        "    yMean = np.mean(y)\n",
        "    yMeanActual = np.mean(mnistLabels)\n",
        "    deltaMean = 0.05\n",
        "    errorMsg = 'Mean of predicted values ' + str(yMean) + \\\n",
        "               ' and actual values ' + str(yMeanActual) + \\\n",
        "               ' differs by >' + str(deltaMean) + '.'\n",
        "    self.assertAlmostEqual(yMean, yMeanActual, delta=deltaMean, msg=errorMsg)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Z6bvqQqrJK_0",
        "outputId": "cf682eda-6a73-44e0-bf00-f7db014ecc24"
      },
      "source": [
        "#@title Train model and run tests\n",
        "\n",
        "model = None\n",
        "# Define\n",
        "model = keras.Sequential()\n",
        "model.add(keras.layers.Dense(mnistData.shape[1],\n",
        "                             activation='relu',\n",
        "                             input_dim=mnistData.shape[1]))\n",
        "model.add(keras.layers.Dropout(dropoutLambda,\n",
        "                               noise_shape=(1, mnistData.shape[1])))\n",
        "model.add(keras.layers.Dense(10, activation='softmax'))\n",
        "# Compile\n",
        "model.compile(optimizer=\"adam\", loss='sparse_categorical_crossentropy', metrics=['accuracy'])\n",
        "# Train\n",
        "trainHistory = model.fit(mnistData, mnistLabels, epochs=10, batch_size=100,\n",
        "                         validation_split=0.1, verbose=0)\n",
        "\n",
        "suite = unittest.TestLoader().loadTestsFromTestCase(mlTest)\n",
        "unittest.TextTestRunner(verbosity=1, stream=sys.stderr).run(suite)"
      ],
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "FF\n",
            "======================================================================\n",
            "FAIL: testMean (__main__.mlTest)\n",
            "----------------------------------------------------------------------\n",
            "Traceback (most recent call last):\n",
            "  File \"<ipython-input-59-f8aa3a0ebb02>\", line 21, in testMean\n",
            "    self.assertAlmostEqual(yMean, yMeanActual, delta=deltaMean, msg=errorMsg)\n",
            "AssertionError: Mean of predicted values 0.1 and actual values 4.4754 differs by >0.05.\n",
            "\n",
            "======================================================================\n",
            "FAIL: testStd (__main__.mlTest)\n",
            "----------------------------------------------------------------------\n",
            "Traceback (most recent call last):\n",
            "  File \"<ipython-input-59-f8aa3a0ebb02>\", line 13, in testStd\n",
            "    self.assertAlmostEqual(yStd, yStdActual, delta=deltaStd, msg=errorMsg)\n",
            "AssertionError: Std. dev. of predicted values 0.28624246 and actual values 2.9147546792140155 differs by >0.05.\n",
            "\n",
            "----------------------------------------------------------------------\n",
            "Ran 2 tests in 0.574s\n",
            "\n",
            "FAILED (failures=2)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<unittest.runner.TextTestResult run=2 errors=0 failures=2>"
            ]
          },
          "metadata": {},
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 643
        },
        "id": "Yej_75j8J-Md",
        "outputId": "34083631-1a5c-4866-c221-7ce974bcdf70"
      },
      "source": [
        "yPred = model.predict(mnistData)\n",
        "plt.hist(yPred, bins=range(11))"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([array([4993.,    7.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
              "            0.]),\n",
              "  array([5000.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
              "            0.]),\n",
              "  array([5000.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
              "            0.]),\n",
              "  array([5000.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
              "            0.]),\n",
              "  array([5000.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
              "            0.]),\n",
              "  array([5000.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
              "            0.]),\n",
              "  array([5000.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
              "            0.]),\n",
              "  array([5000.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
              "            0.]),\n",
              "  array([5000.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
              "            0.]),\n",
              "  array([5000.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
              "            0.])],\n",
              " array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10]),\n",
              " <a list of 10 Lists of Patches objects>)"
            ]
          },
          "metadata": {},
          "execution_count": 63
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W0lr3mzppHr1"
      },
      "source": [
        "## Conclusion\n",
        "\n",
        "The Colab demonstrated the following principles:\n",
        "\n",
        "* Calculate loss correctly for your problem.\n",
        "* Verify and unit test your engineered data.\n",
        "* Find the right model capacity through experimentation.\n",
        "* Find the best regularization through experimentation.\n",
        "* Check quality on data slices."
      ]
    }
  ]
}