algo_example_DT_decision_trees.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Source: [Wikipedia](https://en.wikipedia.org/wiki/Decision_tree_learning) and [Some example](http://dni-institute.in/blogs/gini-index-work-out-example/).\n",
    "\n",
    "## Decision Tree\n",
    "\n",
    "[Decision Tree](https://en.wikipedia.org/wiki/Decision_tree_learning) is one of the simplest and most effective algorithm for classification and regression. Can be used on both numerical and categorical-type dataset.\n",
    "\n",
    "The most common ones are ID3, C4.5, CART (Classification And Regression Tree), CHAID (CHi-squared Automatic Interaction Detector), and MARS.\n",
    "\n",
    "The key idea is to have decision \"fork\" and branches out in a tree strucure, finally arriving at a good degree of segregation between classes. We do have to define a metric that can select good features for us to branch out.\n",
    "\n",
    "![img](https://upload.wikimedia.org/wikipedia/commons/f/f3/CART_tree_titanic_survivors.png)\n",
    "\n",
    "## Metrics\n",
    "\n",
    "We are going to use [Information Gain](https://en.wikipedia.org/wiki/Decision_tree_learning#Information_gain) for this example. \n",
    "\n",
    "Let $ f_i $ be the fraction of data points labeled as class $ i $ in the dataset.\n",
    "\n",
    "Entropy $H$ is\n",
    "\n",
    "$$ H(f) = - \\sum_{i} f_i \\cdot log_2 f_i $$\n",
    "\n",
    "Information Gain $G$ is = Entropy(Parent) - Weighted sum of Entropy(children)\n",
    "\n",
    "$$ G(T,a) = H(T) - \\frac{1}{N} \\sum_{a = 1}^N H(T \\vert a) $$\n",
    "\n",
    "We want to minimize this metric for each chosen cutoff-point.\n",
    "\n",
    "## Coding\n",
    "\n",
    "From 2D dataset, this is going to be a simple 2-layer tree.\n",
    "\n",
    "2 decision nodes (either start at X0 or X1 first) then 4 leaf nodes (the final prediction of class 0 or 1)\n",
    "\n",
    "...\n",
    "\n",
    "..\n",
    "\n",
    "."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from random import randint\n",
    "from pandas import Series,DataFrame\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "import math\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (8, 6)\n",
    "plt.rcParams['font.size'] = 14"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make Random dataset.\n",
    "\n",
    "Source: http://scikit-learn.org/stable/auto_examples/datasets/plot_random_dataset.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.FacetGrid at 0x28854a20>"
      ]
     },
     "execution_count": 263,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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Tx8fx4J77cPL4eNXksfxYbu852OzvJyJqF51+P3Ryfp1+LYjI/zgiSL7U6IR9J/M8mr04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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x28854cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_classification\n",
    "\n",
    "df = pd.DataFrame(columns=['X0','X1','Y'])\n",
    "X, Y = make_classification(n_samples=1000, n_features=2, class_sep=0.7, hypercube=True, \\\n",
    "                           n_informative=2, n_redundant=0, n_classes=2, n_clusters_per_class=1)\n",
    "train_test_split = 0.7\n",
    "train_size = int(X.shape[0]*train_test_split) \n",
    "test_size = X.shape[0] - train_size\n",
    "X_train,Y_train,X_test,Y_test = X[0:train_size],Y[0:train_size],X[train_size:],Y[train_size:] \n",
    "df['X0'],df['X1'],df['Y'] = X[:, 0],X[:, 1],Y\n",
    "df['type'] = 'train'\n",
    "df.loc[train_size:,'type'] = 'test'\n",
    "\n",
    "#plt.title(\"four clusters\", fontsize='small')\n",
    "#plt.scatter(X[:, 0], X[:, 1], marker='o', c=Y)\n",
    "sns.lmplot(x='X0',y='X1',data=df,hue='Y',fit_reg=False, col='type', size=6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from math import log\n",
    "def entropy(Y):\n",
    "    if (len(Y) == 0):\n",
    "        return 0\n",
    "    p = np.count_nonzero(Y)*1.0/Y.shape[0]\n",
    "    if(p == 0 or p == 1):\n",
    "        return 0\n",
    "    else:\n",
    "        return -p*log(p,2) -(1-p)*log(1-p,2)\n",
    "def find_cutoff(X,Y, split_size):\n",
    "    # search tree, try 5 cutoff points, each axis\n",
    "    X_min = np.min(X)\n",
    "    X_max = np.max(X)\n",
    "\n",
    "    E_root = entropy(Y)\n",
    "    E_X_best = E_root\n",
    "    X_cutoff_best = 0.0\n",
    "    print 'X_min = {:.2f},X_max = {:.2f}'.format(X_min,X_max)\n",
    "    print 'root entropy = {:.3f}'.format(E_root)\n",
    "    for i in range(0,split_size):\n",
    "        X_cutoff_point = round(X_min + (X_max - X_min)/(split_size+1)*(i+1),3)\n",
    "\n",
    "        index_lower = (X < X_cutoff_point)\n",
    "        index_higer = np.logical_not(index_lower)\n",
    "        len_lower,len_higher = len(Y[index_lower]),len(Y[index_higer])\n",
    "        len_all = len_lower + len_higher\n",
    "\n",
    "        E_lower = entropy(Y[index_lower])\n",
    "        E_higher = entropy(Y[index_higer])\n",
    "\n",
    "        E_X = 1.0*len_lower/len_all*E_lower + 1.0*len_higher/len_all*E_higher\n",
    "\n",
    "        if(E_X < E_X_best):\n",
    "            E_X_best = E_X\n",
    "            X_cutoff_best = X_cutoff_point\n",
    "            \n",
    "    print 'Chosen X cut_off = {:.2f}, E = {:.3f}'.format(X_cutoff_best,E_X_best)\n",
    "    print ''\n",
    "    return X_cutoff_best,E_X_best"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Start with X0 split, then X1 split.\n",
    "\n",
    "Calculate final entropy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X0\n",
      "X_min = -1.91,X_max = 3.33\n",
      "root entropy = 1.000\n",
      "Chosen X cut_off = -0.17, E = 0.567\n",
      "\n",
      "X1 for X0 left side\n",
      "X_min = -2.81,X_max = 3.85\n",
      "root entropy = 0.665\n",
      "Chosen X cut_off = 0.52, E = 0.174\n",
      "\n",
      "X1 for X0 right side\n",
      "X_min = -2.81,X_max = 2.88\n",
      "root entropy = 0.450\n",
      "Chosen X cut_off = 0.98, E = 0.427\n",
      "\n",
      "final entropy = 0.289\n"
     ]
    }
   ],
   "source": [
    "# search tree, try 5 cutoff points, each axis\n",
    "# Test X0 first\n",
    "print 'X0'\n",
    "L0_cut,E_L0 = find_cutoff(X_train[:,0],Y_train,5)\n",
    "index_left = (X_train[:,0] < L0_cut)\n",
    "index_right = np.logical_not(index_left)\n",
    "\n",
    "#X0 left side, Test X1\n",
    "print 'X1 for X0 left side'\n",
    "L1_left_cut,E_L1_left = find_cutoff(X_train[index_left,1],Y_train[index_left],5)\n",
    "print 'X1 for X0 right side'\n",
    "L1_right_cut,E_L1_right = find_cutoff(X_train[index_right,1],Y_train[index_right],5)\n",
    "\n",
    "len_left,len_right = len(Y_train[index_left]),len(Y_train[index_right])\n",
    "len_all = len_left + len_right\n",
    "E_fin1 = 1.0*len_left/len_all*E_L1_left + 1.0*len_right/len_all*E_L1_right\n",
    "cut = [L0_cut,L1_left_cut,L1_right_cut]\n",
    "print 'final entropy = {:.3f}'.format(E_fin1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now try out X1 first then X0.\n",
    "\n",
    "Calculate final entropy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X1\n",
      "X_min = -1.91,X_max = 3.33\n",
      "root entropy = 1.000\n",
      "Chosen X cut_off = -0.17, E = 0.567\n",
      "\n",
      "X0 for X1 left side\n",
      "X_min = -1.64,X_max = 3.33\n",
      "root entropy = 0.841\n",
      "Chosen X cut_off = 0.01, E = 0.130\n",
      "\n",
      "X0 for X1 right side\n",
      "X_min = -1.91,X_max = 2.66\n",
      "root entropy = 0.821\n",
      "Chosen X cut_off = 0.37, E = 0.630\n",
      "\n",
      "final entropy = 0.381\n"
     ]
    }
   ],
   "source": [
    "# search tree, try 5 cutoff points, each axis\n",
    "# Test X1\n",
    "print 'X1'\n",
    "L0_cut,E_L0 = find_cutoff(X_train[:,0],Y_train,5)\n",
    "index_left = (X_train[:,1] < L0_cut)\n",
    "index_right = np.logical_not(index_left)\n",
    "\n",
    "#X0 left side, Test X1\n",
    "print 'X0 for X1 left side'\n",
    "L1_left_cut,E_L1_left = find_cutoff(X_train[index_left,0],Y_train[index_left],5)\n",
    "print 'X0 for X1 right side'\n",
    "L1_right_cut,E_L1_right = find_cutoff(X_train[index_right,0],Y_train[index_right],5)\n",
    "\n",
    "len_left,len_right = len(Y_train[index_left]),len(Y_train[index_right])\n",
    "len_all = len_left + len_right\n",
    "E_fin2 = 1.0*len_left/len_all*E_L1_left + 1.0*len_right/len_all*E_L1_right\n",
    "print 'final entropy = {:.3f}'.format(E_fin2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Start pop. class 0 and 1 = 355/345\n",
      "=> X0, cutoff at < -0.17, pop. = 66/315\n",
      "===> X1, cutoff at < 0.52,  pop. = 3/305, predict 1\n",
      "===> X1, cutoff at >= 0.52, pop. = 63/10, predict 0\n",
      "=> X0, cutoff at >= -0.17, pop. = 289/30\n",
      "===> X1, cutoff at < 0.98,  pop. = 216/29, predict 0\n",
      "===> X1, cutoff at >= 0.98, pop. = 73/1, predict 0\n"
     ]
    }
   ],
   "source": [
    "var = [0,1]\n",
    "if E_fin2 < E_fin1:\n",
    "    var = [1,0]\n",
    "    cut = [L0_cut,L1_left_cut,L1_right_cut]\n",
    "E_fin = min(E_fin1,E_fin1)\n",
    "\n",
    "i_v0_l = (X_train[:,var[0]] < cut[0])\n",
    "i_v0_h = np.logical_not(i_v0_l)\n",
    "i_v1_ll = (X_train[:,var[1]] < cut[1]) & i_v0_l\n",
    "i_v1_lh = np.logical_not(i_v1_ll) & i_v0_l\n",
    "i_v1_hl = (X_train[:,var[1]] < cut[2]) & i_v0_h\n",
    "i_v1_hh = np.logical_not(i_v1_hl) & i_v0_h\n",
    "\n",
    "p_v1_ll = np.argmax(np.bincount(Y_train[i_v1_ll])) #find mode\n",
    "p_v1_lh = np.argmax(np.bincount(Y_train[i_v1_lh]))\n",
    "p_v1_hl = np.argmax(np.bincount(Y_train[i_v1_hl]))\n",
    "p_v1_hh = np.argmax(np.bincount(Y_train[i_v1_hh]))\n",
    "\n",
    "print 'Start pop. class 0 and 1 = {}/{}'.format(len(Y_train) - np.sum(Y_train),np.sum(Y_train))\n",
    "print '=> X{}, cutoff at < {:.2f}, pop. = {}/{}'.format( var[0],cut[0], \\\n",
    "        len(Y_train[i_v0_l]) - np.sum(Y_train[i_v0_l]),np.sum(Y_train[i_v0_l]))\n",
    "print '===> X{}, cutoff at < {:.2f},  pop. = {}/{}, predict {}'.format(var[1],cut[1], \\\n",
    "        len(Y_train[i_v1_ll]) - np.sum(Y_train[i_v1_ll]),np.sum(Y_train[i_v1_ll]),p_v1_ll)\n",
    "print '===> X{}, cutoff at >= {:.2f}, pop. = {}/{}, predict {}'.format(var[1],cut[1], \\\n",
    "        len(Y_train[i_v1_lh]) - np.sum(Y_train[i_v1_lh]),np.sum(Y_train[i_v1_lh]),p_v1_lh)\n",
    "print '=> X{}, cutoff at >= {:.2f}, pop. = {}/{}'.format( var[0],cut[0], \\\n",
    "        len(Y_train[i_v0_h]) - np.sum(Y_train[i_v0_h]),np.sum(Y_train[i_v0_h]))\n",
    "print '===> X{}, cutoff at < {:.2f},  pop. = {}/{}, predict {}'.format(var[1],cut[2], \\\n",
    "        len(Y_train[i_v1_hl]) - np.sum(Y_train[i_v1_hl]),np.sum(Y_train[i_v1_hl]),p_v1_hl)\n",
    "print '===> X{}, cutoff at >= {:.2f}, pop. = {}/{}, predict {}'.format(var[1],cut[2], \\\n",
    "        len(Y_train[i_v1_hh]) - np.sum(Y_train[i_v1_hh]),np.sum(Y_train[i_v1_hh]),p_v1_hh)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#calculate Y_pred\n",
    "Y_pred = np.zeros(shape=Y_test.shape)\n",
    "\n",
    "t_l = (X_test[:,var[0]] < cut[0])\n",
    "t_h = np.logical_not(t_l)\n",
    "t_ll = (X_test[:,var[1]] < cut[1]) & t_l\n",
    "t_lh = np.logical_not(t_ll) & t_l\n",
    "t_hl = (X_test[:,var[1]] < cut[2]) & t_h\n",
    "t_hh = np.logical_not(t_hl) & t_h\n",
    "\n",
    "Y_pred[t_ll] = p_v1_ll\n",
    "Y_pred[t_lh] = p_v1_lh\n",
    "Y_pred[t_hl] = p_v1_hl\n",
    "Y_pred[t_hh] = p_v1_hh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test set Accuracy = 94.67%\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x28c679e8>"
      ]
     },
     "execution_count": 270,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x24a5f048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "cm_mat = confusion_matrix(Y_test,Y_pred)\n",
    "\n",
    "accuracy = np.trace(cm_mat)*100.0/len(Y_test)\n",
    "print 'Test set Accuracy = {:.2f}%'.format(accuracy)\n",
    "\n",
    "df_temp = pd.DataFrame(cm_mat.flatten()[np.newaxis].T,columns = ['values'])\n",
    "df_temp = pd.DataFrame(cm_mat.flatten()[np.newaxis].T,columns = ['values'])\n",
    "plt.figure(figsize = (6,4),dpi=600)\n",
    "sns.heatmap(cm_mat.T, cbar=True ,annot=True, fmt=',.0f')\n",
    "plt.xlabel('Truth')\n",
    "plt.ylabel('Predicted')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}