feature_sets.ipynb

{
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  "metadata": {
    "colab": {
      "name": "feature_sets.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "JndnmDMp66FL",
        "IGINhMIJ5Wyt",
        "pZa8miwu6_tQ"
      ],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/amemon/testgit/blob/master/feature_sets.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JndnmDMp66FL",
        "colab_type": "text"
      },
      "source": [
        "#### Copyright 2017 Google LLC."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hMqWDc_m6rUC",
        "colab_type": "code",
        "cellView": "both",
        "colab": {}
      },
      "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": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zbIgBK-oXHO7",
        "colab_type": "text"
      },
      "source": [
        "# Feature Sets"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bL04rAQwH3pH",
        "colab_type": "text"
      },
      "source": [
        "**Learning Objective:** Create a minimal set of features that performs just as well as a more complex feature set"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F8Hci6tAH3pH",
        "colab_type": "text"
      },
      "source": [
        "So far, we've thrown all of our features into the model. Models with fewer features use fewer resources and are easier to maintain. Let's see if we can build a model on a minimal set of housing features that will perform equally as well as one that uses all the features in the data set."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F5ZjVwK_qOyR",
        "colab_type": "text"
      },
      "source": [
        "## Setup\n",
        "\n",
        "As before, let's load and prepare the California housing data."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SrOYRILAH3pJ",
        "colab_type": "code",
        "colab": {}
      },
      "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",
        "%tensorflow_version 1.x\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": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dGnXo7flH3pM",
        "colab_type": "code",
        "colab": {}
      },
      "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": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jLXC8y4AqsIy",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "ee1dc563-4344-496c-a894-71ecd965a36e"
      },
      "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": {
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              "<div>\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <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",
              "      <th>median_income</th>\n",
              "      <th>rooms_per_person</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>12000.0</td>\n",
              "      <td>12000.0</td>\n",
              "      <td>12000.0</td>\n",
              "      <td>12000.0</td>\n",
              "      <td>12000.0</td>\n",
              "      <td>12000.0</td>\n",
              "      <td>12000.0</td>\n",
              "      <td>12000.0</td>\n",
              "      <td>12000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>35.6</td>\n",
              "      <td>-119.6</td>\n",
              "      <td>28.6</td>\n",
              "      <td>2644.1</td>\n",
              "      <td>538.7</td>\n",
              "      <td>1431.2</td>\n",
              "      <td>501.1</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>12.5</td>\n",
              "      <td>2187.9</td>\n",
              "      <td>419.4</td>\n",
              "      <td>1170.1</td>\n",
              "      <td>384.1</td>\n",
              "      <td>1.9</td>\n",
              "      <td>1.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>32.5</td>\n",
              "      <td>-124.3</td>\n",
              "      <td>2.0</td>\n",
              "      <td>8.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>3.0</td>\n",
              "      <td>1.0</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>1458.0</td>\n",
              "      <td>296.0</td>\n",
              "      <td>788.0</td>\n",
              "      <td>281.0</td>\n",
              "      <td>2.6</td>\n",
              "      <td>1.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>34.2</td>\n",
              "      <td>-118.5</td>\n",
              "      <td>29.0</td>\n",
              "      <td>2136.0</td>\n",
              "      <td>435.0</td>\n",
              "      <td>1166.0</td>\n",
              "      <td>410.0</td>\n",
              "      <td>3.6</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>3145.2</td>\n",
              "      <td>648.2</td>\n",
              "      <td>1720.0</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>32627.0</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",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "       latitude  longitude  ...  median_income  rooms_per_person\n",
              "count   12000.0    12000.0  ...        12000.0           12000.0\n",
              "mean       35.6     -119.6  ...            3.9               2.0\n",
              "std         2.1        2.0  ...            1.9               1.2\n",
              "min        32.5     -124.3  ...            0.5               0.1\n",
              "25%        33.9     -121.8  ...            2.6               1.5\n",
              "50%        34.2     -118.5  ...            3.6               1.9\n",
              "75%        37.7     -118.0  ...            4.8               2.3\n",
              "max        42.0     -114.3  ...           15.0              55.2\n",
              "\n",
              "[8 rows x 9 columns]"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Validation examples summary:\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <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",
              "      <th>median_income</th>\n",
              "      <th>rooms_per_person</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "      <td>5000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>35.6</td>\n",
              "      <td>-119.6</td>\n",
              "      <td>28.6</td>\n",
              "      <td>2642.7</td>\n",
              "      <td>541.0</td>\n",
              "      <td>1425.8</td>\n",
              "      <td>501.4</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>12.7</td>\n",
              "      <td>2161.0</td>\n",
              "      <td>426.6</td>\n",
              "      <td>1092.7</td>\n",
              "      <td>385.7</td>\n",
              "      <td>1.9</td>\n",
              "      <td>1.0</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>0.0</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>1469.8</td>\n",
              "      <td>298.0</td>\n",
              "      <td>793.8</td>\n",
              "      <td>282.0</td>\n",
              "      <td>2.6</td>\n",
              "      <td>1.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>34.3</td>\n",
              "      <td>-118.5</td>\n",
              "      <td>29.0</td>\n",
              "      <td>2109.5</td>\n",
              "      <td>430.0</td>\n",
              "      <td>1168.0</td>\n",
              "      <td>406.0</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>3165.0</td>\n",
              "      <td>648.2</td>\n",
              "      <td>1722.0</td>\n",
              "      <td>603.0</td>\n",
              "      <td>4.7</td>\n",
              "      <td>2.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>41.9</td>\n",
              "      <td>-114.5</td>\n",
              "      <td>52.0</td>\n",
              "      <td>37937.0</td>\n",
              "      <td>5471.0</td>\n",
              "      <td>16122.0</td>\n",
              "      <td>5189.0</td>\n",
              "      <td>15.0</td>\n",
              "      <td>34.2</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "       latitude  longitude  ...  median_income  rooms_per_person\n",
              "count    5000.0     5000.0  ...         5000.0            5000.0\n",
              "mean       35.6     -119.6  ...            3.9               2.0\n",
              "std         2.1        2.0  ...            1.9               1.0\n",
              "min        32.5     -124.3  ...            0.5               0.0\n",
              "25%        33.9     -121.8  ...            2.6               1.5\n",
              "50%        34.3     -118.5  ...            3.5               1.9\n",
              "75%        37.7     -118.0  ...            4.7               2.3\n",
              "max        41.9     -114.5  ...           15.0              34.2\n",
              "\n",
              "[8 rows x 9 columns]"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Training targets summary:\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
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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>12000.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>207.7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>116.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>15.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>119.9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>180.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>265.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>500.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "       median_house_value\n",
              "count             12000.0\n",
              "mean                207.7\n",
              "std                 116.3\n",
              "min                  15.0\n",
              "25%                 119.9\n",
              "50%                 180.5\n",
              "75%                 265.0\n",
              "max                 500.0"
            ]
          },
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            "tags": []
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        {
          "output_type": "stream",
          "text": [
            "Validation targets summary:\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<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>206.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>115.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>17.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>118.8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>179.8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>265.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>500.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "       median_house_value\n",
              "count              5000.0\n",
              "mean                206.4\n",
              "std                 115.2\n",
              "min                  17.5\n",
              "25%                 118.8\n",
              "50%                 179.8\n",
              "75%                 265.0\n",
              "max                 500.0"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hLvmkugKLany",
        "colab_type": "text"
      },
      "source": [
        "## Task 1: Develop a Good Feature Set\n",
        "\n",
        "**What's the best performance you can get with just 2 or 3 features?**\n",
        "\n",
        "A **correlation matrix** shows pairwise correlations, both for each feature compared to the target and for each feature compared to other features.\n",
        "\n",
        "Here, correlation is defined as the [Pearson correlation coefficient](https://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient).  You don't have to understand the mathematical details for this exercise.\n",
        "\n",
        "Correlation values have the following meanings:\n",
        "\n",
        "  * `-1.0`: perfect negative correlation\n",
        "  * `0.0`: no correlation\n",
        "  * `1.0`: perfect positive correlation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UzoZUSdLIolF",
        "colab_type": "code",
        "cellView": "both",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 359
        },
        "outputId": "894569ea-0704-41f5-fade-4d3b2cb94906"
      },
      "source": [
        "correlation_dataframe = training_examples.copy()\n",
        "correlation_dataframe[\"target\"] = training_targets[\"median_house_value\"]\n",
        "\n",
        "correlation_dataframe.corr()"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <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",
              "      <th>median_income</th>\n",
              "      <th>rooms_per_person</th>\n",
              "      <th>target</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>latitude</th>\n",
              "      <td>1.0</td>\n",
              "      <td>-0.9</td>\n",
              "      <td>0.0</td>\n",
              "      <td>-0.0</td>\n",
              "      <td>-0.1</td>\n",
              "      <td>-0.1</td>\n",
              "      <td>-0.1</td>\n",
              "      <td>-0.1</td>\n",
              "      <td>0.1</td>\n",
              "      <td>-0.1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>longitude</th>\n",
              "      <td>-0.9</td>\n",
              "      <td>1.0</td>\n",
              "      <td>-0.1</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.1</td>\n",
              "      <td>0.1</td>\n",
              "      <td>0.1</td>\n",
              "      <td>-0.0</td>\n",
              "      <td>-0.1</td>\n",
              "      <td>-0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>housing_median_age</th>\n",
              "      <td>0.0</td>\n",
              "      <td>-0.1</td>\n",
              "      <td>1.0</td>\n",
              "      <td>-0.4</td>\n",
              "      <td>-0.3</td>\n",
              "      <td>-0.3</td>\n",
              "      <td>-0.3</td>\n",
              "      <td>-0.1</td>\n",
              "      <td>-0.1</td>\n",
              "      <td>0.1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>total_rooms</th>\n",
              "      <td>-0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>-0.4</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.9</td>\n",
              "      <td>0.9</td>\n",
              "      <td>0.9</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0.1</td>\n",
              "      <td>0.1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>total_bedrooms</th>\n",
              "      <td>-0.1</td>\n",
              "      <td>0.1</td>\n",
              "      <td>-0.3</td>\n",
              "      <td>0.9</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.9</td>\n",
              "      <td>1.0</td>\n",
              "      <td>-0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>population</th>\n",
              "      <td>-0.1</td>\n",
              "      <td>0.1</td>\n",
              "      <td>-0.3</td>\n",
              "      <td>0.9</td>\n",
              "      <td>0.9</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.9</td>\n",
              "      <td>0.0</td>\n",
              "      <td>-0.1</td>\n",
              "      <td>-0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>households</th>\n",
              "      <td>-0.1</td>\n",
              "      <td>0.1</td>\n",
              "      <td>-0.3</td>\n",
              "      <td>0.9</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.9</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>-0.0</td>\n",
              "      <td>0.1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>median_income</th>\n",
              "      <td>-0.1</td>\n",
              "      <td>-0.0</td>\n",
              "      <td>-0.1</td>\n",
              "      <td>0.2</td>\n",
              "      <td>-0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0.7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>rooms_per_person</th>\n",
              "      <td>0.1</td>\n",
              "      <td>-0.1</td>\n",
              "      <td>-0.1</td>\n",
              "      <td>0.1</td>\n",
              "      <td>0.0</td>\n",
              "      <td>-0.1</td>\n",
              "      <td>-0.0</td>\n",
              "      <td>0.2</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>target</th>\n",
              "      <td>-0.1</td>\n",
              "      <td>-0.0</td>\n",
              "      <td>0.1</td>\n",
              "      <td>0.1</td>\n",
              "      <td>0.0</td>\n",
              "      <td>-0.0</td>\n",
              "      <td>0.1</td>\n",
              "      <td>0.7</td>\n",
              "      <td>0.2</td>\n",
              "      <td>1.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                    latitude  longitude  ...  rooms_per_person  target\n",
              "latitude                 1.0       -0.9  ...               0.1    -0.1\n",
              "longitude               -0.9        1.0  ...              -0.1    -0.0\n",
              "housing_median_age       0.0       -0.1  ...              -0.1     0.1\n",
              "total_rooms             -0.0        0.0  ...               0.1     0.1\n",
              "total_bedrooms          -0.1        0.1  ...               0.0     0.0\n",
              "population              -0.1        0.1  ...              -0.1    -0.0\n",
              "households              -0.1        0.1  ...              -0.0     0.1\n",
              "median_income           -0.1       -0.0  ...               0.2     0.7\n",
              "rooms_per_person         0.1       -0.1  ...               1.0     0.2\n",
              "target                  -0.1       -0.0  ...               0.2     1.0\n",
              "\n",
              "[10 rows x 10 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RQpktkNpia2P",
        "colab_type": "text"
      },
      "source": [
        "Features that have strong positive or negative correlations with the target will add information to our model. We can use the correlation matrix to find such strongly correlated features.\n",
        "\n",
        "We'd also like to have features that aren't so strongly correlated with each other, so that they add independent information.\n",
        "\n",
        "Use this information to try removing features.  You can also try developing additional synthetic features, such as ratios of two raw features.\n",
        "\n",
        "For convenience, we've included the training code from the previous exercise."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bjR5jWpFr2xs",
        "colab_type": "code",
        "colab": {}
      },
      "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": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jsvKHzRciH9T",
        "colab_type": "code",
        "colab": {}
      },
      "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": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g3kjQV9WH3pb",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def train_model(\n",
        "    learning_rate,\n",
        "    steps,\n",
        "    batch_size,\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",
        "    batch_size: A non-zero `int`, the batch size.\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.GradientDescentOptimizer(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=construct_feature_columns(training_examples),\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\"], \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",
        "    \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": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "varLu7RNH3pf",
        "colab_type": "text"
      },
      "source": [
        "Spend 5 minutes searching for a good set of features and training parameters. Then check the solution to see what we chose. Don't forget that different features may require different learning parameters."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DSgUxRIlH3pg",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 535
        },
        "outputId": "bc9385d7-267f-4efd-92f2-cce9a233da2c"
      },
      "source": [
        "#\n",
        "# Your code here: add your features of choice as a list of quoted strings.\n",
        "#\n",
        "minimal_features = [\"median_income\",\"rooms_per_person\"\n",
        "]\n",
        "\n",
        "assert minimal_features, \"You must select at least one feature!\"\n",
        "\n",
        "minimal_training_examples = training_examples[minimal_features]\n",
        "minimal_validation_examples = validation_examples[minimal_features]\n",
        "\n",
        "#\n",
        "# Don't forget to adjust these parameters.\n",
        "#\n",
        "train_model(\n",
        "    learning_rate=0.01,\n",
        "    steps=600,\n",
        "    batch_size=6,\n",
        "    training_examples=minimal_training_examples,\n",
        "    training_targets=training_targets,\n",
        "    validation_examples=minimal_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 : 224.54\n",
            "  period 01 : 211.20\n",
            "  period 02 : 198.02\n",
            "  period 03 : 185.07\n",
            "  period 04 : 172.34\n",
            "  period 05 : 159.92\n",
            "  period 06 : 147.93\n",
            "  period 07 : 136.42\n",
            "  period 08 : 125.69\n",
            "  period 09 : 115.61\n",
            "Model training finished.\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tensorflow_estimator.python.estimator.canned.linear.LinearRegressor at 0x7fe5b7d704e0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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USqlkSpORSjxuHlBrIPRaAznL4rnwTT48/zbzOvqSMb0bL/0YTu+pGzl96Yaz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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IGINhMIJ5Wyt",
        "colab_type": "text"
      },
      "source": [
        "### Solution\n",
        "\n",
        "Click below for a solution."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BAGoXFPZ5ZE3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "minimal_features = [\n",
        "  \"median_income\",\n",
        "  \"latitude\",\n",
        "]\n",
        "\n",
        "minimal_training_examples = training_examples[minimal_features]\n",
        "minimal_validation_examples = validation_examples[minimal_features]\n",
        "\n",
        "_ = train_model(\n",
        "    learning_rate=0.01,\n",
        "    steps=500,\n",
        "    batch_size=5,\n",
        "    training_examples=minimal_training_examples,\n",
        "    training_targets=training_targets,\n",
        "    validation_examples=minimal_validation_examples,\n",
        "    validation_targets=validation_targets)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RidI9YhKOiY2",
        "colab_type": "text"
      },
      "source": [
        "## Task 2: Make Better Use of Latitude\n",
        "\n",
        "Plotting `latitude` vs. `median_house_value` shows that there really isn't a linear relationship there.\n",
        "\n",
        "Instead, there are a couple of peaks, which roughly correspond to Los Angeles and San Francisco."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hfGUKj2IR_F1",
        "colab_type": "code",
        "cellView": "both",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "a9b3c507-f040-4ef8-edf6-1d87ba30b3b0"
      },
      "source": [
        "plt.scatter(training_examples[\"latitude\"], training_targets[\"median_house_value\"])"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7fe5b82a6908>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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JdwH4HQB1/ff3ASgzxmb0398CwN3dAoCzAKC/fkl/fwtE9DARHSOiY+fPu1sItaNSrdu+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\ny1ej3pXAIEJTF2/5OoCdG1d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13lNj3GWmNA+uXthm/PyYClVrLHBNNIN1JyjZTuxWGAdd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\nYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6N0p91k2iFCP",
        "colab_type": "text"
      },
      "source": [
        "**Try creating some synthetic features that do a better job with latitude.**\n",
        "\n",
        "For example, you could have a feature that maps `latitude` to a value of `|latitude - 38|`, and call this `distance_from_san_francisco`.\n",
        "\n",
        "Or you could break the space into 10 different buckets.  `latitude_32_to_33`, `latitude_33_to_34`, etc., each showing a value of `1.0` if `latitude` is within that bucket range and a value of `0.0` otherwise.\n",
        "\n",
        "Use the correlation matrix to help guide development, and then add them to your model if you find something that looks good.\n",
        "\n",
        "What's the best validation performance you can get?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wduJ2B28yMFl",
        "colab_type": "code",
        "cellView": "form",
        "colab": {}
      },
      "source": [
        "#\n",
        "# YOUR CODE HERE: Train on a new data set that includes synthetic features based on latitude.\n",
        "#"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pZa8miwu6_tQ",
        "colab_type": "text"
      },
      "source": [
        "### Solution\n",
        "\n",
        "Click below for a solution."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PzABdyjq7IZU",
        "colab_type": "text"
      },
      "source": [
        "Aside from `latitude`, we'll also keep `median_income`, to compare with the previous results.\n",
        "\n",
        "We decided to bucketize the latitude. This is fairly straightforward in Pandas using `Series.apply`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xdVF8siZ7Lup",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        },
        "outputId": "84f605fe-c570-458d-d595-c7249a7900a6"
      },
      "source": [
        "def select_and_transform_features(source_df):\n",
        "  LATITUDE_RANGES = zip(range(32, 44), range(33, 45))\n",
        "  selected_examples = pd.DataFrame()\n",
        "  selected_examples[\"median_income\"] = source_df[\"median_income\"]\n",
        "  for r in LATITUDE_RANGES:\n",
        "    selected_examples[\"latitude_%d_to_%d\" % r] = source_df[\"latitude\"].apply(\n",
        "      lambda l: 1.0 if l >= r[0] and l < r[1] else 0.0)\n",
        "  \n",
        "  #print (selected_examples.columns)\n",
        "  #print (selected_examples.iloc[0:10,7:8])\n",
        "  return selected_examples\n",
        "\n",
        "selected_training_examples = select_and_transform_features(training_examples)\n",
        "selected_validation_examples = select_and_transform_features(validation_examples)\n",
        "print (selected_training_examples.columns)"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Index(['median_income', 'latitude_32_to_33', 'latitude_33_to_34',\n",
            "       'latitude_34_to_35', 'latitude_35_to_36', 'latitude_36_to_37',\n",
            "       'latitude_37_to_38', 'latitude_38_to_39', 'latitude_39_to_40',\n",
            "       'latitude_40_to_41', 'latitude_41_to_42', 'latitude_42_to_43',\n",
            "       'latitude_43_to_44'],\n",
            "      dtype='object')\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U4iAdY6t7Pkh",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 518
        },
        "outputId": "cd94cc02-fe18-407c-9f29-5321624212b8"
      },
      "source": [
        "_ = train_model(\n",
        "    learning_rate=0.01,\n",
        "    steps=500,\n",
        "    batch_size=5,\n",
        "    training_examples=selected_training_examples,\n",
        "    training_targets=training_targets,\n",
        "    validation_examples=selected_validation_examples,\n",
        "    validation_targets=validation_targets)"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Training model...\n",
            "RMSE (on training data):\n",
            "  period 00 : 227.74\n",
            "  period 01 : 217.54\n",
            "  period 02 : 207.44\n",
            "  period 03 : 197.41\n",
            "  period 04 : 187.50\n",
            "  period 05 : 177.75\n",
            "  period 06 : 168.16\n",
            "  period 07 : 158.73\n",
            "  period 08 : 149.53\n",
            "  period 09 : 140.61\n",
            "Model training finished.\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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gbCo6JUoONftB62WQLCPMakWSKfX5oqQb8zqWxTuVJ/83fRuNRq5n/9nrzo5W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\nq7wdaLW0AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}