note/RegressionTree.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 回归树"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 背景"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CART是Classification And Regression Tree，这里以Regression Tree为例预习一下回归树。\n",
    "\n",
    "回归树，或者广义的决策树的工作原理与传统基于梯度下降迭代的Neural Network，或者直接求解析解的线性回归不太一样，它并不是通过某种线性或者非线性的映射，或者变换来进行预测，实现起来也比较反直觉，它的数据结构是一颗二叉树，详细的实现会在下文展示。\n",
    "\n",
    "但是它的目的和Linear Regression，Neural Network的目的是相同的，本质上都是希望经验风险或者结构风险最小化。\n",
    "\n",
    "以一个回归问题为例，Regression Tree的目的也是经验风险或者结构风险最小化，此处以最小化Mean Square Loss为例，当时此处的Loss Function是比较自由的，针对具体的学习任务，换成MAE，或者其他Make Sense的Loss Function也完全可以。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 数据"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "首先我们先用几行代码生成一下数据。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11781b9e8>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd \n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "x = np.linspace(-10, 10, 100).reshape((-1, 1))\n",
    "y = np.linspace(-20, 20, 100) + np.random.normal(loc=0, scale=3.5, size=(100, ))\n",
    "\n",
    "df = pd.DataFrame()\n",
    "df['x'] = x.reshape((-1, ))\n",
    "df['y'] = y\n",
    "\n",
    "df.plot.scatter(x='x', y='y', figsize=(12, 7))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 算法"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们希望最小化："
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\frac{1}{N_1}\\sum (y_k - c_1)^2 + \\frac{1}{N_2}\\sum (y_2 - c_2)^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "只是此处与Linear Regression直接求伪逆与Y的乘积，或者与通过梯度下降与反向传播迭代求解的Neural Network不同，Regression Tree通过以下算法最小化上式的Mean Square Error，具体方法会是这样的：\n",
    "\n",
    "对于一个Shape为$\\ N × M \\ $的数据集$X$，即N行M列的数据集$X$，依次逐列遍历逐行，对j列i行，计算下式："
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \n",
    "\\left\\{\n",
    "\\begin{aligned}\n",
    "c_1 &= \\frac{1}{N_1} \\sum y_{k, j} &  k \\in [0, i)\\\\\n",
    "c_2 &= \\frac{1}{N_2} \\sum y_{k, j} &  k \\in [i, N]\\\\\n",
    "\\end{aligned}\n",
    "\\right.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以看出c1, c2，是对于选定数据集i行j列作为“分割点”后，两个区间内Ground Truth的均值。计算完c1，c2后，将之带入损失函数，计算损失函数的值，并记录之，如果当前c1和c2代表的分割点i, j可以使得损失函数的值最小，那么将这个i, j记为最佳分割，并将数据集切分为$X_1$与$X_2$，构造一个节点（Node），该节点的阈值是$X_{i, j}$，树的深度自增，此时，如果树的深度（Max Depth）为1，那么算法就结束了。通常称这种深度非常浅的决策树（此处为回归树）为决策桩。\n",
    "\n",
    "这个决策桩将会是这样工作的，对于一个给定的输入向量x，如果它$x[j]$，即向量的第j个下标，小于$X_{i, j}$，那么输出c1，否则输出c2，当然，这样的模型性能是不够的，这个算法还将继续下去。\n",
    "\n",
    "之后的操作将会是这样的，对切分后的数据集$X_1$与$X_2$，分别重复以上寻找最佳分割（分裂）点的步骤，并切分数据集，直至达到我们设置的停止条件，如树的深度达到设置的最大深度，或者叶子数达到最大叶子数，或者直至数据集不可再次切分。\n",
    "\n",
    "这个过程中伴随着一颗二叉树的构造，这个构造通常是以深度优先来进行的，即在数据集，或者数据集的子区间完成寻找最佳分割点后，将构造一个树节点，这个节点通常维护了切分点的下标，以及计算出的c1与c2，以及两个孩子节点。详细的数据结构我们会在下文看到。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 实现"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这里以我们生成的数据为例，实现一个简单的回归树，首先我们定义树的结点数据结构："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Node(object):\n",
    "    def __init__(self, i, j, c1, c2, l_node=None, r_node=None):\n",
    "        self.i = i\n",
    "        self.j = j\n",
    "        self.c1 = c1\n",
    "        self.c2 = c2\n",
    "        self.offset = 0\n",
    "        self.l_node = l_node\n",
    "        self.r_node = r_node"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以看出没什么特别的，按照上文描述的，一个节点，维护了最佳切分点的下标，以及给定下标计算出的c1与c2，同时维护了一个下标i相对于原始数据集起始0的偏移，以及左右孩子节点。\n",
    "\n",
    "接下来我们实现回归树的类，用到了基本的递归生成二叉树与二叉树的先根遍历，这里不再赘述了，一些逻辑写在了注释里："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Node(object):\n",
    "    def __init__(self, i, j, c1, c2, l_node=None, r_node=None):\n",
    "        self.i = i\n",
    "        self.j = j\n",
    "        self.c1 = c1\n",
    "        self.c2 = c2\n",
    "        self.offset = 0\n",
    "        self.l_node = l_node\n",
    "        self.r_node = r_node\n",
    "\n",
    "\n",
    "class RegressionTree(object):\n",
    "\n",
    "    def __init__(self):\n",
    "        self._tree = None\n",
    "        self.x_data = None\n",
    "        self.y_data = None\n",
    "        self.num_nodes = 0\n",
    "\n",
    "    def fit(self, x, y, max_depth=3):\n",
    "        self.x_data = x\n",
    "        self.y_data = y\n",
    "        # Calculate nodes.\n",
    "        self.num_nodes = 2 ** max_depth - 1\n",
    "        # Init root node.\n",
    "        root_node = self.make_node(x, y)\n",
    "\n",
    "        def _fit(_x, _y, _node):\n",
    "\n",
    "            if self.num_nodes <= 0:\n",
    "                return\n",
    "\n",
    "            # Make R.\n",
    "            x_r1, y_r1 = _x[:_node.i], _y[:_node.i]\n",
    "            x_r2, y_r2 = _x[_node.i:], _y[_node.i:]\n",
    "\n",
    "            # Make left node.\n",
    "            l_node = self.make_node(x_r1, y_r1)\n",
    "            _node.l_node = l_node\n",
    "\n",
    "            self.num_nodes -= 1\n",
    "\n",
    "            if _node.l_node:\n",
    "                # Update offset.\n",
    "                l_node.offset = _node.offset\n",
    "                _fit(x_r1, y_r1, _node.l_node)\n",
    "\n",
    "            # Make right node.\n",
    "            r_node = self.make_node(x_r2, y_r2)\n",
    "            _node.r_node = r_node\n",
    "\n",
    "            self.num_nodes -= 1\n",
    "\n",
    "            if _node.r_node:\n",
    "                # Update offset.\n",
    "                r_node.offset = _node.i + _node.offset\n",
    "                _fit(x_r2, y_r2, _node.r_node)\n",
    "\n",
    "        _fit(x, y, root_node)\n",
    "\n",
    "        self._tree = root_node\n",
    "\n",
    "    def predict(self, x):\n",
    "\n",
    "        node = self._tree\n",
    "\n",
    "        def _predict(_x, _node):\n",
    "\n",
    "            val = self.x_data[_node.i + _node.offset, _node.j]\n",
    "\n",
    "            if _x[_node.j] < val:\n",
    "                if _node.l_node:\n",
    "                    return _predict(_x, _node.l_node)\n",
    "                else:\n",
    "                    return _node.c1\n",
    "            else:\n",
    "                if _node.r_node:\n",
    "                    return _predict(_x, _node.r_node)\n",
    "                else:\n",
    "                    return _node.c2\n",
    "\n",
    "        return _predict(x, node)\n",
    "\n",
    "    @staticmethod\n",
    "    def make_node(x, y):\n",
    "        # Get shape.\n",
    "        rows, cols = x.shape\n",
    "        if rows <= 1:\n",
    "            return None\n",
    "        # Init params.\n",
    "        best_i, best_j = 1, 1\n",
    "        best_c1, best_c2 = 0, 0\n",
    "        best_loss = np.inf\n",
    "        # Find best split.\n",
    "        for i in range(1, rows):\n",
    "            for j in range(0, cols):\n",
    "                # Calculate c1, c2, loss.\n",
    "                c1 = np.mean(y[:i])\n",
    "                c2 = np.mean(y[i:])\n",
    "                loss = np.mean(y[:i] - c1) + np.mean(y[i:] - c2)\n",
    "                # Update best if need.\n",
    "                if loss < best_loss:\n",
    "                    best_loss = loss\n",
    "                    best_i = i\n",
    "                    best_j = j\n",
    "                    best_c1 = c1\n",
    "                best_c2 = c2\n",
    "        node = Node(best_i, best_j, best_c1, best_c2)\n",
    "        return node"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 实验"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "接下来我们对上文生成的数据以不同的最大深度（Max Depth）构造回归树，并检查它的拟合效果，需要注意的是，最大深度其实直接决定了叶子节点的个数，他们的关系会是这样的：\n",
    "\n",
    "$$\n",
    "Max\\ Leaves = 2^{Max\\ Depth} - 1\n",
    "$$\n",
    "\n",
    "然后，我们构造并拟合数据，设置`max_depth`从2到4，然后观察他们拟合的效果："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'y')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = RegressionTree()\n",
    "\n",
    "df = pd.DataFrame()\n",
    "df['x'] = x.reshape((-1, ))\n",
    "df = df.set_index('x')\n",
    "    \n",
    "for max_depth in range(2, 8):\n",
    "    \n",
    "    t.fit(x, y, max_depth=max_depth)\n",
    "    \n",
    "    y_predict = [t.predict(x[i, :]) for i in range(0, 100)]\n",
    "    \n",
    "    df['MAX_DEPTH_{}'.format(max_depth)] = y_predict\n",
    "    \n",
    "plt.figure(figsize=(12, 7))\n",
    "plt.scatter(x, y, s=10, color='r')\n",
    "\n",
    "for max_depth in range(2, 8):\n",
    "    col_name = 'MAX_DEPTH_{}'.format(max_depth)\n",
    "    plt.plot(x, df[col_name], label=col_name)\n",
    "    \n",
    "plt.title('Regression Tree')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}