FYS-STK4155/doc/LectureNotes/_build/jupyter_execute/chapter6.ipynb

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    "# Decision trees, overarching aims\n",
    "\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",
    "\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**. \n",
    "\n",
    "## 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.\n",
    "\n",
    "\n",
    "## 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.\n",
    "\n",
    "\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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      "2nd degree coefficients:\n",
      "zero power:  4.58641507967355\n",
      "first power:  -0.2107546970521115\n",
      "second power:  0.0003919793592273513\n"
     ]
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_1_1.png"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_1_2.png"
      }
     },
     "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=7)\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",
   "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",
   "metadata": {},
   "source": [
    "$$\n",
    "\\sum_{j=1}^J\\sum_{i\\in R_j}(y_i-\\overline{y}_{R_j})^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where $\\overline{y}_{R_j}$  is the mean response for the training observations \n",
    "within box $j$. \n",
    "\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.\n",
    "\n",
    "\n",
    "### 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",
   "metadata": {},
   "source": [
    "$$\n",
    "\\left\\{X\\vert x_j < s\\right\\},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\left\\{X\\vert x_j \\geq s\\right\\},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "so that we obtain the lowest MSE, that is"
   ]
  },
  {
   "cell_type": "markdown",
   "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",
   "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.\n",
    "\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).\n",
    "\n",
    "\n",
    "For each value of $\\alpha$  there corresponds a subtree $T \\in T_0$ such that"
   ]
  },
  {
   "cell_type": "markdown",
   "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",
   "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",
    "\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 $\\alpha$. \n",
    "\n",
    "\n",
    "### 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",
    "\n",
    "4. Return the subtree from Step 2 that corresponds to the chosen value of $\\alpha$. \n",
    "\n",
    "!eblock\n",
    "\n",
    "\n",
    "\n",
    "## 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.  \n",
    "\n",
    "\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. \n",
    "\n",
    "\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",
   "metadata": {},
   "source": [
    "$$\n",
    "p_{mk} = \\frac{1}{N_m}\\sum_{x_i\\in R_m}I(y_i=k).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "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",
   "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",
   "metadata": {},
   "source": [
    "* Gini index $g$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "g = \\sum_{k=1}^K p_{mk}(1-p_{mk}).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Information entropy or just entropy $s$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "s = -\\sum_{k=1}^K p_{mk}\\log{p_{mk}}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing the Tree, Classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "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": 2,
     "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": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 3,
     "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",
   "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": 4,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "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]')]"
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     },
     "execution_count": 4,
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     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_24_1.png"
      }
     },
     "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",
   "metadata": {},
   "source": [
    "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": 5,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "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",
   "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.\n",
    "\n",
    "### 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",
   "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",
   "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 $max\\_leaf\\_nodes$.\n",
    "\n",
    "\n",
    "### 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",
   "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",
   "metadata": {},
   "source": [
    "Here the MSE for a specific node is defined as"
   ]
  },
  {
   "cell_type": "markdown",
   "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",
   "metadata": {},
   "source": [
    "with"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\overline{y}_{\\mathrm{node}}=\\frac{1}{m_\\mathrm{node}}\\sum_{i\\in \\mathrm{node}}y_i,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "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.\n",
    "\n",
    "\n",
    "\n",
    "### Computing the Gini index\n",
    "\n",
    "The 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 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>\n",
    "\n",
    "### Simple Python Code to read in Data and perform Classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "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": 6,
     "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",
   "metadata": {},
   "source": [
    "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": 7,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "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",
   "metadata": {},
   "source": [
    "## Entropy and the ID3 algorithm\n",
    "\n",
    "The ID3 algorithm  learns decision trees by constructing\n",
    "them in a top down way, beginning with the question **which attribute should be tested at the root of the tree**?\n",
    "\n",
    "1. Each instance attribute is evaluated using a statistical test to determine how well it alone classifies the training examples.\n",
    "\n",
    "2. The best attribute is selected and used as the test at the root node of the tree.\n",
    "\n",
    "3. A descendant of the root node is then created for each possible value of this attribute.\n",
    "\n",
    "4. Training examples are sorted to the appropriate descendant node.\n",
    "\n",
    "5. The entire process is then repeated using the training examples associated with each descendant node to select the best attribute to test at that point in the tree.\n",
    "\n",
    "6. This forms a greedy search for an acceptable decision tree, in which the algorithm never backtracks to reconsider earlier choices. \n",
    "\n",
    "The ID3 algorithm selects which attribute to test at each node in the\n",
    "tree.\n",
    "\n",
    "We would like to select the attribute that is most useful for classifying\n",
    "examples.\n",
    "\n",
    "What is a good quantitative measure of the worth of an attribute?\n",
    "\n",
    "Information gain measures how well a given attribute separates the\n",
    "training examples according to their target classification.\n",
    "\n",
    "The ID3 algorithm uses this information gain measure to select among the candidate\n",
    "attributes at each step while growing the tree.\n",
    "\n",
    "\n",
    "### Cancer Data again now with Decision Trees and other Methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(426, 30)\n",
      "(143, 30)\n",
      "Test set accuracy with Logistic Regression: 0.94\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test set accuracy with SVM: 0.63"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Test set accuracy with Decision Trees: 0.90\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: 0.89\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:460: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
      "\n",
      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
      "Please also refer to the documentation for alternative solver options:\n",
      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
      "  n_iter_i = _check_optimize_result(\n"
     ]
    }
   ],
   "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",
    "\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",
    "# Logistic Regression\n",
    "logreg = LogisticRegression(solver='lbfgs')\n",
    "logreg.fit(X_train, y_train)\n",
    "print(\"Test set accuracy with Logistic Regression: {:.2f}\".format(logreg.score(X_test,y_test)))\n",
    "# Support vector machine\n",
    "svm = SVC(gamma='auto', C=100)\n",
    "svm.fit(X_train, y_train)\n",
    "print(\"Test set accuracy with SVM: {:.2f}\".format(svm.score(X_test,y_test)))\n",
    "# Decision Trees\n",
    "deep_tree_clf = DecisionTreeClassifier(max_depth=None)\n",
    "deep_tree_clf.fit(X_train, y_train)\n",
    "print(\"Test set accuracy with Decision Trees: {:.2f}\".format(deep_tree_clf.score(X_test,y_test)))\n",
    "#now 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)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Another example, the moons again"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_42_0.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from __future__ import division, print_function, unicode_literals\n",
    "\n",
    "# Common imports\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "# to make this notebook's output stable across runs\n",
    "np.random.seed(42)\n",
    "\n",
    "# To plot pretty figures\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",
    "\n",
    "from sklearn.svm import SVC\n",
    "from sklearn import datasets\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.datasets import make_moons\n",
    "from sklearn.tree import export_graphviz\n",
    "\n",
    "Xm, ym = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
    "\n",
    "deep_tree_clf1 = DecisionTreeClassifier(random_state=42)\n",
    "deep_tree_clf2 = DecisionTreeClassifier(min_samples_leaf=4, random_state=42)\n",
    "deep_tree_clf1.fit(Xm, ym)\n",
    "deep_tree_clf2.fit(Xm, ym)\n",
    "\n",
    "\n",
    "def plot_decision_boundary(clf, X, y, axes=[0, 7.5, 0, 3], iris=True, legend=False, plot_training=True):\n",
    "    x1s = np.linspace(axes[0], axes[1], 100)\n",
    "    x2s = np.linspace(axes[2], axes[3], 100)\n",
    "    x1, x2 = np.meshgrid(x1s, x2s)\n",
    "    X_new = np.c_[x1.ravel(), x2.ravel()]\n",
    "    y_pred = clf.predict(X_new).reshape(x1.shape)\n",
    "    custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "    plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)\n",
    "    if not iris:\n",
    "        custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])\n",
    "        plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)\n",
    "    if plot_training:\n",
    "        plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", label=\"Iris-Setosa\")\n",
    "        plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", label=\"Iris-Versicolor\")\n",
    "        plt.plot(X[:, 0][y==2], X[:, 1][y==2], \"g^\", label=\"Iris-Virginica\")\n",
    "        plt.axis(axes)\n",
    "    if iris:\n",
    "        plt.xlabel(\"Petal length\", fontsize=14)\n",
    "        plt.ylabel(\"Petal width\", fontsize=14)\n",
    "    else:\n",
    "        plt.xlabel(r\"$x_1$\", fontsize=18)\n",
    "        plt.ylabel(r\"$x_2$\", fontsize=18, rotation=0)\n",
    "    if legend:\n",
    "        plt.legend(loc=\"lower right\", fontsize=14)\n",
    "plt.figure(figsize=(11, 4))\n",
    "plt.subplot(121)\n",
    "plot_decision_boundary(deep_tree_clf1, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)\n",
    "plt.title(\"No restrictions\", fontsize=16)\n",
    "plt.subplot(122)\n",
    "plot_decision_boundary(deep_tree_clf2, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)\n",
    "plt.title(\"min_samples_leaf = {}\".format(deep_tree_clf2.min_samples_leaf), fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_43_0.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(6)\n",
    "Xs = np.random.rand(100, 2) - 0.5\n",
    "ys = (Xs[:, 0] > 0).astype(np.float32) * 2\n",
    "\n",
    "angle = np.pi/4\n",
    "rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])\n",
    "Xsr = Xs.dot(rotation_matrix)\n",
    "\n",
    "tree_clf_s = DecisionTreeClassifier(random_state=42)\n",
    "tree_clf_s.fit(Xs, ys)\n",
    "tree_clf_sr = DecisionTreeClassifier(random_state=42)\n",
    "tree_clf_sr.fit(Xsr, ys)\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "plt.subplot(121)\n",
    "plot_decision_boundary(tree_clf_s, Xs, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
    "plt.subplot(122)\n",
    "plot_decision_boundary(tree_clf_sr, Xsr, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "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": 12,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "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": 12,
     "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": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_46_0.png"
      }
     },
     "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": 14,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_47_0.png"
      }
     },
     "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",
   "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)\n",
    "\n",
    "### 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."
   ]
  }
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