sparsity_and_l1_regularization.ipynb

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  "metadata": {
    "colab": {
      "name": "sparsity_and_l1_regularization.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [
        "JndnmDMp66FL",
        "yjUCX5LAkxAX"
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      "include_colab_link": true
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "[View in Colaboratory](https://colab.research.google.com/github/diegoreico/machine-learning-crash-course/blob/master/sparsity_and_l1_regularization.ipynb)"
      ]
    },
    {
      "metadata": {
        "id": "JndnmDMp66FL",
        "colab_type": "text"
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      "cell_type": "markdown",
      "source": [
        "#### Copyright 2017 Google LLC."
      ]
    },
    {
      "metadata": {
        "id": "hMqWDc_m6rUC",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "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": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "g4T-_IsVbweU",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Sparsity and L1 Regularization"
      ]
    },
    {
      "metadata": {
        "id": "g8ue2FyFIjnQ",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "**Learning Objectives:**\n",
        "  * Calculate the size of a model\n",
        "  * Apply L1 regularization to reduce the size of a model by increasing sparsity"
      ]
    },
    {
      "metadata": {
        "id": "ME_WXE7cIjnS",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "One way to reduce complexity is to use a regularization function that encourages weights to be exactly zero. For linear models such as regression, a zero weight is equivalent to not using the corresponding feature at all. In addition to avoiding overfitting, the resulting model will be more efficient.\n",
        "\n",
        "L1 regularization is a good way to increase sparsity.\n",
        "\n"
      ]
    },
    {
      "metadata": {
        "id": "fHRzeWkRLrHF",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Setup\n",
        "\n",
        "Run the cells below to load the data and create feature definitions."
      ]
    },
    {
      "metadata": {
        "id": "pb7rSrLKIjnS",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "from __future__ import print_function\n",
        "\n",
        "import math\n",
        "\n",
        "from IPython import display\n",
        "from matplotlib import cm\n",
        "from matplotlib import gridspec\n",
        "from matplotlib import pyplot as plt\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "from sklearn import metrics\n",
        "import tensorflow as tf\n",
        "from tensorflow.python.data import Dataset\n",
        "\n",
        "tf.logging.set_verbosity(tf.logging.ERROR)\n",
        "pd.options.display.max_rows = 10\n",
        "pd.options.display.float_format = '{:.1f}'.format\n",
        "\n",
        "california_housing_dataframe = pd.read_csv(\"https://dl.google.com/mlcc/mledu-datasets/california_housing_train.csv\", sep=\",\")\n",
        "\n",
        "california_housing_dataframe = california_housing_dataframe.reindex(\n",
        "    np.random.permutation(california_housing_dataframe.index))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "3V7q8jk0IjnW",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def preprocess_features(california_housing_dataframe):\n",
        "  \"\"\"Prepares input features from California housing data set.\n",
        "\n",
        "  Args:\n",
        "    california_housing_dataframe: A Pandas DataFrame expected to contain data\n",
        "      from the California housing data set.\n",
        "  Returns:\n",
        "    A DataFrame that contains the features to be used for the model, including\n",
        "    synthetic features.\n",
        "  \"\"\"\n",
        "  selected_features = california_housing_dataframe[\n",
        "    [\"latitude\",\n",
        "     \"longitude\",\n",
        "     \"housing_median_age\",\n",
        "     \"total_rooms\",\n",
        "     \"total_bedrooms\",\n",
        "     \"population\",\n",
        "     \"households\",\n",
        "     \"median_income\"]]\n",
        "  processed_features = selected_features.copy()\n",
        "  # Create a synthetic feature.\n",
        "  processed_features[\"rooms_per_person\"] = (\n",
        "    california_housing_dataframe[\"total_rooms\"] /\n",
        "    california_housing_dataframe[\"population\"])\n",
        "  return processed_features\n",
        "\n",
        "def preprocess_targets(california_housing_dataframe):\n",
        "  \"\"\"Prepares target features (i.e., labels) from California housing data set.\n",
        "\n",
        "  Args:\n",
        "    california_housing_dataframe: A Pandas DataFrame expected to contain data\n",
        "      from the California housing data set.\n",
        "  Returns:\n",
        "    A DataFrame that contains the target feature.\n",
        "  \"\"\"\n",
        "  output_targets = pd.DataFrame()\n",
        "  # Create a boolean categorical feature representing whether the\n",
        "  # median_house_value is above a set threshold.\n",
        "  output_targets[\"median_house_value_is_high\"] = (\n",
        "    california_housing_dataframe[\"median_house_value\"] > 265000).astype(float)\n",
        "  return output_targets"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "pAG3tmgwIjnY",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1229
        },
        "outputId": "5b9fd90b-4613-40f3-f665-f621eb72df13"
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      "cell_type": "code",
      "source": [
        "# Choose the first 12000 (out of 17000) examples for training.\n",
        "training_examples = preprocess_features(california_housing_dataframe.head(12000))\n",
        "training_targets = preprocess_targets(california_housing_dataframe.head(12000))\n",
        "\n",
        "# Choose the last 5000 (out of 17000) examples for validation.\n",
        "validation_examples = preprocess_features(california_housing_dataframe.tail(5000))\n",
        "validation_targets = preprocess_targets(california_housing_dataframe.tail(5000))\n",
        "\n",
        "# Double-check that we've done the right thing.\n",
        "print(\"Training examples summary:\")\n",
        "display.display(training_examples.describe())\n",
        "print(\"Validation examples summary:\")\n",
        "display.display(validation_examples.describe())\n",
        "\n",
        "print(\"Training targets summary:\")\n",
        "display.display(training_targets.describe())\n",
        "print(\"Validation targets summary:\")\n",
        "display.display(validation_targets.describe())"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Training examples summary:\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "       latitude  longitude  housing_median_age  total_rooms  total_bedrooms  \\\n",
              "count   12000.0    12000.0             12000.0      12000.0         12000.0   \n",
              "mean       35.6     -119.6                28.6       2653.9           541.5   \n",
              "std         2.1        2.0                12.6       2206.9           426.4   \n",
              "min        32.5     -124.3                 1.0          2.0             2.0   \n",
              "25%        33.9     -121.8                18.0       1467.8           298.0   \n",
              "50%        34.2     -118.5                29.0       2125.0           434.0   \n",
              "75%        37.7     -118.0                37.0       3158.2           651.0   \n",
              "max        42.0     -114.3                52.0      37937.0          6445.0   \n",
              "\n",
              "       population  households  median_income  rooms_per_person  \n",
              "count     12000.0     12000.0        12000.0           12000.0  \n",
              "mean       1437.9       503.5            3.9               2.0  \n",
              "std        1179.4       390.7            1.9               1.1  \n",
              "min           6.0         2.0            0.5               0.1  \n",
              "25%         789.8       282.8            2.6               1.5  \n",
              "50%        1171.0       409.0            3.5               1.9  \n",
              "75%        1728.2       607.0            4.8               2.3  \n",
              "max       35682.0      6082.0           15.0              55.2  "
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>latitude</th>\n",
              "      <th>longitude</th>\n",
              "      <th>housing_median_age</th>\n",
              "      <th>total_rooms</th>\n",
              "      <th>total_bedrooms</th>\n",
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              "      <th>count</th>\n",
              "      <td>12000.0</td>\n",
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              "      <td>12000.0</td>\n",
              "      <td>12000.0</td>\n",
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              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>35.6</td>\n",
              "      <td>-119.6</td>\n",
              "      <td>28.6</td>\n",
              "      <td>2653.9</td>\n",
              "      <td>541.5</td>\n",
              "      <td>1437.9</td>\n",
              "      <td>503.5</td>\n",
              "      <td>3.9</td>\n",
              "      <td>2.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>2.1</td>\n",
              "      <td>2.0</td>\n",
              "      <td>12.6</td>\n",
              "      <td>2206.9</td>\n",
              "      <td>426.4</td>\n",
              "      <td>1179.4</td>\n",
              "      <td>390.7</td>\n",
              "      <td>1.9</td>\n",
              "      <td>1.1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>32.5</td>\n",
              "      <td>-124.3</td>\n",
              "      <td>1.0</td>\n",
              "      <td>2.0</td>\n",
              "      <td>2.0</td>\n",
              "      <td>6.0</td>\n",
              "      <td>2.0</td>\n",
              "      <td>0.5</td>\n",
              "      <td>0.1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>33.9</td>\n",
              "      <td>-121.8</td>\n",
              "      <td>18.0</td>\n",
              "      <td>1467.8</td>\n",
              "      <td>298.0</td>\n",
              "      <td>789.8</td>\n",
              "      <td>282.8</td>\n",
              "      <td>2.6</td>\n",
              "      <td>1.5</td>\n",
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              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>34.2</td>\n",
              "      <td>-118.5</td>\n",
              "      <td>29.0</td>\n",
              "      <td>2125.0</td>\n",
              "      <td>434.0</td>\n",
              "      <td>1171.0</td>\n",
              "      <td>409.0</td>\n",
              "      <td>3.5</td>\n",
              "      <td>1.9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>37.7</td>\n",
              "      <td>-118.0</td>\n",
              "      <td>37.0</td>\n",
              "      <td>3158.2</td>\n",
              "      <td>651.0</td>\n",
              "      <td>1728.2</td>\n",
              "      <td>607.0</td>\n",
              "      <td>4.8</td>\n",
              "      <td>2.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>42.0</td>\n",
              "      <td>-114.3</td>\n",
              "      <td>52.0</td>\n",
              "      <td>37937.0</td>\n",
              "      <td>6445.0</td>\n",
              "      <td>35682.0</td>\n",
              "      <td>6082.0</td>\n",
              "      <td>15.0</td>\n",
              "      <td>55.2</td>\n",
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            "Validation examples summary:\n"
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            "text/plain": [
              "       latitude  longitude  housing_median_age  total_rooms  total_bedrooms  \\\n",
              "count    5000.0     5000.0              5000.0       5000.0          5000.0   \n",
              "mean       35.6     -119.6                28.6       2619.2           534.5   \n",
              "std         2.1        2.0                12.5       2113.8           409.5   \n",
              "min        32.5     -124.3                 1.0          8.0             1.0   \n",
              "25%        33.9     -121.8                18.0       1447.8           294.0   \n",
              "50%        34.3     -118.5                29.0       2136.5           433.5   \n",
              "75%        37.7     -118.0                37.0       3135.0           646.0   \n",
              "max        41.9     -114.5                52.0      32054.0          5290.0   \n",
              "\n",
              "       population  households  median_income  rooms_per_person  \n",
              "count      5000.0      5000.0         5000.0            5000.0  \n",
              "mean       1409.6       495.8            3.9               2.0  \n",
              "std        1068.1       369.1            1.9               1.2  \n",
              "min           3.0         1.0            0.5               0.0  \n",
              "25%         790.0       279.0            2.6               1.5  \n",
              "50%        1158.0       409.0            3.5               2.0  \n",
              "75%        1702.0       602.0            4.8               2.3  \n",
              "max       15507.0      5050.0           15.0              52.0  "
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>latitude</th>\n",
              "      <th>longitude</th>\n",
              "      <th>housing_median_age</th>\n",
              "      <th>total_rooms</th>\n",
              "      <th>total_bedrooms</th>\n",
              "      <th>population</th>\n",
              "      <th>households</th>\n",
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              "      <th>count</th>\n",
              "      <td>5000.0</td>\n",
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              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>35.6</td>\n",
              "      <td>-119.6</td>\n",
              "      <td>28.6</td>\n",
              "      <td>2619.2</td>\n",
              "      <td>534.5</td>\n",
              "      <td>1409.6</td>\n",
              "      <td>495.8</td>\n",
              "      <td>3.9</td>\n",
              "      <td>2.0</td>\n",
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              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>2.1</td>\n",
              "      <td>2.0</td>\n",
              "      <td>12.5</td>\n",
              "      <td>2113.8</td>\n",
              "      <td>409.5</td>\n",
              "      <td>1068.1</td>\n",
              "      <td>369.1</td>\n",
              "      <td>1.9</td>\n",
              "      <td>1.2</td>\n",
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              "      <th>min</th>\n",
              "      <td>32.5</td>\n",
              "      <td>-124.3</td>\n",
              "      <td>1.0</td>\n",
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              "      <th>25%</th>\n",
              "      <td>33.9</td>\n",
              "      <td>-121.8</td>\n",
              "      <td>18.0</td>\n",
              "      <td>1447.8</td>\n",
              "      <td>294.0</td>\n",
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              "      <td>279.0</td>\n",
              "      <td>2.6</td>\n",
              "      <td>1.5</td>\n",
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              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>34.3</td>\n",
              "      <td>-118.5</td>\n",
              "      <td>29.0</td>\n",
              "      <td>2136.5</td>\n",
              "      <td>433.5</td>\n",
              "      <td>1158.0</td>\n",
              "      <td>409.0</td>\n",
              "      <td>3.5</td>\n",
              "      <td>2.0</td>\n",
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              "      <th>75%</th>\n",
              "      <td>37.7</td>\n",
              "      <td>-118.0</td>\n",
              "      <td>37.0</td>\n",
              "      <td>3135.0</td>\n",
              "      <td>646.0</td>\n",
              "      <td>1702.0</td>\n",
              "      <td>602.0</td>\n",
              "      <td>4.8</td>\n",
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              "      <th>max</th>\n",
              "      <td>41.9</td>\n",
              "      <td>-114.5</td>\n",
              "      <td>52.0</td>\n",
              "      <td>32054.0</td>\n",
              "      <td>5290.0</td>\n",
              "      <td>15507.0</td>\n",
              "      <td>5050.0</td>\n",
              "      <td>15.0</td>\n",
              "      <td>52.0</td>\n",
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            "Training targets summary:\n"
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              "       median_house_value_is_high\n",
              "count                     12000.0\n",
              "mean                          0.2\n",
              "std                           0.4\n",
              "min                           0.0\n",
              "25%                           0.0\n",
              "50%                           0.0\n",
              "75%                           0.0\n",
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              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>median_house_value_is_high</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
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              "      <th>count</th>\n",
              "      <td>12000.0</td>\n",
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              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>0.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>0.4</td>\n",
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              "      <td>0.0</td>\n",
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              "      <td>0.0</td>\n",
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              "      <th>50%</th>\n",
              "      <td>0.0</td>\n",
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              "      <th>75%</th>\n",
              "      <td>0.0</td>\n",
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        {
          "output_type": "stream",
          "text": [
            "Validation targets summary:\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "       median_house_value_is_high\n",
              "count                      5000.0\n",
              "mean                          0.3\n",
              "std                           0.4\n",
              "min                           0.0\n",
              "25%                           0.0\n",
              "50%                           0.0\n",
              "75%                           1.0\n",
              "max                           1.0"
            ],
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              "      <th>median_house_value_is_high</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
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              "      <td>5000.0</td>\n",
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    },
    {
      "metadata": {
        "id": "gHkniRI1Ijna",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def my_input_fn(features, targets, batch_size=1, shuffle=True, num_epochs=None):\n",
        "    \"\"\"Trains a linear regression model.\n",
        "  \n",
        "    Args:\n",
        "      features: pandas DataFrame of features\n",
        "      targets: pandas DataFrame of targets\n",
        "      batch_size: Size of batches to be passed to the model\n",
        "      shuffle: True or False. Whether to shuffle the data.\n",
        "      num_epochs: Number of epochs for which data should be repeated. None = repeat indefinitely\n",
        "    Returns:\n",
        "      Tuple of (features, labels) for next data batch\n",
        "    \"\"\"\n",
        "  \n",
        "    # Convert pandas data into a dict of np arrays.\n",
        "    features = {key:np.array(value) for key,value in dict(features).items()}                                            \n",
        " \n",
        "    # Construct a dataset, and configure batching/repeating.\n",
        "    ds = Dataset.from_tensor_slices((features,targets)) # warning: 2GB limit\n",
        "    ds = ds.batch(batch_size).repeat(num_epochs)\n",
        "    \n",
        "    # Shuffle the data, if specified.\n",
        "    if shuffle:\n",
        "      ds = ds.shuffle(10000)\n",
        "    \n",
        "    # Return the next batch of data.\n",
        "    features, labels = ds.make_one_shot_iterator().get_next()\n",
        "    return features, labels"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "bLzK72jkNJPf",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def get_quantile_based_buckets(feature_values, num_buckets):\n",
        "  quantiles = feature_values.quantile(\n",
        "    [(i+1.)/(num_buckets + 1.) for i in range(num_buckets)])\n",
        "  return [quantiles[q] for q in quantiles.keys()]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "al2YQpKyIjnd",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def construct_feature_columns():\n",
        "  \"\"\"Construct the TensorFlow Feature Columns.\n",
        "\n",
        "  Returns:\n",
        "    A set of feature columns\n",
        "  \"\"\"\n",
        "\n",
        "  bucketized_households = tf.feature_column.bucketized_column(\n",
        "    tf.feature_column.numeric_column(\"households\"),\n",
        "    boundaries=get_quantile_based_buckets(training_examples[\"households\"], 10))\n",
        "  bucketized_longitude = tf.feature_column.bucketized_column(\n",
        "    tf.feature_column.numeric_column(\"longitude\"),\n",
        "    boundaries=get_quantile_based_buckets(training_examples[\"longitude\"], 50))\n",
        "  bucketized_latitude = tf.feature_column.bucketized_column(\n",
        "    tf.feature_column.numeric_column(\"latitude\"),\n",
        "    boundaries=get_quantile_based_buckets(training_examples[\"latitude\"], 50))\n",
        "  bucketized_housing_median_age = tf.feature_column.bucketized_column(\n",
        "    tf.feature_column.numeric_column(\"housing_median_age\"),\n",
        "    boundaries=get_quantile_based_buckets(\n",
        "      training_examples[\"housing_median_age\"], 10))\n",
        "  bucketized_total_rooms = tf.feature_column.bucketized_column(\n",
        "    tf.feature_column.numeric_column(\"total_rooms\"),\n",
        "    boundaries=get_quantile_based_buckets(training_examples[\"total_rooms\"], 10))\n",
        "  bucketized_total_bedrooms = tf.feature_column.bucketized_column(\n",
        "    tf.feature_column.numeric_column(\"total_bedrooms\"),\n",
        "    boundaries=get_quantile_based_buckets(training_examples[\"total_bedrooms\"], 10))\n",
        "  bucketized_population = tf.feature_column.bucketized_column(\n",
        "    tf.feature_column.numeric_column(\"population\"),\n",
        "    boundaries=get_quantile_based_buckets(training_examples[\"population\"], 10))\n",
        "  bucketized_median_income = tf.feature_column.bucketized_column(\n",
        "    tf.feature_column.numeric_column(\"median_income\"),\n",
        "    boundaries=get_quantile_based_buckets(training_examples[\"median_income\"], 10))\n",
        "  bucketized_rooms_per_person = tf.feature_column.bucketized_column(\n",
        "    tf.feature_column.numeric_column(\"rooms_per_person\"),\n",
        "    boundaries=get_quantile_based_buckets(\n",
        "      training_examples[\"rooms_per_person\"], 10))\n",
        "\n",
        "  long_x_lat = tf.feature_column.crossed_column(\n",
        "    set([bucketized_longitude, bucketized_latitude]), hash_bucket_size=1000)\n",
        "\n",
        "  feature_columns = set([\n",
        "    long_x_lat,\n",
        "    bucketized_longitude,\n",
        "    bucketized_latitude,\n",
        "    bucketized_housing_median_age,\n",
        "    bucketized_total_rooms,\n",
        "    bucketized_total_bedrooms,\n",
        "    bucketized_population,\n",
        "    bucketized_households,\n",
        "    bucketized_median_income,\n",
        "    bucketized_rooms_per_person])\n",
        "  \n",
        "  return feature_columns"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "hSBwMrsrE21n",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Calculate the Model Size\n",
        "\n",
        "To calculate the model size, we simply count the number of parameters that are non-zero. We provide a helper function below to do that. The function uses intimate knowledge of the Estimators API - don't worry about understanding how it works."
      ]
    },
    {
      "metadata": {
        "id": "e6GfTI0CFhB8",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def model_size(estimator):\n",
        "  variables = estimator.get_variable_names()\n",
        "  size = 0\n",
        "  for variable in variables:\n",
        "    if not any(x in variable \n",
        "               for x in ['global_step',\n",
        "                         'centered_bias_weight',\n",
        "                         'bias_weight',\n",
        "                         'Ftrl']\n",
        "              ):\n",
        "      size += np.count_nonzero(estimator.get_variable_value(variable))\n",
        "  return size"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "XabdAaj67GfF",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Reduce the Model Size\n",
        "\n",
        "Your team needs to build a highly accurate Logistic Regression model on the *SmartRing*, a ring that is so smart it can sense the demographics of a city block ('median_income', 'avg_rooms', 'households', ..., etc.) and tell you whether the given city block is high cost city block or not.\n",
        "\n",
        "Since the SmartRing is small, the engineering team has determined that it can only handle a model that has **no more than 600 parameters**. On the other hand, the product management team has determined that the model is not launchable unless the **LogLoss is less than 0.35** on the holdout test set.\n",
        "\n",
        "Can you use your secret weapon—L1 regularization—to tune the model to satisfy both the size and accuracy constraints?"
      ]
    },
    {
      "metadata": {
        "id": "G79hGRe7qqej",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Task 1: Find a good regularization coefficient.\n",
        "\n",
        "**Find an L1 regularization strength parameter which satisfies both constraints — model size is less than 600 and log-loss is less than 0.35 on validation set.**\n",
        "\n",
        "The following code will help you get started. There are many ways to apply regularization to your model. Here, we chose to do it using `FtrlOptimizer`, which is designed to give better results with L1 regularization than standard gradient descent.\n",
        "\n",
        "Again, the model will train on the entire data set, so expect it to run slower than normal."
      ]
    },
    {
      "metadata": {
        "id": "1Fcdm0hpIjnl",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def train_linear_classifier_model(\n",
        "    learning_rate,\n",
        "    regularization_strength,\n",
        "    steps,\n",
        "    batch_size,\n",
        "    feature_columns,\n",
        "    training_examples,\n",
        "    training_targets,\n",
        "    validation_examples,\n",
        "    validation_targets):\n",
        "  \"\"\"Trains a linear regression model.\n",
        "  \n",
        "  In addition to training, this function also prints training progress information,\n",
        "  as well as a plot of the training and validation loss over time.\n",
        "  \n",
        "  Args:\n",
        "    learning_rate: A `float`, the learning rate.\n",
        "    regularization_strength: A `float` that indicates the strength of the L1\n",
        "       regularization. A value of `0.0` means no regularization.\n",
        "    steps: A non-zero `int`, the total number of training steps. A training step\n",
        "      consists of a forward and backward pass using a single batch.\n",
        "    feature_columns: A `set` specifying the input feature columns to use.\n",
        "    training_examples: A `DataFrame` containing one or more columns from\n",
        "      `california_housing_dataframe` to use as input features for training.\n",
        "    training_targets: A `DataFrame` containing exactly one column from\n",
        "      `california_housing_dataframe` to use as target for training.\n",
        "    validation_examples: A `DataFrame` containing one or more columns from\n",
        "      `california_housing_dataframe` to use as input features for validation.\n",
        "    validation_targets: A `DataFrame` containing exactly one column from\n",
        "      `california_housing_dataframe` to use as target for validation.\n",
        "      \n",
        "  Returns:\n",
        "    A `LinearClassifier` object trained on the training data.\n",
        "  \"\"\"\n",
        "\n",
        "  periods = 7\n",
        "  steps_per_period = steps / periods\n",
        "\n",
        "  # Create a linear classifier object.\n",
        "  my_optimizer = tf.train.FtrlOptimizer(learning_rate=learning_rate, l1_regularization_strength=regularization_strength)\n",
        "  my_optimizer = tf.contrib.estimator.clip_gradients_by_norm(my_optimizer, 5.0)\n",
        "  linear_classifier = tf.estimator.LinearClassifier(\n",
        "      feature_columns=feature_columns,\n",
        "      optimizer=my_optimizer\n",
        "  )\n",
        "  \n",
        "  # Create input functions.\n",
        "  training_input_fn = lambda: my_input_fn(training_examples, \n",
        "                                          training_targets[\"median_house_value_is_high\"], \n",
        "                                          batch_size=batch_size)\n",
        "  predict_training_input_fn = lambda: my_input_fn(training_examples, \n",
        "                                                  training_targets[\"median_house_value_is_high\"], \n",
        "                                                  num_epochs=1, \n",
        "                                                  shuffle=False)\n",
        "  predict_validation_input_fn = lambda: my_input_fn(validation_examples, \n",
        "                                                    validation_targets[\"median_house_value_is_high\"], \n",
        "                                                    num_epochs=1, \n",
        "                                                    shuffle=False)\n",
        "  \n",
        "  # Train the model, but do so inside a loop so that we can periodically assess\n",
        "  # loss metrics.\n",
        "  print(\"Training model...\")\n",
        "  print(\"LogLoss (on validation data):\")\n",
        "  training_log_losses = []\n",
        "  validation_log_losses = []\n",
        "  for period in range (0, periods):\n",
        "    # Train the model, starting from the prior state.\n",
        "    linear_classifier.train(\n",
        "        input_fn=training_input_fn,\n",
        "        steps=steps_per_period\n",
        "    )\n",
        "    # Take a break and compute predictions.\n",
        "    training_probabilities = linear_classifier.predict(input_fn=predict_training_input_fn)\n",
        "    training_probabilities = np.array([item['probabilities'] for item in training_probabilities])\n",
        "    \n",
        "    validation_probabilities = linear_classifier.predict(input_fn=predict_validation_input_fn)\n",
        "    validation_probabilities = np.array([item['probabilities'] for item in validation_probabilities])\n",
        "    \n",
        "    # Compute training and validation loss.\n",
        "    training_log_loss = metrics.log_loss(training_targets, training_probabilities)\n",
        "    validation_log_loss = metrics.log_loss(validation_targets, validation_probabilities)\n",
        "    # Occasionally print the current loss.\n",
        "    print(\"  period %02d : %0.2f\" % (period, validation_log_loss))\n",
        "    # Add the loss metrics from this period to our list.\n",
        "    training_log_losses.append(training_log_loss)\n",
        "    validation_log_losses.append(validation_log_loss)\n",
        "  print(\"Model training finished.\")\n",
        "\n",
        "  # Output a graph of loss metrics over periods.\n",
        "  plt.ylabel(\"LogLoss\")\n",
        "  plt.xlabel(\"Periods\")\n",
        "  plt.title(\"LogLoss vs. Periods\")\n",
        "  plt.tight_layout()\n",
        "  plt.plot(training_log_losses, label=\"training\")\n",
        "  plt.plot(validation_log_losses, label=\"validation\")\n",
        "  plt.legend()\n",
        "\n",
        "  return linear_classifier"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "9H1CKHSzIjno",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 599
        },
        "outputId": "062462c6-388a-4aa7-cc31-18bf855245f1"
      },
      "cell_type": "code",
      "source": [
        "linear_classifier = train_linear_classifier_model(\n",
        "    learning_rate=0.1,\n",
        "    # TWEAK THE REGULARIZATION VALUE BELOW\n",
        "    regularization_strength=0.1,\n",
        "    steps=300,\n",
        "    batch_size=100,\n",
        "    feature_columns=construct_feature_columns(),\n",
        "    training_examples=training_examples,\n",
        "    training_targets=training_targets,\n",
        "    validation_examples=validation_examples,\n",
        "    validation_targets=validation_targets)\n",
        "print(\"Model size:\", model_size(linear_classifier))"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Training model...\n",
            "LogLoss (on validation data):\n",
            "  period 00 : 0.33\n",
            "  period 01 : 0.30\n",
            "  period 02 : 0.28\n",
            "  period 03 : 0.27\n",
            "  period 04 : 0.27\n",
            "  period 05 : 0.26\n",
            "  period 06 : 0.26\n",
            "Model training finished.\n",
            "Model size: 783\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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YhVaj5eOYz0grzlA7JCGEEK2YFDNNYEhPP4b38iMxo4iVW2JbxViSIOd2/K7L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\nRK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f6807113850>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "yjUCX5LAkxAX",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Solution\n",
        "\n",
        "Click below to see a possible solution."
      ]
    },
    {
      "metadata": {
        "id": "hgGhy-okmkWL",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "A regularization strength of 0.1 should be sufficient. Note that there is a compromise to be struck:\n",
        "stronger regularization gives us smaller models, but can affect the classification loss."
      ]
    },
    {
      "metadata": {
        "id": "_rV8YQWZIjns",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 599
        },
        "outputId": "df90ee33-3e37-43c8-ca28-a2852ea0edf6"
      },
      "cell_type": "code",
      "source": [
        "linear_classifier = train_linear_classifier_model(\n",
        "    learning_rate=0.1,\n",
        "    regularization_strength=0.1,\n",
        "    steps=300,\n",
        "    batch_size=100,\n",
        "    feature_columns=construct_feature_columns(),\n",
        "    training_examples=training_examples,\n",
        "    training_targets=training_targets,\n",
        "    validation_examples=validation_examples,\n",
        "    validation_targets=validation_targets)\n",
        "print(\"Model size:\", model_size(linear_classifier))"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Training model...\n",
            "LogLoss (on validation data):\n",
            "  period 00 : 0.33\n",
            "  period 01 : 0.30\n",
            "  period 02 : 0.28\n",
            "  period 03 : 0.27\n",
            "  period 04 : 0.27\n",
            "  period 05 : 0.26\n",
            "  period 06 : 0.26\n",
            "Model training finished.\n",
            "Model size: 743\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ol+1jKS522D6bXcyaXWcI8XclKkyvdlgmodVo+XvEPbwR9y6/JG3E38mXKN/u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\niIiISERTmBEREZGI9v8B/7ziAMWzQjUAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f6808c412d0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}