FYS-STK4155/doc/pub/week46/ipynb/week46.ipynb

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    "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
    "doconce format html week46.do.txt --no_mako -->\n",
    "<!-- dom:TITLE: Week 46: Decision Trees, Ensemble methods  and Random Forests -->"
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    "# Week 46: Decision Trees, Ensemble methods  and Random Forests\n",
    "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
    "\n",
    "Date: **Week 46, November 11-15**"
   ]
  },
  {
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   "source": [
    "## Plan for week 46\n",
    "\n",
    "**Lab sessions on Tuesday and Wednesday.**\n",
    "\n",
    "1. Work on and discussions of project 3\n",
    "\n",
    "**Material for the lecture on Monday November 11, 2024.**\n",
    "\n",
    "Basics of decision trees, classification and regression algorithms and ensemble models \n",
    "1. Readings and Videos:\n",
    "\n",
    "a. Lecture notes at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/pub/week46/ipynb/week46.ipynb>\n",
    "<!-- * [Video of lecture](https://youtu.be/PMswUwhYa7k) -->\n",
    "<!-- * [Whiteboard notes](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesNov16.pdf) -->\n",
    "\n",
    "b. Video on Decision trees at <https://www.youtube.com/watch?v=RmajweUFKvM&ab_channel=Simplilearn>\n",
    "\n",
    "c. Decision Trees: Rashcka et al chapter 3 pages 86-98, and chapter 7 on Ensemble methods, Voting and Bagging and Gradient Boosting. See also lecture from STK-IN4300, lecture 7 at <https://www.uio.no/studier/emner/matnat/math/STK-IN4300/h20/slides/lecture_7.pdf>."
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    "## Decision trees, overarching aims\n",
    "\n",
    "We start here with the most basic algorithm, the so-called decision\n",
    "tree. With this basic algorithm we can in turn build more complex\n",
    "networks, spanning from homogeneous and heterogenous forests (bagging,\n",
    "random forests and more) to one of the most popular supervised\n",
    "algorithms nowadays, the extreme gradient boosting, or just\n",
    "XGBoost. But let us start with the simplest possible ingredient.\n",
    "\n",
    "Decision trees are supervised learning algorithms used for both,\n",
    "classification and regression tasks.\n",
    "\n",
    "The main idea of decision trees\n",
    "is to find those descriptive features which contain the most\n",
    "**information** regarding the target feature and then split the dataset\n",
    "along the values of these features such that the target feature values\n",
    "for the resulting underlying datasets are as pure as possible.\n",
    "\n",
    "The descriptive features which reproduce best the target/output features are normally  said\n",
    "to be the most informative ones. The process of finding the **most\n",
    "informative** feature is done until we accomplish a stopping criteria\n",
    "where we then finally end up in so called **leaf nodes**."
   ]
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    "## Basics of a tree\n",
    "\n",
    "A decision tree is typically divided into a **root node**, the **interior nodes**,\n",
    "and the final **leaf nodes** or just **leaves**. These entities are then connected by so-called **branches**.\n",
    "\n",
    "The leaf nodes\n",
    "contain the predictions we will make for new query instances presented\n",
    "to our trained model. This is possible since the model has \n",
    "learned the underlying structure of the training data and hence can,\n",
    "given some assumptions, make predictions about the target feature value\n",
    "(class) of unseen query instances."
   ]
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    "## A typical Decision Tree with its pertinent Jargon, Classification Problem\n",
    "\n",
    "<!-- dom:FIGURE: [DataFiles/cancer.png, width=600 frac=0.8] -->\n",
    "<!-- begin figure -->\n",
    "\n",
    "<img src=\"DataFiles/cancer.png\" width=\"600\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
    "<!-- end figure -->\n",
    "\n",
    "This tree was produced using the Wisconsin cancer data (discussed here as well, see code examples below) using **Scikit-Learn**'s decision tree classifier. Here we have used the so-called **gini** index (see below) to split the various branches."
   ]
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    "## General Features\n",
    "\n",
    "The overarching approach to decision trees is a top-down approach.\n",
    "\n",
    "* A leaf provides the classification of a given instance.\n",
    "\n",
    "* A node specifies a test of some attribute of the instance.\n",
    "\n",
    "* A branch corresponds to a possible values of an attribute.\n",
    "\n",
    "* An instance is classified by starting at the root node of the tree, testing the attribute specified by this node, then moving down the tree branch corresponding to the value of the attribute in the given example.\n",
    "\n",
    "This process is then repeated for the subtree rooted at the new\n",
    "node."
   ]
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    "## How do we set it up?\n",
    "\n",
    "In simplified terms, the process of training a decision tree and\n",
    "predicting the target features of query instances is as follows:\n",
    "\n",
    "1. Present a dataset containing of a number of training instances characterized by a number of descriptive features and a target feature\n",
    "\n",
    "2. Train the decision tree model by continuously splitting the target feature along the values of the descriptive features using a measure of information gain during the training process\n",
    "\n",
    "3. Grow the tree until we accomplish a stopping criteria create leaf nodes which represent the *predictions* we want to make for new query instances\n",
    "\n",
    "4. Show query instances to the tree and run down the tree until we arrive at leaf nodes\n",
    "\n",
    "Then we are essentially done!"
   ]
  },
  {
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   "id": "b87f6367",
   "metadata": {},
   "source": [
    "## Decision trees and Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a74fdf82",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2nd degree coefficients:\n",
      "zero power:  -2.9520023319082793\n",
      "first power:  0.0013216492385537202\n",
      "second power:  4.285303587898884e-05\n"
     ]
    },
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "steps=250\n",
    "\n",
    "distance=0\n",
    "x=0\n",
    "distance_list=[]\n",
    "steps_list=[]\n",
    "while x<steps:\n",
    "    distance+=np.random.randint(-1,2)\n",
    "    distance_list.append(distance)\n",
    "    x+=1\n",
    "    steps_list.append(x)\n",
    "plt.plot(steps_list,distance_list, color='green', label=\"Random Walk Data\")\n",
    "\n",
    "steps_list=np.asarray(steps_list)\n",
    "distance_list=np.asarray(distance_list)\n",
    "\n",
    "X=steps_list[:,np.newaxis]\n",
    "\n",
    "#Polynomial fits\n",
    "\n",
    "#Degree 2\n",
    "poly_features=PolynomialFeatures(degree=2, include_bias=False)\n",
    "X_poly=poly_features.fit_transform(X)\n",
    "\n",
    "lin_reg=LinearRegression()\n",
    "poly_fit=lin_reg.fit(X_poly,distance_list)\n",
    "b=lin_reg.coef_\n",
    "c=lin_reg.intercept_\n",
    "print (\"2nd degree coefficients:\")\n",
    "print (\"zero power: \",c)\n",
    "print (\"first power: \", b[0])\n",
    "print (\"second power: \",b[1])\n",
    "\n",
    "z = np.arange(0, steps, .01)\n",
    "z_mod=b[1]*z**2+b[0]*z+c\n",
    "\n",
    "fit_mod=b[1]*X**2+b[0]*X+c\n",
    "plt.plot(z, z_mod, color='r', label=\"2nd Degree Fit\")\n",
    "plt.title(\"Polynomial Regression\")\n",
    "\n",
    "plt.xlabel(\"Steps\")\n",
    "plt.ylabel(\"Distance\")\n",
    "\n",
    "#Degree 10\n",
    "poly_features10=PolynomialFeatures(degree=10, include_bias=False)\n",
    "X_poly10=poly_features10.fit_transform(X)\n",
    "\n",
    "poly_fit10=lin_reg.fit(X_poly10,distance_list)\n",
    "\n",
    "y_plot=poly_fit10.predict(X_poly10)\n",
    "plt.plot(X, y_plot, color='black', label=\"10th Degree Fit\")\n",
    "\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "#Decision Tree Regression\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "regr_1=DecisionTreeRegressor(max_depth=2)\n",
    "regr_2=DecisionTreeRegressor(max_depth=5)\n",
    "regr_3=DecisionTreeRegressor(max_depth=13)\n",
    "regr_1.fit(X, distance_list)\n",
    "regr_2.fit(X, distance_list)\n",
    "regr_3.fit(X, distance_list)\n",
    "\n",
    "X_test = np.arange(0.0, steps, 0.01)[:, np.newaxis]\n",
    "y_1 = regr_1.predict(X_test)\n",
    "y_2 = regr_2.predict(X_test)\n",
    "y_3=regr_3.predict(X_test)\n",
    "\n",
    "# Plot the results\n",
    "plt.figure()\n",
    "plt.scatter(X, distance_list, s=2.5, c=\"black\", label=\"data\")\n",
    "plt.plot(X_test, y_1, color=\"red\",\n",
    "         label=\"max_depth=2\", linewidth=2)\n",
    "plt.plot(X_test, y_2, color=\"green\", label=\"max_depth=5\", linewidth=2)\n",
    "plt.plot(X_test, y_3, color=\"m\", label=\"max_depth=7\", linewidth=2)\n",
    "\n",
    "plt.xlabel(\"Data\")\n",
    "plt.ylabel(\"Darget\")\n",
    "plt.title(\"Decision Tree Regression\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d0e6ee5",
   "metadata": {},
   "source": [
    "## Building a tree, regression\n",
    "\n",
    "There are mainly two steps\n",
    "1. We split the predictor space (the set of possible values $x_1,x_2,\\dots, x_p$) into $J$ distinct and non-non-overlapping regions, $R_1,R_2,\\dots,R_J$.  \n",
    "\n",
    "2. For every observation that falls into the region $R_j$ , we make the same prediction, which is simply the mean of the response values for the training observations in $R_j$.\n",
    "\n",
    "How do we construct the regions $R_1,\\dots,R_J$?  In theory, the\n",
    "regions could have any shape. However, we choose to divide the\n",
    "predictor space into high-dimensional rectangles, or boxes, for\n",
    "simplicity and for ease of interpretation of the resulting predictive\n",
    "model. The goal is to find boxes $R_1,\\dots,R_J$ that minimize the\n",
    "MSE, given by"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5c1c351",
   "metadata": {},
   "source": [
    "$$\n",
    "\\sum_{j=1}^J\\sum_{i\\in R_j}(y_i-\\overline{y}_{R_j})^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "810a4087",
   "metadata": {},
   "source": [
    "where $\\overline{y}_{R_j}$  is the mean response for the training observations \n",
    "within box $j$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5629755a",
   "metadata": {},
   "source": [
    "## A top-down approach, recursive binary splitting\n",
    "\n",
    "Unfortunately, it is computationally infeasible to consider every\n",
    "possible partition of the feature space into $J$ boxes.  The common\n",
    "strategy is to take a top-down approach\n",
    "\n",
    "The approach is top-down because it begins at the top of the tree (all\n",
    "observations belong to a single region) and then successively splits\n",
    "the predictor space; each split is indicated via two new branches\n",
    "further down on the tree. It is greedy because at each step of the\n",
    "tree-building process, the best split is made at that particular step,\n",
    "rather than looking ahead and picking a split that will lead to a\n",
    "better tree in some future step."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f3102c6",
   "metadata": {},
   "source": [
    "## Making a tree\n",
    "\n",
    "In order to implement the recursive binary splitting we start by selecting\n",
    "the predictor $x_j$ and a cutpoint $s$ that splits the predictor space into two regions $R_1$ and $R_2$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6e4959c",
   "metadata": {},
   "source": [
    "$$\n",
    "\\left\\{X\\vert x_j < s\\right\\},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46f332ab",
   "metadata": {},
   "source": [
    "and"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4f43761",
   "metadata": {},
   "source": [
    "$$\n",
    "\\left\\{X\\vert x_j \\geq s\\right\\},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58b2f5b5",
   "metadata": {},
   "source": [
    "so that we obtain the lowest MSE, that is"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97388edc",
   "metadata": {},
   "source": [
    "$$\n",
    "\\sum_{i:x_i\\in R_j}(y_i-\\overline{y}_{R_1})^2+\\sum_{i:x_i\\in R_2}(y_i-\\overline{y}_{R_2})^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2ed2edb",
   "metadata": {},
   "source": [
    "which we want to minimize by considering all predictors\n",
    "$x_1,x_2,\\dots,x_p$.  We consider also all possible values of $s$ for\n",
    "each predictor. These values could be determined by randomly assigned\n",
    "numbers or by starting at the midpoint and then proceed till we find\n",
    "an optimal value.\n",
    "\n",
    "For any $j$ and $s$, we define the pair of half-planes where\n",
    "$\\overline{y}_{R_1}$ is the mean response for the training\n",
    "observations in $R_1(j,s)$, and $\\overline{y}_{R_2}$ is the mean\n",
    "response for the training observations in $R_2(j,s)$.\n",
    "\n",
    "Finding the values of $j$ and $s$ that minimize the above equation can be\n",
    "done quite quickly, especially when the number of features $p$ is not\n",
    "too large.\n",
    "\n",
    "Next, we repeat the process, looking\n",
    "for the best predictor and best cutpoint in order to split the data\n",
    "further so as to minimize the MSE within each of the resulting\n",
    "regions. However, this time, instead of splitting the entire predictor\n",
    "space, we split one of the two previously identified regions. We now\n",
    "have three regions. Again, we look to split one of these three regions\n",
    "further, so as to minimize the MSE. The process continues until a\n",
    "stopping criterion is reached; for instance, we may continue until no\n",
    "region contains more than five observations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "433e9a7c",
   "metadata": {},
   "source": [
    "## Pruning the tree\n",
    "\n",
    "The above procedure is rather straightforward, but leads often to\n",
    "overfitting and unnecessarily large and complicated trees. The basic\n",
    "idea is to grow a large tree $T_0$ and then prune it back in order to\n",
    "obtain a subtree. A smaller tree with fewer splits (fewer regions) can\n",
    "lead to smaller variance and better interpretation at the cost of a\n",
    "little more bias.\n",
    "\n",
    "The so-called Cost complexity pruning algorithm gives us a\n",
    "way to do just this. Rather than considering every possible subtree,\n",
    "we consider a sequence of trees indexed by a nonnegative tuning\n",
    "parameter $\\alpha$.\n",
    "\n",
    "Read more at the following [Scikit-Learn link on pruning](https://scikit-learn.org/stable/auto_examples/tree/plot_cost_complexity_pruning.html#sphx-glr-auto-examples-tree-plot-cost-complexity-pruning-py)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf126778",
   "metadata": {},
   "source": [
    "## Cost complexity pruning\n",
    "\n",
    "For each value of $\\alpha$  there corresponds a subtree $T \\in T_0$ such that"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd0b65f1",
   "metadata": {},
   "source": [
    "$$\n",
    "\\sum_{m=1}^{\\overline{T}}\\sum_{i:x_i\\in R_m}(y_i-\\overline{y}_{R_m})^2+\\alpha\\overline{T},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cb61a07",
   "metadata": {},
   "source": [
    "is as small as possible. Here $\\overline{T}$ is \n",
    "the number of terminal nodes of the tree $T$ , $R_m$ is the\n",
    "rectangle (i.e. the subset of predictor space)  corresponding to the $m$-th terminal node.\n",
    "\n",
    "The tuning parameter $\\alpha$ controls a trade-off between the subtree’s\n",
    "complexity and its fit to the training data. When $\\alpha = 0$, then the\n",
    "subtree $T$ will simply equal $T_0$, \n",
    "because then the above equation just measures the\n",
    "training error. \n",
    "However, as $\\alpha$ increases, there is a price to pay for\n",
    "having a tree with many terminal nodes. The above equation will\n",
    "tend to be minimized for a smaller subtree. \n",
    "\n",
    "It turns out that as we increase $\\alpha$ from zero\n",
    "branches get pruned from the tree in a nested and predictable fashion,\n",
    "so obtaining the whole sequence of subtrees as a function of $\\alpha$ is\n",
    "easy. We can select a value of $\\alpha$ using a validation set or using\n",
    "cross-validation. We then return to the full data set and obtain the\n",
    "subtree corresponding to $\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73748b5a",
   "metadata": {},
   "source": [
    "## Schematic Regression Procedure\n",
    "\n",
    "**Building a Regression Tree.**\n",
    "\n",
    "1. Use recursive binary splitting to grow a large tree on the training data, stopping only when each terminal node has fewer than some minimum number of observations.\n",
    "\n",
    "2. Apply cost complexity pruning to the large tree in order to obtain a sequence of best subtrees, as a function of $\\alpha$.\n",
    "\n",
    "3. Use for example $K$-fold cross-validation to choose $\\alpha$. Divide the training observations into $K$ folds. For each $k=1,2,\\dots,K$ we: \n",
    "\n",
    "  * repeat steps 1 and 2 on all but the $k$-th fold of the training data. \n",
    "\n",
    "  * Then we valuate the mean squared prediction error on the data in the left-out $k$-th fold, as a function of $\\alpha$.\n",
    "\n",
    "  * Finally  we average the results for each value of $\\alpha$, and pick $\\alpha$ to minimize the average error.\n",
    "\n",
    "4. Return the subtree from Step 2 that corresponds to the chosen value of $\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b1da6d3",
   "metadata": {},
   "source": [
    "## A Classification Tree\n",
    "\n",
    "A classification tree is very similar to a regression tree, except\n",
    "that it is used to predict a qualitative response rather than a\n",
    "quantitative one. Recall that for a regression tree, the predicted\n",
    "response for an observation is given by the mean response of the\n",
    "training observations that belong to the same terminal node. In\n",
    "contrast, for a classification tree, we predict that each observation\n",
    "belongs to the most commonly occurring class of training observations\n",
    "in the region to which it belongs. In interpreting the results of a\n",
    "classification tree, we are often interested not only in the class\n",
    "prediction corresponding to a particular terminal node region, but\n",
    "also in the class proportions among the training observations that\n",
    "fall into that region."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02b48bdf",
   "metadata": {},
   "source": [
    "## Growing a classification tree\n",
    "\n",
    "The task of growing a\n",
    "classification tree is quite similar to the task of growing a\n",
    "regression tree. Just as in the regression setting, we use recursive\n",
    "binary splitting to grow a classification tree. However, in the\n",
    "classification setting, the MSE cannot be used as a criterion for making\n",
    "the binary splits.  A natural alternative to MSE is the **classification\n",
    "error rate**. Since we plan to assign an observation in a given region\n",
    "to the most commonly occurring error rate class of training\n",
    "observations in that region, the classification error rate is simply\n",
    "the fraction of the training observations in that region that do not\n",
    "belong to the most common class. \n",
    "\n",
    "When building a classification tree, either the Gini index or the\n",
    "entropy are typically used to evaluate the quality of a particular\n",
    "split, since these two approaches are more sensitive to node purity\n",
    "than is the classification error rate."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d679c00",
   "metadata": {},
   "source": [
    "## Classification tree, how to split nodes\n",
    "\n",
    "If our targets are the outcome of a classification process that takes\n",
    "for example $k=1,2,\\dots,K$ values, the only thing we need to think of\n",
    "is to set up the splitting criteria for each node.\n",
    "\n",
    "We define a PDF $p_{mk}$ that represents the number of observations of\n",
    "a class $k$ in a region $R_m$ with $N_m$ observations. We represent\n",
    "this likelihood function in terms of the proportion $I(y_i=k)$ of\n",
    "observations of this class in the region $R_m$ as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04bae309",
   "metadata": {},
   "source": [
    "$$\n",
    "p_{mk} = \\frac{1}{N_m}\\sum_{x_i\\in R_m}I(y_i=k).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b060012",
   "metadata": {},
   "source": [
    "We let $p_{mk}$ represent the majority class of observations in region\n",
    "$m$. The three most common ways of splitting a node are given by\n",
    "\n",
    "* Misclassification error"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f56fef9d",
   "metadata": {},
   "source": [
    "$$\n",
    "p_{mk} = \\frac{1}{N_m}\\sum_{x_i\\in R_m}I(y_i\\ne k) = 1-p_{mk}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1fac4cf",
   "metadata": {},
   "source": [
    "* Gini index $g$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c832a60f",
   "metadata": {},
   "source": [
    "$$\n",
    "g = \\sum_{k=1}^K p_{mk}(1-p_{mk}).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90832db4",
   "metadata": {},
   "source": [
    "* Information entropy or just entropy $s$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0215b6b4",
   "metadata": {},
   "source": [
    "$$\n",
    "s = -\\sum_{k=1}^K p_{mk}\\log{p_{mk}}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8591f16d",
   "metadata": {},
   "source": [
    "## Visualizing the Tree, Classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "113d51d1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     mean radius  mean texture  mean perimeter  mean area  mean smoothness  \\\n",
      "0          17.99         10.38          122.80     1001.0          0.11840   \n",
      "1          20.57         17.77          132.90     1326.0          0.08474   \n",
      "2          19.69         21.25          130.00     1203.0          0.10960   \n",
      "3          11.42         20.38           77.58      386.1          0.14250   \n",
      "4          20.29         14.34          135.10     1297.0          0.10030   \n",
      "..           ...           ...             ...        ...              ...   \n",
      "564        21.56         22.39          142.00     1479.0          0.11100   \n",
      "565        20.13         28.25          131.20     1261.0          0.09780   \n",
      "566        16.60         28.08          108.30      858.1          0.08455   \n",
      "567        20.60         29.33          140.10     1265.0          0.11780   \n",
      "568         7.76         24.54           47.92      181.0          0.05263   \n",
      "\n",
      "     mean compactness  mean concavity  mean concave points  mean symmetry  \\\n",
      "0             0.27760         0.30010              0.14710         0.2419   \n",
      "1             0.07864         0.08690              0.07017         0.1812   \n",
      "2             0.15990         0.19740              0.12790         0.2069   \n",
      "3             0.28390         0.24140              0.10520         0.2597   \n",
      "4             0.13280         0.19800              0.10430         0.1809   \n",
      "..                ...             ...                  ...            ...   \n",
      "564           0.11590         0.24390              0.13890         0.1726   \n",
      "565           0.10340         0.14400              0.09791         0.1752   \n",
      "566           0.10230         0.09251              0.05302         0.1590   \n",
      "567           0.27700         0.35140              0.15200         0.2397   \n",
      "568           0.04362         0.00000              0.00000         0.1587   \n",
      "\n",
      "     mean fractal dimension  ...  worst radius  worst texture  \\\n",
      "0                   0.07871  ...        25.380          17.33   \n",
      "1                   0.05667  ...        24.990          23.41   \n",
      "2                   0.05999  ...        23.570          25.53   \n",
      "3                   0.09744  ...        14.910          26.50   \n",
      "4                   0.05883  ...        22.540          16.67   \n",
      "..                      ...  ...           ...            ...   \n",
      "564                 0.05623  ...        25.450          26.40   \n",
      "565                 0.05533  ...        23.690          38.25   \n",
      "566                 0.05648  ...        18.980          34.12   \n",
      "567                 0.07016  ...        25.740          39.42   \n",
      "568                 0.05884  ...         9.456          30.37   \n",
      "\n",
      "     worst perimeter  worst area  worst smoothness  worst compactness  \\\n",
      "0             184.60      2019.0           0.16220            0.66560   \n",
      "1             158.80      1956.0           0.12380            0.18660   \n",
      "2             152.50      1709.0           0.14440            0.42450   \n",
      "3              98.87       567.7           0.20980            0.86630   \n",
      "4             152.20      1575.0           0.13740            0.20500   \n",
      "..               ...         ...               ...                ...   \n",
      "564           166.10      2027.0           0.14100            0.21130   \n",
      "565           155.00      1731.0           0.11660            0.19220   \n",
      "566           126.70      1124.0           0.11390            0.30940   \n",
      "567           184.60      1821.0           0.16500            0.86810   \n",
      "568            59.16       268.6           0.08996            0.06444   \n",
      "\n",
      "     worst concavity  worst concave points  worst symmetry  \\\n",
      "0             0.7119                0.2654          0.4601   \n",
      "1             0.2416                0.1860          0.2750   \n",
      "2             0.4504                0.2430          0.3613   \n",
      "3             0.6869                0.2575          0.6638   \n",
      "4             0.4000                0.1625          0.2364   \n",
      "..               ...                   ...             ...   \n",
      "564           0.4107                0.2216          0.2060   \n",
      "565           0.3215                0.1628          0.2572   \n",
      "566           0.3403                0.1418          0.2218   \n",
      "567           0.9387                0.2650          0.4087   \n",
      "568           0.0000                0.0000          0.2871   \n",
      "\n",
      "     worst fractal dimension  \n",
      "0                    0.11890  \n",
      "1                    0.08902  \n",
      "2                    0.08758  \n",
      "3                    0.17300  \n",
      "4                    0.07678  \n",
      "..                       ...  \n",
      "564                  0.07115  \n",
      "565                  0.06637  \n",
      "566                  0.07820  \n",
      "567                  0.12400  \n",
      "568                  0.07039  \n",
      "\n",
      "[569 rows x 30 columns]\n",
      "     malignant  benign\n",
      "0         True   False\n",
      "1         True   False\n",
      "2         True   False\n",
      "3         True   False\n",
      "4         True   False\n",
      "..         ...     ...\n",
      "564       True   False\n",
      "565       True   False\n",
      "566       True   False\n",
      "567       True   False\n",
      "568      False    True\n",
      "\n",
      "[569 rows x 2 columns]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import os\n",
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import confusion_matrix\n",
    "from sklearn.tree import export_graphviz\n",
    "\n",
    "from IPython.display import Image \n",
    "from pydot import graph_from_dot_data\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "cancer = load_breast_cancer()\n",
    "X = pd.DataFrame(cancer.data, columns=cancer.feature_names)\n",
    "print(X)\n",
    "y = pd.Categorical.from_codes(cancer.target, cancer.target_names)\n",
    "y = pd.get_dummies(y)\n",
    "print(y)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)\n",
    "tree_clf = DecisionTreeClassifier(max_depth=5)\n",
    "tree_clf.fit(X_train, y_train)\n",
    "\n",
    "export_graphviz(\n",
    "    tree_clf,\n",
    "    out_file=\"DataFiles/cancer.dot\",\n",
    "    feature_names=cancer.feature_names,\n",
    "    class_names=cancer.target_names,\n",
    "    rounded=True,\n",
    "    filled=True\n",
    ")\n",
    "cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'\n",
    "os.system(cmd)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc99e81f",
   "metadata": {},
   "source": [
    "## Visualizing the Tree, The Moons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f4f56adb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Common imports\n",
    "import numpy as np\n",
    "from sklearn.model_selection import  train_test_split \n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.datasets import make_moons\n",
    "from sklearn.tree import export_graphviz\n",
    "from pydot import graph_from_dot_data\n",
    "import pandas as pd\n",
    "import os\n",
    "\n",
    "np.random.seed(42)\n",
    "X, y = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X,y,random_state=0)\n",
    "tree_clf = DecisionTreeClassifier(max_depth=5)\n",
    "tree_clf.fit(X_train, y_train)\n",
    "\n",
    "export_graphviz(\n",
    "    tree_clf,\n",
    "    out_file=\"DataFiles/moons.dot\",\n",
    "    rounded=True,\n",
    "    filled=True\n",
    ")\n",
    "cmd = 'dot -Tpng DataFiles/moons.dot -o DataFiles/moons.png'\n",
    "os.system(cmd)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf0845ba",
   "metadata": {},
   "source": [
    "## Other ways of visualizing the trees\n",
    "\n",
    "**Scikit-Learn** has also another way to visualize the trees which is very useful, here with the Iris data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f7344f0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0.5, 0.9166666666666666, 'x[2] <= 2.45\\ngini = 0.667\\nsamples = 150\\nvalue = [50, 50, 50]'),\n",
       " Text(0.4230769230769231, 0.75, 'gini = 0.0\\nsamples = 50\\nvalue = [50, 0, 0]'),\n",
       " Text(0.5769230769230769, 0.75, 'x[3] <= 1.75\\ngini = 0.5\\nsamples = 100\\nvalue = [0, 50, 50]'),\n",
       " Text(0.3076923076923077, 0.5833333333333334, 'x[2] <= 4.95\\ngini = 0.168\\nsamples = 54\\nvalue = [0, 49, 5]'),\n",
       " Text(0.15384615384615385, 0.4166666666666667, 'x[3] <= 1.65\\ngini = 0.041\\nsamples = 48\\nvalue = [0, 47, 1]'),\n",
       " Text(0.07692307692307693, 0.25, 'gini = 0.0\\nsamples = 47\\nvalue = [0, 47, 0]'),\n",
       " Text(0.23076923076923078, 0.25, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 0, 1]'),\n",
       " Text(0.46153846153846156, 0.4166666666666667, 'x[3] <= 1.55\\ngini = 0.444\\nsamples = 6\\nvalue = [0, 2, 4]'),\n",
       " Text(0.38461538461538464, 0.25, 'gini = 0.0\\nsamples = 3\\nvalue = [0, 0, 3]'),\n",
       " Text(0.5384615384615384, 0.25, 'x[2] <= 5.45\\ngini = 0.444\\nsamples = 3\\nvalue = [0, 2, 1]'),\n",
       " Text(0.46153846153846156, 0.08333333333333333, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 2, 0]'),\n",
       " Text(0.6153846153846154, 0.08333333333333333, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 0, 1]'),\n",
       " Text(0.8461538461538461, 0.5833333333333334, 'x[2] <= 4.85\\ngini = 0.043\\nsamples = 46\\nvalue = [0, 1, 45]'),\n",
       " Text(0.7692307692307693, 0.4166666666666667, 'x[1] <= 3.1\\ngini = 0.444\\nsamples = 3\\nvalue = [0, 1, 2]'),\n",
       " Text(0.6923076923076923, 0.25, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 0, 2]'),\n",
       " Text(0.8461538461538461, 0.25, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 1, 0]'),\n",
       " Text(0.9230769230769231, 0.4166666666666667, 'gini = 0.0\\nsamples = 43\\nvalue = [0, 0, 43]')]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn import tree\n",
    "X, y = load_iris(return_X_y=True)\n",
    "tree_clf = tree.DecisionTreeClassifier()\n",
    "tree_clf = tree_clf.fit(X, y)\n",
    "# and then plot the tree\n",
    "tree.plot_tree(tree_clf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fb6fd52",
   "metadata": {},
   "source": [
    "## Printing out as text\n",
    "\n",
    "Alternatively, the tree can also be exported in textual format with the function exporttext.\n",
    "This method doesn’t require the installation of external libraries and is more compact:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d0d96130",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "|--- petal width (cm) <= 0.80\n",
      "|   |--- class: 0\n",
      "|--- petal width (cm) >  0.80\n",
      "|   |--- petal width (cm) <= 1.75\n",
      "|   |   |--- class: 1\n",
      "|   |--- petal width (cm) >  1.75\n",
      "|   |   |--- class: 2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.tree import export_text\n",
    "iris = load_iris()\n",
    "decision_tree = DecisionTreeClassifier(random_state=0, max_depth=2)\n",
    "decision_tree = decision_tree.fit(iris.data, iris.target)\n",
    "r = export_text(decision_tree, feature_names=iris['feature_names'])\n",
    "print(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6574f042",
   "metadata": {},
   "source": [
    "## Algorithms for Setting up Decision Trees\n",
    "\n",
    "Two algorithms stand out in the set up of decision trees:\n",
    "1. The CART (Classification And Regression Tree) algorithm for both classification and regression\n",
    "\n",
    "2. The ID3 algorithm based on the computation of the information gain for classification\n",
    "\n",
    "We discuss both algorithms with applications here. The popular library\n",
    "**Scikit-Learn** uses the CART algorithm. For classification problems\n",
    "you can use either the **gini** index or the **entropy** to split a tree\n",
    "in two branches."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8ec4915",
   "metadata": {},
   "source": [
    "## The CART algorithm for Classification\n",
    "\n",
    "For classification, the CART algorithm splits the data set in two subsets using a single feature $k$ and a threshold $t_k$.\n",
    "This could be for example a threshold set by a number below a certain circumference of a malign tumor.\n",
    "\n",
    "How do we find these two quantities?\n",
    "We search for the pair $(k,t_k)$ that produces the purest subset using for example the **gini** factor $G$.\n",
    "The cost function it tries to minimize is then"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eff9d046",
   "metadata": {},
   "source": [
    "$$\n",
    "C(k,t_k) = \\frac{m_{\\mathrm{left}}}{m}G_{\\mathrm{left}}+ \\frac{m_{\\mathrm{right}}}{m}G_{\\mathrm{right}},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ec161df",
   "metadata": {},
   "source": [
    "where $G_{\\mathrm{left/right}}$ measures the impurity of the left/right subset  and $m_{\\mathrm{left/right}}$\n",
    " is the number of instances in the left/right subset\n",
    "\n",
    "Once it has successfully split the training set in two, it splits the subsets using the same logic, then the subsubsets\n",
    "and so on, recursively. It stops recursing once it reaches the maximum depth (defined by the\n",
    "$max\\_depth$ hyperparameter), or if it cannot find a split that will reduce impurity. A few other\n",
    "hyperparameters control additional stopping conditions such as the $min\\_samples\\_split$,\n",
    "$min\\_samples\\_leaf$, $min\\_weight\\_fraction\\_leaf$, and $max\\_leaf\\_nodes$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6284da65",
   "metadata": {},
   "source": [
    "## The CART algorithm for Regression\n",
    "\n",
    "The CART algorithm for regression works is similar to the one for classification except that instead of trying to split the\n",
    "training set in a way that minimizes say the **gini** or **entropy** impurity, it now tries to split the training set in a way that minimizes our well-known mean-squared error (MSE). The cost function is now"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af4b8a85",
   "metadata": {},
   "source": [
    "$$\n",
    "C(k,t_k) = \\frac{m_{\\mathrm{left}}}{m}\\mathrm{MSE}_{\\mathrm{left}}+ \\frac{m_{\\mathrm{right}}}{m}\\mathrm{MSE}_{\\mathrm{right}}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75de258a",
   "metadata": {},
   "source": [
    "Here the MSE for a specific node is defined as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b537a97",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathrm{MSE}_{\\mathrm{node}}=\\frac{1}{m_\\mathrm{node}}\\sum_{i\\in \\mathrm{node}}(\\overline{y}_{\\mathrm{node}}-y_i)^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7778645a",
   "metadata": {},
   "source": [
    "with"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80609ac3",
   "metadata": {},
   "source": [
    "$$\n",
    "\\overline{y}_{\\mathrm{node}}=\\frac{1}{m_\\mathrm{node}}\\sum_{i\\in \\mathrm{node}}y_i,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4dfdfc42",
   "metadata": {},
   "source": [
    "the mean value of all observations in a specific node.\n",
    "\n",
    "Without any regularization, the regression task for decision trees, \n",
    "just like for classification tasks, is  prone to overfitting."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f109fa64",
   "metadata": {},
   "source": [
    "## Why binary splits?\n",
    "\n",
    "It is custom to split to a tree uising binary splits. The reason is\n",
    "that multiway splits fragment the data too quickly, leaving\n",
    "insufficient data at the next level down.  Multiway splits can be\n",
    "achieved by a series of binary split and this is normally preferred."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d922699",
   "metadata": {},
   "source": [
    "## Computing a Tree using the Gini Index\n",
    "\n",
    "Consider the following example with attributes/features and two\n",
    "possible outcomes (classes)  for each attribute.  Assume we wish to find some\n",
    "correlations between the average grade of a student as function of the\n",
    "number of hours studied and hours slept. We want also to correlate the\n",
    "grade in a given course with the general trend, whether the students\n",
    "recently has gotten grades below average or above.\n",
    "\n",
    "We have three features/attributes\n",
    "1. Trend of average grades before present course, classified as either below  or above  the average grade of the whole class  \n",
    "\n",
    "2. The number of hours studies, classified again as either higher (more than 3 hours per day) or lower . Here we have used a standard for one $ECTS$ which is scaled to 25-30 hours of work for a semester which lasts 18 weeks, with 15 weeks of lectures and 3 weeks for exams, assuming a total of 30 ECTS per semester. \n",
    "\n",
    "3. The number of hours slept as high for more than $8$ hours and below  for less than 8 hours of sleep, classified again as either high or low\n",
    "\n",
    "4. The final grade whether it is above or below average"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b3caaf3",
   "metadata": {},
   "source": [
    "## The Table\n",
    "\n",
    "<table class=\"dotable\" border=\"1\">\n",
    "<thead>\n",
    "<tr><th align=\"center\">Grade Trend</th> <th align=\"center\">Hours slept</th> <th align=\"center\">Hours Studied</th> <th align=\"center\">Grade</th> </tr>\n",
    "</thead>\n",
    "<tbody>\n",
    "<tr><td align=\"center\">   Above          </td> <td align=\"center\">   Low            </td> <td align=\"center\">   High             </td> <td align=\"center\">   Above    </td> </tr>\n",
    "<tr><td align=\"center\">   Below          </td> <td align=\"center\">   High           </td> <td align=\"center\">   Low              </td> <td align=\"center\">   Below    </td> </tr>\n",
    "<tr><td align=\"center\">   Above          </td> <td align=\"center\">   Low            </td> <td align=\"center\">   High             </td> <td align=\"center\">   Above    </td> </tr>\n",
    "<tr><td align=\"center\">   Above          </td> <td align=\"center\">   High           </td> <td align=\"center\">   High             </td> <td align=\"center\">   Above    </td> </tr>\n",
    "<tr><td align=\"center\">   Below          </td> <td align=\"center\">   Low            </td> <td align=\"center\">   High             </td> <td align=\"center\">   Below    </td> </tr>\n",
    "<tr><td align=\"center\">   Above          </td> <td align=\"center\">   Low            </td> <td align=\"center\">   Low              </td> <td align=\"center\">   Below    </td> </tr>\n",
    "<tr><td align=\"center\">   Below          </td> <td align=\"center\">   High           </td> <td align=\"center\">   High             </td> <td align=\"center\">   Below    </td> </tr>\n",
    "<tr><td align=\"center\">   Below          </td> <td align=\"center\">   Low            </td> <td align=\"center\">   High             </td> <td align=\"center\">   Below    </td> </tr>\n",
    "<tr><td align=\"center\">   Above          </td> <td align=\"center\">   Low            </td> <td align=\"center\">   Low              </td> <td align=\"center\">   Below    </td> </tr>\n",
    "<tr><td align=\"center\">   Above          </td> <td align=\"center\">   High           </td> <td align=\"center\">   High             </td> <td align=\"center\">   Above    </td> </tr>\n",
    "</tbody>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95856cd8",
   "metadata": {},
   "source": [
    "## Computing the various Gini Indices\n",
    "\n",
    "In computations we will translate all classes into numbers. Being\n",
    "these binary classes, they can easily be split into ones and zeros.\n",
    "\n",
    "**Gini index for Average trend.**\n",
    "\n",
    "[See handwritten notes November 3](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2022/NotesNov32022.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "177279e1",
   "metadata": {},
   "source": [
    "## Computing the various Gini Indices, Hours slept\n",
    "\n",
    "**Gini index for hour slept.**\n",
    "\n",
    "[See handwritten notes November 3](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2022/NotesNov32022.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44c2ba1c",
   "metadata": {},
   "source": [
    "## Computing the various Gini Indices, Hours studied\n",
    "\n",
    "**Gini index for hour studied.**\n",
    "\n",
    "[See handwritten notes November 3](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2022/NotesNov32022.pdf)\n",
    "\n",
    "For final tree, see the above handwritten notes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82a317dc",
   "metadata": {},
   "source": [
    "## A possible code using Scikit-Learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e55268fa",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Common imports\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.tree import export_graphviz\n",
    "from sklearn.preprocessing import StandardScaler, OneHotEncoder\n",
    "from sklearn.compose import ColumnTransformer\n",
    "from IPython.display import Image \n",
    "from pydot import graph_from_dot_data\n",
    "import os\n",
    "\n",
    "# Where to save the figures and data files\n",
    "PROJECT_ROOT_DIR = \"Results\"\n",
    "FIGURE_ID = \"Results/FigureFiles\"\n",
    "DATA_ID = \"DataFiles/\"\n",
    "\n",
    "if not os.path.exists(PROJECT_ROOT_DIR):\n",
    "    os.mkdir(PROJECT_ROOT_DIR)\n",
    "\n",
    "if not os.path.exists(FIGURE_ID):\n",
    "    os.makedirs(FIGURE_ID)\n",
    "\n",
    "if not os.path.exists(DATA_ID):\n",
    "    os.makedirs(DATA_ID)\n",
    "\n",
    "def image_path(fig_id):\n",
    "    return os.path.join(FIGURE_ID, fig_id)\n",
    "\n",
    "def data_path(dat_id):\n",
    "    return os.path.join(DATA_ID, dat_id)\n",
    "\n",
    "def save_fig(fig_id):\n",
    "    plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
    "\n",
    "infile = open(data_path(\"grades.csv\"),'r')\n",
    "\n",
    "# Read the experimental data with Pandas\n",
    "from IPython.display import display\n",
    "grades = pd.read_csv(infile)\n",
    "grades = pd.DataFrame(grades)\n",
    "display(grades)\n",
    "# Features and targets\n",
    "X = grades.loc[:, grades.columns != 'Grade'].values\n",
    "y = grades.loc[:, grades.columns == 'Grade'].values\n",
    "print(X)\n",
    "# Then do a Classification tree\n",
    "tree_clf = DecisionTreeClassifier(max_depth=2)\n",
    "tree_clf.fit(X, y)\n",
    "print(\"Train set accuracy with Decision Tree: {:.2f}\".format(tree_clf.score(X,y)))\n",
    "#transfer to a decision tree graph\n",
    "export_graphviz(\n",
    "    tree_clf,\n",
    "    out_file=\"DataFiles/grade.dot\",\n",
    "    rounded=True,\n",
    "    filled=True\n",
    ")\n",
    "cmd = 'dot -Tpng DataFiles/grade.dot -o DataFiles/grades.png'\n",
    "os.system(cmd)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47a5e24c",
   "metadata": {},
   "source": [
    "## Further example: Computing the Gini index\n",
    "\n",
    "The next example we will look at is a classical one in many Machine\n",
    "Learning applications. Based on various meteorological features, we\n",
    "have several so-called attributes which decide whether we at the end\n",
    "will do some outdoor activity like skiing, going for a bike ride etc\n",
    "etc.  The table here contains the feautures **outlook**, **temperature**,\n",
    "**humidity** and **wind**.  The target or output is whether we ride\n",
    "(True=1) or whether we do something else that day (False=0). The\n",
    "attributes for each feature are then sunny, overcast and rain for the\n",
    "outlook, hot, cold and mild for temperature, high and normal for\n",
    "humidity and weak and strong for wind.\n",
    "\n",
    "The table here summarizes the various attributes and\n",
    "<table class=\"dotable\" border=\"1\">\n",
    "<thead>\n",
    "<tr><th align=\"center\">Day</th> <th align=\"center\">Outlook </th> <th align=\"center\">Temperature</th> <th align=\"center\">Humidity</th> <th align=\"center\"> Wind </th> <th align=\"center\">Ride</th> </tr>\n",
    "</thead>\n",
    "<tbody>\n",
    "<tr><td align=\"center\">   1      </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Hot            </td> <td align=\"center\">   High        </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   0       </td> </tr>\n",
    "<tr><td align=\"center\">   2      </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Hot            </td> <td align=\"center\">   High        </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   3      </td> <td align=\"center\">   Overcast    </td> <td align=\"center\">   Hot            </td> <td align=\"center\">   High        </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   4      </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   High        </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   5      </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Cool           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   6      </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Cool           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   0       </td> </tr>\n",
    "<tr><td align=\"center\">   7      </td> <td align=\"center\">   Overcast    </td> <td align=\"center\">   Cool           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   8      </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   High        </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   0       </td> </tr>\n",
    "<tr><td align=\"center\">   9      </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Cool           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   10     </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   11     </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   12     </td> <td align=\"center\">   Overcast    </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   High        </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   13     </td> <td align=\"center\">   Overcast    </td> <td align=\"center\">   Hot            </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   14     </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   High        </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   0       </td> </tr>\n",
    "</tbody>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "434a4333",
   "metadata": {},
   "source": [
    "## Simple Python Code to read in Data and perform Classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "894efbe3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  (0, 0)\t1.0\n",
      "  (0, 7)\t1.0\n",
      "  (0, 9)\t1.0\n",
      "  (0, 13)\t1.0\n",
      "  (1, 3)\t1.0\n",
      "  (1, 5)\t1.0\n",
      "  (1, 8)\t1.0\n",
      "  (1, 12)\t1.0\n",
      "  (2, 3)\t1.0\n",
      "  (2, 5)\t1.0\n",
      "  (2, 8)\t1.0\n",
      "  (2, 11)\t1.0\n",
      "  (3, 1)\t1.0\n",
      "  (3, 5)\t1.0\n",
      "  (3, 8)\t1.0\n",
      "  (3, 12)\t1.0\n",
      "  (4, 2)\t1.0\n",
      "  (4, 6)\t1.0\n",
      "  (4, 8)\t1.0\n",
      "  (4, 12)\t1.0\n",
      "  (5, 2)\t1.0\n",
      "  (5, 4)\t1.0\n",
      "  (5, 10)\t1.0\n",
      "  (5, 12)\t1.0\n",
      "  (6, 2)\t1.0\n",
      "  :\t:\n",
      "  (8, 12)\t1.0\n",
      "  (9, 3)\t1.0\n",
      "  (9, 4)\t1.0\n",
      "  (9, 10)\t1.0\n",
      "  (9, 12)\t1.0\n",
      "  (10, 2)\t1.0\n",
      "  (10, 6)\t1.0\n",
      "  (10, 10)\t1.0\n",
      "  (10, 12)\t1.0\n",
      "  (11, 3)\t1.0\n",
      "  (11, 6)\t1.0\n",
      "  (11, 10)\t1.0\n",
      "  (11, 11)\t1.0\n",
      "  (12, 1)\t1.0\n",
      "  (12, 6)\t1.0\n",
      "  (12, 8)\t1.0\n",
      "  (12, 11)\t1.0\n",
      "  (13, 1)\t1.0\n",
      "  (13, 5)\t1.0\n",
      "  (13, 10)\t1.0\n",
      "  (13, 12)\t1.0\n",
      "  (14, 2)\t1.0\n",
      "  (14, 6)\t1.0\n",
      "  (14, 8)\t1.0\n",
      "  (14, 11)\t1.0\n",
      "Train set accuracy with Decision Tree: 0.73\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Common imports\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.tree import export_graphviz\n",
    "from sklearn.preprocessing import StandardScaler, OneHotEncoder\n",
    "from sklearn.compose import ColumnTransformer\n",
    "from IPython.display import Image \n",
    "from pydot import graph_from_dot_data\n",
    "import os\n",
    "\n",
    "# Where to save the figures and data files\n",
    "PROJECT_ROOT_DIR = \"Results\"\n",
    "FIGURE_ID = \"Results/FigureFiles\"\n",
    "DATA_ID = \"DataFiles/\"\n",
    "\n",
    "if not os.path.exists(PROJECT_ROOT_DIR):\n",
    "    os.mkdir(PROJECT_ROOT_DIR)\n",
    "\n",
    "if not os.path.exists(FIGURE_ID):\n",
    "    os.makedirs(FIGURE_ID)\n",
    "\n",
    "if not os.path.exists(DATA_ID):\n",
    "    os.makedirs(DATA_ID)\n",
    "\n",
    "def image_path(fig_id):\n",
    "    return os.path.join(FIGURE_ID, fig_id)\n",
    "\n",
    "def data_path(dat_id):\n",
    "    return os.path.join(DATA_ID, dat_id)\n",
    "\n",
    "def save_fig(fig_id):\n",
    "    plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
    "\n",
    "infile = open(data_path(\"rideclass.csv\"),'r')\n",
    "\n",
    "# Read the experimental data with Pandas\n",
    "from IPython.display import display\n",
    "ridedata = pd.read_csv(infile,names = ('Outlook','Temperature','Humidity','Wind','Ride'))\n",
    "ridedata = pd.DataFrame(ridedata)\n",
    "\n",
    "# Features and targets\n",
    "X = ridedata.loc[:, ridedata.columns != 'Ride'].values\n",
    "y = ridedata.loc[:, ridedata.columns == 'Ride'].values\n",
    "\n",
    "# Create the encoder.\n",
    "encoder = OneHotEncoder(handle_unknown=\"ignore\")\n",
    "# Assume for simplicity all features are categorical.\n",
    "encoder.fit(X)    \n",
    "# Apply the encoder.\n",
    "X = encoder.transform(X)\n",
    "print(X)\n",
    "# Then do a Classification tree\n",
    "tree_clf = DecisionTreeClassifier(max_depth=2)\n",
    "tree_clf.fit(X, y)\n",
    "print(\"Train set accuracy with Decision Tree: {:.2f}\".format(tree_clf.score(X,y)))\n",
    "#transfer to a decision tree graph\n",
    "export_graphviz(\n",
    "    tree_clf,\n",
    "    out_file=\"DataFiles/ride.dot\",\n",
    "    rounded=True,\n",
    "    filled=True\n",
    ")\n",
    "cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'\n",
    "os.system(cmd)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce70cb1f",
   "metadata": {},
   "source": [
    "## Computing the Gini Factor\n",
    "\n",
    "The above functions (gini, entropy and misclassification error) are\n",
    "important components of the so-called CART algorithm. We will discuss\n",
    "this algorithm below after we have discussed the information gain\n",
    "algorithm ID3.\n",
    "\n",
    "In the example here we have converted all our attributes into numerical values $0,1,2$ etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "57fd167f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 1.000 Gini=0.394\n",
      "X1 < 2.000 Gini=0.394\n",
      "X1 < 2.000 Gini=0.394\n",
      "X1 < 2.000 Gini=0.394\n",
      "X1 < 1.000 Gini=0.394\n",
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 2.000 Gini=0.394\n",
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 1.000 Gini=0.394\n",
      "X1 < 1.000 Gini=0.394\n",
      "X1 < 2.000 Gini=0.394\n",
      "X2 < 0.000 Gini=0.408\n",
      "X2 < 0.000 Gini=0.408\n",
      "X2 < 0.000 Gini=0.408\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 2.000 Gini=0.407\n",
      "X2 < 2.000 Gini=0.407\n",
      "X2 < 2.000 Gini=0.407\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 2.000 Gini=0.407\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 0.000 Gini=0.408\n",
      "X2 < 1.000 Gini=0.407\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 1.000 Gini=0.405\n",
      "Split: [X3 < 1.000]\n"
     ]
    }
   ],
   "source": [
    "# Split a dataset based on an attribute and an attribute value\n",
    "def test_split(index, value, dataset):\n",
    "\tleft, right = list(), list()\n",
    "\tfor row in dataset:\n",
    "\t\tif row[index] < value:\n",
    "\t\t\tleft.append(row)\n",
    "\t\telse:\n",
    "\t\t\tright.append(row)\n",
    "\treturn left, right\n",
    " \n",
    "# Calculate the Gini index for a split dataset\n",
    "def gini_index(groups, classes):\n",
    "\t# count all samples at split point\n",
    "\tn_instances = float(sum([len(group) for group in groups]))\n",
    "\t# sum weighted Gini index for each group\n",
    "\tgini = 0.0\n",
    "\tfor group in groups:\n",
    "\t\tsize = float(len(group))\n",
    "\t\t# avoid divide by zero\n",
    "\t\tif size == 0:\n",
    "\t\t\tcontinue\n",
    "\t\tscore = 0.0\n",
    "\t\t# score the group based on the score for each class\n",
    "\t\tfor class_val in classes:\n",
    "\t\t\tp = [row[-1] for row in group].count(class_val) / size\n",
    "\t\t\tscore += p * p\n",
    "\t\t# weight the group score by its relative size\n",
    "\t\tgini += (1.0 - score) * (size / n_instances)\n",
    "\treturn gini\n",
    "\n",
    "# Select the best split point for a dataset\n",
    "def get_split(dataset):\n",
    "\tclass_values = list(set(row[-1] for row in dataset))\n",
    "\tb_index, b_value, b_score, b_groups = 999, 999, 999, None\n",
    "\tfor index in range(len(dataset[0])-1):\n",
    "\t\tfor row in dataset:\n",
    "\t\t\tgroups = test_split(index, row[index], dataset)\n",
    "\t\t\tgini = gini_index(groups, class_values)\n",
    "\t\t\tprint('X%d < %.3f Gini=%.3f' % ((index+1), row[index], gini))\n",
    "\t\t\tif gini < b_score:\n",
    "\t\t\t\tb_index, b_value, b_score, b_groups = index, row[index], gini, groups\n",
    "\treturn {'index':b_index, 'value':b_value, 'groups':b_groups}\n",
    " \n",
    "dataset = [[0,0,0,0,0],\n",
    "            [0,0,0,1,1],\n",
    "            [1,0,0,0,1],\n",
    "            [2,1,0,0,1],\n",
    "            [2,2,1,0,1],\n",
    "            [2,2,1,1,0],\n",
    "            [1,2,1,1,1],\n",
    "            [0,1,0,0,0],\n",
    "            [0,2,1,0,1],\n",
    "            [2,1,1,0,1],\n",
    "            [0,1,1,1,1],\n",
    "            [1,1,0,1,1],\n",
    "            [1,0,1,0,1],\n",
    "            [2,1,0,1,0]]\n",
    "\n",
    "split = get_split(dataset)\n",
    "print('Split: [X%d < %.3f]' % ((split['index']+1), split['value']))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15373d99",
   "metadata": {},
   "source": [
    "## Regression trees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "41a7e5f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Quadratic training set + noise\n",
    "np.random.seed(42)\n",
    "m = 200\n",
    "X = np.random.rand(m, 1)\n",
    "y = 4 * (X - 0.5) ** 2\n",
    "y = y + np.random.randn(m, 1) / 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d7c9965b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>DecisionTreeRegressor(max_depth=2, random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">DecisionTreeRegressor</label><div class=\"sk-toggleable__content\"><pre>DecisionTreeRegressor(max_depth=2, random_state=42)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "DecisionTreeRegressor(max_depth=2, random_state=42)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "tree_reg = DecisionTreeRegressor(max_depth=2, random_state=42)\n",
    "tree_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb82e5ae",
   "metadata": {},
   "source": [
    "## Final regressor code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5810e45a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "tree_reg1 = DecisionTreeRegressor(random_state=42, max_depth=2)\n",
    "tree_reg2 = DecisionTreeRegressor(random_state=42, max_depth=3)\n",
    "tree_reg1.fit(X, y)\n",
    "tree_reg2.fit(X, y)\n",
    "\n",
    "def plot_regression_predictions(tree_reg, X, y, axes=[0, 1, -0.2, 1], ylabel=\"$y$\"):\n",
    "    x1 = np.linspace(axes[0], axes[1], 500).reshape(-1, 1)\n",
    "    y_pred = tree_reg.predict(x1)\n",
    "    plt.axis(axes)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    if ylabel:\n",
    "        plt.ylabel(ylabel, fontsize=18, rotation=0)\n",
    "    plt.plot(X, y, \"b.\")\n",
    "    plt.plot(x1, y_pred, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "plt.subplot(121)\n",
    "plot_regression_predictions(tree_reg1, X, y)\n",
    "for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
    "    plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
    "plt.text(0.21, 0.65, \"Depth=0\", fontsize=15)\n",
    "plt.text(0.01, 0.2, \"Depth=1\", fontsize=13)\n",
    "plt.text(0.65, 0.8, \"Depth=1\", fontsize=13)\n",
    "plt.legend(loc=\"upper center\", fontsize=18)\n",
    "plt.title(\"max_depth=2\", fontsize=14)\n",
    "\n",
    "plt.subplot(122)\n",
    "plot_regression_predictions(tree_reg2, X, y, ylabel=None)\n",
    "for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
    "    plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
    "for split in (0.0458, 0.1298, 0.2873, 0.9040):\n",
    "    plt.plot([split, split], [-0.2, 1], \"k:\", linewidth=1)\n",
    "plt.text(0.3, 0.5, \"Depth=2\", fontsize=13)\n",
    "plt.title(\"max_depth=3\", fontsize=14)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "cbba33cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tree_reg1 = DecisionTreeRegressor(random_state=42)\n",
    "tree_reg2 = DecisionTreeRegressor(random_state=42, min_samples_leaf=10)\n",
    "tree_reg1.fit(X, y)\n",
    "tree_reg2.fit(X, y)\n",
    "\n",
    "x1 = np.linspace(0, 1, 500).reshape(-1, 1)\n",
    "y_pred1 = tree_reg1.predict(x1)\n",
    "y_pred2 = tree_reg2.predict(x1)\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(x1, y_pred1, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "plt.axis([0, 1, -0.2, 1.1])\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", fontsize=18, rotation=0)\n",
    "plt.legend(loc=\"upper center\", fontsize=18)\n",
    "plt.title(\"No restrictions\", fontsize=14)\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(x1, y_pred2, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "plt.axis([0, 1, -0.2, 1.1])\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.title(\"min_samples_leaf={}\".format(tree_reg2.min_samples_leaf), fontsize=14)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d0dc01f",
   "metadata": {},
   "source": [
    "## Pros and cons of trees, pros\n",
    "\n",
    "* White box, easy to interpret model. Some people believe that decision trees more closely mirror human decision-making than do the regression and classification approaches discussed earlier (think of support vector machines)\n",
    "\n",
    "* Trees are very easy to explain to people. In fact, they are even easier to explain than linear regression!\n",
    "\n",
    "* No feature normalization needed\n",
    "\n",
    "* Tree models can handle both continuous and categorical data (Classification and Regression Trees)\n",
    "\n",
    "* Can model nonlinear relationships\n",
    "\n",
    "* Can model interactions between the different descriptive features\n",
    "\n",
    "* Trees can be displayed graphically, and are easily interpreted even by a non-expert (especially if they are small)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "875b55f8",
   "metadata": {},
   "source": [
    "## Disadvantages\n",
    "\n",
    "* Unfortunately, trees generally do not have the same level of predictive accuracy as some of the other regression and classification approaches\n",
    "\n",
    "* If continuous features are used the tree may become quite large and hence less interpretable\n",
    "\n",
    "* Decision trees are prone to overfit the training data and hence do not well generalize the data if no stopping criteria or improvements like pruning, boosting or bagging are implemented\n",
    "\n",
    "* Small changes in the data may lead to a completely different tree. This issue can be addressed by using ensemble methods like bagging, boosting or random forests\n",
    "\n",
    "* Unbalanced datasets where some target feature values occur much more frequently than others may lead to biased trees since the frequently occurring feature values are preferred over the less frequently occurring ones. \n",
    "\n",
    "* If the number of features is relatively large (high dimensional) and the number of instances is relatively low, the tree might overfit the data\n",
    "\n",
    "* Features with many levels may be preferred over features with less levels since for them it is *more easy* to split the dataset such that the sub datasets only contain pure target feature values. This issue can be addressed by preferring for instance the information gain ratio as splitting criteria over information gain\n",
    "\n",
    "However, by aggregating many decision trees, using methods like\n",
    "bagging, random forests, and boosting, the predictive performance of\n",
    "trees can be substantially improved."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0ec4472",
   "metadata": {},
   "source": [
    "## Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods\n",
    "\n",
    "As stated above and seen in many of the examples discussed here about\n",
    "a single decision tree, we often end up overfitting our training\n",
    "data. This normally means that we have a high variance. Can we reduce\n",
    "the variance of a statistical learning method?\n",
    "\n",
    "This leads us to a set of different methods that can combine different\n",
    "machine learning algorithms or just use one of them to construct\n",
    "forests and jungles of trees, homogeneous ones or heterogenous\n",
    "ones. These methods are recognized by different names which we will\n",
    "try to explain here. These are\n",
    "\n",
    "1. Voting classifiers\n",
    "\n",
    "2. Bagging and Pasting\n",
    "\n",
    "3. Random forests\n",
    "\n",
    "4. Boosting methods, from adaptive to Extreme Gradient Boosting (XGBoost)\n",
    "\n",
    "We discuss these methods here."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "532012c9",
   "metadata": {},
   "source": [
    "## An Overview of Ensemble Methods\n",
    "\n",
    "<!-- dom:FIGURE: [DataFiles/ensembleoverview.png, width=600 frac=0.8] -->\n",
    "<!-- begin figure -->\n",
    "\n",
    "<img src=\"DataFiles/ensembleoverview.png\" width=\"600\"><p style=\"font-size: 0.9em\"><i>Figure 1: </i></p>\n",
    "<!-- end figure -->"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d055f1bf",
   "metadata": {},
   "source": [
    "## Why Voting?\n",
    "\n",
    "The idea behind boosting, and voting as well can be phrased as follows:\n",
    "**Can a group of people somehow arrive at highly\n",
    "reasoned decisions, despite the weak judgement of the individual\n",
    "members?**\n",
    "\n",
    "The aim is to create a good classifier by combining several weak classifiers.\n",
    "**A weak classifier is a classifier which is able to produce results that are only slightly better than guessing at random.**\n",
    "\n",
    "The basic approach is to apply repeatedly (in boosting this is done in an iterative way) a weak classifier to modifications of the data.\n",
    "In voting we simply apply the law of large numbers while in boosting we give more weight to misclassified data in\n",
    "each iteration.  \n",
    "\n",
    "Decision trees play an important role as our weak classifier. They serve as the basic method."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9eadfafd",
   "metadata": {},
   "source": [
    "## Tossing coins\n",
    "\n",
    "The simplest case is a so-called voting ensemble. To illustrate this,\n",
    "think of yourself tossing coins with a biased outcome of 51 per cent\n",
    "for heads and 49% for tails. With only few tosses,\n",
    "you may not clearly see this distribution for heads and tails. However, after some\n",
    "thousands of tosses, there will be a clear majority of heads.  With 2000 tosses\n",
    "you should see approximately 1020 heads and 980 tails.\n",
    "\n",
    "We can then state that the outcome is a clear majority of heads. If\n",
    "you do this ten thousand times, it is easy to see that there is a 97%\n",
    "likelihood of a majority of heads.\n",
    "\n",
    "Another example would be to collect all polls before an\n",
    "election. Different polls may show different likelihoods for a\n",
    "candidate winning with say a majority  of the popular vote. The majority vote\n",
    "would then consist in many polls indicating that this candidate will\n",
    "actually win.\n",
    "\n",
    "The example here shows how we can implement the coin tossing case,\n",
    "clealry demostrating that after some tosses we see the [law of large](https://en.wikipedia.org/wiki/Law_of_large_numbers)\n",
    "numbers kicking in."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd224ee4",
   "metadata": {},
   "source": [
    "## Standard imports first"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2d51d494",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Common imports\n",
    "from IPython.display import Image \n",
    "from pydot import graph_from_dot_data\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.tree import export_graphviz\n",
    "from sklearn.preprocessing import StandardScaler, OneHotEncoder\n",
    "from sklearn.compose import ColumnTransformer\n",
    "from IPython.display import Image \n",
    "from pydot import graph_from_dot_data\n",
    "import os\n",
    "\n",
    "# Where to save the figures and data files\n",
    "PROJECT_ROOT_DIR = \"Results\"\n",
    "FIGURE_ID = \"Results/FigureFiles\"\n",
    "DATA_ID = \"DataFiles/\"\n",
    "\n",
    "if not os.path.exists(PROJECT_ROOT_DIR):\n",
    "    os.mkdir(PROJECT_ROOT_DIR)\n",
    "\n",
    "if not os.path.exists(FIGURE_ID):\n",
    "    os.makedirs(FIGURE_ID)\n",
    "\n",
    "if not os.path.exists(DATA_ID):\n",
    "    os.makedirs(DATA_ID)\n",
    "\n",
    "def image_path(fig_id):\n",
    "    return os.path.join(FIGURE_ID, fig_id)\n",
    "\n",
    "def data_path(dat_id):\n",
    "    return os.path.join(DATA_ID, dat_id)\n",
    "\n",
    "def save_fig(fig_id):\n",
    "    plt.savefig(image_path(fig_id) + \".png\", format='png')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d03687f5",
   "metadata": {},
   "source": [
    "## Simple Voting Example, head or tail"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "54b4f008",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# Common imports\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.colors import ListedColormap\n",
    "plt.rcParams['axes.labelsize'] = 14\n",
    "plt.rcParams['xtick.labelsize'] = 12\n",
    "plt.rcParams['ytick.labelsize'] = 12\n",
    "\n",
    "heads_proba = 0.51\n",
    "coin_tosses = (np.random.rand(10000, 10) < heads_proba).astype(np.int32)\n",
    "cumulative_heads_ratio = np.cumsum(coin_tosses, axis=0) / np.arange(1, 10001).reshape(-1, 1)\n",
    "plt.figure(figsize=(8,3.5))\n",
    "plt.plot(cumulative_heads_ratio)\n",
    "plt.plot([0, 10000], [0.51, 0.51], \"k--\", linewidth=2, label=\"51%\")\n",
    "plt.plot([0, 10000], [0.5, 0.5], \"k-\", label=\"50%\")\n",
    "plt.xlabel(\"Number of coin tosses\")\n",
    "plt.ylabel(\"Heads ratio\")\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.axis([0, 10000, 0.42, 0.58])\n",
    "save_fig(\"votingsimple\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9706454",
   "metadata": {},
   "source": [
    "## Using the Voting Classifier\n",
    "\n",
    "We can use the voting classifier on other data sets, here the exciting binary case of two distinct objects using the make moons functionality of **Scikit-Learn**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a175cf2b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LogisticRegression 0.864\n",
      "RandomForestClassifier 0.872\n",
      "SVC 0.888\n",
      "VotingClassifier 0.896\n",
      "LogisticRegression 0.864\n",
      "RandomForestClassifier 0.872\n",
      "SVC 0.888\n",
      "VotingClassifier 0.912\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.datasets import make_moons\n",
    "\n",
    "X, y = make_moons(n_samples=500, noise=0.30, random_state=42)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n",
    "\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.ensemble import VotingClassifier\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.svm import SVC\n",
    "\n",
    "log_clf = LogisticRegression(solver=\"liblinear\", random_state=42)\n",
    "rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)\n",
    "svm_clf = SVC(gamma=\"auto\", random_state=42)\n",
    "\n",
    "voting_clf = VotingClassifier(\n",
    "    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],\n",
    "    voting='hard')\n",
    "\n",
    "voting_clf.fit(X_train, y_train)\n",
    "\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "for clf in (log_clf, rnd_clf, svm_clf, voting_clf):\n",
    "    clf.fit(X_train, y_train)\n",
    "    y_pred = clf.predict(X_test)\n",
    "    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))\n",
    "\n",
    "log_clf = LogisticRegression(solver=\"liblinear\", random_state=42)\n",
    "rnd_clf = RandomForestClassifier(n_estimators=10, random_state=42)\n",
    "svm_clf = SVC(gamma=\"auto\", probability=True, random_state=42)\n",
    "voting_clf = VotingClassifier(\n",
    "    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],\n",
    "    voting='soft')\n",
    "voting_clf.fit(X_train, y_train)\n",
    "\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "for clf in (log_clf, rnd_clf, svm_clf, voting_clf):\n",
    "    clf.fit(X_train, y_train)\n",
    "    y_pred = clf.predict(X_test)\n",
    "    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bc53786",
   "metadata": {},
   "source": [
    "## Voting and Bagging"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "1fff4626",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>VotingClassifier(estimators=[(&#x27;lr&#x27;, LogisticRegression(random_state=42)),\n",
       "                             (&#x27;rf&#x27;, RandomForestClassifier(random_state=42)),\n",
       "                             (&#x27;svc&#x27;, SVC(random_state=42))])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" ><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">VotingClassifier</label><div class=\"sk-toggleable__content\"><pre>VotingClassifier(estimators=[(&#x27;lr&#x27;, LogisticRegression(random_state=42)),\n",
       "                             (&#x27;rf&#x27;, RandomForestClassifier(random_state=42)),\n",
       "                             (&#x27;svc&#x27;, SVC(random_state=42))])</pre></div></div></div><div class=\"sk-parallel\"><div class=\"sk-parallel-item\"><div class=\"sk-item\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><label>lr</label></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" ><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression(random_state=42)</pre></div></div></div></div></div></div><div class=\"sk-parallel-item\"><div class=\"sk-item\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><label>rf</label></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" ><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">RandomForestClassifier</label><div class=\"sk-toggleable__content\"><pre>RandomForestClassifier(random_state=42)</pre></div></div></div></div></div></div><div class=\"sk-parallel-item\"><div class=\"sk-item\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><label>svc</label></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-5\" type=\"checkbox\" ><label for=\"sk-estimator-id-5\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">SVC</label><div class=\"sk-toggleable__content\"><pre>SVC(random_state=42)</pre></div></div></div></div></div></div></div></div></div></div>"
      ],
      "text/plain": [
       "VotingClassifier(estimators=[('lr', LogisticRegression(random_state=42)),\n",
       "                             ('rf', RandomForestClassifier(random_state=42)),\n",
       "                             ('svc', SVC(random_state=42))])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.datasets import make_moons\n",
    "\n",
    "X, y = make_moons(n_samples=500, noise=0.30, random_state=42)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.ensemble import VotingClassifier\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.svm import SVC\n",
    "\n",
    "log_clf = LogisticRegression(random_state=42)\n",
    "rnd_clf = RandomForestClassifier(random_state=42)\n",
    "svm_clf = SVC(random_state=42)\n",
    "\n",
    "voting_clf = VotingClassifier(\n",
    "    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],\n",
    "    voting='hard')\n",
    "voting_clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e3a4bb0f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LogisticRegression 0.864\n",
      "RandomForestClassifier 0.896\n",
      "SVC 0.896\n",
      "VotingClassifier 0.912\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "for clf in (log_clf, rnd_clf, svm_clf, voting_clf):\n",
    "    clf.fit(X_train, y_train)\n",
    "    y_pred = clf.predict(X_test)\n",
    "    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "fef61b5a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-3 {color: black;}#sk-container-id-3 pre{padding: 0;}#sk-container-id-3 div.sk-toggleable {background-color: white;}#sk-container-id-3 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-3 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-3 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-3 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-3 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-3 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-3 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-3 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-3 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-3 div.sk-item {position: relative;z-index: 1;}#sk-container-id-3 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-3 div.sk-item::before, #sk-container-id-3 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-3 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-3 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-3 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-3 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-3 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-3 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-3 div.sk-label-container {text-align: center;}#sk-container-id-3 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-3 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>VotingClassifier(estimators=[(&#x27;lr&#x27;, LogisticRegression(random_state=42)),\n",
       "                             (&#x27;rf&#x27;, RandomForestClassifier(random_state=42)),\n",
       "                             (&#x27;svc&#x27;, SVC(probability=True, random_state=42))],\n",
       "                 voting=&#x27;soft&#x27;)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-6\" type=\"checkbox\" ><label for=\"sk-estimator-id-6\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">VotingClassifier</label><div class=\"sk-toggleable__content\"><pre>VotingClassifier(estimators=[(&#x27;lr&#x27;, LogisticRegression(random_state=42)),\n",
       "                             (&#x27;rf&#x27;, RandomForestClassifier(random_state=42)),\n",
       "                             (&#x27;svc&#x27;, SVC(probability=True, random_state=42))],\n",
       "                 voting=&#x27;soft&#x27;)</pre></div></div></div><div class=\"sk-parallel\"><div class=\"sk-parallel-item\"><div class=\"sk-item\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><label>lr</label></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-7\" type=\"checkbox\" ><label for=\"sk-estimator-id-7\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression(random_state=42)</pre></div></div></div></div></div></div><div class=\"sk-parallel-item\"><div class=\"sk-item\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><label>rf</label></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-8\" type=\"checkbox\" ><label for=\"sk-estimator-id-8\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">RandomForestClassifier</label><div class=\"sk-toggleable__content\"><pre>RandomForestClassifier(random_state=42)</pre></div></div></div></div></div></div><div class=\"sk-parallel-item\"><div class=\"sk-item\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><label>svc</label></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-9\" type=\"checkbox\" ><label for=\"sk-estimator-id-9\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">SVC</label><div class=\"sk-toggleable__content\"><pre>SVC(probability=True, random_state=42)</pre></div></div></div></div></div></div></div></div></div></div>"
      ],
      "text/plain": [
       "VotingClassifier(estimators=[('lr', LogisticRegression(random_state=42)),\n",
       "                             ('rf', RandomForestClassifier(random_state=42)),\n",
       "                             ('svc', SVC(probability=True, random_state=42))],\n",
       "                 voting='soft')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_clf = LogisticRegression(random_state=42)\n",
    "rnd_clf = RandomForestClassifier(random_state=42)\n",
    "svm_clf = SVC(probability=True, random_state=42)\n",
    "\n",
    "voting_clf = VotingClassifier(\n",
    "    estimators=[('lr', log_clf), ('rf', rnd_clf), ('svc', svm_clf)],\n",
    "    voting='soft')\n",
    "voting_clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2cd36a0a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LogisticRegression 0.864\n",
      "RandomForestClassifier 0.896\n",
      "SVC 0.896\n",
      "VotingClassifier 0.92\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "for clf in (log_clf, rnd_clf, svm_clf, voting_clf):\n",
    "    clf.fit(X_train, y_train)\n",
    "    y_pred = clf.predict(X_test)\n",
    "    print(clf.__class__.__name__, accuracy_score(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f31db625",
   "metadata": {},
   "source": [
    "## Bagging\n",
    "\n",
    "The **plain** decision trees suffer from high\n",
    "variance. This means that if we split the training data into two parts\n",
    "at random, and fit a decision tree to both halves, the results that we\n",
    "get could be quite different. In contrast, a procedure with low\n",
    "variance will yield similar results if applied repeatedly to distinct\n",
    "data sets; linear regression tends to have low variance, if the ratio\n",
    "of $n$ to $p$ is moderately large. \n",
    "\n",
    "**Bootstrap aggregation**, or just **bagging**, is a\n",
    "general-purpose procedure for reducing the variance of a statistical\n",
    "learning method."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce89108a",
   "metadata": {},
   "source": [
    "## More bagging\n",
    "\n",
    "Bagging typically results in improved accuracy\n",
    "over prediction using a single tree. Unfortunately, however, it can be\n",
    "difficult to interpret the resulting model. Recall that one of the\n",
    "advantages of decision trees is the attractive and easily interpreted\n",
    "diagram that results.\n",
    "\n",
    "However, when we bag a large number of trees, it is no longer\n",
    "possible to represent the resulting statistical learning procedure\n",
    "using a single tree, and it is no longer clear which variables are\n",
    "most important to the procedure. Thus, bagging improves prediction\n",
    "accuracy at the expense of interpretability.  Although the collection\n",
    "of bagged trees is much more difficult to interpret than a single\n",
    "tree, one can obtain an overall summary of the importance of each\n",
    "predictor using the MSE (for bagging regression trees) or the Gini\n",
    "index (for bagging classification trees). In the case of bagging\n",
    "regression trees, we can record the total amount that the MSE is\n",
    "decreased due to splits over a given predictor, averaged over all $B$ possible\n",
    "trees. A large value indicates an important predictor. Similarly, in\n",
    "the context of bagging classification trees, we can add up the total\n",
    "amount that the Gini index  is decreased by splits over a given\n",
    "predictor, averaged over all $B$ trees."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cdece01",
   "metadata": {},
   "source": [
    "## Making your own Bootstrap: Changing the Level of the Decision Tree\n",
    "\n",
    "Let us bring up our good old boostrap example from the linear regression lectures. We change the linerar regression algorithm with\n",
    "a decision tree wth different depths and perform a bootstrap aggregate (in this case we perform as many bootstraps as data points $n$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "324a964b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Polynomial degree: 1\n",
      "Error: 0.06380941468319971\n",
      "Bias^2: 0.05160313473529168\n",
      "Var: 0.01220627994790804\n",
      "0.06380941468319971 >= 0.05160313473529168 + 0.01220627994790804 = 0.06380941468319971\n",
      "Polynomial degree: 2\n",
      "Error: 0.043464037468677004\n",
      "Bias^2: 0.02659851591375224\n",
      "Var: 0.01686552155492476\n",
      "0.043464037468677004 >= 0.02659851591375224 + 0.01686552155492476 = 0.043464037468677\n",
      "Polynomial degree: 3\n",
      "Error: 0.020716391693769383\n",
      "Bias^2: 0.01159033914386312\n",
      "Var: 0.00912605254990626\n",
      "0.020716391693769383 >= 0.01159033914386312 + 0.00912605254990626 = 0.02071639169376938\n",
      "Polynomial degree: 4\n",
      "Error: 0.02063627410934057\n",
      "Bias^2: 0.0117496656370668\n",
      "Var: 0.008886608472273775\n",
      "0.02063627410934057 >= 0.0117496656370668 + 0.008886608472273775 = 0.020636274109340574\n",
      "Polynomial degree: 5\n",
      "Error: 0.02087627881701288\n",
      "Bias^2: 0.01349183949256158\n",
      "Var: 0.007384439324451296\n",
      "0.02087627881701288 >= 0.01349183949256158 + 0.007384439324451296 = 0.020876278817012876\n",
      "Polynomial degree: 6\n",
      "Error: 0.02069601123831537\n",
      "Bias^2: 0.013918526350129823\n",
      "Var: 0.0067774848881855445\n",
      "0.02069601123831537 >= 0.013918526350129823 + 0.0067774848881855445 = 0.020696011238315368\n",
      "Polynomial degree: 7\n",
      "Error: 0.022964339924731444\n",
      "Bias^2: 0.01550381208433455\n",
      "Var: 0.007460527840396904\n",
      "0.022964339924731444 >= 0.01550381208433455 + 0.007460527840396904 = 0.022964339924731455\n",
      "Simple tree: 0.5148389267750961\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.utils import resample\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "n = 100\n",
    "n_boostraps = 100\n",
    "maxdepth = 8\n",
    "\n",
    "# Make data set.\n",
    "x = np.linspace(-3, 3, n).reshape(-1, 1)\n",
    "y = np.exp(-x**2) + 1.5 * np.exp(-(x-2)**2)+ np.random.normal(0, 0.1, x.shape)\n",
    "error = np.zeros(maxdepth)\n",
    "bias = np.zeros(maxdepth)\n",
    "variance = np.zeros(maxdepth)\n",
    "polydegree = np.zeros(maxdepth)\n",
    "X_train, X_test, y_train, y_test = train_test_split(x, y, test_size=0.2)\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(X_train)\n",
    "X_train_scaled = scaler.transform(X_train)\n",
    "X_test_scaled = scaler.transform(X_test)\n",
    "\n",
    "# we produce a simple tree first as benchmark\n",
    "simpletree = DecisionTreeRegressor(max_depth=3) \n",
    "simpletree.fit(X_train_scaled, y_train)\n",
    "simpleprediction = simpletree.predict(X_test_scaled)\n",
    "for degree in range(1,maxdepth):\n",
    "    model = DecisionTreeRegressor(max_depth=degree) \n",
    "    y_pred = np.empty((y_test.shape[0], n_boostraps))\n",
    "    for i in range(n_boostraps):\n",
    "        x_, y_ = resample(X_train_scaled, y_train)\n",
    "        model.fit(x_, y_)\n",
    "        y_pred[:, i] = model.predict(X_test_scaled)#.ravel()\n",
    "\n",
    "    polydegree[degree] = degree\n",
    "    error[degree] = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )\n",
    "    bias[degree] = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )\n",
    "    variance[degree] = np.mean( np.var(y_pred, axis=1, keepdims=True) )\n",
    "    print('Polynomial degree:', degree)\n",
    "    print('Error:', error[degree])\n",
    "    print('Bias^2:', bias[degree])\n",
    "    print('Var:', variance[degree])\n",
    "    print('{} >= {} + {} = {}'.format(error[degree], bias[degree], variance[degree], bias[degree]+variance[degree]))\n",
    " \n",
    "mse_simpletree= np.mean( np.mean((y_test - simpleprediction)**2))\n",
    "print(\"Simple tree:\",mse_simpletree)\n",
    "plt.xlim(1,maxdepth)\n",
    "plt.plot(polydegree, error, label='MSE')\n",
    "plt.plot(polydegree, bias, label='bias')\n",
    "plt.plot(polydegree, variance, label='Variance')\n",
    "plt.legend()\n",
    "save_fig(\"baggingboot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33074a97",
   "metadata": {},
   "source": [
    "## Random forests\n",
    "\n",
    "Random forests provide an improvement over bagged trees by way of a\n",
    "small tweak that decorrelates the trees. \n",
    "\n",
    "As in bagging, we build a\n",
    "number of decision trees on bootstrapped training samples. But when\n",
    "building these decision trees, each time a split in a tree is\n",
    "considered, a random sample of $m$ predictors is chosen as split\n",
    "candidates from the full set of $p$ predictors. The split is allowed to\n",
    "use only one of those $m$ predictors. \n",
    "\n",
    "A fresh sample of $m$ predictors is\n",
    "taken at each split, and typically we choose"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8140eb76",
   "metadata": {},
   "source": [
    "$$\n",
    "m\\approx \\sqrt{p}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ba57277",
   "metadata": {},
   "source": [
    "In building a random forest, at\n",
    "each split in the tree, the algorithm is not even allowed to consider\n",
    "a majority of the available predictors. \n",
    "\n",
    "The reason for this is rather clever. Suppose that there is one very\n",
    "strong predictor in the data set, along with a number of other\n",
    "moderately strong predictors. Then in the collection of bagged\n",
    "variable importance random forest trees, most or all of the trees will\n",
    "use this strong predictor in the top split. Consequently, all of the\n",
    "bagged trees will look quite similar to each other. Hence the\n",
    "predictions from the bagged trees will be highly correlated.\n",
    "Unfortunately, averaging many highly correlated quantities does not\n",
    "lead to as large of a reduction in variance as averaging many\n",
    "uncorrelated quantities. In particular, this means that bagging will\n",
    "not lead to a substantial reduction in variance over a single tree in\n",
    "this setting."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7dce23d",
   "metadata": {},
   "source": [
    "## Random Forest Algorithm\n",
    "The algorithm described here can be applied to both classification and regression problems.\n",
    "\n",
    "We will grow of forest of say $B$ trees.\n",
    "1. For $b=1:B$\n",
    "\n",
    "  * Draw a bootstrap sample from the training data organized in our $\\boldsymbol{X}$ matrix.\n",
    "\n",
    "  * We grow then a random forest tree $T_b$ based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached\n",
    "\n",
    "1. we select $m \\le p$ variables at random from the $p$ predictors/features\n",
    "\n",
    "2. pick the best split point among the $m$ features using for example the CART algorithm and create a new node\n",
    "\n",
    "3. split the node into daughter nodes\n",
    "\n",
    "4. Output then the ensemble of trees $\\{T_b\\}_1^{B}$ and make predictions for either a regression type of problem or a classification type of problem."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4e3455f",
   "metadata": {},
   "source": [
    "## Random Forests Compared with other Methods on the Cancer Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "9f530afd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(426, 30)\n",
      "(143, 30)\n",
      "Test set accuracy Logistic Regression with scaled data: 0.96\n",
      "Test set accuracy SVM with scaled data: 0.96\n",
      "Test set accuracy with Decision Trees and scaled data: 0.87\n",
      "[0.93333333 0.73333333 0.93333333 1.         1.         0.92857143\n",
      " 1.         0.92857143 0.92857143 0.92857143]\n",
      "Test set accuracy with Random Forests and scaled data: 0.98\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.model_selection import  train_test_split \n",
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.ensemble import BaggingClassifier\n",
    "\n",
    "# Load the data\n",
    "cancer = load_breast_cancer()\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
    "print(X_train.shape)\n",
    "print(X_test.shape)\n",
    "#define methods\n",
    "# Logistic Regression\n",
    "logreg = LogisticRegression(solver='lbfgs')\n",
    "# Support vector machine\n",
    "svm = SVC(gamma='auto', C=100)\n",
    "# Decision Trees\n",
    "deep_tree_clf = DecisionTreeClassifier(max_depth=None)\n",
    "#Scale the data\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(X_train)\n",
    "X_train_scaled = scaler.transform(X_train)\n",
    "X_test_scaled = scaler.transform(X_test)\n",
    "# Logistic Regression\n",
    "logreg.fit(X_train_scaled, y_train)\n",
    "print(\"Test set accuracy Logistic Regression with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
    "# Support Vector Machine\n",
    "svm.fit(X_train_scaled, y_train)\n",
    "print(\"Test set accuracy SVM with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
    "# Decision Trees\n",
    "deep_tree_clf.fit(X_train_scaled, y_train)\n",
    "print(\"Test set accuracy with Decision Trees and scaled data: {:.2f}\".format(deep_tree_clf.score(X_test_scaled,y_test)))\n",
    "\n",
    "\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "from sklearn.model_selection import cross_validate\n",
    "# Data set not specificied\n",
    "#Instantiate the model with 500 trees and entropy as splitting criteria\n",
    "Random_Forest_model = RandomForestClassifier(n_estimators=500,criterion=\"entropy\")\n",
    "Random_Forest_model.fit(X_train_scaled, y_train)\n",
    "#Cross validation\n",
    "accuracy = cross_validate(Random_Forest_model,X_test_scaled,y_test,cv=10)['test_score']\n",
    "print(accuracy)\n",
    "print(\"Test set accuracy with Random Forests and scaled data: {:.2f}\".format(Random_Forest_model.score(X_test_scaled,y_test)))\n",
    "\n",
    "\n",
    "import scikitplot as skplt\n",
    "y_pred = Random_Forest_model.predict(X_test_scaled)\n",
    "skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)\n",
    "plt.show()\n",
    "y_probas = Random_Forest_model.predict_proba(X_test_scaled)\n",
    "skplt.metrics.plot_roc(y_test, y_probas)\n",
    "plt.show()\n",
    "skplt.metrics.plot_cumulative_gain(y_test, y_probas)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "813c8183",
   "metadata": {},
   "source": [
    "Recall that the cumulative gains curve shows the percentage of the\n",
    "overall number of cases in a given category *gained* by targeting a\n",
    "percentage of the total number of cases.\n",
    "\n",
    "Similarly, the receiver operating characteristic curve, or ROC curve,\n",
    "displays the diagnostic ability of a binary classifier system as its\n",
    "discrimination threshold is varied. It plots the true positive rate against the false positive rate."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0723ecc",
   "metadata": {},
   "source": [
    "## Compare  Bagging on Trees with Random Forests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "ea6c0862",
   "metadata": {},
   "outputs": [],
   "source": [
    "bag_clf = BaggingClassifier(\n",
    "    DecisionTreeClassifier(splitter=\"random\", max_leaf_nodes=16, random_state=42),\n",
    "    n_estimators=500, max_samples=1.0, bootstrap=True, n_jobs=-1, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "851aee9e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9790209790209791"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bag_clf.fit(X_train, y_train)\n",
    "y_pred = bag_clf.predict(X_test)\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "rnd_clf = RandomForestClassifier(n_estimators=500, max_leaf_nodes=16, n_jobs=-1, random_state=42)\n",
    "rnd_clf.fit(X_train, y_train)\n",
    "y_pred_rf = rnd_clf.predict(X_test)\n",
    "np.sum(y_pred == y_pred_rf) / len(y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "287af61b",
   "metadata": {},
   "source": [
    "## Boosting, a Bird's Eye View\n",
    "\n",
    "The basic idea is to combine weak classifiers in order to create a good\n",
    "classifier. With a weak classifier we often intend a classifier which\n",
    "produces results which are only slightly better than we would get by\n",
    "random guesses.\n",
    "\n",
    "This is done by applying in an iterative way a weak (or a standard\n",
    "classifier like decision trees) to modify the data. In each iteration\n",
    "we emphasize those observations which are misclassified by weighting\n",
    "them with a factor."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99fa95d1",
   "metadata": {},
   "source": [
    "## What is boosting? Additive Modelling/Iterative Fitting\n",
    "\n",
    "Boosting is a way of fitting an additive expansion in a set of\n",
    "elementary basis functions like for example some simple polynomials.\n",
    "Assume for example that we have a function"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0843532",
   "metadata": {},
   "source": [
    "$$\n",
    "f_M(x) = \\sum_{i=1}^M \\beta_m b(x;\\gamma_m),\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0036ded",
   "metadata": {},
   "source": [
    "where $\\beta_m$ are the expansion parameters to be determined in a\n",
    "minimization process and $b(x;\\gamma_m)$ are some simple functions of\n",
    "the multivariable parameter $x$ which is characterized by the\n",
    "parameters $\\gamma_m$.\n",
    "\n",
    "As an example, consider the Sigmoid function we used in logistic\n",
    "regression. In that case, we can translate the function\n",
    "$b(x;\\gamma_m)$ into the Sigmoid function"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64b3db1f",
   "metadata": {},
   "source": [
    "$$\n",
    "\\sigma(t) = \\frac{1}{1+\\exp{(-t)}},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b53e923c",
   "metadata": {},
   "source": [
    "where $t=\\gamma_0+\\gamma_1 x$ and the parameters $\\gamma_0$ and\n",
    "$\\gamma_1$ were determined by the Logistic Regression fitting\n",
    "algorithm.\n",
    "\n",
    "As another example, consider the cost function we defined for linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2fe6aab6",
   "metadata": {},
   "source": [
    "$$\n",
    "C(\\boldsymbol{y},\\boldsymbol{f}) = \\frac{1}{n} \\sum_{i=0}^{n-1}(y_i-f(x_i))^2.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02f7e570",
   "metadata": {},
   "source": [
    "In this case the function $f(x)$ was replaced by the design matrix\n",
    "$\\boldsymbol{X}$ and the unknown linear regression parameters $\\boldsymbol{\\beta}$,\n",
    "that is $\\boldsymbol{f}=\\boldsymbol{X}\\boldsymbol{\\beta}$. In linear regression we can \n",
    "simply invert a matrix and obtain the parameters $\\beta$ by"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d5428ac",
   "metadata": {},
   "source": [
    "$$\n",
    "\\boldsymbol{\\beta}=\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25a66005",
   "metadata": {},
   "source": [
    "In iterative fitting or additive modeling, we minimize the cost function with respect to the parameters $\\beta_m$ and $\\gamma_m$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "819e870d",
   "metadata": {},
   "source": [
    "## Iterative Fitting, Regression and Squared-error Cost Function\n",
    "\n",
    "The way we proceed is as follows (here we specialize to the squared-error cost function)\n",
    "\n",
    "1. Establish a cost function, here $C(\\boldsymbol{y},\\boldsymbol{f}) = \\frac{1}{n} \\sum_{i=0}^{n-1}(y_i-f_M(x_i))^2$ with $f_M(x) = \\sum_{i=1}^M \\beta_m b(x;\\gamma_m)$.\n",
    "\n",
    "2. Initialize with a guess $f_0(x)$. It could be one or even zero or some random numbers.\n",
    "\n",
    "3. For $m=1:M$\n",
    "\n",
    "a. minimize $\\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta b(x;\\gamma))^2$ wrt $\\gamma$ and $\\beta$\n",
    "\n",
    "b. This gives the optimal values $\\beta_m$ and $\\gamma_m$\n",
    "\n",
    "c. Determine then the new values $f_m(x)=f_{m-1}(x) +\\beta_m b(x;\\gamma_m)$\n",
    "\n",
    "We could use any of the algorithms we have discussed till now. If we\n",
    "use trees, $\\gamma$ parameterizes the split variables and split points\n",
    "at the internal nodes, and the predictions at the terminal nodes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2b40fd6",
   "metadata": {},
   "source": [
    "## Squared-Error Example and Iterative Fitting\n",
    "\n",
    "To better understand what happens, let us develop the steps for the iterative fitting using the above squared error function.\n",
    "\n",
    "For simplicity we assume also that our functions $b(x;\\gamma)=1+\\gamma x$. \n",
    "\n",
    "This means that for every iteration $m$, we need to optimize"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "afdbae5d",
   "metadata": {},
   "source": [
    "$$\n",
    "(\\beta_m,\\gamma_m) = \\mathrm{argmin}_{\\beta,\\lambda}\\hspace{0.1cm} \\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta b(x;\\gamma))^2=\\sum_{i=0}^{n-1}(y_i-f_{m-1}(x_i)-\\beta(1+\\gamma x_i))^2.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b5a9a94",
   "metadata": {},
   "source": [
    "We start our iteration by simply setting $f_0(x)=0$. \n",
    "Taking the derivatives  with respect to $\\beta$ and $\\gamma$ we obtain"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "071ce45d",
   "metadata": {},
   "source": [
    "$$\n",
    "\\frac{\\partial {\\cal C}}{\\partial \\beta} = -2\\sum_{i}(1+\\gamma x_i)(y_i-\\beta(1+\\gamma x_i))=0,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b64e74a0",
   "metadata": {},
   "source": [
    "and"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "006f6950",
   "metadata": {},
   "source": [
    "$$\n",
    "\\frac{\\partial {\\cal C}}{\\partial \\gamma} =-2\\sum_{i}\\beta x_i(y_i-\\beta(1+\\gamma x_i))=0.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a6cb700",
   "metadata": {},
   "source": [
    "We can then rewrite these equations as (defining $\\boldsymbol{w}=\\boldsymbol{e}+\\gamma \\boldsymbol{x})$ with $\\boldsymbol{e}$ being the unit vector)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9792edc",
   "metadata": {},
   "source": [
    "$$\n",
    "\\gamma \\boldsymbol{w}^T(\\boldsymbol{y}-\\beta\\gamma \\boldsymbol{w})=0,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad4e3e77",
   "metadata": {},
   "source": [
    "which gives us $\\beta = \\boldsymbol{w}^T\\boldsymbol{y}/(\\boldsymbol{w}^T\\boldsymbol{w})$. Similarly we have"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4422c86",
   "metadata": {},
   "source": [
    "$$\n",
    "\\beta\\gamma \\boldsymbol{x}^T(\\boldsymbol{y}-\\beta(1+\\gamma \\boldsymbol{x}))=0,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9095127",
   "metadata": {},
   "source": [
    "which leads to $\\gamma =(\\boldsymbol{x}^T\\boldsymbol{y}-\\beta\\boldsymbol{x}^T\\boldsymbol{e})/(\\beta\\boldsymbol{x}^T\\boldsymbol{x})$.  Inserting\n",
    "for $\\beta$ gives us an equation for $\\gamma$. This is a non-linear equation in the unknown $\\gamma$ and has to be solved numerically. \n",
    "\n",
    "The solution to these two equations gives us in turn $\\beta_1$ and $\\gamma_1$ leading to the new expression for $f_1(x)$ as\n",
    "$f_1(x) = \\beta_1(1+\\gamma_1x)$. Doing this $M$ times results in our final estimate for the function $f$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7e4c3c3",
   "metadata": {},
   "source": [
    "## Iterative Fitting, Classification and AdaBoost\n",
    "\n",
    "Let us consider a binary classification problem with two outcomes $y_i \\in \\{-1,1\\}$ and $i=0,1,2,\\dots,n-1$ as our set of\n",
    "observations. We define a classification function $G(x)$ which produces a prediction taking one or the other of the two values \n",
    "$\\{-1,1\\}$.\n",
    "\n",
    "The error rate of the training sample is then"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3e78fb3",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathrm{\\overline{err}}=\\frac{1}{n} \\sum_{i=0}^{n-1} I(y_i\\ne G(x_i)).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8efd60b4",
   "metadata": {},
   "source": [
    "The iterative procedure starts with defining a weak classifier whose\n",
    "error rate is barely better than random guessing.  The iterative\n",
    "procedure in boosting is to sequentially apply a  weak\n",
    "classification algorithm to repeatedly modified versions of the data\n",
    "producing a sequence of weak classifiers $G_m(x)$.\n",
    "\n",
    "Here we will express our  function $f(x)$ in terms of $G(x)$. That is"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df99945c",
   "metadata": {},
   "source": [
    "$$\n",
    "f_M(x) = \\sum_{i=1}^M \\beta_m b(x;\\gamma_m),\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc416763",
   "metadata": {},
   "source": [
    "will be a function of"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "389d2723",
   "metadata": {},
   "source": [
    "$$\n",
    "G_M(x) = \\mathrm{sign} \\sum_{i=1}^M \\alpha_m G_m(x).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1eec60f",
   "metadata": {},
   "source": [
    "## Adaptive Boosting, AdaBoost\n",
    "\n",
    "In our iterative procedure we define thus"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8de59939",
   "metadata": {},
   "source": [
    "$$\n",
    "f_m(x) = f_{m-1}(x)+\\beta_mG_m(x).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ffc9c90",
   "metadata": {},
   "source": [
    "The simplest possible cost function which leads (also simple from a computational point of view) to the AdaBoost algorithm is the\n",
    "exponential cost/loss function defined as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b8ad6ea",
   "metadata": {},
   "source": [
    "$$\n",
    "C(\\boldsymbol{y},\\boldsymbol{f}) = \\sum_{i=0}^{n-1}\\exp{(-y_i(f_{m-1}(x_i)+\\beta G(x_i))}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "290ecb27",
   "metadata": {},
   "source": [
    "We optimize $\\beta$ and $G$ for each value of $m=1:M$ as we did in the regression case.\n",
    "This is normally done in two steps. Let us however first rewrite the cost function as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b835bd84",
   "metadata": {},
   "source": [
    "$$\n",
    "C(\\boldsymbol{y},\\boldsymbol{f}) = \\sum_{i=0}^{n-1}w_i^{m}\\exp{(-y_i\\beta G(x_i))},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b38ce14f",
   "metadata": {},
   "source": [
    "where we have defined $w_i^m= \\exp{(-y_if_{m-1}(x_i))}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e37dc59e",
   "metadata": {},
   "source": [
    "## Building up AdaBoost\n",
    "\n",
    "First, for any $\\beta > 0$, we optimize $G$ by setting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63ea786a",
   "metadata": {},
   "source": [
    "$$\n",
    "G_m(x) = \\mathrm{sign} \\sum_{i=0}^{n-1} w_i^m I(y_i \\ne G_(x_i)),\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1a81aa0",
   "metadata": {},
   "source": [
    "which is the classifier that minimizes the weighted error rate in predicting $y$.\n",
    "\n",
    "We can do this by rewriting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75be4ffe",
   "metadata": {},
   "source": [
    "$$\n",
    "\\exp{-(\\beta)}\\sum_{y_i=G(x_i)}w_i^m+\\exp{(\\beta)}\\sum_{y_i\\ne G(x_i)}w_i^m,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4f28a57",
   "metadata": {},
   "source": [
    "which can be rewritten as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b446ff3f",
   "metadata": {},
   "source": [
    "$$\n",
    "(\\exp{(\\beta)}-\\exp{-(\\beta)})\\sum_{i=0}^{n-1}w_i^mI(y_i\\ne G(x_i))+\\exp{(-\\beta)}\\sum_{i=0}^{n-1}w_i^m=0,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08d10f84",
   "metadata": {},
   "source": [
    "which leads to"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bda97977",
   "metadata": {},
   "source": [
    "$$\n",
    "\\beta_m = \\frac{1}{2}\\log{\\frac{1-\\mathrm{\\overline{err}}}{\\mathrm{\\overline{err}}}},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c96cfaa",
   "metadata": {},
   "source": [
    "where we have redefined the error as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "399edb04",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathrm{\\overline{err}}_m=\\frac{1}{n}\\frac{\\sum_{i=0}^{n-1}w_i^mI(y_i\\ne G(x_i)}{\\sum_{i=0}^{n-1}w_i^m},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20bfce2f",
   "metadata": {},
   "source": [
    "which leads to an update of"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "282c44ac",
   "metadata": {},
   "source": [
    "$$\n",
    "f_m(x) = f_{m-1}(x) +\\beta_m G_m(x).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a8ddb16",
   "metadata": {},
   "source": [
    "This leads to the new weights"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bf9bda1",
   "metadata": {},
   "source": [
    "$$\n",
    "w_i^{m+1} = w_i^m \\exp{(-y_i\\beta_m G_m(x_i))}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4b681cd",
   "metadata": {},
   "source": [
    "## Adaptive boosting: AdaBoost, Basic Algorithm\n",
    "\n",
    "The algorithm here is rather straightforward. Assume that our weak\n",
    "classifier is a decision tree and we consider a binary set of outputs\n",
    "with $y_i \\in \\{-1,1\\}$ and $i=0,1,2,\\dots,n-1$ as our set of\n",
    "observations. Our design matrix is given in terms of the\n",
    "feature/predictor vectors\n",
    "$\\boldsymbol{X}=[\\boldsymbol{x}_0\\boldsymbol{x}_1\\dots\\boldsymbol{x}_{p-1}]$. Finally, we define also a\n",
    "classifier determined by our data via a function $G(x)$. This function tells us how well we are able to classify our outputs/targets $\\boldsymbol{y}$. \n",
    "\n",
    "We have already defined the misclassification error $\\mathrm{err}$ as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1eb4a855",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathrm{err}=\\frac{1}{n}\\sum_{i=0}^{n-1}I(y_i\\ne G(x_i)),\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "238ee6db",
   "metadata": {},
   "source": [
    "where the function $I()$ is one if we misclassify and zero if we classify correctly."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd0b8fe3",
   "metadata": {},
   "source": [
    "## Basic Steps of AdaBoost\n",
    "\n",
    "With the above definitions we are now ready to set up the algorithm for AdaBoost.\n",
    "The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases.\n",
    "1. We start by initializing all weights to $w_i = 1/n$, with $i=0,1,2,\\dots n-1$. It is easy to see that we must have $\\sum_{i=0}^{n-1}w_i = 1$.\n",
    "\n",
    "2. We rewrite the misclassification error as"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79ae4017",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathrm{\\overline{err}}_m=\\frac{\\sum_{i=0}^{n-1}w_i^m I(y_i\\ne G(x_i))}{\\sum_{i=0}^{n-1}w_i},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a963b267",
   "metadata": {},
   "source": [
    "1. Then we start looping over all attempts at classifying, namely we start an iterative process for $m=1:M$, where $M$ is the final number of classifications. Our given classifier could for example be a plain decision tree.\n",
    "\n",
    "a. Fit then a given classifier to the training set using the weights $w_i$.\n",
    "\n",
    "b. Compute then $\\mathrm{err}$ and figure out which events are classified properly and which are classified wrongly.\n",
    "\n",
    "c. Define a quantity $\\alpha_{m} = \\log{(1-\\mathrm{\\overline{err}}_m)/\\mathrm{\\overline{err}}_m}$\n",
    "\n",
    "d. Set the new weights to $w_i = w_i\\times \\exp{(\\alpha_m I(y_i\\ne G(x_i)}$.\n",
    "\n",
    "5. Compute the new classifier $G(x)= \\sum_{i=0}^{n-1}\\alpha_m I(y_i\\ne G(x_i)$.\n",
    "\n",
    "For the iterations with $m \\le 2$ the weights are modified\n",
    "individually at each steps. The observations which were misclassified\n",
    "at iteration $m-1$ have a weight which is larger than those which were\n",
    "classified properly. As this proceeds, the observations which were\n",
    "difficult to classifiy correctly are given a larger influence. Each\n",
    "new classification step $m$ is then forced to concentrate on those\n",
    "observations that are missed in the previous iterations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22277568",
   "metadata": {},
   "source": [
    "## AdaBoost Examples\n",
    "\n",
    "Using **Scikit-Learn** it is easy to apply the adaptive boosting algorithm, as done here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "2c8adda4",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.ensemble import AdaBoostClassifier\n",
    "\n",
    "ada_clf = AdaBoostClassifier(\n",
    "    DecisionTreeClassifier(max_depth=1), n_estimators=200,\n",
    "    algorithm=\"SAMME.R\", learning_rate=0.5, random_state=42)\n",
    "ada_clf.fit(X_train, y_train)\n",
    "\n",
    "from sklearn.ensemble import AdaBoostClassifier\n",
    "\n",
    "ada_clf = AdaBoostClassifier(\n",
    "    DecisionTreeClassifier(max_depth=1), n_estimators=200,\n",
    "    algorithm=\"SAMME.R\", learning_rate=0.5, random_state=42)\n",
    "ada_clf.fit(X_train_scaled, y_train)\n",
    "y_pred = ada_clf.predict(X_test_scaled)\n",
    "skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)\n",
    "plt.show()\n",
    "y_probas = ada_clf.predict_proba(X_test_scaled)\n",
    "skplt.metrics.plot_roc(y_test, y_probas)\n",
    "plt.show()\n",
    "skplt.metrics.plot_cumulative_gain(y_test, y_probas)\n",
    "plt.show()"
   ]
  }
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