{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# %load ../../../preconfig.py\n",
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set(color_codes=True)\n",
    "#sns.set(font='SimHei')\n",
    "#plt.rcParams['axes.grid'] = False\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "import pandas as pd\n",
    "pd.options.display.max_rows = 20\n",
    "\n",
    "#import sklearn\n",
    "\n",
    "#import itertools\n",
    "\n",
    "import logging\n",
    "logger = logging.getLogger()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "决策树简介和 Python 实现\n",
    "======================\n",
    "参考：\n",
    "\n",
    "+ [Building a decision tree from scratch - a beginner tutorial](http://www.patricklamle.com/Tutorials/Decision%20tree%20python/tuto_decision%20tree.html)\n",
    "\n",
    "+ 9.2 Tree-Based Methods - The Elements of Statistical Learning\n",
    "\n",
    "+ [Classification and Regression Trees (CART) Theory and Applications](http://edoc.hu-berlin.de/master/timofeev-roman-2004-12-20/PDF/timofeev.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 0. 基本介绍\n",
    "本文主要是参照 Tree-Based Methods - The Elements of Statistical Learning 来实现一个简化版范例，其算法是 CART。\n",
    "\n",
    "决策树的思想本身非常朴素，关于它的基本介绍在网上已经非常丰富，比如：\n",
    "\n",
    "+ [算法杂货铺——分类算法之决策树(Decision tree)](http://www.cnblogs.com/leoo2sk/archive/2010/09/19/decision-tree.html)\n",
    "\n",
    "其主要问题是在每次决策时找到一个分割点，让生成的子集尽可能地纯净。这里涉及到四个问题:\n",
    "\n",
    "1. 如何分割样本？\n",
    "\n",
    "2. 如何评价子集的纯净度？\n",
    "\n",
    "3. 如何找到单个最佳的分割点，其子集最为纯净？\n",
    "\n",
    "4. 如何找到最佳的分割点序列，其最终分割子集总体最为纯净？\n",
    "\n",
    "接下来，围绕上述问题，一一概要说明，并加以演示。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 加载数据\n",
    "\n",
    "古话说，「三军未动，粮草先行」。\n",
    "\n",
    "我们先加载演示数据，使用的是 sklearn 自带的测试用例。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "data = load_iris()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length  sepal_width  petal_length  petal_width\n",
       "0           5.1          3.5           1.4          0.2\n",
       "1           4.9          3.0           1.4          0.2"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 准备特征数据\n",
    "X = pd.DataFrame(data.data, \n",
    "                 columns=[\"sepal_length\", \"sepal_width\", \"petal_length\", \"petal_width\"])\n",
    "X.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   target\n",
       "0  setosa\n",
       "1  setosa\n",
       "2  setosa"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 准备标签数据\n",
    "y = pd.DataFrame(data.target, columns=['target'])\n",
    "y.replace(to_replace=range(3), value=data.target_names, inplace=True)\n",
    "y.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length  sepal_width  petal_length  petal_width  target\n",
       "0           5.1          3.5           1.4          0.2  setosa\n",
       "1           4.9          3.0           1.4          0.2  setosa\n",
       "2           4.7          3.2           1.3          0.2  setosa"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 组建样本 [特征，标签]\n",
    "samples = pd.concat([X, y], axis=1) #, keys=[\"x\", \"y\"])\n",
    "samples.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.0 如何分割样本\n",
    "决策树的分割方法是取一个特征 $f$ 和阈值 $t$，以此为界将样本 $X$ 拆分为两个子集 $X_l, X_r$。其数学表达形同：\n",
    "\n",
    "\\begin{align}\n",
    "    X = \\begin{cases}\n",
    "        X_l, \\ \\text{if } X[f] < t \\\\\n",
    "        X_r, \\ \\text{if } X[f] \\geq t\n",
    "    \\end{cases}\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def splitter(samples, feature, threshold):\n",
    "    # 按特征 f 和阈值 t 分割样本\n",
    "    \n",
    "    left_nodes = samples.query(\"{f} < {t}\".format(f=feature, t=threshold))\n",
    "    right_nodes = samples.query(\"{f} >= {t}\".format(f=feature, t=threshold))\n",
    "    \n",
    "    return {\"left_nodes\": left_nodes, \"right_nodes\": right_nodes}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "setosa        20\n",
       "versicolor     1\n",
       "virginica      1\n",
       "Name: target, dtype: int64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "split = splitter(samples, \"sepal_length\", 5)\n",
    "\n",
    "# 左子集\n",
    "x_l = split[\"left_nodes\"].loc[:, \"target\"].value_counts()\n",
    "x_l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "virginica     49\n",
       "versicolor    49\n",
       "setosa        30\n",
       "Name: target, dtype: int64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 右子集\n",
    "x_r = split[\"right_nodes\"].loc[:, \"target\"].value_counts()\n",
    "x_r"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. 如何评价子集的纯净度？\n",
    "\n",
    "从常理来说，我们希望分割子集尽可能地纯净，最好是单个子集就只含有一类标签，从而保证决策结果精准。\n",
    "\n",
    "那么什么样的评价函数，可以用来度量各子集的纯净度呢？\n",
    "\n",
    "以刚才计算结果为例， $x_l$ 主要标签是 setosa，非常纯净，而 $x_r$ 则三种标签势均力敌，非常混杂。所以思路是，若一种标签在子集中占比非常大，则此子集就较纯净；若各标签占比差别不大，就较为混杂。\n",
    "\n",
    "常用的评价函数正是计算各标签 $c_k$ 在子集中的占比 $p_k = c_k / \\sum (c_k)$，并通过组合 $p_k$ 来描述占比集中或分散。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calc_class_proportion(node):\n",
    "    # 计算各标签在集合中的占比\n",
    "    \n",
    "    y = node[\"target\"]\n",
    "    return y.value_counts() / y.count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "setosa        0.909091\n",
       "versicolor    0.045455\n",
       "virginica     0.045455\n",
       "Name: target, dtype: float64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calc_class_proportion(split[\"left_nodes\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "virginica     0.382812\n",
       "versicolor    0.382812\n",
       "setosa        0.234375\n",
       "Name: target, dtype: float64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calc_class_proportion(split[\"right_nodes\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "主要的评价函数有三种，它们评价的是集合的不纯度（值越大，集合越混杂）。\n",
    "\n",
    "先做些数学定义以便于描述：     \n",
    "假设对于集合 $m$ 有 $N_m$ 个样本，可分割成 $R_m$ 子集。     \n",
    "若总的标签类别有 $K$ 种，则标签 $k$ 在此集合中的占比为：\n",
    "\n",
    "\\begin{equation}\n",
    "    \\hat{p}_{m k} = \\frac{1}{N_m} \\displaystyle \\sum_{x_i \\in R_m} I(y_i = k)\n",
    "\\end{equation}\n",
    "\n",
    "且令标签 $k$ 是占比最大的标签，即 $k(m) = \\operatorname{arg max}_k \\hat{p}_{m k}$.\n",
    "\n",
    "##### 1. Misclassification error\n",
    "我们一般把集合的分类结果定义为占比最大的标签，那么落在此集合中的其它标签就是误分类。其比率是 $1 - \\hat{p}_{m k}(m)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def misclassification_error(node):\n",
    "    p_mk = calc_class_proportion(node)\n",
    "    \n",
    "    return 1 - p_mk.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.090909090909090939"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "misclassification_error(split[\"left_nodes\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6171875"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "misclassification_error(split[\"right_nodes\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对于二分类问题，"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>p</th>\n",
       "      <th>1-p</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02</td>\n",
       "      <td>0.98</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      p   1-p\n",
       "0  0.00  1.00\n",
       "1  0.01  0.99\n",
       "2  0.02  0.98"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binary_class = pd.Series(np.arange(0, 1.01, 0.01)).to_frame(name=\"p\")\n",
    "binary_class[\"1-p\"] = 1 - binary_class[\"p\"]\n",
    "binary_class.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "误分类率和占比 $p$ 的关系可划图为："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x114376080>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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1xXLzR6/CjoG2CcMwtHT9QVVUNSh7fLJS+vc0+yQADpeZnqRRg69X8fHz2rDr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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114376470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "binary_class[\"misclass\"] = binary_class.apply(lambda x: 1 - x.max(), axis=1)\n",
    "binary_class.plot(x=\"p\", y=\"misclass\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "当 $p=0.5$，两种标签各占一半，不纯度最高；当 $p=0$ 或 $p=1$, 只含有其中一种标签时，不纯度最低。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2. Gini index\n",
    "这里的基尼系数并非是经济上测量分配公平的指标。\n",
    "\n",
    "它的思路是从集合中随机抽取元素 $a \\in K_p$，再以 $K_p$ 在集合中的分布为参考随机给 $a$ 分配标签，那么误分配率就是基尼系数。\n",
    "\n",
    "具体到决策树的节点 $m$ 上，标签 $k_i$ 的占比为 $p_{k_i m}$。则抽中属于标签 $k_i$ 的元素概率是 $p_{k_i m}$，误分配到其它标签的概率是 $\\sum_{k' \\neq k_i} p_{k_i m} p_{k' m}$。对于整个集合的标签则是：\n",
    "\n",
    "\\begin{equation}\n",
    "    G(m) = \\displaystyle \\sum_{k \\neq k'} p_{k m} p_{k' m} \\, \\overset{乘法分配律}{=} \\sum_{k = 1}^{K} p_{k m} (1 - p_{k m})\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gini_index(node):\n",
    "    p_mk = calc_class_proportion(node)\n",
    "    \n",
    "    return (p_mk * (1 - p_mk)).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1694214876033058"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gini_index(split[\"left_nodes\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6519775390625"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gini_index(split[\"right_nodes\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在二分类中，基尼系数和占比 $p$ 的关系可划图为："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1143a2630>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ioaUJoiORm1MqFHju4UzkpIwf7n59VxlMZpY02Q4LmhzOgM6AV98rQVe/HuuWJuDhZQmi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\nkQP6/wGN/Cjo34jR5AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1142fbeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "binary_class[\"gini\"] = (binary_class[\"p\"] * binary_class[\"1-p\"] * 2)\n",
    "binary_class.plot(x=\"p\", y=\"gini\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 3. Cross-entropy\n",
    "ref:    \n",
    "[Qualitively what is Cross Entropy](http://stats.stackexchange.com/questions/80967/qualitively-what-is-cross-entropy)\n",
    "\n",
    "这个损失函数的思路来源于信息论：若某事件的发生概率是 $p$，则需至少 $\\log_2 (1/p)$ 位编码。那么对于所有事件，其最优编码的平均字长为 $\\sum_i p_i \\log_2 (1 / p_i)$。\n",
    "\n",
    "借用其思路，对于节点来说，其内容越混杂，就需要越多字长来区分。所以这里 cross-entropy 定义为：\n",
    "\n",
    "\\begin{equation}\n",
    "    C(m) = \\displaystyle \\sum_{k=1}^K p_{m k} \\log (1 / p_{m k}) \\, = - \\sum_{k=1}^K p_{m k} \\log p_{m k}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def cross_entropy(node):\n",
    "    p_mk = calc_class_proportion(node)\n",
    "    \n",
    "    return - (p_mk * p_mk.apply(np.log)).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.36764947740014225"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_entropy(split[\"left_nodes\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.075199711851601"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cross_entropy(split[\"right_nodes\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在二分类中，cross-entropy 和占比 $p$ 的关系可划图为："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x116c16668>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4q23GAg3CYE40bf4/kZ6ejtzcXGRkZAAAsrKykJOTA4PBgBUrVuDZZ5/F6tWr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\nTogBTURE5IQY0ERERE7o/wMX4mupHpqJ5wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116c1f978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = binary_class[[\"p\", \"1-p\"]]\n",
    "binary_class[\"cross_entropy\"] = -(x * np.log(x)).sum(axis=1)\n",
    "binary_class.plot(x=\"p\", y=\"cross_entropy\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在二分类问题中，三种评价函数的比较如图:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x116dacb00>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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R673ljiQIgpO4d+pE8N/uxWE0UvThfBxms9yRhIskCrqDcFgsFC6cj8NoIPie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\nAgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116db8470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "binary_class.plot(x=\"p\", y=[\"misclass\", \"gini\", \"cross_entropy\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "为了便于比较，我们将 cross_entropy 也放缩到 $(0.5, 0.5)$。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x116d3d4a8>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ow668OERuTT7vJL3P+eps4vw781jveYTZaZ1me4xzYbmONz9PApmMJ+/qQzt/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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116c16438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "binary_class[\"cross_entropy_scaled\"] = binary_class[\"cross_entropy\"] / binary_class[\"cross_entropy\"].max() * 0.5\n",
    "binary_class.plot(x=\"p\", y=[\"misclass\", \"gini\", \"cross_entropy_scaled\"], ylim=[0,0.55])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以看到，识分类率在整个区间是均一的，而 cross_entropy 越靠近纯净，其值变化越剧烈。所以 cross_entropy 对纯净更敏感的特性，有利于让结果子集更纯净，其使用相对较多。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "####  3. 如何找到单个最佳的分割点，其子集最为纯净？\n",
    "单个最佳分割点，涉及三个问题：\n",
    "\n",
    "1. 对于单次分割，分割前和分割后，集合的纯净度提升了多少？\n",
    "\n",
    "2. 给定一个特征，纯净度提升最大的阈值是多少？\n",
    "\n",
    "3. 对于多个特征，哪一个特征的最佳阈值对纯净度提升最大？\n",
    "\n",
    "\n",
    "##### 3.1 对于单次分割，分割前和分割后，集合的纯净度提升了多少？\n",
    "令测量不纯度的函数为 $G$,    \n",
    "对一个节点 $m$ 来说，若其按分割方法 $f$ 得到子集 $m_l$ 和 $m_r$，则总的不纯度减少量为：\n",
    "\n",
    "\\begin{equation}\n",
    "    G(m) - G(m_l) - G(m_r)\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def calc_impurity_measure(node, feathure, threshold, measure, min_nodes=5):\n",
    "    child = splitter(node, feathure, threshold)\n",
    "    left = child[\"left_nodes\"]\n",
    "    right = child[\"right_nodes\"]\n",
    "    \n",
    "    if left.shape[0] <= min_nodes or right.shape[0] <= min_nodes:\n",
    "        return 0\n",
    "    \n",
    "    \n",
    "    impurity = pd.DataFrame([], \n",
    "                       columns=[\"score\", \"rate\"],\n",
    "                       index=[])\n",
    "    \n",
    "    impurity.loc[\"all\"] = [measure(node), node.shape[0]]\n",
    "    impurity.loc[\"left\"] = [-measure(left), left.shape[0]]\n",
    "    impurity.loc[\"right\"] = [-measure(right), right.shape[0]]\n",
    "    \n",
    "    impurity[\"rate\"] /= impurity.at[\"all\", \"rate\"]\n",
    "    \n",
    "    logger.info(impurity)\n",
    "    \n",
    "    return (impurity[\"score\"] * impurity[\"rate\"]).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08546401515151514"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calc_impurity_measure(samples, \"sepal_length\", 5, gini_index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calc_impurity_measure(samples, \"sepal_length\", 1, gini_index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 3.2. 给定一个特征，纯净度提升最大的阈值是多少？\n",
    "\n",
    "对于一个给定的特征，理论上通过枚取所有可能的阈值，从中找到最大减少量的阈值点，就是此特征的最佳分隔点。\n",
    "\n",
    "但现实中，很多特征是连续的，或者阈值点太多，全部穷尽并不现实，往往需要用到最优化的寻优方法。这里为了简易起见，我们对特征的值由小到大设了10个分位点，进行计算。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def find_best_threshold(node, feature, measure):\n",
    "    threshold_candidates = node[feature].quantile(np.arange(0, 1, 0.2))\n",
    "    \n",
    "    res = pd.Series([], name=feature)\n",
    "    for t in threshold_candidates:\n",
    "        res[t] = calc_impurity_measure(node, feature, t, measure)\n",
    "    \n",
    "    logger.info(res)\n",
    "    \n",
    "    if res.max() == 0:\n",
    "        return None\n",
    "    else:\n",
    "        return res.argmax()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.3999999999999999"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "find_best_threshold(samples, \"sepal_width\", gini_index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.5999999999999996"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "find_best_threshold(samples, \"sepal_length\", gini_index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 3.3. 对于多个特征，哪一个特征的最佳阈值对纯净度提升最大？\n",
    "显然，最暴力的方法是：每次分割，我们穷尽所有特征，即可找到对此节点最佳分割点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def find_best_split(node, measure):\n",
    "    if node[\"target\"].unique().shape[0] <= 1:\n",
    "        return None\n",
    "    \n",
    "    purity_gain = pd.Series([], name=\"feature\")\n",
    "    \n",
    "    for f in node.drop(\"target\", axis=1).columns:\n",
    "        purity_gain[f] = find_best_threshold(node, f, measure)\n",
    "        \n",
    "    if pd.isnull(purity_gain.max()):\n",
    "        return None\n",
    "    else:\n",
    "        best_split = {\"feature\": purity_gain.argmax(), \"threshold\": purity_gain.max()}\n",
    "        best_split[\"child\"] = splitter(node, **best_split)\n",
    "\n",
    "        return best_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['sepal_length', 5.5999999999999996]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_split = find_best_split(samples, gini_index)\n",
    "[best_split[x] for x in [\"feature\", \"threshold\"]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####  4. 如何找到最佳的分割点序列，其最终分割子集总体最为纯净？\n",
    "搜索全局最优解在目前还没有有效的方法，所以退一步，我们用贪婪的思想，在每次分割时取最优，希望由局部最优的分割序列能够达到全局最优的效果。\n",
    "\n",
    "我们使用递归的方法由上而下依次计算，在处理节点顺序时使用深度优先方法组建出决策树。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class BinaryNode:\n",
    "    def __init__(self, samples, max_depth, measure=gini_index):\n",
    "        self.samples = samples\n",
    "        self.max_depth = max_depth\n",
    "        self.measure = measure\n",
    "        \n",
    "        self.is_leaf = False\n",
    "        self.class_ = None\n",
    "        \n",
    "        self.left = None\n",
    "        self.right = None\n",
    "        \n",
    "        self.best_split = None\n",
    "    \n",
    "    def split(self, depth):\n",
    "        if depth > self.max_depth:\n",
    "            self.is_leaf = True\n",
    "            self.class_ = self.samples[\"target\"].value_counts().argmax()\n",
    "            return\n",
    "        \n",
    "        best_split = find_best_split(self.samples, self.measure)\n",
    "        if pd.isnull(best_split):\n",
    "            self.is_leaf = True\n",
    "            self.class_ = self.samples[\"target\"].value_counts().argmax()\n",
    "            return\n",
    "\n",
    "        self.best_split = best_split\n",
    "        left = self.best_split[\"child\"][\"left_nodes\"]\n",
    "        self.left = BinaryNode(left.drop(best_split[\"feature\"], axis=1), self.max_depth)\n",
    "        \n",
    "        right = self.best_split[\"child\"][\"right_nodes\"]\n",
    "        self.right = BinaryNode(right.drop(best_split[\"feature\"], axis=1), self.max_depth)\n",
    "\n",
    "        # 先序深度优先\n",
    "        self.left.split(depth+1)\n",
    "        self.right.split(depth+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "binaryNode = BinaryNode(samples, 3)\n",
    "binaryNode.split(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def show(node, depth):\n",
    "    if node.left:\n",
    "        show(node.left, depth+1)\n",
    "    \n",
    "    if node.is_leaf:\n",
    "        print(\"{}{}\".format(\"\\t\"*(depth+2), node.class_))\n",
    "        return \n",
    "    else:\n",
    "        print(\"{}{}: {}\".format(\"\\t\"*depth,\n",
    "                                node.best_split[\"feature\"],\n",
    "                                node.best_split[\"threshold\"]))\n",
    "    if node.right:\n",
    "        show(node.right, depth+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\t\t\t\tversicolor\n",
      "\tsepal_width: 2.8200000000000003\n",
      "\t\t\t\t\tsetosa\n",
      "\t\tpetal_length: 1.6\n",
      "\t\t\t\t\t\tsetosa\n",
      "\t\t\tpetal_width: 0.4\n",
      "\t\t\t\t\t\tsetosa\n",
      "sepal_length: 5.6\n",
      "\t\t\t\t\tversicolor\n",
      "\t\tsepal_width: 3.1\n",
      "\t\t\t\t\tversicolor\n",
      "\tpetal_length: 4.8\n",
      "\t\t\t\t\t\tversicolor\n",
      "\t\t\tpetal_width: 1.8\n",
      "\t\t\t\t\t\tvirginica\n",
      "\t\tsepal_width: 2.9\n",
      "\t\t\t\t\t\tvirginica\n",
      "\t\t\tpetal_width: 2.0\n",
      "\t\t\t\t\t\tvirginica\n"
     ]
    }
   ],
   "source": [
    "show(binaryNode, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "观察可知，这颗树是有问题的，如 petal_width: 0.4 下两个叶子的类别均是 setosa。在树生成后，可以通过后续的剪枝操作，让整颗树更精简。这里不再详述。"
   ]
  }
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