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    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Decision-Tree-(Classification)\" data-toc-modified-id=\"Decision-Tree-(Classification)-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Decision Tree (Classification)</a></span><ul class=\"toc-item\"><li><span><a href=\"#Splitting-criteria-for-classification-trees\" data-toc-modified-id=\"Splitting-criteria-for-classification-trees-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>Splitting criteria for classification trees</a></span></li><li><span><a href=\"#Impurity\" data-toc-modified-id=\"Impurity-1.2\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>Impurity</a></span><ul class=\"toc-item\"><li><span><a href=\"#Entropy\" data-toc-modified-id=\"Entropy-1.2.1\"><span class=\"toc-item-num\">1.2.1&nbsp;&nbsp;</span>Entropy</a></span></li><li><span><a href=\"#Gini-Index\" data-toc-modified-id=\"Gini-Index-1.2.2\"><span class=\"toc-item-num\">1.2.2&nbsp;&nbsp;</span>Gini Index</a></span></li></ul></li><li><span><a href=\"#Concrete-Example\" data-toc-modified-id=\"Concrete-Example-1.3\"><span class=\"toc-item-num\">1.3&nbsp;&nbsp;</span>Concrete Example</a></span></li><li><span><a href=\"#When-To-Stop-Recursing\" data-toc-modified-id=\"When-To-Stop-Recursing-1.4\"><span class=\"toc-item-num\">1.4&nbsp;&nbsp;</span>When To Stop Recursing</a></span></li><li><span><a href=\"#Implementation\" data-toc-modified-id=\"Implementation-1.5\"><span class=\"toc-item-num\">1.5&nbsp;&nbsp;</span>Implementation</a></span></li></ul></li><li><span><a href=\"#Reference\" data-toc-modified-id=\"Reference-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Reference</a></span></li></ul></div>"
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   "source": [
    "# code for loading the format for the notebook\n",
    "import os\n",
    "\n",
    "# path : store the current path to convert back to it later\n",
    "path = os.getcwd()\n",
    "os.chdir(os.path.join('..', 'notebook_format'))\n",
    "from formats import load_style\n",
    "load_style(css_style = 'custom2.css')"
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   "metadata": {},
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     "text": [
      "Ethen 2017-09-30 09:58:00 \n",
      "\n",
      "CPython 3.5.2\n",
      "IPython 6.1.0\n",
      "\n",
      "numpy 1.13.1\n",
      "pandas 0.20.3\n",
      "matplotlib 2.0.0\n",
      "sklearn 0.18.1\n"
     ]
    }
   ],
   "source": [
    "os.chdir(path)\n",
    "\n",
    "# 1. magic for inline plot\n",
    "# 2. magic to print version\n",
    "# 3. magic so that the notebook will reload external python modules\n",
    "# 4. magic to enable retina (high resolution) plots\n",
    "# https://gist.github.com/minrk/3301035\n",
    "%matplotlib inline\n",
    "%load_ext watermark\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from graphviz import Source\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.metrics import accuracy_score\n",
    "from sklearn.tree import export_graphviz\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "\n",
    "%watermark -a 'Ethen' -d -t -v -p numpy,pandas,matplotlib,sklearn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Decision Tree (Classification)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "Let us first create a scenario: say I want to buy a house and wish to borrow a loan from the bank. Now before giving me the loan, the bank is going to look at my history record like my credit, what has it been like in the past? How much money do I make? (and maybe some other information) and use them to determine whether loaning me money is a risky thing or not (whether I'm going to default). So how can the bank do this with decision trees?\n",
    "\n",
    "Decision trees are formed by a collection of rules (**if-then** statements that partition the data) based on variables available from the data set. So in the example above, a very simple decision tree model could look like this:\n",
    "\n",
    "```\n",
    "if Credit = excellent then\n",
    "    Outcome = Yes\n",
    "else if Credit = poor then\n",
    "    if Income = high then\n",
    "        Outcome = Yes\n",
    "    else if Income = low then\n",
    "        Outcome = No\n",
    "```\n",
    "\n",
    "The algorithm works by starting at the top of the tree (the root node), then it will traverse down the branches of this decision tree and ask a series of questions. In the end it will reach the bottom of the tree (the leaf node) that contains the final outcome. For example, if somebody has a credit that's poor and his/her income is high, then the bank will say a Yes, we will give him/her the loan. \n",
    "\n",
    "Our task now is to learn how to generate the tree to create these decision rules for us. Thankfully, the core method for learning a decision tree can be viewed as a recursive algorithm. A decision tree can be \"learned\" by splitting the dataset into subsets based on the input features/attributes' value. This process is repeated on each derived subset in a recursive manner called recursive partitioning:\n",
    "\n",
    "1. Start at the tree's root node\n",
    "2. Select the best rule/feature that splits the data into two subsets (child node) for the current node\n",
    "3. Repeated step 2 on each of the derived subset until the tree can't be further splitted. As we'll later see, we can set restrictions to decide when the tree should stop growing.\n",
    "\n",
    "There are a few additional details that we need to make more concrete. Including how to pick the rule/feature to split on and because it is a recursive algorithm, we have to figure out when to stop the recursion, in other words, when to not go and split another node in the tree."
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Splitting criteria for classification trees"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first question is what is the best rule/feature to split on and how do we measure that? One way to determine this is by choosing the one that maximizes the **Information Gain (IG)** at each split.\n",
    "\n",
    "$$IG(D_{p}, a) = I(D_{p}) - p_{left} I(D_{left}) - p_{right} I(D_{right})$$\n",
    "\n",
    "- $IG$: Information Gain\n",
    "- $a$: feature to perform the split\n",
    "- $I$: Some impurity measure that we'll look at in the subsequent section\n",
    "- $D_{p}$: training subset of the parent node\n",
    "- $D_{left}$, $D_{right}$ :training subset of the left/right child node\n",
    "- $p_{left}$, $p_{right}$: proportion of parent node samples that ended up in the left/right child node after the split. $\\frac{N_{left}}{N_p}$ or $\\frac{N_{right}}{N_p}$. Where:\n",
    "    - $N_p$: number of samples in the parent node\n",
    "    - $N_{left}$: number of samples in the left child node\n",
    "    - $N_{right}$: number of samples in the right child node"
   ]
  },
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   "source": [
    "## Impurity\n",
    "\n",
    "The two most common impurity measure are entropy and gini index."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Entropy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Entropy is defined as:\n",
    "\n",
    "$$I_E(t) = - \\sum_{i =1}^{C} p(i \\mid t) \\;log_2 \\,p(i \\mid t)$$\n",
    "\n",
    "for all non-empty classes, $p(i \\mid t) \\neq 0$, where:\n",
    "\n",
    "- $p(i \\mid t)$ is the proportion (or frequency or probability) of the samples that belong to class $i$ for a particular node $t$\n",
    "- $C$ is the number of unique class labels\n",
    "\n",
    "The entropy is therefore 0 if all samples at a node belong to the same class, and the entropy is maximal if we have an uniform class distribution. For example, in a binary class setting, the entropy is 0 if  $p(i =1 \\mid t) =1$ or $p(i =0 \\mid t) =1$. And if the classes are distributed uniformly with $p(i =1 \\mid t) = 0.5$ and $p(i =0 \\mid t) =0.5$ the entropy is 1, which we can visualize by plotting the entropy for binary class setting below."
   ]
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  {
   "cell_type": "code",
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    {
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nT0/R/1w8Q4lRzutdu6radP2Te1VUz8z4AAIXoR4AJoiC+nbd+NReFQx4czop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0fflCTA3LXk5662E1tdErCa6aTV9mUZvjKy/OA1/LuSJC3KUC9J0uy4GnhZVdXWG6rqncAZ7eoT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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113eba198>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 379,
       "width": 506
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def entropy(p):\n",
    "    return - p * np.log2(p) - (1 - p) * np.log2(1 - p)\n",
    "\n",
    "# change default figure and font size\n",
    "plt.rcParams['figure.figsize'] = 8, 6 \n",
    "plt.rcParams['font.size'] = 12\n",
    "\n",
    "x = np.arange(0.0, 1.0, 0.01)\n",
    "ent = [entropy(p) if p != 0 else None for p in x]\n",
    "plt.plot(x, ent)\n",
    "plt.axhline(y = 1.0, linewidth = 1, color = 'k', linestyle = '--')\n",
    "plt.ylim([ 0, 1.1 ])\n",
    "plt.xlabel('p(i=1)')\n",
    "plt.ylabel('Entropy')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gini Index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gini Index is defined as:\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "I_G(t) &= \\sum_{i =1}^{C} p(i \\mid t) \\big(1-p(i \\mid t)\\big) \\nonumber \\\\ \n",
    "       &= \\sum_{i =1}^{C} p(i \\mid t) - p(i \\mid t)^2 \\nonumber \\\\ \n",
    "       &= \\sum_{i =1}^{C} p(i \\mid t) - \\sum_{i =1}^{C} p(i \\mid t)^2 \\nonumber \\\\ \n",
    "       &= 1 - \\sum_{i =1}^{C} p(i \\mid t)^2\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "Compared to Entropy, the maximum value of the Gini index is 0.5, which occurs when the classes are perfectly balanced in a node. On the other hand, the minimum value of the Gini index is 0 and occurs when there is only one class represented in a node (A node with a lower Gini index is said to be more \"pure\").\n",
    "\n",
    "This time we plot Entropy and Gini index together to compare them against each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UXN2oP35erDX7Kjvcb0g6b0iUrhufqKRwRsYAPeWMhFA9NSdDm4tq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bMjCo6eweVZv+HKuh2AKEquK01Kw8kXZ+DSzAWIeP4xBIzlzhmi+qCyUWBoS08sqT4e+3Q2hnM8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\nNPXr4J0hsWJ7275ahqIMnDh45SV3RZkNr/1RG19/2xPrctJ/q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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1143abf60>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 464,
       "width": 562
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def gini(p):\n",
    "    return p * (1 - p) + (1 - p) * ( 1 - (1 - p) )\n",
    "\n",
    "gi = gini(x)\n",
    "\n",
    "# plot\n",
    "for i, lab in zip([ent, gi], ['Entropy', 'Gini Index']):\n",
    "    plt.plot(x, i, label = lab)\n",
    "\n",
    "plt.legend(loc = 'upper center', bbox_to_anchor = (0.5, 1.15),\n",
    "           ncol = 3, fancybox = True, shadow = False)\n",
    "plt.axhline(y = 0.5, linewidth = 1, color = 'k', linestyle = '--')\n",
    "plt.axhline(y = 1.0, linewidth = 1, color = 'k', linestyle = '--')\n",
    "plt.ylim([ 0, 1.1 ])\n",
    "plt.xlabel('p(i=1)')\n",
    "plt.ylabel('Impurity')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see from the plot, there is not much differences (as in they both increase and decrease at similar range). In practice, Gini Index and Entropy typically yield very similar results and it is often not worth spending much time on evaluating decision tree models using different impurity criteria. As for which one to use, maybe consider Gini Index, because this way, we don’t need to compute the log, which can make it a bit computationly faster.\n",
    "\n",
    "Decision trees can also be used on regression task. It's just instead of using gini index or entropy as the impurity function, we use criteria such as MSE (mean square error):\n",
    "\n",
    "$$I_{MSE}(t) = \\frac{1}{N_t} \\sum_i^{N_t}(y_i - \\bar{y})^2$$\n",
    "\n",
    "Where $\\bar{y}$ is the averages of the response at node $t$, and $N_t$ is the number of observations that reached node $t$. This is simply saying, we compute the differences between all $N_t$ observation's reponse to the average response, square it and take the average."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Concrete Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we'll calculate the Entropy score by hand to hopefully make things a bit more concrete. Using the bank loan example again, suppose at a particular node, there are 80 observations, of whom 40 were classified as Yes (the bank will issue the loan) and 40 were classified as No.\n",
    "\n",
    "We can first calculate the Entropy before making a split:\n",
    "\n",
    "$$I_E(D_{p}) = - \\left( \\frac{40}{80} log_2(\\frac{40}{80}) + \\frac{40}{80} log_2(\\frac{40}{80}) \\right) = 1$$\n",
    "\n",
    "Suppose we try splitting on Income and the child nodes turn out to be.\n",
    "\n",
    "- Left (Income = high): 30 Yes and 10 No\n",
    "- Right (Income = low): 10 Yes and 30 No\n",
    "\n",
    "$$I_E(D_{left}) = - \\left( \\frac{30}{40} log_2(\\frac{30}{40}) + \\frac{10}{40} log_2(\\frac{10}{40}) \\right) = 0.81$$\n",
    "$$I_E(D_{right}) = - \\left( \\frac{10}{40} log_2(\\frac{10}{40}) + \\frac{30}{40} log_2(\\frac{30}{40}) \\right) = 0.81$$\n",
    "$$IG(D_{p}, Income) = 1 - \\frac{40}{80} (0.81) - \\frac{40}{80} (0.81) = 0.19$$\n",
    "\n",
    "Next we repeat the same process and evaluate the split based on splitting by Credit.\n",
    "\n",
    "- Left (Credit = excellent): 20 Yes and 0 No\n",
    "- Right (Credit = poot): 20 Yes and 40 No\n",
    "\n",
    "$$I_E(D_{left}) = - \\left( \\frac{20}{20} log_2(\\frac{20}{20}) + \\frac{0}{20} log_2(\\frac{0}{20}) \\right) = 0$$\n",
    "$$I_E(D_{right}) = - \\left( \\frac{20}{60} log_2(\\frac{20}{60}) + \\frac{40}{60} log_2(\\frac{40}{60}) \\right) = 0.92$$\n",
    "$$IG(D_{p}, Credit) = 1 - \\frac{20}{80} (0) - \\frac{60}{80} (0.92) = 0.31$$\n",
    "\n",
    "In this case, it will choose Credit as the feature to split upon.\n",
    "\n",
    "If we were to have more features, the decision tree algorithm will simply try every possible split, and will choose the split that maximizes the information gain. If the feature is a continuous variable, then we can simply get the unique values of that feature in a sorted order, then try all possible split values (threshold) by using cutoff point (average) between every two values (e.g. a unique value of 1, 2, 3 will result in trying the split on the value 1.5 and 2.5). Or to speed up computations, we can bin the unqiue values into buckets, and split on the buckets."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## When To Stop Recursing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The other question that we need to address is when to stop the tree from growing. There are some early stopping criteria that is commonly used to prevent the tree from overfitting.\n",
    "\n",
    "- **Maximum depth** The length of the longest path from a root node to a leaf node will not exceed this value. This is the most commonly tuned hyperparameter for tree-based method\n",
    "- **Minimum sample split:** The minimum number of samples required to split a node should be greater than this number\n",
    "- **Minimum information gain** The minimum information gain required for splitting on the best feature\n",
    "\n",
    "And that's pretty much it for classification trees! For a more visual appealing explanation, the following link this a website that uses interactive visualization to demonstrate how decision trees work. [A Visual Introduction to Machine Learning](http://www.r2d3.us/visual-intro-to-machine-learning-part-1/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With all of that in mind, the following section implements a toy classification tree algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Tree:\n",
    "    \"\"\"\n",
    "    Classification tree using information gain with entropy as impurity\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    max_features : int or None, default None\n",
    "        The number of features to consider when looking for the best split,\n",
    "        None uses all features\n",
    "\n",
    "    min_samples_split : int, default 10\n",
    "        The minimum number of samples required to split an internal node\n",
    "\n",
    "    max_depth : int, default 3\n",
    "        Maximum depth of the tree\n",
    "\n",
    "    minimum_gain : float, default 1e-7\n",
    "        Minimum information gain required for splitting\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, max_depth = 3, max_features = None,\n",
    "                 minimum_gain = 1e-7, min_samples_split = 10):\n",
    "        self.max_depth = max_depth\n",
    "        self.max_features = max_features\n",
    "        self.minimum_gain = minimum_gain\n",
    "        self.min_samples_split = min_samples_split\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        \"\"\"pass in the 2d-array dataset and the response column\"\"\"\n",
    "        self.n_class = np.unique(y).shape[0]\n",
    "\n",
    "        # in the case you're wondering why we have this implementation of\n",
    "        # choosing the number of features to consider when looking\n",
    "        # for the best split, it will become much clearer when we\n",
    "        # start discussing Random Forest algorithm\n",
    "        if self.max_features is None or self.max_features > X.shape[1]:\n",
    "            self.max_features = X.shape[1]\n",
    "\n",
    "        self.feature_importance = np.zeros(X.shape[1])\n",
    "        self.tree = _create_decision_tree(X, y, self.max_depth,\n",
    "                                          self.minimum_gain, self.max_features,\n",
    "                                          self.min_samples_split, self.n_class,\n",
    "                                          self.feature_importance, X.shape[0])\n",
    "        self.feature_importance /= np.sum(self.feature_importance)\n",
    "        return self\n",
    "\n",
    "    def predict(self, X):\n",
    "        proba = self.predict_proba(X)\n",
    "        pred = np.argmax(proba, axis = 1)\n",
    "        return pred\n",
    "\n",
    "    def predict_proba(self, X):\n",
    "        proba = np.empty((X.shape[0], self.n_class))\n",
    "        for i in range(X.shape[0]):\n",
    "            proba[i] = self._predict_row(X[i, :], self.tree)\n",
    "\n",
    "        return proba\n",
    "\n",
    "    def _predict_row(self, row, tree):\n",
    "        \"\"\"Predict single row\"\"\"\n",
    "        if tree['is_leaf']:\n",
    "            return tree['prob']\n",
    "        else:\n",
    "            if row[tree['split_col']] <= tree['threshold']:\n",
    "                return self._predict_row(row, tree['left'])\n",
    "            else:\n",
    "                return self._predict_row(row, tree['right'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def _create_decision_tree(X, y, max_depth,\n",
    "                          minimum_gain, max_features,\n",
    "                          min_samples_split, n_class,\n",
    "                          feature_importance, n_row):\n",
    "    \"\"\"recursively grow the decision tree until it reaches the stopping criteria\"\"\"\n",
    "    try:\n",
    "        assert max_depth > 0\n",
    "        assert X.shape[0] > min_samples_split\n",
    "        column, value, gain = _find_best_split(X, y, max_features)\n",
    "        assert gain > minimum_gain\n",
    "        feature_importance[column] += (X.shape[0] / n_row) * gain\n",
    "\n",
    "        # split the dataset and grow left and right child\n",
    "        left_X, right_X, left_y, right_y = _split(X, y, column, value)\n",
    "        left_child = _create_decision_tree(left_X, left_y, max_depth - 1,\n",
    "                                           minimum_gain, max_features,\n",
    "                                           min_samples_split, n_class,\n",
    "                                           feature_importance, n_row)\n",
    "        right_child = _create_decision_tree(right_X, right_y, max_depth - 1,\n",
    "                                            minimum_gain, max_features,\n",
    "                                            min_samples_split, n_class,\n",
    "                                            feature_importance, n_row)\n",
    "    except AssertionError:\n",
    "        # if criteria reached, compute the classification\n",
    "        # probability and return it as a leaf node\n",
    "\n",
    "        # note that some leaf node may only contain partial classes,\n",
    "        # thus specify the minlength so class that don't appear will\n",
    "        # still get assign a probability of 0\n",
    "        counts = np.bincount(y, minlength = n_class)\n",
    "        prob = counts / y.shape[0]\n",
    "        leaf = {'is_leaf': True, 'prob': prob}\n",
    "        return leaf\n",
    "\n",
    "    node = {'is_leaf': False,\n",
    "            'left': left_child,\n",
    "            'right': right_child,\n",
    "            'split_col': column,\n",
    "            'threshold': value}\n",
    "    return node\n",
    "\n",
    "\n",
    "def _find_best_split(X, y, max_features):\n",
    "    \"\"\"Greedy algorithm to find the best feature and value for a split\"\"\"\n",
    "    subset = np.random.choice(X.shape[1], max_features, replace = False)\n",
    "    max_col, max_val, max_gain = None, None, None\n",
    "    parent_entropy = _compute_entropy(y)\n",
    "\n",
    "    for column in subset:\n",
    "        split_values = _find_splits(X, column)\n",
    "        for value in split_values:\n",
    "            splits = _split(X, y, column, value, return_X = False)\n",
    "            gain = parent_entropy - _compute_splits_entropy(y, splits)\n",
    "\n",
    "            if max_gain is None or gain > max_gain:\n",
    "                max_col, max_val, max_gain = column, value, gain\n",
    "\n",
    "    return max_col, max_val, max_gain\n",
    "\n",
    "\n",
    "def _compute_entropy(split):\n",
    "    \"\"\"entropy score using a fix log base 2\"\"\"\n",
    "    _, counts = np.unique(split, return_counts = True)\n",
    "    p = counts / split.shape[0]\n",
    "    entropy = -np.sum(p * np.log2(p))\n",
    "    return entropy\n",
    "\n",
    "\n",
    "def _find_splits(X, column):\n",
    "    \"\"\"\n",
    "    find all possible split values (threshold),\n",
    "    by getting unique values in a sorted order\n",
    "    and finding cutoff point (average) between every two values\n",
    "    \"\"\"\n",
    "    X_unique = np.unique(X[:, column])\n",
    "    split_values = np.empty(X_unique.shape[0] - 1)\n",
    "    for i in range(1, X_unique.shape[0]):\n",
    "        average = (X_unique[i - 1] + X_unique[i]) / 2\n",
    "        split_values[i - 1] = average\n",
    "\n",
    "    return split_values\n",
    "\n",
    "\n",
    "def _compute_splits_entropy(y, splits):\n",
    "    \"\"\"compute the entropy for the splits (the two child nodes)\"\"\"\n",
    "    splits_entropy = 0\n",
    "    for split in splits:\n",
    "        splits_entropy += (split.shape[0] / y.shape[0]) * _compute_entropy(split)\n",
    "\n",
    "    return splits_entropy\n",
    "\n",
    "\n",
    "def _split(X, y, column, value, return_X = True):\n",
    "    \"\"\"split the response column using the cutoff threshold\"\"\"\n",
    "    left_mask = X[:, column] <= value\n",
    "    right_mask = X[:, column] > value\n",
    "    left_y, right_y = y[left_mask], y[right_mask]\n",
    "\n",
    "    if not return_X:\n",
    "        return left_y, right_y\n",
    "    else:\n",
    "        left_X, right_X = X[left_mask], X[right_mask]\n",
    "        return left_X, right_X, left_y, right_y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will load the [Iris dataset](http://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_iris.html), and use it as a sample dataset to test our algorithm. This data sets consists of 3 different types of irises’ (Setosa, Versicolour, and Virginica). It is stored as a 150x4 numpy.ndarray, where the rows are the samples and the columns being Sepal Length, Sepal Width, Petal Length and Petal Width."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "classification distribution:  [50 48 52]\n",
      "accuracy score:  0.973333333333\n"
     ]
    }
   ],
   "source": [
    "# load a sample dataset\n",
    "iris = load_iris()\n",
    "X = iris.data\n",
    "y = iris.target\n",
    "\n",
    "# train model and print the accuracy score\n",
    "tree = Tree()\n",
    "tree.fit(X, y)\n",
    "y_pred = tree.predict(X)\n",
    "print('classification distribution: ', np.bincount(y_pred))\n",
    "print('accuracy score: ', accuracy_score(y, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "classification distribution:  [50 48 52]\n",
      "accuracy score:  0.973333333333\n"
     ]
    }
   ],
   "source": [
    "# use library to confirm results are comparable\n",
    "clf = DecisionTreeClassifier(criterion = 'entropy', min_samples_split = 10, max_depth = 3)\n",
    "clf.fit(X, y)\n",
    "y_pred = clf.predict(X)\n",
    "print('classification distribution: ', np.bincount(y_pred))\n",
    "print('accuracy score: ', accuracy_score(y, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Advantages of decision trees:**\n",
    "\n",
    "\n",
    "- Features don't require scaling or normalization\n",
    "- Great at dealing with data that have lots of categorical features\n",
    "- Can be displayed graphically, thus making it highly interpretable (in the next code chunk)\n",
    "- It is non-parametric, thus it will outperform linear models if relationship between features and response is highly non-linear\n",
    "\n",
    "For visualizing the decision tree, you might need to have graphviz installed. For the mac user, try doing `brew install graphviz` or follow the instructions in this [link](http://macappstore.org/graphviz-2/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
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   "source": [
    "# visualize the decision tree\n",
    "\n",
    "# export it as .dot file, other common parameters include\n",
    "# `rounded` (boolean to round the score on each node)\n",
    "export_graphviz(clf, feature_names = iris.feature_names, filled = True,\n",
    "                class_names = iris.target_names, out_file = 'tree.dot')\n",
    "\n",
    "# read it in and visualize it, or if we wish to\n",
    "# convert the .dot file into other formats, we can do:\n",
    "# import os\n",
    "# os.system('dot -Tpng tree.dot -o tree.jpeg')\n",
    "with open('tree.dot') as f:\n",
    "    dot_graph = f.read()\n",
    "\n",
    "Source(dot_graph)"
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   "metadata": {},
   "source": [
    "# Reference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [scikit-learn Documentation: Decision Trees](http://scikit-learn.org/stable/modules/tree.html)\n",
    "- [Blog: The advantages of the different impurity metrics](http://sebastianraschka.com/faq/docs/decision-tree-binary.html)\n",
    "- [Notebook: Cheatsheet for Decision Tree Classification](http://nbviewer.jupyter.org/github/rasbt/pattern_classification/blob/master/machine_learning/decision_trees/decision-tree-cheatsheet.ipynb)\n",
    "- [Github: Minimal and clean examples of machine learning algorithms](https://github.com/rushter/MLAlgorithms/blob/master/mla/ensemble/tree.py)"
   ]
  }
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