boston_housing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 机器学习工程师纳米学位\n",
    "## 模型评价与验证\n",
    "## 项目 1: 预测波士顿房价\n",
    "\n",
    "\n",
    "欢迎来到机器学习工程师纳米学位的第一个项目！在此文件中，有些示例代码已经提供给你，但你还需要实现更多的功能来让项目成功运行。除非有明确要求，你无须修改任何已给出的代码。以**编程练习**开始的标题表示接下来的内容中有需要你必须实现的功能。每一部分都会有详细的指导，需要实现的部分也会在注释中以**TODO**标出。请仔细阅读所有的提示！\n",
    "\n",
    "除了实现代码外，你还**必须**回答一些与项目和实现有关的问题。每一个需要你回答的问题都会以**'问题 X'**为标题。请仔细阅读每个问题，并且在问题后的**'回答'**文字框中写出完整的答案。你的项目将会根据你对问题的回答和撰写代码所实现的功能来进行评分。\n",
    "\n",
    ">**提示：**Code 和 Markdown 区域可通过 **Shift + Enter** 快捷键运行。此外，Markdown可以通过双击进入编辑模式。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第一步. 导入数据\n",
    "在这个项目中，你将利用马萨诸塞州波士顿郊区的房屋信息数据训练和测试一个模型，并对模型的性能和预测能力进行测试。通过该数据训练后的好的模型可以被用来对房屋做特定预测---尤其是对房屋的价值。对于房地产经纪等人的日常工作来说，这样的预测模型被证明非常有价值。\n",
    "\n",
    "此项目的数据集来自[UCI机器学习知识库(数据集已下线)](https://archive.ics.uci.edu/ml/datasets.html)。波士顿房屋这些数据于1978年开始统计，共506个数据点，涵盖了麻省波士顿不同郊区房屋14种特征的信息。本项目对原始数据集做了以下处理：\n",
    "- 有16个`'MEDV'` 值为50.0的数据点被移除。 这很可能是由于这些数据点包含**遗失**或**看不到的值**。\n",
    "- 有1个数据点的 `'RM'` 值为8.78. 这是一个异常值，已经被移除。\n",
    "- 对于本项目，房屋的`'RM'`， `'LSTAT'`，`'PTRATIO'`以及`'MEDV'`特征是必要的，其余不相关特征已经被移除。\n",
    "- `'MEDV'`特征的值已经过必要的数学转换，可以反映35年来市场的通货膨胀效应。\n",
    "\n",
    "运行下面区域的代码以载入波士顿房屋数据集，以及一些此项目所需的Python库。如果成功返回数据集的大小，表示数据集已载入成功。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 载入此项目所需要的库\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import visuals as vs # Supplementary code\n",
    "\n",
    "# 检查你的Python版本\n",
    "from sys import version_info\n",
    "if version_info.major != 2 and version_info.minor != 7:\n",
    "    raise Exception('请使用Python 2.7来完成此项目')\n",
    "    \n",
    "# 让结果在notebook中显示\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Boston housing dataset has 489 data points with 4 variables each.\n"
     ]
    }
   ],
   "source": [
    "# 载入波士顿房屋的数据集\n",
    "data = pd.read_csv('housing.csv')\n",
    "prices = data['MEDV']\n",
    "features = data.drop('MEDV', axis = 1)\n",
    "    \n",
    "# 完成\n",
    "print \"Boston housing dataset has {} data points with {} variables each.\".format(*data.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第二步. 分析数据\n",
    "在项目的第一个部分，你会对波士顿房地产数据进行初步的观察并给出你的分析。通过对数据的探索来熟悉数据可以让你更好地理解和解释你的结果。\n",
    "\n",
    "由于这个项目的最终目标是建立一个预测房屋价值的模型，我们需要将数据集分为**特征(features)**和**目标变量(target variable)**。\n",
    "- **特征** `'RM'`， `'LSTAT'`，和 `'PTRATIO'`，给我们提供了每个数据点的数量相关的信息。\n",
    "- **目标变量**：` 'MEDV'`，是我们希望预测的变量。\n",
    "\n",
    "他们分别被存在`features`和`prices`两个变量名中。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 1：基础统计运算\n",
    "你的第一个编程练习是计算有关波士顿房价的描述统计数据。我们已为你导入了` numpy `，你需要使用这个库来执行必要的计算。这些统计数据对于分析模型的预测结果非常重要的。\n",
    "在下面的代码中，你要做的是：\n",
    "- 计算`prices`中的`'MEDV'`的最小值、最大值、均值、中值和标准差；\n",
    "- 将运算结果储存在相应的变量中。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statistics for Boston housing dataset:\n",
      "\n",
      "Minimum price: $105,000.00\n",
      "Maximum price: $1,024,800.00\n",
      "Mean price: $454,342.94\n",
      "Median price $438,900.00\n",
      "Standard deviation of prices: $165,171.13\n"
     ]
    }
   ],
   "source": [
    "#TODO 1\n",
    "\n",
    "#目标：计算价值的最小值\n",
    "minimum_price = np.min(prices)\n",
    "\n",
    "#目标：计算价值的最大值\n",
    "maximum_price = np.max(prices)\n",
    "\n",
    "#目标：计算价值的平均值\n",
    "mean_price = np.mean(prices)\n",
    "\n",
    "#目标：计算价值的中值\n",
    "median_price = np.median(prices)\n",
    "\n",
    "#目标：计算价值的标准差\n",
    "std_price = np.std(prices)\n",
    "\n",
    "#目标：输出计算的结果\n",
    "print \"Statistics for Boston housing dataset:\\n\"\n",
    "print \"Minimum price: ${:,.2f}\".format(minimum_price)\n",
    "print \"Maximum price: ${:,.2f}\".format(maximum_price)\n",
    "print \"Mean price: ${:,.2f}\".format(mean_price)\n",
    "print \"Median price ${:,.2f}\".format(median_price)\n",
    "print \"Standard deviation of prices: ${:,.2f}\".format(std_price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 1 - 特征观察\n",
    "\n",
    "如前文所述，本项目中我们关注的是其中三个值:`'RM'`、`'LSTAT'` 和`'PTRATIO'`，对每一个数据点:\n",
    "- `'RM'` 是该地区中每个房屋的平均房间数量；\n",
    "- `'LSTAT'` 是指该地区有多少百分比的房东属于是低收入阶层（有工作但收入微薄）；\n",
    "- `'PTRATIO'` 是该地区的中学和小学里，学生和老师的数目比（`学生/老师`）。\n",
    "\n",
    "_凭直觉，上述三个特征中对每一个来说，你认为增大该特征的数值，`'MEDV'`的值会是**增大**还是**减小**呢？每一个答案都需要你给出理由。_\n",
    "\n",
    "**提示：**你预期一个`'RM'` 值是6的房屋跟`'RM'` 值是7的房屋相比，价值更高还是更低呢？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 1 - 回答：'RM' 增大，价值更高，显然房间越多的房子价值越高；‘LSTAT’增大，说明该地区的低收入人群占比重越大，相应的房价也倾向于偏低；'PTRATIO'增大，说明该地区的学校里老师数量比较少，房价会比老师多的地区要偏低。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 2: 数据分割与重排\n",
    "接下来，你需要把波士顿房屋数据集分成训练和测试两个子集。通常在这个过程中，数据也会被重排列，以消除数据集中由于顺序而产生的偏差。\n",
    "在下面的代码中，你需要\n",
    "\n",
    "使用 `sklearn.model_selection` 中的 `train_test_split`， 将`features`和`prices`的数据都分成用于训练的数据子集和用于测试的数据子集。\n",
    "  - 分割比例为：80%的数据用于训练，20%用于测试；\n",
    "  - 选定一个数值以设定 `train_test_split` 中的 `random_state` ，这会确保结果的一致性；"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# TODO 2\n",
    "\n",
    "# 提示： 导入train_test_split\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(features, prices, test_size=0.2, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 2 - 训练及测试\n",
    "*将数据集按一定比例分为训练用的数据集和测试用的数据集对学习算法有什么好处？*\n",
    "\n",
    "*如果用模型已经见过的数据，例如部分训练集数据进行测试，又有什么坏处？*\n",
    "\n",
    "**提示：** 如果没有数据来对模型进行测试，会出现什么问题？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 2 - 回答: 把训练集分割出来，可以利用交叉验证的方法调整参数得到最优的模型而不造成data leakage；如果不用独立的测试集来测试模型而用部分训练集来进行测试，模型可能会得到不符合实际的高分数，因为事实上模型已经遇到过这些数据也已经知道了这些数据中的信息，而如果用独立的测试集就可以避免这个问题。我们通过比较模型在训练集和测试集上的表现，可以评估得到模型在未知数据集上的泛化能力。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第三步. 模型衡量标准\n",
    "在项目的第三步中，你需要了解必要的工具和技巧来让你的模型进行预测。用这些工具和技巧对每一个模型的表现做精确的衡量可以极大地增强你预测的信心。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习3：定义衡量标准\n",
    "如果不能对模型的训练和测试的表现进行量化地评估，我们就很难衡量模型的好坏。通常我们会定义一些衡量标准，这些标准可以通过对某些误差或者拟合程度的计算来得到。在这个项目中，你将通过运算[*决定系数*](http://stattrek.com/statistics/dictionary.aspx?definition=coefficient_of_determination) R<sup>2</sup> 来量化模型的表现。模型的决定系数是回归分析中十分常用的统计信息，经常被当作衡量模型预测能力好坏的标准。\n",
    "\n",
    "R<sup>2</sup>的数值范围从0至1，表示**目标变量**的预测值和实际值之间的相关程度平方的百分比。一个模型的R<sup>2</sup> 值为0还不如直接用**平均值**来预测效果好；而一个R<sup>2</sup> 值为1的模型则可以对目标变量进行完美的预测。从0至1之间的数值，则表示该模型中目标变量中有百分之多少能够用**特征**来解释。_模型也可能出现负值的R<sup>2</sup>，这种情况下模型所做预测有时会比直接计算目标变量的平均值差很多。_\n",
    "\n",
    "在下方代码的 `performance_metric` 函数中，你要实现：\n",
    "- 使用 `sklearn.metrics` 中的 [`r2_score`](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.r2_score.html) 来计算 `y_true` 和 `y_predict`的R<sup>2</sup>值，作为对其表现的评判。\n",
    "- 将他们的表现评分储存到`score`变量中。\n",
    "\n",
    "或 \n",
    "\n",
    "- (可选) 不使用任何外部库，参考[决定系数的定义](https://en.wikipedia.org/wiki/Coefficient_of_determination)进行计算，这也可以帮助你更好的理解决定系数在什么情况下等于0或等于1。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# TODO 3\n",
    "\n",
    "# 提示： 导入r2_score\n",
    "from sklearn.metrics import r2_score\n",
    "\n",
    "def performance_metric(y_true, y_predict):\n",
    "    \"\"\"计算并返回预测值相比于预测值的分数\"\"\"\n",
    "    \n",
    "    score = r2_score(y_true, y_predict)\n",
    "\n",
    "    return score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# TODO 3 可选\n",
    "\n",
    "# 不允许导入任何计算决定系数的库\n",
    "\n",
    "def performance_metric2(y_true, y_predict):\n",
    "    \"\"\"计算并返回预测值相比于预测值的分数\"\"\"\n",
    "    \n",
    "    score = None\n",
    "\n",
    "    return score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 3 - 拟合程度\n",
    "\n",
    "假设一个数据集有五个数据且一个模型做出下列目标变量的预测：\n",
    "\n",
    "| 真实数值 | 预测数值 |\n",
    "| :-------------: | :--------: |\n",
    "| 3.0 | 2.5 |\n",
    "| -0.5 | 0.0 |\n",
    "| 2.0 | 2.1 |\n",
    "| 7.0 | 7.8 |\n",
    "| 4.2 | 5.3 |\n",
    "*你觉得这个模型已成功地描述了目标变量的变化吗？如果成功，请解释为什么，如果没有，也请给出原因。*  \n",
    "\n",
    "**提示**：运行下方的代码，使用`performance_metric`函数来计算模型的决定系数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model has a coefficient of determination, R^2, of 0.923.\n"
     ]
    }
   ],
   "source": [
    "# 计算这个模型的预测结果的决定系数\n",
    "score = performance_metric([3, -0.5, 2, 7, 4.2], [2.5, 0.0, 2.1, 7.8, 5.3])\n",
    "print \"Model has a coefficient of determination, R^2, of {:.3f}.\".format(score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 3 - 回答: 模型对目标变量的变化描述的比较准确，因为其决定系数接近1，根据决定系数的公式，系数接近1说明residual sum of squares 相对于数据的n倍方差（total sum of squares）是比较小的，预测值与真实数值的差别不大。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第四步. 分析模型的表现\n",
    "在项目的第四步，我们来看一下不同参数下，模型在训练集和验证集上的表现。这里，我们专注于一个特定的算法（带剪枝的决策树，但这并不是这个项目的重点），和这个算法的一个参数 `'max_depth'`。用全部训练集训练，选择不同`'max_depth'` 参数，观察这一参数的变化如何影响模型的表现。画出模型的表现来对于分析过程十分有益，这可以让我们看到一些单看结果看不到的行为。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 学习曲线\n",
    "下方区域内的代码会输出四幅图像，它们是一个决策树模型在不同最大深度下的表现。每一条曲线都直观得显示了随着训练数据量的增加，模型学习曲线的在训练集评分和验证集评分的变化，评分使用决定系数R<sup>2</sup>。曲线的阴影区域代表的是该曲线的不确定性（用标准差衡量）。\n",
    "\n",
    "运行下方区域中的代码，并利用输出的图形回答下面的问题。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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T7w5nW/QaG2MKRGQmcLdjQf0rNgHFIUChMWaOMeY1EXkBG5N0H+BasPpjn4FXGmM2iMir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\nO+fyZvYR4Btmdppz7j3M3Pf9+cDeYB4PzOybwOXAAxO2+zPgL4H3zqb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k3CCmm/NJZLno\n7etlW/e2KcfuGaYLCCIiUlX6VZmHuw7cRbaQXTTjkXKFHJlCxs9qFkyE2p5spz3dTnO8WVdaRaTh\n5Ao5HjzyIG85d/qLUQqSRESkmvSrMg879+0kHolz4doL6/L6xQQAxUH/yWiSlemVtKXaSMfSCopE\npOHtPbaXTCEz7SSyoCBJRESqS78q83DbvtvYvmY7TfGmmr9WcTLT0fwonvMAaIo30dPSQ2vCH8Sv\nblkistQUkzZMldkOwOEUJImISFXpV2WOjg4f5cEjD/Kei95Tk+M758gUxua/cc7RkmhhXeu6UmYz\nnRSIyFK3u283rYlWNrZtLLvecx6xSGxZTnItIiK1o7PsObpt/20AXLyhOuORyk0KuiKxgp62HpoT\nzaRjaU3oKiLLTm9fL+esOmfKVPd5L6+JZEVEpOoUJM3Rzn07aUu2sa1725z2L2We87KYMyKRCG3J\nNta2rqUp3kQ6ntaVURFZ1rKFLI8cfYTfOu+3ptym4BUWpMuziIgsLwqS5sA5x237buOi9RdV3LqT\n9/KM5kfJFXKAP8i4PdVOR7qDdCxNKpbSpKAiIiEPHXmInJebNmlDwWkiWRERqb6aB0lm9grgr4Eo\n8CXn3CcnrN8B/A6QBw4Db3POPVXrcs3HE/1PcHDwIG+/4O1TblPMPJf38gAko0k60520JdtIx9Mk\no0kFRSKyIBq1Hq4kaUPeyytIEhGRqqtpkGRmUeB64FeA/cCdZnajc+6B0Gb3Ahc454bN7PeBvwR+\nrZblmq9d+3YBk8cj5b08A5kBAFLxFKuaV7EiuUKZ50Skbhq5Hu7t66Uj1cHa1rVTb+SU/ltERKqv\n1r8szwf2OuceBzCzbwKXA6UfZ+fcLaHtbweurHGZ5m3nvp2sX7F+UralkdwIq1tWs7Z1LfFovE6l\nExEZp2Hr4ZmSNhQpSBIRkWqrdWaAdcC+0PP9wbKpXAV8r9wKM7vazO4ys7sOHz5cxSLOTt7Lc8f+\nO3jRhheVXdeabFWAJCKLSdXqYRhfFx85cqRKRZxsJDfC3mN7p+1qV6Q6V0REqq3WQVK5y3+u7IZm\nVwIXAH9Vbr1z7gvOuQuccxd0d3dXsYizc/+z9zOUG5oy9beuaIrIIlO1ehjG18VdXV1VKuJkDx55\nkIIrcG7P1EkbiqKm6RFERKS6an1Gvx/YEHq+HjgwcSMzuxS4Fvgl51ymxmWal137dmEYF62/aNI6\nMyMe0RVNEVlUGrIeLiVt6J6hJcl0cUpERKqv1i1JdwJbzOxUM0sAbwZuDG9gZtuBvwde45zrq3F5\n5m3nvp1sW7WN9lT7pHXOOf1Yi8hi05D1cG9fL91N3fS09Ey5Td7Lk4gklClURESqrqZBknMuD7wD\n+AHwIPBt59weM/uYmb0m2OyvgBbgBjO7z8xunOJwdTeYHeTnh35edjyScw4zU5AkIotKo9bDxaQN\n0yl4BZKx5AKVSERElpOan9E7524Gbp6w7EOhx5fWugzV8rNnfkbBFcqOR8p7eZIxzX0kIotPo9XD\ng9lBHj/+OK/a8qppt8t7eZrjzQtUKhERWU5q3d1uSdm1bxepWIrz15w/aV3BFUjH0nUolYjI0vLA\n4QdwuBmTNhRcQRPJiohITShImoWd+3ZywdoLyk4Mm/fypKL6sRYRma9Kkzaou52IiNSKgqQKHRo8\nxOPHHy87Hgn8ICkdV0uSiMh89fb1srZ1LSubVs64rcaBiohILShIqtCufbsAppwfCSjbwiQiIrOz\nu2/3zKm/AwqSRESkFhQkVWjnvp10NXVx5sozy65X+m8Rkfk7MXqCp088XdEksqAgSUREakNBUgU8\n53Hbvtt44foXTpm9zjDiUU0kKyIyH3sO7wGYMf03oGkXRESkZhQkVeCRo49wdOTotF3tHGpJEhGZ\nr2LShm3d26bdzjmHYUQj0YUoloiILDMKkipQHI80VdKGglcgEU0QMX2cIiLz0dvXy8a2jbSl2qbd\nrjg3nYiISC3orL4CO/ftZHPHZnpaesqu14+1iEh17O7bXVFXO82RJCIitaQgaQaZfIa7Dtw1bVe7\nvJfXRLIiIvN0dPgoBwYOcO6qmZM25L08yaguTomISG0oSJrBPYfuYTQ/OnOQpDmSRETmpfdwMIls\nJS1JnlqSRESkdhQkzeC2fbcRi8R4/rrnT7mNh6crmiIi89Tb14thnN199ozbeniam05ERGpGQdIM\ndu7byXN7nktLomXKbcwpDa2IyHz19vVyasep09a3RYbqXRERqR0FSdM4PnKcPX17pu1qV6Q5kkRE\n5mf3s5UlbShSkCQiIrWiIGkatz9zOw43ZervEoN4REGSiMhcPTv4LIeHD1eUtKFIQZKIiNSKgqRp\n3LbvNloSLZzbM/WPtuc8TWgoIjJPs0naAJrAW0REaktB0jR27tvJC9a9YNofYqX/FhGZv96+XiIW\nYWvX1hm3LXgF4pE4ZrYAJRMRkeVIQdIUnj7xNPtP7p+xq50mkhURmb/evl5O7zy9oukUCq6gjKIi\nIlJTCpKmsHPfToAZkzYUvAJN8aaFKJKIyJLknJtV0gZdnBIRkVpTkDSFXU/vYk3LGja1b5p2u7yX\n14SGIiLzcGDgAMdHj1ectEETyYqISK0pSCqj4BW4/ZnbuXjDxTP2eTdM6b9FROaht292SRvyXl7d\n7UREpKYUJJWx5/AeTmZOzpz6G2VYEhGZr96+XuKROGd1nVXxPro4JSIitaQgqYzieKQXbnjhjNua\nmeZIEhGZh919uzlj5RkkoomK99HFKRERqSUFSWXsenoXZ3efTWe6c9rtnHOAfqxFRObKOUdvX2/F\nXe2KVO+KiEgtKUiaYDg3zL2H7uWF62duRSqmodVcHSIic/P0iacZyA5UnLShSEGSiIjUUs2DJDN7\nhZk9bGZ7zeyaMuuTZvatYP0dZrap1mWazp0H7iTn5Soaj6TMdiLSCBZzPTzbpA3OOcxMQZKIiNRU\nTYMkM4sC1wOvBM4Gft3Mzp6w2VXAcefc6cBngE/Vskwz2fX0LhLRBM9b+7wZt1WQJCKL3WKvh3v7\neklEE5zeeXpF22siWRERWQi1bkl6PrDXOfe4cy4LfBO4fMI2lwNfCR5/B/hlq2P/tV37dnHB2gsq\nCn7yXl4TyYrIYreo6+HdfbvZ2rW14mx1BU9BkoiI1F6tg6R1wL7Q8/3BsrLbOOfywAlgZY3LVdbh\nocM8cuyRisYjgd/tQ2loRWSRW7T1cMErsOfwnlmNR8p7eZIxBUkiIlJbtQ6Syl2JdHPYBjO72szu\nMrO7Dh8+XJXCTbRr/y6AisYjBWVS+m8RWeyqVg/D+Lr4yJEj8yrYk/1PMpwbnlVmu4IrqJuziIjU\nXK2DpP3AhtDz9cCBqbYxsxjQBhybeCDn3Beccxc45y7o7u6uSWF3Pb2LjlQHW7u3VrS9c5pIVkQW\nvarVwzC+Lu7q6ppXwXb37QYqT9oAQXc7tSSJiEiN1TpIuhPYYmanmlkCeDNw44RtbgR+M3j8BuAn\nrjgB0QJyzrFz305euOGFRKzyj0Xd7URkkVu09XBvXy/pWJrTOk6reB9Dme1ERKT2avpL45zLm9k7\ngB8AUeDLzrk9ZvYx4C7n3I3APwBfM7O9+Fcu31zLMk3lseOPcXj4MBdvuLii7QtegVgkNquASkRk\noS3meri3r5ezu88mGonOaj8FSSIiUms1/6Vxzt0M3Dxh2YdCj0eBN9a6HDPZuW8nABevrzBIcgXS\n8XQtiyQiUhWLsR7Oe3keOPwAv37Or896XwVJIiJSa2oGCex6eheb2jaxbsXEpE/l5Qo5UlENHhYR\nmYu9x/aSKWRmNR4JwKGxoCIiUnsKkoBsIcvPDvyMizdW1ooEakkSEZmP3r5eYHZJGzznEbWoujmL\niEjN6ZcGuP/Z+xnODVec+huUhlZEZD56+3ppSbRwSvspFe+T9/Kqd0VEZEFYHRLJzZuZDZBgHx6F\nuhUiQpQcozi8OezdBcxvgpH6a/T3oPLXX6O/h9mW/xTnXG3mL6gTMxskwdMLVhcbERweeTJVOuJy\n+xtcjBr9Paj89bfs62KpjUbt2P2wy7gL6l2IuTKzu5xr3PJD478Hlb/+Gv09NHr5q+Qh1cX10+jl\nh8Z/Dyp//S2F9yCLk7rbiYiIiIiIhChIEhERERERCWnUIOkL9S7APDV6+aHx34PKX3+N/h4avfzV\n0Oifgcpff43+HlT++lsK70EWoYZM3CAiIiIiIlIrjdqSJCIiIiIiUhMKkkREREREREIaKkgys1eY\n2cNmttfMrql3eSplZk+a2W4zu8/M7gqWdZrZf5jZo8F9R73LWWRmXzazPjPrDS0rW17z/U3wndxv\nZufXr+RjpngPHzGzZ4Lv4T4ze1Vo3Z8E7+FhM3t5fUo9xsw2mNktZvagme0xsz8KljfE9zBN+Rvi\nOzCzlJn9zMx+HpT/o8HyU83sjuDz/5aZJYLlyeD53mD9pnqWv9YasS5utHoYGr8uVj28KL4D1cUi\nc+Wca4gbEAUeA04DEsDPgbPrXa4Ky/4k0DVh2V8C1wSPrwE+Ve9yhsr2i8D5QO9M5QVeBXwPMOAi\n4I56l3+a9/AR4L1ltj07+HtKAqcGf2fROpd/DXB+8LgVeCQoZ0N8D9OUvyG+g+BzbAkex4E7gs/1\n28Cbg+WfB34/ePwHwOeDx28GvlXPz7/Gn01D1sWNVg8HZWroulj18KL4DlQX1/k70K1xb43UkvR8\nYK9z7nHnXBb4JnB5ncs0H5cDXwkefwV4bR3LMo5z7r+AYxMWT1Xey4GvOt/tQLuZrVmYkk5tivcw\nlcuBbzrnMs65J4C9+H9vdeOcO+icuyd4PAA8CKyjQb6Haco/lUX1HQSf42DwNB7cHPARM2n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tnkcuCrzp/R9nYza7f/z96dhzlyl/ei/74qLa1ep3t67/F4xjPexjO2xwwwOTkhOPgEnAfH3ATC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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a513350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 根据不同的训练集大小，和最大深度，生成学习曲线\n",
    "vs.ModelLearning(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 4 - 学习曲线\n",
    "*选择上述图像中的其中一个，并给出其最大深度。随着训练数据量的增加，训练集曲线的评分有怎样的变化？验证集曲线呢？如果有更多的训练数据，是否能有效提升模型的表现呢？*\n",
    "\n",
    "**提示：**学习曲线的评分是否最终会收敛到特定的值？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 4 - 回答: 在上述图像中，当最大深度为3时决策树的模型表现最好。当最大深度为1时，模型过于简单并不能很好的描述数据；而当最大深度为10时，模型已经过拟合以至于不能对训练集的数据进行很好的泛化预测。最大深度为3时，随着训练数据的增加，训练集曲线的评分会从1 开始呈现下降趋势，因为在最初训练数据的增加会导致更多的error；验证集的分数曲线会随着训练数据的增加而增加，因为训练数据的增加能够让模型更精确的描述数据。但是当数据达到一定程度时，比如最大深度为3的时候，训练集中的数据达到250个点的时候，学习曲线会趋于收敛，因为这时训练数据量已经足够多模型可以比较好的预测数据了。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 复杂度曲线\n",
    "下列代码内的区域会输出一幅图像，它展示了一个已经经过训练和验证的决策树模型在不同最大深度条件下的表现。这个图形将包含两条曲线，一个是训练集的变化，一个是验证集的变化。跟**学习曲线**相似，阴影区域代表该曲线的不确定性，模型训练和测试部分的评分都用的 `performance_metric` 函数。\n",
    "\n",
    "运行下方区域中的代码，并利用输出的图形并回答下面的两个问题。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KqVHL74eGhq7b5ZcnrlFdcAH8/Oc2tNrbuwLL6+39OUQgJwdyc+0tfH/MmK7HeXld6/Py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\ny8FsZ729ItIviPNtTEhZ4jOmZWuBSU6BURd1q2V8DAx1Bnb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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ade9b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 根据不同的最大深度参数，生成复杂度曲线\n",
    "vs.ModelComplexity(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 5 - 偏差（bias）与方差（variance）之间的权衡取舍\n",
    "*当模型以最大深度 1训练时，模型的预测是出现很大的偏差还是出现了很大的方差？当模型以最大深度10训练时，情形又如何呢？图形中的哪些特征能够支持你的结论？*\n",
    "  \n",
    "**提示：** 你如何得知模型是否出现了偏差很大或者方差很大的问题？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 5 - 回答: 当最大深度为1时，图形中模型的预测出现了很大的偏差，因为无论是训练集还是数据集，模型的评分都比较低只有0.4， 说明模型并不能很好的对数据进行预测；而当最大深度为10时， 模型的预测出现了很大的方差，因为训练集的评分比较好而测试集的评分很差，说明模型过拟合也失去了泛化的能力，并不能对测试数据进行很好的预测。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 6- 最优模型的猜测\n",
    "*结合问题 5 中的图，你认为最大深度是多少的模型能够最好地对未见过的数据进行预测？你得出这个答案的依据是什么？*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 6 - 回答: 我认为最大深度为3时模型最好。首先，最大深度为3时，测试集的评分是所有深度里最高的，而且此时数据集和测试集的评分差别最小，说明学习的模型既能够比较好的代表数据集，也能比较好的对测试集的数据做出预测；如果数据集加上测试集认为是真实数据的话，那么这个模型就是最贴近真实情况的模型了。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## 第五步. 选择最优参数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 7- 网格搜索（Grid Search）\n",
    "*什么是网格搜索法？如何用它来优化模型？*\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 7 - 回答: 网格搜索法是对一个模型的给定的不同参数组合进行遍历搜索，通过交叉验证得到模型的最优参数的一种方法。当我们用一个模型学习现有数据，可以定义不同的参数组合，网络搜索法就可以分别用这些参数进行排列组合来拟合，最终通过交叉验证找到最适合的模型。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 8 - 交叉验证\n",
    "- 什么是K折交叉验证法（k-fold cross-validation）？\n",
    "- [GridSearchCV](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html)是如何结合交叉验证来完成对最佳参数组合的选择的？\n",
    "- [GridSearchCV](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html)中的`'cv_results_'`属性能告诉我们什么？\n",
    "- 网格搜索时如果不使用交叉验证会有什么问题？交叉验证又是如何解决这个问题的？\n",
    "\n",
    "**提示：** 在下面 fit_model函数最后加入 `print pd.DataFrame(grid.cv_results_)` 可以帮你查看更多信息。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 8 - 回答：k折交叉验证法，默认情况下是把训练集按顺序平均分成k份，每一份都分别做一次验证集，其余的k-1份做为训练数据集，进行k次交叉验证，取k次评分的均值作为最后的评分结果。GridSearchCV最终在选取最优化的模型时，就是根据不同参数组合的交叉验证评分结果来判断的。'cv_results_'属性会告诉我们交叉验证中拆分数据集的规则，比如是用默认的3折还是自定义的k折交叉验证或者其他的分割方法。另外 ，从'cv_results_'的结果还可以看到每次拟合所用的平均时间、平均测试时间、训练集的分数和验证集的分数还有他们的标准差，还有分成的k份数据的每个split的训练集的分数和验证集的分数。\n",
    "### 网格搜索法如果不使用交叉验证，只是简单的把数据集分成训练集和验证集的话，无论训练集还是验证集的数据会变少，都不能够精确的代表整个数据集中的数据，有可能会导致根据训练集找到的参数组合在验证集中的表现很差，也就是说找到的参数组合并不是最优的。而交叉验证能解决这个问题，能够避免因为对数据集划分的偶然性造成的模型评分偏高/偏低的问题，因为交叉验证能够保证所有的数据都能被用来训练和验证，找到的参数更精确。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 4：训练最优模型\n",
    "在这个练习中，你将需要将所学到的内容整合，使用**决策树算法**训练一个模型。为了得出的是一个最优模型，你需要使用网格搜索法训练模型，以找到最佳的 `'max_depth'` 参数。你可以把`'max_depth'` 参数理解为决策树算法在做出预测前，允许其对数据提出问题的数量。决策树是**监督学习算法**中的一种。\n",
    "\n",
    "在下方 `fit_model` 函数中，你需要做的是：\n",
    "1. **定义 `'cross_validator'` 变量**: 使用 `sklearn.model_selection` 中的 [`KFold`](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.KFold.html) 创建一个交叉验证生成器对象;\n",
    "2. **定义 `'regressor'` 变量**: 使用  `sklearn.tree` 中的 [`DecisionTreeRegressor`](http://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeRegressor.html) 创建一个决策树的回归函数;\n",
    "3. **定义 `'params'` 变量**: 为 `'max_depth'` 参数创造一个字典，它的值是从1至10的数组;\n",
    "4. **定义 `'scoring_fnc'` 变量**: 使用 `sklearn.metrics` 中的 [`make_scorer`](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.make_scorer.html)  创建一个评分函数；\n",
    " 将 `‘performance_metric’` 作为参数传至这个函数中；\n",
    "5. **定义 `'grid'` 变量**: 使用 `sklearn.model_selection` 中的 [`GridSearchCV`](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html) 创建一个网格搜索对象；将变量`'regressor'`, `'params'`, `'scoring_fnc'`和 `'cross_validator'` 作为参数传至这个对象构造函数中；\n",
    "  \n",
    "如果你对python函数的默认参数定义和传递不熟悉，可以参考这个MIT课程的[视频](http://cn-static.udacity.com/mlnd/videos/MIT600XXT114-V004200_DTH.mp4)。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# TODO 4\n",
    "\n",
    "#提示: 导入 'KFold' 'DecisionTreeRegressor' 'make_scorer' 'GridSearchCV' \n",
    "from sklearn.model_selection import KFold\n",
    "from sklearn import tree\n",
    "from sklearn.metrics import make_scorer\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "\n",
    "def fit_model(X, y):\n",
    "    \"\"\" 基于输入数据 [X,y]，利于网格搜索找到最优的决策树模型\"\"\"\n",
    "    \n",
    "    cross_validator = KFold(n_splits=5, random_state=None, shuffle=False)\n",
    "    \n",
    "    regressor = tree.DecisionTreeRegressor()\n",
    "\n",
    "    params = {\"max_depth\":range(1,11)}\n",
    "\n",
    "    scoring_fnc = make_scorer(score_func=performance_metric)\n",
    "\n",
    "    grid = GridSearchCV(estimator=regressor, param_grid=params, scoring=scoring_fnc, cv=cross_validator)\n",
    "\n",
    "    # 基于输入数据 [X,y]，进行网格搜索\n",
    "    grid = grid.fit(X, y)\n",
    "    \n",
    "    print pd.DataFrame(grid.cv_results_)\n",
    "\n",
    "    # 返回网格搜索后的最优模型\n",
    "    return grid.best_estimator_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 4：训练最优模型 （可选）\n",
    "在这个练习中，你将需要将所学到的内容整合，使用**决策树算法**训练一个模型。为了得出的是一个最优模型，你需要使用网格搜索法训练模型，以找到最佳的 `'max_depth'` 参数。你可以把`'max_depth'` 参数理解为决策树算法在做出预测前，允许其对数据提出问题的数量。决策树是**监督学习算法**中的一种。\n",
    "\n",
    "在下方 `fit_model` 函数中，你需要做的是：\n",
    "\n",
    "- 遍历参数`‘max_depth’`的可选值 1～10，构造对应模型\n",
    "- 计算当前模型的交叉验证分数\n",
    "- 返回最优交叉验证分数对应的模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# TODO 4 可选\n",
    "\n",
    "'''\n",
    "不允许使用 DecisionTreeRegressor 以外的任何 sklearn 库\n",
    "\n",
    "提示: 你可能需要实现下面的 cross_val_score 函数\n",
    "\n",
    "def cross_val_score(estimator, X, y, scoring = performance_metric, cv=3):\n",
    "    \"\"\" 返回每组交叉验证的模型分数的数组 \"\"\"\n",
    "    scores = [0,0,0]\n",
    "    return scores\n",
    "'''\n",
    "\n",
    "def fit_model2(X, y):\n",
    "    \"\"\" 基于输入数据 [X,y]，利于网格搜索找到最优的决策树模型\"\"\"\n",
    "    \n",
    "    #最优交叉验证分数对应的最优模型\n",
    "    best_estimator = None\n",
    "    \n",
    "    return best_estimator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 9 - 最优模型\n",
    "*最优模型的最大深度（maximum depth）是多少？此答案与你在**问题 6**所做的猜测是否相同？*\n",
    "\n",
    "运行下方区域内的代码，将决策树回归函数代入训练数据的集合，以得到最优化的模型。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   mean_fit_time  mean_score_time  mean_test_score  mean_train_score  \\\n",
      "0       0.000884         0.000295         0.369945          0.464526   \n",
      "1       0.001338         0.000383         0.646221          0.724819   \n",
      "2       0.001026         0.000307         0.750120          0.827132   \n",
      "3       0.000846         0.000285         0.783205          0.869918   \n",
      "4       0.000924         0.000307         0.774892          0.905068   \n",
      "5       0.000892         0.000257         0.739760          0.933147   \n",
      "6       0.000924         0.000250         0.736796          0.953271   \n",
      "7       0.000893         0.000240         0.727163          0.967387   \n",
      "8       0.000940         0.000242         0.707774          0.980051   \n",
      "9       0.000986         0.000254         0.704591          0.987937   \n",
      "\n",
      "  param_max_depth              params  rank_test_score  split0_test_score  \\\n",
      "0               1   {u'max_depth': 1}               10           0.441798   \n",
      "1               2   {u'max_depth': 2}                9           0.650624   \n",
      "2               3   {u'max_depth': 3}                3           0.764262   \n",
      "3               4   {u'max_depth': 4}                1           0.774103   \n",
      "4               5   {u'max_depth': 5}                2           0.777923   \n",
      "5               6   {u'max_depth': 6}                4           0.774340   \n",
      "6               7   {u'max_depth': 7}                5           0.765230   \n",
      "7               8   {u'max_depth': 8}                6           0.762445   \n",
      "8               9   {u'max_depth': 9}                7           0.763898   \n",
      "9              10  {u'max_depth': 10}                8           0.737592   \n",
      "\n",
      "   split0_train_score  split1_test_score       ...         split2_test_score  \\\n",
      "0            0.459329           0.372028       ...                  0.299578   \n",
      "1            0.737756           0.704460       ...                  0.573730   \n",
      "2            0.832384           0.736814       ...                  0.746905   \n",
      "3            0.870743           0.748659       ...                  0.770054   \n",
      "4            0.909865           0.746128       ...                  0.770841   \n",
      "5            0.936857           0.705113       ...                  0.743113   \n",
      "6            0.958631           0.693522       ...                  0.724807   \n",
      "7            0.973887           0.709700       ...                  0.725632   \n",
      "8            0.983567           0.681319       ...                  0.694345   \n",
      "9            0.990612           0.656601       ...                  0.732761   \n",
      "\n",
      "   split2_train_score  split3_test_score  split3_train_score  \\\n",
      "0            0.460173           0.383378            0.460642   \n",
      "1            0.722491           0.636724            0.725419   \n",
      "2            0.833427           0.722750            0.814270   \n",
      "3            0.874686           0.786015            0.853319   \n",
      "4            0.912729           0.804478            0.888359   \n",
      "5            0.938664           0.768893            0.919637   \n",
      "6            0.959737           0.760286            0.943559   \n",
      "7            0.973031           0.753988            0.959618   \n",
      "8            0.984732           0.726613            0.971164   \n",
      "9            0.989649           0.737815            0.979868   \n",
      "\n",
      "   split4_test_score  split4_train_score  std_fit_time  std_score_time  \\\n",
      "0           0.352021            0.474948      0.000113        0.000032   \n",
      "1           0.665510            0.728807      0.000491        0.000070   \n",
      "2           0.779686            0.830499      0.000119        0.000026   \n",
      "3           0.837313            0.872484      0.000031        0.000042   \n",
      "4           0.775053            0.902649      0.000112        0.000090   \n",
      "5           0.706899            0.930687      0.000133        0.000023   \n",
      "6           0.739771            0.946685      0.000069        0.000016   \n",
      "7           0.683599            0.962718      0.000011        0.000003   \n",
      "8           0.671978            0.981079      0.000015        0.000003   \n",
      "9           0.657765            0.989683      0.000073        0.000020   \n",
      "\n",
      "   std_test_score  std_train_score  \n",
      "0        0.046172         0.005979  \n",
      "1        0.042674         0.009165  \n",
      "2        0.020040         0.007045  \n",
      "3        0.029579         0.008681  \n",
      "4        0.018569         0.009069  \n",
      "5        0.029463         0.007460  \n",
      "6        0.026027         0.006757  \n",
      "7        0.028896         0.005592  \n",
      "8        0.033740         0.004784  \n",
      "9        0.038670         0.004049  \n",
      "\n",
      "[10 rows x 21 columns]\n",
      "Parameter 'max_depth' is 4 for the optimal model.\n"
     ]
    }
   ],
   "source": [
    "# 基于训练数据，获得最优模型\n",
    "optimal_reg = fit_model(X_train, y_train)\n",
    "\n",
    "# 输出最优模型的 'max_depth' 参数\n",
    "print \"Parameter 'max_depth' is {} for the optimal model.\".format(optimal_reg.get_params()['max_depth'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 9 - 回答：最优模型的最大深度为4，与问题6中的猜测类似。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 第六步. 做出预测\n",
    "当我们用数据训练出一个模型，它现在就可用于对新的数据进行预测。在决策树回归函数中，模型已经学会对新输入的数据*提问*，并返回对**目标变量**的预测值。你可以用这个预测来获取数据未知目标变量的信息，这些数据必须是不包含在训练数据之内的。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 10 - 预测销售价格\n",
    "想像你是一个在波士顿地区的房屋经纪人，并期待使用此模型以帮助你的客户评估他们想出售的房屋。你已经从你的三个客户收集到以下的资讯:\n",
    "\n",
    "| 特征 | 客戶 1 | 客戶 2 | 客戶 3 |\n",
    "| :---: | :---: | :---: | :---: |\n",
    "| 房屋内房间总数 | 5 间房间 | 4 间房间 | 8 间房间 |\n",
    "| 社区贫困指数（％被认为是贫困阶层） | 17% | 32% | 3% |\n",
    "| 邻近学校的学生-老师比例 | 15：1 | 22：1 | 12：1 |\n",
    "\n",
    "*你会建议每位客户的房屋销售的价格为多少？从房屋特征的数值判断，这样的价格合理吗？为什么？* \n",
    "\n",
    "**提示：**用你在**分析数据**部分计算出来的统计信息来帮助你证明你的答案。\n",
    "\n",
    "运行下列的代码区域，使用你优化的模型来为每位客户的房屋价值做出预测。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted selling price for Client 1's home: $403,025.00\n",
      "Predicted selling price for Client 2's home: $237,478.72\n",
      "Predicted selling price for Client 3's home: $931,636.36\n"
     ]
    }
   ],
   "source": [
    "# 生成三个客户的数据\n",
    "client_data = [[5, 17, 15], # 客户 1\n",
    "               [4, 32, 22], # 客户 2\n",
    "               [8, 3, 12]]  # 客户 3\n",
    "\n",
    "# 进行预测\n",
    "predicted_price = optimal_reg.predict(client_data)\n",
    "for i, price in enumerate(predicted_price):\n",
    "    print \"Predicted selling price for Client {}'s home: ${:,.2f}\".format(i+1, price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 10 - 回答：每位客户的房屋售价建议分别是: 403,025.00/237,478.72和931,636.36。其中第二位客户的房屋售价最低，因为所在地区的贫困阶层的比例比较高，学校的老师比较少，因此在房间数同等条件下这个地区的房屋售价会偏低，而第二位客户的房间数是最少的，因此售价最低；类似的原因，第三位客户房屋所在区域的贫困阶层比较少，学校中老师比例高，而且房间数最多，因此它的售价最高；另外，根据统计信息来看，这个地区的房价分布在 \\$105,000.00和\\$1,024,800.00之间，而客户2和客户3的特征分别对应了这个地区相对较低和较高的房价并且在统计值的范围内，客户1的房屋特征介于他们2者之间，比较接近统计数据的中值， 因此这个预测结果是符合预期的。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 编程练习 5\n",
    "你刚刚预测了三个客户的房子的售价。在这个练习中，你将用你的最优模型在整个测试数据上进行预测, 并计算相对于目标变量的决定系数 R<sup>2</sup>的值**。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal model has R^2 score 0.84 on test data\n"
     ]
    }
   ],
   "source": [
    "#TODO 5\n",
    "\n",
    "# 提示：你可能需要用到 X_test, y_test, optimal_reg, performance_metric\n",
    "# 提示：你可能需要参考问题10的代码进行预测\n",
    "# 提示：你可能需要参考问题3的代码来计算R^2的值\n",
    "y_predicted = optimal_reg.predict(X_test)\n",
    "\n",
    "r2 = performance_metric(y_test, y_predicted)\n",
    "\n",
    "#r2 = 1\n",
    "\n",
    "print \"Optimal model has R^2 score {:,.2f} on test data\".format(r2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题11 - 分析决定系数\n",
    "\n",
    "你刚刚计算了最优模型在测试集上的决定系数，你会如何评价这个结果？"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题11 - 回答: r2为0.84，说明大概有80%的price是能够用现在的feature准确的预测出来的，不算非常准确，但这个结果可以给房产经纪人一个初步的考量，大概的估计房屋售价。如果能够考虑到房屋的其他特性，比方说修建时间、周边的交通情况（例如是不是靠近地铁站之类的），预测结果应该会更好。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 模型健壮性\n",
    "\n",
    "一个最优的模型不一定是一个健壮模型。有的时候模型会过于复杂或者过于简单，以致于难以泛化新增添的数据；有的时候模型采用的学习算法并不适用于特定的数据结构；有的时候样本本身可能有太多噪点或样本过少，使得模型无法准确地预测目标变量。这些情况下我们会说模型是欠拟合的。\n",
    "\n",
    "### 问题 12 - 模型健壮性\n",
    "\n",
    "模型是否足够健壮来保证预测的一致性？\n",
    "\n",
    "**提示**: 执行下方区域中的代码，采用不同的训练和测试集执行 `fit_model` 函数10次。注意观察对一个特定的客户来说，预测是如何随训练数据的变化而变化的。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trial 1: $391,183.33\n",
      "Trial 2: $411,417.39\n",
      "Trial 3: $415,800.00\n",
      "Trial 4: $420,622.22\n",
      "Trial 5: $413,334.78\n",
      "Trial 6: $411,931.58\n",
      "Trial 7: $399,663.16\n",
      "Trial 8: $407,232.00\n",
      "Trial 9: $402,531.82\n",
      "Trial 10: $413,700.00\n",
      "\n",
      "Range in prices: $29,438.89\n"
     ]
    }
   ],
   "source": [
    "# 请先注释掉 fit_model 函数里的所有 print 语句\n",
    "vs.PredictTrials(features, prices, fit_model, client_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 12 - 回答：从10次预测的结果来看，每次的预测结果变化幅度不大，模型已经足够健壮对训练数据的变化不敏感。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 13 - 实用性探讨\n",
    "*简单地讨论一下你建构的模型能否在现实世界中使用？* \n",
    "\n",
    "提示：回答以下几个问题，并给出相应结论的理由：\n",
    "- *1978年所采集的数据，在已考虑通货膨胀的前提下，在今天是否仍然适用？*\n",
    "- *数据中呈现的特征是否足够描述一个房屋？*\n",
    "- *在波士顿这样的大都市采集的数据，能否应用在其它乡镇地区？*\n",
    "- *你觉得仅仅凭房屋所在社区的环境来判断房屋价值合理吗？*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题 13 - 回答：如果用现在模型在现实生活中预测房价，预测结果是不准确的。因为在这个模型中，我们只考虑了3个feature；其实在现实生活中，还有很多其他的因素也会影响房价，比如像在上一题提到的，房屋的修建时间、周边的交通情况，还有社区的治安情况和生活设施等都会影响一个地区的房价。另外，在考虑通货膨胀的前提下，我们仍然用1978年的数据是不合适的，通常通货膨胀会导致房价的普遍上涨，用将近30年前的数据会导致预测结果偏低。另外，在波士顿这样的大都市采集的数据，对预测乡镇地区的房价没有意义；即便是在波士顿采集的数据，去预测类似的大都市例如纽约也是不准确的，因为不同地区的房价具有非常大的差别，只有同一个地区的房价才有参考的意义。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 可选问题 - 预测北京房价\n",
    "\n",
    "（本题结果不影响项目是否通过）通过上面的实践，相信你对机器学习的一些常用概念有了很好的领悟和掌握。但利用70年代的波士顿房价数据进行建模的确对我们来说意义不是太大。现在你可以把你上面所学应用到北京房价数据集中 `bj_housing.csv`。\n",
    "\n",
    "免责声明：考虑到北京房价受到宏观经济、政策调整等众多因素的直接影响，预测结果仅供参考。\n",
    "\n",
    "这个数据集的特征有：\n",
    "- Area：房屋面积，平方米\n",
    "- Room：房间数，间\n",
    "- Living: 厅数，间\n",
    "- School: 是否为学区房，0或1\n",
    "- Year: 房屋建造时间，年\n",
    "- Floor: 房屋所处楼层，层\n",
    "\n",
    "目标变量：\n",
    "- Value: 房屋人民币售价，万\n",
    "\n",
    "你可以参考上面学到的内容，拿这个数据集来练习数据分割与重排、定义衡量标准、训练模型、评价模型表现、使用网格搜索配合交叉验证对参数进行调优并选出最佳参数，比较两者的差别，最终得出最佳模型对验证集的预测分数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter 'max_depth' is 9 for the optimal model.\n",
      "Optimal model has R^2 score 0.57 on test data\n",
      "Trial 1: $526.25\n",
      "Trial 2: $483.36\n",
      "Trial 3: $465.89\n",
      "Trial 4: $430.05\n",
      "Trial 5: $490.97\n",
      "Trial 6: $441.65\n",
      "Trial 7: $423.77\n",
      "Trial 8: $531.43\n",
      "Trial 9: $429.25\n",
      "Trial 10: $460.22\n",
      "\n",
      "Range in prices: $107.66\n"
     ]
    }
   ],
   "source": [
    "# TODO 6\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import visuals as vs # Supplementary code\n",
    "from sklearn.metrics import r2_score\n",
    "from sklearn.cross_validation import KFold\n",
    "from sklearn import tree\n",
    "from sklearn.metrics import make_scorer\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "data = pd.read_csv('bj_housing.csv')\n",
    "prices = data['Value']\n",
    "features = data.drop('Value', axis = 1)\n",
    "\n",
    "\n",
    "def performance_metric(y_true, y_predict):\n",
    " \n",
    "    \n",
    "    score = r2_score(y_true, y_predict)\n",
    "\n",
    "    return score\n",
    "\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(features, prices, test_size=0.2, random_state=42)\n",
    "\n",
    "\n",
    "\n",
    "def fit_model(X, y):\n",
    "\n",
    "    \n",
    "    cross_validator = KFold(n=len(y), n_folds=10, random_state=None, shuffle=False)\n",
    "    \n",
    "    regressor = tree.DecisionTreeRegressor()\n",
    "\n",
    "    params = {\"max_depth\":range(1,11)}\n",
    "    #print \"params\", params[\"max_depth\"]\n",
    "\n",
    "    scoring_fnc = make_scorer(score_func=performance_metric)\n",
    "\n",
    "    grid = GridSearchCV(regressor, params, scoring=scoring_fnc, cv=cross_validator)\n",
    "\n",
    "    grid = grid.fit(X, y)\n",
    "\n",
    "    return grid.best_estimator_\n",
    "\n",
    "\n",
    "optimal_reg = fit_model(X_train, y_train)\n",
    "print \"Parameter 'max_depth' is {} for the optimal model.\".format(optimal_reg.get_params()['max_depth'])\n",
    "\n",
    "\n",
    "y_test_predicted = optimal_reg.predict(X_test)\n",
    "r2 = performance_metric(y_test, y_test_predicted)\n",
    "print \"Optimal model has R^2 score {:,.2f} on test data\".format(r2)\n",
    "\n",
    "client_data = [[128, 3, 1, 1, 2004, 21]]\n",
    "vs.PredictTrials(features, prices, fit_model, client_data)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题14 - 北京房价预测\n",
    "你成功的用新的数据集构建了模型了吗？他能对测试数据进行验证吗？它的表现是否符合你的预期？交叉验证是否有助于提升你模型的表现？\n",
    "\n",
    "**提示：**如果你是从零开始构建机器学习的代码会让你一时觉得无从下手。这时不要着急，你要做的只是查看之前写的代码，把每一行都看明白，然后逐步构建你的模型。当中遇到什么问题也可以在我们论坛寻找答案。也许你会发现你所构建的模型的表现并没有达到你的预期，这说明机器学习并非是一项简单的任务，构建一个表现良好的模型需要长时间的研究和测试。这也是我们接下来的课程中会逐渐学到的。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 问题14 - 回答: 用从北京采集的数据构建的模型，误差比较大，r2决定系数只有0.58，意味着大约一半的房价预测是可以用现有的特征来解释，另外一半数据是不能够用现有的特征来解释的。我选取了bj_housing的第一个房屋来进行预测，真实房价是370万，而根据不同训练集测试集预测的结果大都是450万到500万之间，这与实际值相差悬殊。另外，我观察bj_housing中的数据，有一部分房屋的价格非常高，但是根据现有特征很难得出价格高的原因，我猜想其中应该还有其他影响因素并没有考虑，如果多增加一些考量的特征，就可以尝试构建一个更准确的模型，提高决定系数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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