feature_crosses.ipynb

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  "metadata": {
    "colab": {
      "name": "feature_crosses.ipynb",
      "version": "0.3.2",
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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/guruRockz/Machine-Learning-Course-Python-implementation/blob/master/feature_crosses.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",
        "cellView": "both",
        "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": [
        "# Feature Crosses"
      ]
    },
    {
      "metadata": {
        "id": "F7dke6skIK-k",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "**Learning Objectives:**\n",
        "  * Improve a linear regression model with the addition of additional synthetic features (this is a continuation of the previous exercise)\n",
        "  * Use an input function to convert pandas `DataFrame` objects to `Tensors` and invoke the input function in `fit()` and `predict()` operations\n",
        "  * Use the FTRL optimization algorithm for model training\n",
        "  * Create new synthetic features through one-hot encoding, binning, and feature crosses"
      ]
    },
    {
      "metadata": {
        "id": "NS_fcQRd8B97",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Setup"
      ]
    },
    {
      "metadata": {
        "id": "4IdzD8IdIK-l",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "First, as we've done in previous exercises, let's define the input and create the data-loading code."
      ]
    },
    {
      "metadata": {
        "id": "CsfdiLiDIK-n",
        "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://download.mlcc.google.com/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": "10rhoflKIK-s",
        "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",
        "  # Scale the target to be in units of thousands of dollars.\n",
        "  output_targets[\"median_house_value\"] = (\n",
        "    california_housing_dataframe[\"median_house_value\"] / 1000.0)\n",
        "  return output_targets"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "ufplEkjN8KUp",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1205
        },
        "outputId": "5cccd685-4966-4523-9743-55651e9821fa"
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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": 3,
      "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     -119.5                28.5       2638.6           538.5   \n",
              "std         2.1        2.0                12.6       2173.0           421.2   \n",
              "min        32.5     -124.3                 1.0         11.0             3.0   \n",
              "25%        33.9     -121.8                18.0       1461.0           296.0   \n",
              "50%        34.2     -118.5                29.0       2127.0           434.0   \n",
              "75%        37.7     -118.0                37.0       3142.2           647.0   \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       1430.0       500.5            3.9               2.0  \n",
              "std        1164.8       384.8            1.9               1.1  \n",
              "min           8.0         2.0            0.5               0.0  \n",
              "25%         789.0       281.0            2.6               1.5  \n",
              "50%        1166.0       408.0            3.5               1.9  \n",
              "75%        1724.2       602.2            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>households</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",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>35.6</td>\n",
              "      <td>-119.5</td>\n",
              "      <td>28.5</td>\n",
              "      <td>2638.6</td>\n",
              "      <td>538.5</td>\n",
              "      <td>1430.0</td>\n",
              "      <td>500.5</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>2173.0</td>\n",
              "      <td>421.2</td>\n",
              "      <td>1164.8</td>\n",
              "      <td>384.8</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>11.0</td>\n",
              "      <td>3.0</td>\n",
              "      <td>8.0</td>\n",
              "      <td>2.0</td>\n",
              "      <td>0.5</td>\n",
              "      <td>0.0</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>1461.0</td>\n",
              "      <td>296.0</td>\n",
              "      <td>789.0</td>\n",
              "      <td>281.0</td>\n",
              "      <td>2.6</td>\n",
              "      <td>1.5</td>\n",
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              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>34.2</td>\n",
              "      <td>-118.5</td>\n",
              "      <td>29.0</td>\n",
              "      <td>2127.0</td>\n",
              "      <td>434.0</td>\n",
              "      <td>1166.0</td>\n",
              "      <td>408.0</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>3142.2</td>\n",
              "      <td>647.0</td>\n",
              "      <td>1724.2</td>\n",
              "      <td>602.2</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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              "  </tbody>\n",
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          "text": [
            "Validation examples summary:\n"
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          "data": {
            "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       35.7     -119.6                28.7       2655.9           541.6   \n",
              "std         2.1        2.0                12.6       2196.6           422.4   \n",
              "min        32.6     -124.3                 1.0          2.0             1.0   \n",
              "25%        33.9     -121.8                18.0       1464.0           297.0   \n",
              "50%        34.3     -118.5                29.0       2129.5           433.0   \n",
              "75%        37.7     -118.0                37.0       3174.2           654.0   \n",
              "max        42.0     -114.5                52.0      30405.0          4492.0   \n",
              "\n",
              "       population  households  median_income  rooms_per_person  \n",
              "count      5000.0      5000.0         5000.0            5000.0  \n",
              "mean       1428.5       503.0            3.9               2.0  \n",
              "std        1106.3       383.8            1.9               1.3  \n",
              "min           3.0         1.0            0.5               0.1  \n",
              "25%         791.0       282.0            2.5               1.5  \n",
              "50%        1171.0       410.0            3.5               1.9  \n",
              "75%        1715.0       609.2            4.7               2.3  \n",
              "max       12873.0      4372.0           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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              "      <td>5000.0</td>\n",
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              "      <td>5000.0</td>\n",
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              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>35.7</td>\n",
              "      <td>-119.6</td>\n",
              "      <td>28.7</td>\n",
              "      <td>2655.9</td>\n",
              "      <td>541.6</td>\n",
              "      <td>1428.5</td>\n",
              "      <td>503.0</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>12.6</td>\n",
              "      <td>2196.6</td>\n",
              "      <td>422.4</td>\n",
              "      <td>1106.3</td>\n",
              "      <td>383.8</td>\n",
              "      <td>1.9</td>\n",
              "      <td>1.3</td>\n",
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              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>32.6</td>\n",
              "      <td>-124.3</td>\n",
              "      <td>1.0</td>\n",
              "      <td>2.0</td>\n",
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              "      <td>0.1</td>\n",
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              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>33.9</td>\n",
              "      <td>-121.8</td>\n",
              "      <td>18.0</td>\n",
              "      <td>1464.0</td>\n",
              "      <td>297.0</td>\n",
              "      <td>791.0</td>\n",
              "      <td>282.0</td>\n",
              "      <td>2.5</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>2129.5</td>\n",
              "      <td>433.0</td>\n",
              "      <td>1171.0</td>\n",
              "      <td>410.0</td>\n",
              "      <td>3.5</td>\n",
              "      <td>1.9</td>\n",
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              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>37.7</td>\n",
              "      <td>-118.0</td>\n",
              "      <td>37.0</td>\n",
              "      <td>3174.2</td>\n",
              "      <td>654.0</td>\n",
              "      <td>1715.0</td>\n",
              "      <td>609.2</td>\n",
              "      <td>4.7</td>\n",
              "      <td>2.3</td>\n",
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              "      <th>max</th>\n",
              "      <td>42.0</td>\n",
              "      <td>-114.5</td>\n",
              "      <td>52.0</td>\n",
              "      <td>30405.0</td>\n",
              "      <td>4492.0</td>\n",
              "      <td>12873.0</td>\n",
              "      <td>4372.0</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\n",
              "count             12000.0\n",
              "mean                206.8\n",
              "std                 115.4\n",
              "min                  15.0\n",
              "25%                 119.4\n",
              "50%                 180.4\n",
              "75%                 263.8\n",
              "max                 500.0"
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              "    </tr>\n",
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              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>12000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>206.8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>115.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>15.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>119.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>180.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>263.8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>500.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Validation targets summary:\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "       median_house_value\n",
              "count              5000.0\n",
              "mean                208.6\n",
              "std                 117.3\n",
              "min                  15.0\n",
              "25%                 119.6\n",
              "50%                 180.1\n",
              "75%                 267.4\n",
              "max                 500.0"
            ],
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
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              "\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>median_house_value</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>5000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>208.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>117.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>15.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>119.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>180.1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>267.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>500.0</td>\n",
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      ]
    },
    {
      "metadata": {
        "id": "oJlrB4rJ_2Ma",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def construct_feature_columns(input_features):\n",
        "  \"\"\"Construct the TensorFlow Feature Columns.\n",
        "\n",
        "  Args:\n",
        "    input_features: The names of the numerical input features to use.\n",
        "  Returns:\n",
        "    A set of feature columns\n",
        "  \"\"\"\n",
        "  return set([tf.feature_column.numeric_column(my_feature)\n",
        "              for my_feature in input_features])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "NBxoAfp2AcB6",
        "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": "hweDyy31LBsV",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## FTRL Optimization Algorithm\n",
        "\n",
        "High dimensional linear models benefit from using a variant of gradient-based optimization called FTRL. This algorithm has the benefit of scaling the learning rate differently for different coefficients, which can be useful if some features rarely take non-zero values (it also is well suited to support L1 regularization). We can apply FTRL using the [FtrlOptimizer](https://www.tensorflow.org/api_docs/python/tf/train/FtrlOptimizer)."
      ]
    },
    {
      "metadata": {
        "id": "S0SBf1X1IK_O",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def train_model(\n",
        "    learning_rate,\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",
        "    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 `LinearRegressor` object trained on the training data.\n",
        "  \"\"\"\n",
        "\n",
        "  periods = 10\n",
        "  steps_per_period = steps / periods\n",
        "\n",
        "  # Create a linear regressor object.\n",
        "  my_optimizer = tf.train.FtrlOptimizer(learning_rate=learning_rate)\n",
        "  my_optimizer = tf.contrib.estimator.clip_gradients_by_norm(my_optimizer, 5.0)\n",
        "  linear_regressor = tf.estimator.LinearRegressor(\n",
        "      feature_columns=feature_columns,\n",
        "      optimizer=my_optimizer\n",
        "  )\n",
        "  \n",
        "  training_input_fn = lambda: my_input_fn(training_examples, \n",
        "                                          training_targets[\"median_house_value\"], \n",
        "                                          batch_size=batch_size)\n",
        "  predict_training_input_fn = lambda: my_input_fn(training_examples, \n",
        "                                                  training_targets[\"median_house_value\"], \n",
        "                                                  num_epochs=1, \n",
        "                                                  shuffle=False)\n",
        "  predict_validation_input_fn = lambda: my_input_fn(validation_examples, \n",
        "                                                    validation_targets[\"median_house_value\"], \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(\"RMSE (on training data):\")\n",
        "  training_rmse = []\n",
        "  validation_rmse = []\n",
        "  for period in range (0, periods):\n",
        "    # Train the model, starting from the prior state.\n",
        "    linear_regressor.train(\n",
        "        input_fn=training_input_fn,\n",
        "        steps=steps_per_period\n",
        "    )\n",
        "    # Take a break and compute predictions.\n",
        "    training_predictions = linear_regressor.predict(input_fn=predict_training_input_fn)\n",
        "    training_predictions = np.array([item['predictions'][0] for item in training_predictions])\n",
        "    validation_predictions = linear_regressor.predict(input_fn=predict_validation_input_fn)\n",
        "    validation_predictions = np.array([item['predictions'][0] for item in validation_predictions])\n",
        "    \n",
        "    # Compute training and validation loss.\n",
        "    training_root_mean_squared_error = math.sqrt(\n",
        "        metrics.mean_squared_error(training_predictions, training_targets))\n",
        "    validation_root_mean_squared_error = math.sqrt(\n",
        "        metrics.mean_squared_error(validation_predictions, validation_targets))\n",
        "    # Occasionally print the current loss.\n",
        "    print(\"  period %02d : %0.2f\" % (period, training_root_mean_squared_error))\n",
        "    # Add the loss metrics from this period to our list.\n",
        "    training_rmse.append(training_root_mean_squared_error)\n",
        "    validation_rmse.append(validation_root_mean_squared_error)\n",
        "  print(\"Model training finished.\")\n",
        "\n",
        "  \n",
        "  # Output a graph of loss metrics over periods.\n",
        "  plt.ylabel(\"RMSE\")\n",
        "  plt.xlabel(\"Periods\")\n",
        "  plt.title(\"Root Mean Squared Error vs. Periods\")\n",
        "  plt.tight_layout()\n",
        "  plt.plot(training_rmse, label=\"training\")\n",
        "  plt.plot(validation_rmse, label=\"validation\")\n",
        "  plt.legend()\n",
        "\n",
        "  return linear_regressor"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "1Cdr02tLIK_Q",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 622
        },
        "outputId": "69a62857-abf4-4dae-a3d9-0919559fafa2"
      },
      "cell_type": "code",
      "source": [
        "_ = train_model(\n",
        "    learning_rate=1.0,\n",
        "    steps=500,\n",
        "    batch_size=100,\n",
        "    feature_columns=construct_feature_columns(training_examples),\n",
        "    training_examples=training_examples,\n",
        "    training_targets=training_targets,\n",
        "    validation_examples=validation_examples,\n",
        "    validation_targets=validation_targets)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Training model...\n",
            "RMSE (on training data):\n",
            "  period 00 : 326.23\n",
            "  period 01 : 168.80\n",
            "  period 02 : 239.19\n",
            "  period 03 : 168.50\n",
            "  period 04 : 189.45\n",
            "  period 05 : 126.55\n",
            "  period 06 : 130.68\n",
            "  period 07 : 129.37\n",
            "  period 08 : 122.32\n",
            "  period 09 : 135.77\n",
            "Model training finished.\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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sD4dKj9gdR0REpFlSgalnToeDeP8kALbn6r5IIiIivqAC4wOdYzoAsEV3phYR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\nwIiIiEjS+f/FW3oG1L3yEAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f09f885bad0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "i4lGvqajDWlw",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## One-Hot Encoding for Discrete Features\n",
        "\n",
        "Discrete (i.e. strings, enumerations, integers) features are usually converted into families of binary features before training a logistic regression model.\n",
        "\n",
        "For example, suppose we created a synthetic feature that can take any of the values `0`, `1` or `2`, and that we have a few training points:\n",
        "\n",
        "| # | feature_value |\n",
        "|---|---------------|\n",
        "| 0 |             2 |\n",
        "| 1 |             0 |\n",
        "| 2 |             1 |\n",
        "\n",
        "For each possible categorical value, we make a new **binary** feature of **real values** that can take one of just two possible values: 1.0 if the example has that value, and 0.0 if not. In the example above, the categorical feature would be converted into three features, and the training points now look like:\n",
        "\n",
        "| # | feature_value_0 | feature_value_1 | feature_value_2 |\n",
        "|---|-----------------|-----------------|-----------------|\n",
        "| 0 |             0.0 |             0.0 |             1.0 |\n",
        "| 1 |             1.0 |             0.0 |             0.0 |\n",
        "| 2 |             0.0 |             1.0 |             0.0 |"
      ]
    },
    {
      "metadata": {
        "id": "KnssXowblKm7",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Bucketized (Binned) Features\n",
        "\n",
        "Bucketization is also known as binning.\n",
        "\n",
        "We can bucketize `population` into the following 3 buckets (for instance):\n",
        "- `bucket_0` (`< 5000`): corresponding to less populated blocks\n",
        "- `bucket_1` (`5000 - 25000`): corresponding to mid populated blocks\n",
        "- `bucket_2` (`> 25000`): corresponding to highly populated blocks\n",
        "\n",
        "Given the preceding bucket definitions, the following `population` vector:\n",
        "\n",
        "    [[10001], [42004], [2500], [18000]]\n",
        "\n",
        "becomes the following bucketized feature vector:\n",
        "\n",
        "    [[1], [2], [0], [1]]\n",
        "\n",
        "The feature values are now the bucket indices. Note that these indices are considered to be discrete features. Typically, these will be further converted in one-hot representations as above, but this is done transparently.\n",
        "\n",
        "To define feature columns for bucketized features, instead of using `numeric_column`, we can use [`bucketized_column`](https://www.tensorflow.org/api_docs/python/tf/feature_column/bucketized_column), which takes a numeric column as input and transforms it to a bucketized feature using the bucket boundaries specified in the `boundardies` argument. The following code defines bucketized feature columns for `households` and `longitude`; the `get_quantile_based_boundaries` function calculates boundaries based on quantiles, so that each bucket contains an equal number of elements."
      ]
    },
    {
      "metadata": {
        "id": "cc9qZrtRy-ED",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def get_quantile_based_boundaries(feature_values, num_buckets):\n",
        "  boundaries = np.arange(1.0, num_buckets) / num_buckets\n",
        "  quantiles = feature_values.quantile(boundaries)\n",
        "  return [quantiles[q] for q in quantiles.keys()]\n",
        "\n",
        "# Divide households into 7 buckets.\n",
        "households = tf.feature_column.numeric_column(\"households\")\n",
        "bucketized_households = tf.feature_column.bucketized_column(\n",
        "  households, boundaries=get_quantile_based_boundaries(\n",
        "    california_housing_dataframe[\"households\"], 7))\n",
        "\n",
        "# Divide longitude into 10 buckets.\n",
        "longitude = tf.feature_column.numeric_column(\"longitude\")\n",
        "bucketized_longitude = tf.feature_column.bucketized_column(\n",
        "  longitude, boundaries=get_quantile_based_boundaries(\n",
        "    california_housing_dataframe[\"longitude\"], 10))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "U-pQDAa0MeN3",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Task 1: Train the Model on Bucketized Feature Columns\n",
        "**Bucketize all the real valued features in our example, train the model and see if the results improve.**\n",
        "\n",
        "In the preceding code block, two real valued columns (namely `households` and `longitude`) have been transformed into bucketized feature columns. Your task is to bucketize the rest of the columns, then run the code to train the model. There are various heuristics to find the range of the buckets. This exercise uses a quantile-based technique, which chooses the bucket boundaries in such a way that each bucket has the same number of examples."
      ]
    },
    {
      "metadata": {
        "id": "YFXV9lyMLedy",
        "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",
        "  households = tf.feature_column.numeric_column(\"households\")\n",
        "  longitude = tf.feature_column.numeric_column(\"longitude\")\n",
        "  latitude = tf.feature_column.numeric_column(\"latitude\")\n",
        "  housing_median_age = tf.feature_column.numeric_column(\"housing_median_age\")\n",
        "  median_income = tf.feature_column.numeric_column(\"median_income\")\n",
        "  rooms_per_person = tf.feature_column.numeric_column(\"rooms_per_person\")\n",
        "  \n",
        "  # Divide households into 7 buckets.\n",
        "  bucketized_households = tf.feature_column.bucketized_column(\n",
        "    households, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"households\"], 7))\n",
        "\n",
        "  # Divide longitude into 10 buckets.\n",
        "  bucketized_longitude = tf.feature_column.bucketized_column(\n",
        "    longitude, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"longitude\"], 10))\n",
        "\n",
        "  #\n",
        "  # YOUR CODE HERE: bucketize the following columns, following the example above:\n",
        "  #\n",
        "  bucketized_latitude = tf.feature_column.bucketized_column(\n",
        "    latitude, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"latitude\"], 10))\n",
        "  bucketized_housing_median_age = tf.feature_column.bucketized_column(\n",
        "    housing_median_age, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"housing_median_age\"], 10))\n",
        "  bucketized_median_income = tf.feature_column.bucketized_column(\n",
        "    median_income, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"median_income\"], 7))\n",
        "  bucketized_rooms_per_person = tf.feature_column.bucketized_column(\n",
        "    rooms_per_person, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"rooms_per_person\"], 7))\n",
        "  \n",
        "  feature_columns = set([\n",
        "    bucketized_longitude,\n",
        "    bucketized_latitude,\n",
        "    bucketized_housing_median_age,\n",
        "    bucketized_households,\n",
        "    bucketized_median_income,\n",
        "    bucketized_rooms_per_person])\n",
        "  \n",
        "  return feature_columns\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "0FfUytOTNJhL",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 622
        },
        "outputId": "e5a7eaa7-2ea3-4427-cba9-8b48102e10cb"
      },
      "cell_type": "code",
      "source": [
        "_ = train_model(\n",
        "    learning_rate=1.0,\n",
        "    steps=500,\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)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Training model...\n",
            "RMSE (on training data):\n",
            "  period 00 : 169.16\n",
            "  period 01 : 142.91\n",
            "  period 02 : 126.47\n",
            "  period 03 : 115.44\n",
            "  period 04 : 107.59\n",
            "  period 05 : 101.82\n",
            "  period 06 : 97.46\n",
            "  period 07 : 93.94\n",
            "  period 08 : 91.08\n",
            "  period 09 : 88.73\n",
            "Model training finished.\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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LemO5pDf1YzHnwLQ0emsddw/2p7zCyJp98QDYWdkS7j+CkspStlzaYeYKhRBC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\nQgghhMg4UsAIIYQQIuP8f+rhryQJGo/rAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f09ef266350>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "ZTDHHM61NPTw",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Solution\n",
        "\n",
        "Click below for a solution."
      ]
    },
    {
      "metadata": {
        "id": "JQHnUhL_NRwA",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "You may be wondering how to determine how many buckets to use. That is of course data-dependent. Here, we just selected arbitrary values so as to obtain a not-too-large model."
      ]
    },
    {
      "metadata": {
        "id": "Ro5civQ3Ngh_",
        "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",
        "  households = tf.feature_column.numeric_column(\"households\")\n",
        "  longitude = tf.feature_column.numeric_column(\"longitude\")\n",
        "  latitude = tf.feature_column.numeric_column(\"latitude\")\n",
        "  housing_median_age = tf.feature_column.numeric_column(\"housing_median_age\")\n",
        "  median_income = tf.feature_column.numeric_column(\"median_income\")\n",
        "  rooms_per_person = tf.feature_column.numeric_column(\"rooms_per_person\")\n",
        "  \n",
        "  # Divide households into 7 buckets.\n",
        "  bucketized_households = tf.feature_column.bucketized_column(\n",
        "    households, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"households\"], 7))\n",
        "\n",
        "  # Divide longitude into 10 buckets.\n",
        "  bucketized_longitude = tf.feature_column.bucketized_column(\n",
        "    longitude, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"longitude\"], 10))\n",
        "  \n",
        "  # Divide latitude into 10 buckets.\n",
        "  bucketized_latitude = tf.feature_column.bucketized_column(\n",
        "    latitude, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"latitude\"], 10))\n",
        "\n",
        "  # Divide housing_median_age into 7 buckets.\n",
        "  bucketized_housing_median_age = tf.feature_column.bucketized_column(\n",
        "    housing_median_age, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"housing_median_age\"], 7))\n",
        "  \n",
        "  # Divide median_income into 7 buckets.\n",
        "  bucketized_median_income = tf.feature_column.bucketized_column(\n",
        "    median_income, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"median_income\"], 7))\n",
        "  \n",
        "  # Divide rooms_per_person into 7 buckets.\n",
        "  bucketized_rooms_per_person = tf.feature_column.bucketized_column(\n",
        "    rooms_per_person, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"rooms_per_person\"], 7))\n",
        "  \n",
        "  feature_columns = set([\n",
        "    bucketized_longitude,\n",
        "    bucketized_latitude,\n",
        "    bucketized_housing_median_age,\n",
        "    bucketized_households,\n",
        "    bucketized_median_income,\n",
        "    bucketized_rooms_per_person])\n",
        "  \n",
        "  return feature_columns"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "RNgfYk6OO8Sy",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "_ = train_model(\n",
        "    learning_rate=1.0,\n",
        "    steps=500,\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)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "AFJ1qoZPlQcs",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Feature Crosses\n",
        "\n",
        "Crossing two (or more) features is a clever way to learn non-linear relations using a linear model. In our problem, if we just use the feature `latitude` for learning, the model might learn that city blocks at a particular latitude (or within a particular range of latitudes since we have bucketized it) are more likely to be expensive than others. Similarly for the feature `longitude`. However, if we cross `longitude` by `latitude`, the crossed feature represents a well defined city block. If the model learns that certain city blocks (within range of latitudes and longitudes) are more likely to be more expensive than others, it is a stronger signal than two features considered individually.\n",
        "\n",
        "Currently, the feature columns API only supports discrete features for crosses. To cross two continuous values, like `latitude` or `longitude`, we can bucketize them.\n",
        "\n",
        "If we cross the `latitude` and `longitude` features (supposing, for example, that `longitude` was bucketized into `2` buckets, while `latitude` has `3` buckets), we actually get six crossed binary features. Each of these features will get its own separate weight when we train the model."
      ]
    },
    {
      "metadata": {
        "id": "-Rk0c1oTYaVH",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Task 2: Train the Model Using Feature Crosses\n",
        "\n",
        "**Add a feature cross of `longitude` and `latitude` to your model, train it, and determine whether the results improve.**\n",
        "\n",
        "Refer to the TensorFlow API docs for [`crossed_column()`](https://www.tensorflow.org/api_docs/python/tf/feature_column/crossed_column) to build the feature column for your cross. Use a `hash_bucket_size` of `1000`."
      ]
    },
    {
      "metadata": {
        "id": "-eYiVEGeYhUi",
        "colab_type": "code",
        "cellView": "both",
        "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",
        "  households = tf.feature_column.numeric_column(\"households\")\n",
        "  longitude = tf.feature_column.numeric_column(\"longitude\")\n",
        "  latitude = tf.feature_column.numeric_column(\"latitude\")\n",
        "  housing_median_age = tf.feature_column.numeric_column(\"housing_median_age\")\n",
        "  median_income = tf.feature_column.numeric_column(\"median_income\")\n",
        "  rooms_per_person = tf.feature_column.numeric_column(\"rooms_per_person\")\n",
        "  \n",
        "  # Divide households into 7 buckets.\n",
        "  bucketized_households = tf.feature_column.bucketized_column(\n",
        "    households, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"households\"], 7))\n",
        "\n",
        "  # Divide longitude into 10 buckets.\n",
        "  bucketized_longitude = tf.feature_column.bucketized_column(\n",
        "    longitude, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"longitude\"], 10))\n",
        "  \n",
        "  # Divide latitude into 10 buckets.\n",
        "  bucketized_latitude = tf.feature_column.bucketized_column(\n",
        "    latitude, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"latitude\"], 10))\n",
        "\n",
        "  # Divide housing_median_age into 7 buckets.\n",
        "  bucketized_housing_median_age = tf.feature_column.bucketized_column(\n",
        "    housing_median_age, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"housing_median_age\"], 7))\n",
        "  \n",
        "  # Divide median_income into 7 buckets.\n",
        "  bucketized_median_income = tf.feature_column.bucketized_column(\n",
        "    median_income, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"median_income\"], 7))\n",
        "  \n",
        "  # Divide rooms_per_person into 7 buckets.\n",
        "  bucketized_rooms_per_person = tf.feature_column.bucketized_column(\n",
        "    rooms_per_person, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"rooms_per_person\"], 7))\n",
        "  \n",
        "  # YOUR CODE HERE: Make a feature column for the long_x_lat feature cross\n",
        "  long_x_lat = tf.feature_column.crossed_column([bucketized_longitude, bucketized_latitude], 1000)\n",
        "  \n",
        "  feature_columns = set([\n",
        "    bucketized_longitude,\n",
        "    bucketized_latitude,\n",
        "    bucketized_housing_median_age,\n",
        "    bucketized_households,\n",
        "    bucketized_median_income,\n",
        "    bucketized_rooms_per_person,\n",
        "    long_x_lat])\n",
        "  \n",
        "  return feature_columns"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "xZuZMp3EShkM",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 622
        },
        "outputId": "a771304a-2aa4-414c-b68d-f45b323ee173"
      },
      "cell_type": "code",
      "source": [
        "_ = train_model(\n",
        "    learning_rate=1.0,\n",
        "    steps=500,\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)"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Training model...\n",
            "RMSE (on training data):\n",
            "  period 00 : 162.84\n",
            "  period 01 : 134.67\n",
            "  period 02 : 117.68\n",
            "  period 03 : 106.57\n",
            "  period 04 : 98.72\n",
            "  period 05 : 93.08\n",
            "  period 06 : 88.73\n",
            "  period 07 : 85.46\n",
            "  period 08 : 82.74\n",
            "  period 09 : 80.47\n",
            "Model training finished.\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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o4xNO+7Boks8c5+e0XY4sT0REpFpTgKlCLRoG0Kx+LeITMjiQnA3AoMh+WAwL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\nEGlHChghhBBCpB0pYIQQQgiRdv4/VQhMnSc2GFoAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f09e0e1e4d0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "0i7vGo9PTaZl",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Solution\n",
        "\n",
        "Click below for the solution."
      ]
    },
    {
      "metadata": {
        "id": "3tAWu8qSTe2v",
        "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",
        "  households = tf.feature_column.numeric_column(\"households\")\n",
        "  longitude = tf.feature_column.numeric_column(\"longitude\")\n",
        "  latitude = tf.feature_column.numeric_column(\"latitude\")\n",
        "  housing_median_age = tf.feature_column.numeric_column(\"housing_median_age\")\n",
        "  median_income = tf.feature_column.numeric_column(\"median_income\")\n",
        "  rooms_per_person = tf.feature_column.numeric_column(\"rooms_per_person\")\n",
        "  \n",
        "  # Divide households into 7 buckets.\n",
        "  bucketized_households = tf.feature_column.bucketized_column(\n",
        "    households, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"households\"], 7))\n",
        "\n",
        "  # Divide longitude into 10 buckets.\n",
        "  bucketized_longitude = tf.feature_column.bucketized_column(\n",
        "    longitude, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"longitude\"], 10))\n",
        "  \n",
        "  # Divide latitude into 10 buckets.\n",
        "  bucketized_latitude = tf.feature_column.bucketized_column(\n",
        "    latitude, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"latitude\"], 10))\n",
        "\n",
        "  # Divide housing_median_age into 7 buckets.\n",
        "  bucketized_housing_median_age = tf.feature_column.bucketized_column(\n",
        "    housing_median_age, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"housing_median_age\"], 7))\n",
        "  \n",
        "  # Divide median_income into 7 buckets.\n",
        "  bucketized_median_income = tf.feature_column.bucketized_column(\n",
        "    median_income, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"median_income\"], 7))\n",
        "  \n",
        "  # Divide rooms_per_person into 7 buckets.\n",
        "  bucketized_rooms_per_person = tf.feature_column.bucketized_column(\n",
        "    rooms_per_person, boundaries=get_quantile_based_boundaries(\n",
        "      training_examples[\"rooms_per_person\"], 7))\n",
        "  \n",
        "  # YOUR CODE HERE: Make a feature column for the long_x_lat feature cross\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",
        "    bucketized_longitude,\n",
        "    bucketized_latitude,\n",
        "    bucketized_housing_median_age,\n",
        "    bucketized_households,\n",
        "    bucketized_median_income,\n",
        "    bucketized_rooms_per_person,\n",
        "    long_x_lat])\n",
        "  \n",
        "  return feature_columns"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "-_vvNYIyTtPC",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "_ = train_model(\n",
        "    learning_rate=1.0,\n",
        "    steps=500,\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)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "ymlHJ-vrhLZw",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Optional Challenge: Try Out More Synthetic Features\n",
        "\n",
        "So far, we've tried simple bucketized columns and feature crosses, but there are many more combinations that could potentially improve the results. For example, you could cross multiple columns. What happens if you vary the number of buckets? What other synthetic features can you think of? Do they improve the model?"
      ]
    }
  ]
}