1.Machine_Learning/11.DecisionTree,Bagging,RandomForest.ipynb

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    "## Decision Trees, Bagging, and Random Forest \n",
    "\n",
    "In this tutorial, we will implement Decision Trees for Classification and Regression from scratch. Next, we will highlight their shortcommings through the Bias-Variance Decomposition. Finaly, we will show how the Random Forest algoorthm emerges from Bagging and Decision Trees.\n",
    "\n",
    "\n",
    "This tutorial is based on amazing lectures of Kilian Weinberger\n",
    "[Lecture 17](https://www.cs.cornell.edu/courses/cs4780/2018fa/lectures/lecturenote17.html) and \n",
    "[Lecture 18](https://www.cs.cornell.edu/courses/cs4780/2018fa/lectures/lecturenote18.html). "
   ]
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    "### Motivation for Decision Trees\n",
    "Advantages of kNN\n",
    "In low dimensions kNN is actually quite powerful \n",
    "1. It can learn non-linear decision boundaries and \n",
    "2. It can handle multi-class problems. \n",
    "Disadvantages\n",
    "1. kNN needs the entire training data stored, i.e,. it requires a lot of storage\n",
    "2. As the size of training data increases$ testing time increases as we need to compute distances to all training inputs, \n",
    "3. We need to find a good distance metric.\n",
    "\n",
    "\n",
    "__Decision trees__ do not need even a single training data stored. Instead, we store learned rules. More specifically, we use the training data to build a tree structure that recursively divides the space into regions with similar labels."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcbc9248",
   "metadata": {},
   "source": [
    "# Decision Tree"
   ]
  },
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   "source": [
    "### SETUP\n",
    "$\\mathcal D = \\{ (x_i,y_i) \\}_{i=1} ^n ,$ where $y_i \\in \\{1,\\dots,c\\}$. Let $\\mathcal D_k \\subseteq \\mathcal D$, where $\\mathcal D_k = \\{(x,y) \\in \\mathcal D : y=k \\}$ all inputs with label $k$.\n",
    "\n",
    "The fract of inputs in the dataset with label $k$ is computed as \n",
    "$$ p_k = \\frac{|\\mathcal D_k |}{ | \\mathcal D |}$$\n",
    "\n",
    "\n",
    "## Gini Impurity\n",
    "\n",
    "$$ G(\\mathcal D) = \\sum_{k=1} ^c p_k (1 - p_k)$$\n",
    "Note that $c$ is the number of classes."
   ]
  },
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    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Gini Impurity Binary 2p(1-p)')"
      ]
     },
     "execution_count": 1,
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     "output_type": "execute_result"
    },
    {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import load_iris,load_diabetes\n",
    "import pandas as pd\n",
    "\n",
    "p=np.linspace(0, 1, 100, endpoint=True)\n",
    "np.sum(p*(1-p))\n",
    "plt.plot(p,2*p*(1-p))\n",
    "plt.title('Gini Impurity Binary 2p(1-p)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9af428e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length  sepal_width  petal_length  petal_width\n",
       "0           5.1          3.5           1.4          0.2\n",
       "1           4.9          3.0           1.4          0.2\n",
       "2           4.7          3.2           1.3          0.2\n",
       "3           4.6          3.1           1.5          0.2\n",
       "4           5.0          3.6           1.4          0.2"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data=load_iris()\n",
    "data.keys()\n",
    "X=pd.DataFrame(data['data'],columns=data['feature_names'])\n",
    "y=pd.Series(data['target'])\n",
    "del data\n",
    "# Easy selecting\n",
    "def rename_columns(x):\n",
    "    x=x.replace(' (cm)','')\n",
    "    return x.replace(\" \", \"_\")\n",
    "X.columns=pd.Index(rename_columns(x) for x in X.columns) \n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d153254e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X.sepal_width,X.sepal_length,c=y)\n",
    "plt.xlabel('Sepal Width')\n",
    "plt.ylabel('Sepal Length')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8c458a45",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The spliting cretarion and the value \n",
    "sepal_length_split = 6.0\n",
    "\n",
    "# Ploting the original plot\n",
    "plt.scatter(X.sepal_width,X.sepal_length,c=y)\n",
    "plt.xlabel('Sepal Width')\n",
    "plt.ylabel('Sepal Length')\n",
    "plt.grid()\n",
    "\n",
    "plt.axhline(sepal_length_split, label='Spliting criteria', color='red')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "822a576a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gini_impurity(y):\n",
    "  '''\n",
    "  Given a Pandas Series, it calculates the Gini Impurity. \n",
    "  y: variable with which calculate Gini Impurity.\n",
    "  '''\n",
    "  if isinstance(y, pd.Series):\n",
    "    # Probability of class label k\n",
    "    p_k=y.value_counts()/y.shape[0]\n",
    "    return (p_k*(1-p_k)).sum()\n",
    "  else:\n",
    "    raise('Object must be a Pandas Series.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4996d1a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6666666666666667"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gini_impurity(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "08d79550",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5605352859487438"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Left Split\n",
    "gini_impurity(y[X[X['sepal_length']<=sepal_length_split].index])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b131c37f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.44074173609244827"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Right Split\n",
    "gini_impurity(y[X[X['sepal_length']>sepal_length_split].index])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "114284ec",
   "metadata": {},
   "source": [
    "$$ \\text{Going on direction where sepal length is larger than its mean is advantages}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a602e649",
   "metadata": {},
   "outputs": [],
   "source": [
    "class DecisionClassificationNode:\n",
    "    def __init__(self, *, id, max_depth, depth):\n",
    "        self.id = id\n",
    "        self.max_depth = max_depth\n",
    "        self.depth = depth\n",
    "        self.left, self.right = None, None\n",
    "        self.best_feature, self.feature_val = None, None\n",
    "        self.gini_gain = None\n",
    "        self.class_probability = dict()\n",
    "        self.yhat = None\n",
    "\n",
    "    def __str__(self):\n",
    "        m = f'{self.id}\\tDepth:{self.depth}\\tFeature:{self.best_feature}\\t'\n",
    "        if self.feature_val is not None:\n",
    "            m += f'Val:{self.feature_val:.3f}\\tGiniGain:{self.gini_gain:.3f}\\tPred:{self.class_probability}'\n",
    "        return m\n",
    "\n",
    "    @staticmethod\n",
    "    def best_split(X, y):\n",
    "        features = list(X.columns)\n",
    "\n",
    "        df = X.copy()\n",
    "        y = y.copy()\n",
    "        df['y'] = y\n",
    "\n",
    "        max_gain = 0\n",
    "        best_feature = None\n",
    "        best_feature_avg = None\n",
    "\n",
    "        for feature in features:\n",
    "\n",
    "            gini_base = gini_impurity(y)\n",
    "            mean_of_feature = df[feature].mean()\n",
    "\n",
    "            dfleft, dfright = df[df[feature] <= mean_of_feature], df[df[feature] > mean_of_feature]\n",
    "\n",
    "            lleft, lright = len(dfleft), len(dfright)\n",
    "            lenght = lleft + lright\n",
    "\n",
    "            w_left, w_right = lleft / lenght, lright / lenght\n",
    "\n",
    "            gini_left, gini_right = gini_impurity(dfleft['y']), gini_impurity(dfright['y'])\n",
    "            # Calculating the weighted GINI impurity\n",
    "            weighted_gini = w_left * gini_left + w_right * gini_right\n",
    "            gini_gain = gini_base - weighted_gini\n",
    "            # print(\n",
    "            #    f'Feature:{feature}\\t Mean Value:{mean_of_feature:.3f},\\t Weighted Gini:{weighted_gini:.3f},\\t Gini Gain:{gini_gain:.3f}')\n",
    "            if gini_gain > max_gain:\n",
    "                best_feature = feature\n",
    "                best_feature_avg = mean_of_feature\n",
    "                # Setting the best gain to the current one\n",
    "                max_gain = gini_gain\n",
    "        return best_feature, best_feature_avg, max_gain\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        features = list(X.columns)\n",
    "        self.best_feature, self.feature_val, self.gini_gain = self.best_split(X, y)\n",
    "        self.yhat = y.value_counts() / len(y)\n",
    "\n",
    "        # print(f'Feature:{feature}\\t Mean Value:{mean_of_feature:.3f},\\t Weighted Gini:{weighted_gini:.3f},\\t Gini Gain:{gini_gain:.3f}')\n",
    "\n",
    "        df = X.copy()\n",
    "        y = y.copy()\n",
    "        df['y'] = y\n",
    "        if self.depth > self.max_depth or (self.best_feature is None):\n",
    "            return self\n",
    "\n",
    "        dfleft, dfright = df[df[self.best_feature] <= self.feature_val], df[\n",
    "            df[self.best_feature] > self.feature_val]\n",
    "\n",
    "        left_classes = dfleft['y'].value_counts().index.to_list()\n",
    "        left_probs = (dfleft['y'].value_counts() / len(dfleft)).to_list()\n",
    "        self.class_probability['Left'] = dict(zip(left_classes, left_probs))\n",
    "\n",
    "        right_classes = dfright['y'].value_counts().index.to_list()\n",
    "        right_probs = (dfright['y'].value_counts() / len(dfright)).to_list()\n",
    "\n",
    "        self.class_probability['Right'] = dict(zip(right_classes, right_probs))\n",
    "        self.left = DecisionClassificationNode(id=self.id + '_left', max_depth=self.max_depth, depth=self.depth + 1).fit(\n",
    "            dfleft[features], dfleft['y'])\n",
    "        self.right = DecisionClassificationNode(id=self.id + '_right', max_depth=self.max_depth, depth=self.depth + 1).fit(\n",
    "            dfright[features], dfright['y'])\n",
    "        # IF we reach here, then stopping criteria is fulfilled\n",
    "        return self\n",
    "\n",
    "    def predict(self, x):\n",
    "        if self.best_feature is None:\n",
    "            label, prob = self.yhat.index.values, self.yhat.values\n",
    "            return label[prob.argmax()]\n",
    "\n",
    "        boolean_output = x[self.best_feature] <= self.feature_val\n",
    "\n",
    "        if boolean_output and self.left is not None:\n",
    "            # Turn Left\n",
    "            return self.left.predict(x)\n",
    "        elif (boolean_output == False) and self.right is not None:\n",
    "            # turn Right\n",
    "            return self.right.predict(x)\n",
    "        else:\n",
    "            label, prob = self.yhat.index.values, self.yhat.values\n",
    "            return label[prob.argmax()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2adc4046",
   "metadata": {},
   "outputs": [],
   "source": [
    "class DecisionTree:\n",
    "    def __init__(self, max_depth=None):\n",
    "        self.X, self.y = None, None\n",
    "        self.features = None\n",
    "        # Saving the hyper parameters\n",
    "        self.max_depth = max_depth if max_depth else 200\n",
    "        self.root = None\n",
    "\n",
    "    def fit(self, X, y,type_of_node=None):\n",
    "        self.root = type_of_node(id='Root', max_depth=self.max_depth, depth=0).fit(X.copy(), y.copy())\n",
    "        return self\n",
    "\n",
    "    def __str__(self):\n",
    "        return str(self.root)\n",
    "\n",
    "    def predict(self, X):\n",
    "        preds = []\n",
    "        for index, x in X.iterrows():\n",
    "            preds.append(self.root.predict(x))\n",
    "        return np.array(preds).flatten()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb49fc45",
   "metadata": {},
   "source": [
    "#### Max depth = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a6b562b5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9466666666666667\n"
     ]
    }
   ],
   "source": [
    "preds = DecisionTree(max_depth=1).fit(X, y,DecisionClassificationNode).predict(X)\n",
    "print((preds == y).mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76314ad2",
   "metadata": {},
   "source": [
    "#### Max depth = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b299fe3f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.96\n"
     ]
    }
   ],
   "source": [
    "preds = DecisionTree(max_depth=3).fit(X, y,DecisionClassificationNode).predict(X)\n",
    "print((preds == y).mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a63c0aae",
   "metadata": {},
   "source": [
    "#### Max depth = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f8588aea",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.96\n"
     ]
    }
   ],
   "source": [
    "preds = DecisionTree(max_depth=3).fit(X, y,DecisionClassificationNode).predict(X)\n",
    "print((preds == y).mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "137af579",
   "metadata": {},
   "source": [
    "#### Max depth = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "5156397f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.98\n"
     ]
    }
   ],
   "source": [
    "preds = DecisionTree(max_depth=5).fit(X, y,DecisionClassificationNode).predict(X)\n",
    "print((preds == y).mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b5c76bf",
   "metadata": {},
   "source": [
    "#### Max depth = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "712b90df",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    }
   ],
   "source": [
    "preds = DecisionTree(max_depth=10).fit(X, y,DecisionClassificationNode).predict(X)\n",
    "print((preds == y).mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c788484a",
   "metadata": {},
   "source": [
    "### Using scikit-learn for Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "05439c47",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn import tree\n",
    "iris = load_iris()\n",
    "X, y = iris.data, iris.target\n",
    "clf = tree.DecisionTreeClassifier()\n",
    "clf = clf.fit(X, y)\n",
    "tree.plot_tree(clf);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "ef24d1b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n",
       " -->\n",
       "<!-- Title: Tree Pages: 1 -->\n",
       "<svg width=\"857pt\" height=\"671pt\"\n",
       " viewBox=\"0.00 0.00 857.00 671.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 667)\">\n",
       "<title>Tree</title>\n",
       "<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-667 853,-667 853,4 -4,4\"/>\n",
       "<!-- 0 -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>0</title>\n",
       "<path fill=\"#ffffff\" stroke=\"#000000\" d=\"M517.5,-663C517.5,-663 381.5,-663 381.5,-663 375.5,-663 369.5,-657 369.5,-651 369.5,-651 369.5,-592 369.5,-592 369.5,-586 375.5,-580 381.5,-580 381.5,-580 517.5,-580 517.5,-580 523.5,-580 529.5,-586 529.5,-592 529.5,-592 529.5,-651 529.5,-651 529.5,-657 523.5,-663 517.5,-663\"/>\n",
       "<text text-anchor=\"start\" x=\"377.5\" y=\"-647.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">petal length (cm) ≤ 2.45</text>\n",
       "<text text-anchor=\"start\" x=\"414\" y=\"-632.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">gini = 0.667</text>\n",
       "<text text-anchor=\"start\" x=\"404.5\" y=\"-617.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">samples = 150</text>\n",
       "<text text-anchor=\"start\" x=\"391.5\" y=\"-602.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">value = [50, 50, 50]</text>\n",
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       "</g>\n",
       "<!-- 1 -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>1</title>\n",
       "<path fill=\"#e58139\" stroke=\"#000000\" d=\"M419,-536.5C419,-536.5 326,-536.5 326,-536.5 320,-536.5 314,-530.5 314,-524.5 314,-524.5 314,-480.5 314,-480.5 314,-474.5 320,-468.5 326,-468.5 326,-468.5 419,-468.5 419,-468.5 425,-468.5 431,-474.5 431,-480.5 431,-480.5 431,-524.5 431,-524.5 431,-530.5 425,-536.5 419,-536.5\"/>\n",
       "<text text-anchor=\"start\" x=\"344.5\" y=\"-521.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">gini = 0.0</text>\n",
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       "</g>\n",
       "<!-- 0&#45;&gt;1 -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>0&#45;&gt;1</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M422.5691,-579.8796C415.3117,-568.6636 407.4497,-556.5131 400.1535,-545.2372\"/>\n",
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       "<text text-anchor=\"middle\" x=\"389.4656\" y=\"-557.56\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">True</text>\n",
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       "<!-- 2 -->\n",
       "<g id=\"node3\" class=\"node\">\n",
       "<title>2</title>\n",
       "<path fill=\"#ffffff\" stroke=\"#000000\" d=\"M592,-544C592,-544 461,-544 461,-544 455,-544 449,-538 449,-532 449,-532 449,-473 449,-473 449,-467 455,-461 461,-461 461,-461 592,-461 592,-461 598,-461 604,-467 604,-473 604,-473 604,-532 604,-532 604,-538 598,-544 592,-544\"/>\n",
       "<text text-anchor=\"start\" x=\"457\" y=\"-528.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">petal width (cm) ≤ 1.75</text>\n",
       "<text text-anchor=\"start\" x=\"498.5\" y=\"-513.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">gini = 0.5</text>\n",
       "<text text-anchor=\"start\" x=\"481.5\" y=\"-498.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">samples = 100</text>\n",
       "<text text-anchor=\"start\" x=\"472\" y=\"-483.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">value = [0, 50, 50]</text>\n",
       "<text text-anchor=\"start\" x=\"474\" y=\"-468.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">class = versicolor</text>\n",
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       "<!-- 0&#45;&gt;2 -->\n",
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       "<title>0&#45;&gt;2</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M476.4309,-579.8796C482.0837,-571.1434 488.1033,-561.8404 493.9366,-552.8253\"/>\n",
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       "<text text-anchor=\"middle\" x=\"504.6924\" y=\"-565.0431\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">False</text>\n",
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       "<!-- 3 -->\n",
       "<g id=\"node4\" class=\"node\">\n",
       "<title>3</title>\n",
       "<path fill=\"#4de88e\" stroke=\"#000000\" d=\"M482.5,-425C482.5,-425 346.5,-425 346.5,-425 340.5,-425 334.5,-419 334.5,-413 334.5,-413 334.5,-354 334.5,-354 334.5,-348 340.5,-342 346.5,-342 346.5,-342 482.5,-342 482.5,-342 488.5,-342 494.5,-348 494.5,-354 494.5,-354 494.5,-413 494.5,-413 494.5,-419 488.5,-425 482.5,-425\"/>\n",
       "<text text-anchor=\"start\" x=\"342.5\" y=\"-409.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">petal length (cm) ≤ 4.95</text>\n",
       "<text text-anchor=\"start\" x=\"379\" y=\"-394.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">gini = 0.168</text>\n",
       "<text text-anchor=\"start\" x=\"373.5\" y=\"-379.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">samples = 54</text>\n",
       "<text text-anchor=\"start\" x=\"364\" y=\"-364.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">value = [0, 49, 5]</text>\n",
       "<text text-anchor=\"start\" x=\"362\" y=\"-349.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">class = versicolor</text>\n",
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       "<!-- 2&#45;&gt;3 -->\n",
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       "<title>2&#45;&gt;3</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M487.3278,-460.8796C478.7665,-451.7832 469.6268,-442.0722 460.8168,-432.7116\"/>\n",
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       "</g>\n",
       "<!-- 12 -->\n",
       "<g id=\"node13\" class=\"node\">\n",
       "<title>12</title>\n",
       "<path fill=\"#843de6\" stroke=\"#000000\" d=\"M706.5,-425C706.5,-425 570.5,-425 570.5,-425 564.5,-425 558.5,-419 558.5,-413 558.5,-413 558.5,-354 558.5,-354 558.5,-348 564.5,-342 570.5,-342 570.5,-342 706.5,-342 706.5,-342 712.5,-342 718.5,-348 718.5,-354 718.5,-354 718.5,-413 718.5,-413 718.5,-419 712.5,-425 706.5,-425\"/>\n",
       "<text text-anchor=\"start\" x=\"566.5\" y=\"-409.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">petal length (cm) ≤ 4.85</text>\n",
       "<text text-anchor=\"start\" x=\"603\" y=\"-394.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">gini = 0.043</text>\n",
       "<text text-anchor=\"start\" x=\"597.5\" y=\"-379.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">samples = 46</text>\n",
       "<text text-anchor=\"start\" x=\"588\" y=\"-364.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">value = [0, 1, 45]</text>\n",
       "<text text-anchor=\"start\" x=\"590\" y=\"-349.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">class = virginica</text>\n",
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       "<!-- 2&#45;&gt;12 -->\n",
       "<g id=\"edge12\" class=\"edge\">\n",
       "<title>2&#45;&gt;12</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M565.6722,-460.8796C574.2335,-451.7832 583.3732,-442.0722 592.1832,-432.7116\"/>\n",
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       "</g>\n",
       "<!-- 4 -->\n",
       "<g id=\"node5\" class=\"node\">\n",
       "<title>4</title>\n",
       "<path fill=\"#3de684\" stroke=\"#000000\" d=\"M261,-306C261,-306 130,-306 130,-306 124,-306 118,-300 118,-294 118,-294 118,-235 118,-235 118,-229 124,-223 130,-223 130,-223 261,-223 261,-223 267,-223 273,-229 273,-235 273,-235 273,-294 273,-294 273,-300 267,-306 261,-306\"/>\n",
       "<text text-anchor=\"start\" x=\"126\" y=\"-290.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">petal width (cm) ≤ 1.65</text>\n",
       "<text text-anchor=\"start\" x=\"160\" y=\"-275.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">gini = 0.041</text>\n",
       "<text text-anchor=\"start\" x=\"154.5\" y=\"-260.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">samples = 48</text>\n",
       "<text text-anchor=\"start\" x=\"145\" y=\"-245.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">value = [0, 47, 1]</text>\n",
       "<text text-anchor=\"start\" x=\"143\" y=\"-230.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">class = versicolor</text>\n",
       "</g>\n",
       "<!-- 3&#45;&gt;4 -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>3&#45;&gt;4</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M337.9044,-341.8796C319.483,-331.8697 299.6918,-321.1156 280.8974,-310.9031\"/>\n",
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       "<!-- 7 -->\n",
       "<g id=\"node8\" class=\"node\">\n",
       "<title>7</title>\n",
       "<path fill=\"#c09cf2\" stroke=\"#000000\" d=\"M480,-306C480,-306 349,-306 349,-306 343,-306 337,-300 337,-294 337,-294 337,-235 337,-235 337,-229 343,-223 349,-223 349,-223 480,-223 480,-223 486,-223 492,-229 492,-235 492,-235 492,-294 492,-294 492,-300 486,-306 480,-306\"/>\n",
       "<text text-anchor=\"start\" x=\"345\" y=\"-290.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">petal width (cm) ≤ 1.55</text>\n",
       "<text text-anchor=\"start\" x=\"379\" y=\"-275.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">gini = 0.444</text>\n",
       "<text text-anchor=\"start\" x=\"377\" y=\"-260.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">samples = 6</text>\n",
       "<text text-anchor=\"start\" x=\"367.5\" y=\"-245.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">value = [0, 2, 4]</text>\n",
       "<text text-anchor=\"start\" x=\"366\" y=\"-230.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">class = virginica</text>\n",
       "</g>\n",
       "<!-- 3&#45;&gt;7 -->\n",
       "<g id=\"edge7\" class=\"edge\">\n",
       "<title>3&#45;&gt;7</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M414.5,-341.8796C414.5,-333.6838 414.5,-324.9891 414.5,-316.5013\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"418.0001,-316.298 414.5,-306.2981 411.0001,-316.2981 418.0001,-316.298\"/>\n",
       "</g>\n",
       "<!-- 5 -->\n",
       "<g id=\"node6\" class=\"node\">\n",
       "<title>5</title>\n",
       "<path fill=\"#39e581\" stroke=\"#000000\" d=\"M109,-179.5C109,-179.5 12,-179.5 12,-179.5 6,-179.5 0,-173.5 0,-167.5 0,-167.5 0,-123.5 0,-123.5 0,-117.5 6,-111.5 12,-111.5 12,-111.5 109,-111.5 109,-111.5 115,-111.5 121,-117.5 121,-123.5 121,-123.5 121,-167.5 121,-167.5 121,-173.5 115,-179.5 109,-179.5\"/>\n",
       "<text text-anchor=\"start\" x=\"32.5\" y=\"-164.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">gini = 0.0</text>\n",
       "<text text-anchor=\"start\" x=\"19.5\" y=\"-149.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">samples = 47</text>\n",
       "<text text-anchor=\"start\" x=\"10\" y=\"-134.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">value = [0, 47, 0]</text>\n",
       "<text text-anchor=\"start\" x=\"8\" y=\"-119.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">class = versicolor</text>\n",
       "</g>\n",
       "<!-- 4&#45;&gt;5 -->\n",
       "<g id=\"edge5\" class=\"edge\">\n",
       "<title>4&#45;&gt;5</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M148.2836,-222.8796C134.9358,-211.1138 120.4215,-198.3197 107.1096,-186.5855\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"109.2448,-183.8019 99.4287,-179.8149 104.616,-189.0531 109.2448,-183.8019\"/>\n",
       "</g>\n",
       "<!-- 6 -->\n",
       "<g id=\"node7\" class=\"node\">\n",
       "<title>6</title>\n",
       "<path fill=\"#8139e5\" stroke=\"#000000\" d=\"M240,-179.5C240,-179.5 151,-179.5 151,-179.5 145,-179.5 139,-173.5 139,-167.5 139,-167.5 139,-123.5 139,-123.5 139,-117.5 145,-111.5 151,-111.5 151,-111.5 240,-111.5 240,-111.5 246,-111.5 252,-117.5 252,-123.5 252,-123.5 252,-167.5 252,-167.5 252,-173.5 246,-179.5 240,-179.5\"/>\n",
       "<text text-anchor=\"start\" x=\"167.5\" y=\"-164.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">gini = 0.0</text>\n",
       "<text text-anchor=\"start\" x=\"158\" y=\"-149.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"start\" x=\"148.5\" y=\"-134.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">value = [0, 0, 1]</text>\n",
       "<text text-anchor=\"start\" x=\"147\" y=\"-119.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">class = virginica</text>\n",
       "</g>\n",
       "<!-- 4&#45;&gt;6 -->\n",
       "<g id=\"edge6\" class=\"edge\">\n",
       "<title>4&#45;&gt;6</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M195.5,-222.8796C195.5,-212.2134 195.5,-200.7021 195.5,-189.9015\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"199.0001,-189.8149 195.5,-179.8149 192.0001,-189.815 199.0001,-189.8149\"/>\n",
       "</g>\n",
       "<!-- 8 -->\n",
       "<g id=\"node9\" class=\"node\">\n",
       "<title>8</title>\n",
       "<path fill=\"#8139e5\" stroke=\"#000000\" d=\"M371,-179.5C371,-179.5 282,-179.5 282,-179.5 276,-179.5 270,-173.5 270,-167.5 270,-167.5 270,-123.5 270,-123.5 270,-117.5 276,-111.5 282,-111.5 282,-111.5 371,-111.5 371,-111.5 377,-111.5 383,-117.5 383,-123.5 383,-123.5 383,-167.5 383,-167.5 383,-173.5 377,-179.5 371,-179.5\"/>\n",
       "<text text-anchor=\"start\" x=\"298.5\" y=\"-164.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">gini = 0.0</text>\n",
       "<text text-anchor=\"start\" x=\"289\" y=\"-149.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
       "<text text-anchor=\"start\" x=\"279.5\" y=\"-134.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">value = [0, 0, 3]</text>\n",
       "<text text-anchor=\"start\" x=\"278\" y=\"-119.3\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">class = virginica</text>\n",
       "</g>\n",
       "<!-- 7&#45;&gt;8 -->\n",
       "<g id=\"edge8\" class=\"edge\">\n",
       "<title>7&#45;&gt;8</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M383.7219,-222.8796C375.3464,-211.5536 366.2662,-199.2748 357.8589,-187.9058\"/>\n",
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       "<!-- 9 -->\n",
       "<g id=\"node10\" class=\"node\">\n",
       "<title>9</title>\n",
       "<path fill=\"#9cf2c0\" stroke=\"#000000\" d=\"M552,-187C552,-187 413,-187 413,-187 407,-187 401,-181 401,-175 401,-175 401,-116 401,-116 401,-110 407,-104 413,-104 413,-104 552,-104 552,-104 558,-104 564,-110 564,-116 564,-116 564,-175 564,-175 564,-181 558,-187 552,-187\"/>\n",
       "<text text-anchor=\"start\" x=\"409\" y=\"-171.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">sepal length (cm) ≤ 6.95</text>\n",
       "<text text-anchor=\"start\" x=\"447\" y=\"-156.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">gini = 0.444</text>\n",
       "<text text-anchor=\"start\" x=\"445\" y=\"-141.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
       "<text text-anchor=\"start\" x=\"435.5\" y=\"-126.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">value = [0, 2, 1]</text>\n",
       "<text text-anchor=\"start\" x=\"430\" y=\"-111.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">class = versicolor</text>\n",
       "</g>\n",
       "<!-- 7&#45;&gt;9 -->\n",
       "<g id=\"edge9\" class=\"edge\">\n",
       "<title>7&#45;&gt;9</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M438.2831,-222.8796C443.2237,-214.2335 448.4816,-205.0322 453.5833,-196.1042\"/>\n",
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       "<!-- 10 -->\n",
       "<g id=\"node11\" class=\"node\">\n",
       "<title>10</title>\n",
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       "<text text-anchor=\"start\" x=\"386.5\" y=\"-52.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">gini = 0.0</text>\n",
       "<text text-anchor=\"start\" x=\"377\" y=\"-37.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">samples = 2</text>\n",
       "<text text-anchor=\"start\" x=\"367.5\" y=\"-22.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">value = [0, 2, 0]</text>\n",
       "<text text-anchor=\"start\" x=\"362\" y=\"-7.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">class = versicolor</text>\n",
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       "<!-- 9&#45;&gt;10 -->\n",
       "<g id=\"edge10\" class=\"edge\">\n",
       "<title>9&#45;&gt;10</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M457.1793,-103.9815C451.7984,-95.1585 446.1068,-85.8258 440.6941,-76.9506\"/>\n",
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       "<g id=\"node12\" class=\"node\">\n",
       "<title>11</title>\n",
       "<path fill=\"#8139e5\" stroke=\"#000000\" d=\"M594,-68C594,-68 505,-68 505,-68 499,-68 493,-62 493,-56 493,-56 493,-12 493,-12 493,-6 499,0 505,0 505,0 594,0 594,0 600,0 606,-6 606,-12 606,-12 606,-56 606,-56 606,-62 600,-68 594,-68\"/>\n",
       "<text text-anchor=\"start\" x=\"521.5\" y=\"-52.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">gini = 0.0</text>\n",
       "<text text-anchor=\"start\" x=\"512\" y=\"-37.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">samples = 1</text>\n",
       "<text text-anchor=\"start\" x=\"502.5\" y=\"-22.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">value = [0, 0, 1]</text>\n",
       "<text text-anchor=\"start\" x=\"501\" y=\"-7.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">class = virginica</text>\n",
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       "<!-- 9&#45;&gt;11 -->\n",
       "<g id=\"edge11\" class=\"edge\">\n",
       "<title>9&#45;&gt;11</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M507.4483,-103.9815C512.7501,-95.1585 518.3581,-85.8258 523.6911,-76.9506\"/>\n",
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       "<g id=\"node14\" class=\"node\">\n",
       "<title>13</title>\n",
       "<path fill=\"#c09cf2\" stroke=\"#000000\" d=\"M701.5,-306C701.5,-306 575.5,-306 575.5,-306 569.5,-306 563.5,-300 563.5,-294 563.5,-294 563.5,-235 563.5,-235 563.5,-229 569.5,-223 575.5,-223 575.5,-223 701.5,-223 701.5,-223 707.5,-223 713.5,-229 713.5,-235 713.5,-235 713.5,-294 713.5,-294 713.5,-300 707.5,-306 701.5,-306\"/>\n",
       "<text text-anchor=\"start\" x=\"571.5\" y=\"-290.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">sepal width (cm) ≤ 3.1</text>\n",
       "<text text-anchor=\"start\" x=\"603\" y=\"-275.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">gini = 0.444</text>\n",
       "<text text-anchor=\"start\" x=\"601\" y=\"-260.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">samples = 3</text>\n",
       "<text text-anchor=\"start\" x=\"591.5\" y=\"-245.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">value = [0, 1, 2]</text>\n",
       "<text text-anchor=\"start\" x=\"590\" y=\"-230.8\" font-family=\"Helvetica,sans-Serif\" font-size=\"14.00\" fill=\"#000000\">class = virginica</text>\n",
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       "<!-- 12&#45;&gt;13 -->\n",
       "<g id=\"edge13\" class=\"edge\">\n",
       "<title>12&#45;&gt;13</title>\n",
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       "<!-- 16 -->\n",
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       "<title>16</title>\n",
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       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.files.Source at 0x7f7f9f12dbe0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import graphviz \n",
    "dot_data = tree.export_graphviz(clf, out_file=None) \n",
    "graph = graphviz.Source(dot_data) \n",
    "graph.render(\"iris\") \n",
    "dot_data = tree.export_graphviz(clf, out_file=None, feature_names=iris.feature_names,  \n",
    "                                class_names=iris.target_names,  \n",
    "                                filled=True, rounded=True,  special_characters=True)  \n",
    "graph = graphviz.Source(dot_data)  \n",
    "graph "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1dc6c3a",
   "metadata": {},
   "source": [
    "### Predictions are very interpretable aren't they :) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fec74b62",
   "metadata": {},
   "source": [
    "# Decision Regression Tree\n",
    "\n",
    "$$ \\mathcal L (S) = \\frac{1}{|S|} \\sum_{(x_i, y_i ) \\in S} (y - \\mu)^2$$\n",
    "where $\\mu = \\frac{1}{|S|} \\sum_{(x_i, y_i ) \\in S} y_i$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71cbf069",
   "metadata": {},
   "source": [
    "### Runtime Complexity in training\n",
    "\n",
    "Cost of constructing a decision $$ \\mathcal O (|\\mathcal D| \\times |d| \\times log(|\\mathcal D|)),\\; \\text{ where } \\forall i x_i \\in \\mathbb R ^d $$\n",
    "\n",
    "Cost of constructing a decision Tree $$ \\mathcal O (|\\mathcal D|^2 \\times |d| \\times log(|\\mathcal D|)),\\; \\text{ where } \\forall i x_i \\in \\mathbb R ^d $$\n",
    "\n",
    "\n",
    "[By using this heuristic](https://youtu.be/0LB1cy2sCXc?t=1027), we would get $$ \\mathcal O (|\\mathcal D| \\times |d| \\times log(|\\mathcal D|))$$\n",
    "\n",
    "### Runtime Prediction \n",
    "\n",
    "$$ \\mathcal O (log(|\\mathcal D|))$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "728c1fe6",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>bmi</th>\n",
       "      <th>bp</th>\n",
       "      <th>s1</th>\n",
       "      <th>s2</th>\n",
       "      <th>s3</th>\n",
       "      <th>s4</th>\n",
       "      <th>s5</th>\n",
       "      <th>s6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.038076</td>\n",
       "      <td>0.050680</td>\n",
       "      <td>0.061696</td>\n",
       "      <td>0.021872</td>\n",
       "      <td>-0.044223</td>\n",
       "      <td>-0.034821</td>\n",
       "      <td>-0.043401</td>\n",
       "      <td>-0.002592</td>\n",
       "      <td>0.019908</td>\n",
       "      <td>-0.017646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.001882</td>\n",
       "      <td>-0.044642</td>\n",
       "      <td>-0.051474</td>\n",
       "      <td>-0.026328</td>\n",
       "      <td>-0.008449</td>\n",
       "      <td>-0.019163</td>\n",
       "      <td>0.074412</td>\n",
       "      <td>-0.039493</td>\n",
       "      <td>-0.068330</td>\n",
       "      <td>-0.092204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.085299</td>\n",
       "      <td>0.050680</td>\n",
       "      <td>0.044451</td>\n",
       "      <td>-0.005671</td>\n",
       "      <td>-0.045599</td>\n",
       "      <td>-0.034194</td>\n",
       "      <td>-0.032356</td>\n",
       "      <td>-0.002592</td>\n",
       "      <td>0.002864</td>\n",
       "      <td>-0.025930</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.089063</td>\n",
       "      <td>-0.044642</td>\n",
       "      <td>-0.011595</td>\n",
       "      <td>-0.036656</td>\n",
       "      <td>0.012191</td>\n",
       "      <td>0.024991</td>\n",
       "      <td>-0.036038</td>\n",
       "      <td>0.034309</td>\n",
       "      <td>0.022692</td>\n",
       "      <td>-0.009362</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.005383</td>\n",
       "      <td>-0.044642</td>\n",
       "      <td>-0.036385</td>\n",
       "      <td>0.021872</td>\n",
       "      <td>0.003935</td>\n",
       "      <td>0.015596</td>\n",
       "      <td>0.008142</td>\n",
       "      <td>-0.002592</td>\n",
       "      <td>-0.031991</td>\n",
       "      <td>-0.046641</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        age       sex       bmi        bp        s1        s2        s3  \\\n",
       "0  0.038076  0.050680  0.061696  0.021872 -0.044223 -0.034821 -0.043401   \n",
       "1 -0.001882 -0.044642 -0.051474 -0.026328 -0.008449 -0.019163  0.074412   \n",
       "2  0.085299  0.050680  0.044451 -0.005671 -0.045599 -0.034194 -0.032356   \n",
       "3 -0.089063 -0.044642 -0.011595 -0.036656  0.012191  0.024991 -0.036038   \n",
       "4  0.005383 -0.044642 -0.036385  0.021872  0.003935  0.015596  0.008142   \n",
       "\n",
       "         s4        s5        s6  \n",
       "0 -0.002592  0.019908 -0.017646  \n",
       "1 -0.039493 -0.068330 -0.092204  \n",
       "2 -0.002592  0.002864 -0.025930  \n",
       "3  0.034309  0.022692 -0.009362  \n",
       "4 -0.002592 -0.031991 -0.046641  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = load_diabetes()\n",
    "data.keys()\n",
    "X = pd.DataFrame(data['data'], columns=data['feature_names'])\n",
    "y = pd.Series(data['target'])\n",
    "del data\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "88b1a25a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def avg_squared_difference(y):\n",
    "    if isinstance(y, pd.Series):\n",
    "        return np.mean((y - y.mean()) ** 2)\n",
    "    else:\n",
    "        raise ('Object must be a Pandas Series.')\n",
    "\n",
    "\n",
    "class DecisionRegressionNode:\n",
    "    def __init__(self, *, id, max_depth, depth):\n",
    "        self.id = id\n",
    "        self.max_depth = max_depth\n",
    "        self.depth = depth\n",
    "        self.left, self.right = None, None\n",
    "        self.best_feature, self.feature_val = None, None\n",
    "        self.gini_gain = None\n",
    "        self.class_probability = dict()\n",
    "        self.yhat = None\n",
    "\n",
    "    def __str__(self):\n",
    "        m = f'{self.id}\\tDepth:{self.depth}\\tFeature:{self.best_feature}\\t'\n",
    "        if self.feature_val is not None:\n",
    "            m += f'Val:{self.feature_val:.3f}\\tGiniGain:{self.gini_gain:.3f}\\tPred:{self.class_probability}'\n",
    "        return m\n",
    "\n",
    "    @staticmethod\n",
    "    def best_split(X, y):\n",
    "        features = list(X.columns)\n",
    "\n",
    "        df = X.copy()\n",
    "        y = y.copy()\n",
    "        df['y'] = y\n",
    "\n",
    "        max_gain = 0\n",
    "        best_feature = None\n",
    "        best_feature_avg = None\n",
    "\n",
    "        for feature in features:\n",
    "\n",
    "            gini_base = avg_squared_difference(y)\n",
    "            mean_of_feature = df[feature].mean()\n",
    "\n",
    "            dfleft, dfright = df[df[feature] <= mean_of_feature], df[df[feature] > mean_of_feature]\n",
    "\n",
    "            lleft, lright = len(dfleft), len(dfright)\n",
    "            lenght = lleft + lright\n",
    "\n",
    "            w_left, w_right = lleft / lenght, lright / lenght\n",
    "\n",
    "            gini_left, gini_right = avg_squared_difference(dfleft['y']), avg_squared_difference(dfright['y'])\n",
    "            # Calculating the weighted GINI impurity\n",
    "            weighted_gini = w_left * gini_left + w_right * gini_right\n",
    "            gini_gain = gini_base - weighted_gini\n",
    "            # print(\n",
    "            #    f'Feature:{feature}\\t Mean Value:{mean_of_feature:.3f},\\t Weighted Gini:{weighted_gini:.3f},\\t Gini Gain:{gini_gain:.3f}')\n",
    "            if gini_gain > max_gain:\n",
    "                best_feature = feature\n",
    "                best_feature_avg = mean_of_feature\n",
    "                # Setting the best gain to the current one\n",
    "                max_gain = gini_gain\n",
    "        return best_feature, best_feature_avg, max_gain\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        features = list(X.columns)\n",
    "        self.best_feature, self.feature_val, self.gini_gain = self.best_split(X, y)\n",
    "        self.yhat = y.mean()\n",
    "\n",
    "        df = X.copy()\n",
    "        y = y.copy()\n",
    "        df['y'] = y\n",
    "        if self.depth > self.max_depth or (self.best_feature is None):\n",
    "            return self\n",
    "\n",
    "        dfleft, dfright = df[df[self.best_feature] <= self.feature_val], df[\n",
    "            df[self.best_feature] > self.feature_val]\n",
    "\n",
    "        left_classes = dfleft['y'].value_counts().index.to_list()\n",
    "        left_probs = (dfleft['y'].value_counts() / len(dfleft)).to_list()\n",
    "        self.class_probability['Left'] = dict(zip(left_classes, left_probs))\n",
    "\n",
    "        right_classes = dfright['y'].value_counts().index.to_list()\n",
    "        right_probs = (dfright['y'].value_counts() / len(dfright)).to_list()\n",
    "\n",
    "        self.class_probability['Right'] = dict(zip(right_classes, right_probs))\n",
    "        self.left = DecisionRegressionNode(id=self.id + '_left', max_depth=self.max_depth, depth=self.depth + 1).fit(\n",
    "            dfleft[features], dfleft['y'])\n",
    "        self.right = DecisionRegressionNode(id=self.id + '_right', max_depth=self.max_depth, depth=self.depth + 1).fit(\n",
    "            dfright[features], dfright['y'])\n",
    "        # IF we reach here, then stopping criteria is fulfilled\n",
    "        return self\n",
    "\n",
    "    def predict(self, x):\n",
    "        if self.best_feature is None:\n",
    "            return  self.yhat.mean()\n",
    "\n",
    "        boolean_output = x[self.best_feature] <= self.feature_val\n",
    "\n",
    "        if boolean_output and self.left is not None:\n",
    "            # Turn Left\n",
    "            return self.left.predict(x)\n",
    "        elif (boolean_output == False) and self.right is not None:\n",
    "            # turn Right\n",
    "            return self.right.predict(x)\n",
    "        else:\n",
    "            return self.yhat.mean()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7b2a29e",
   "metadata": {},
   "source": [
    "# Decision Tree Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "6a5a042c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f7f9ef7e8e0>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Define a true function \n",
    "def f(x):\n",
    "    return np.sin(x)\n",
    "\n",
    "def generate_input(n):\n",
    "    return np.linspace(-2, 2, num=n)\n",
    "\n",
    "N = 50    # number of training points.\n",
    "s = 0.05    # noise variance.\n",
    "\n",
    "X = generate_input(N)\n",
    "Y = f(X)+s*np.random.randn(N)\n",
    "plt.scatter(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "09b0bed4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f7f9f06c2e0>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XIzMz0+V7t23bhn//+9+YO3eu28+RJAl79uyBRsP/cxAReVN4mIDCHC0AczLTmeV5YY4W5XV6tyutuBqL/MnnQ1QLFixAbm4ubrjhBmRkZOC1117D0aNHMW/ePADm4aPjx4/j7bfftnnfypUrMWrUKCQnJ9uVWVRUhPT0dFxzzTUwGo1YtmwZ9uzZg5dfftnXzSEiCjnZyRqsmJli1/Oi/rXnZYJWjdElW5yutBIALN6wD4DgMqaotA4TtGoOV5FX+DzBmTFjBk6dOoUlS5ZAp9MhOTkZGzdutK6K0ul0dnviGAwGrFu3Di+88ILDMs+cOYP7778fer0eoihi5MiR2L59O9LS0nzdHCKikJSdrMEErdrh3JmKw6fcrrTSG1tdlt95NVbGoFjvVp5CkiBJUshtXmA0GiGKIgwGA6Kjo3u6OkREQe3jPcfx0Ht7vFLWC3ddj9uvv8IrZZHyePL7zcM2iYioW+SutPJ3WRTaeNgmERF1a+m2nJVWCdGRAAScMLpfjUXkDUxwiIhCXHeXbltWWuWvroYA2CQwlhRp8RTzgcmuYgpztJxgTF7DISoiohDmraXblpVWatF2iEktqrBiZgqykzWyYoi8hZOMOcmYiEJUh0nC6JItTldAWYaNvlo4XnbPCncyJl/y5PebQ1RERCHKk4M05S7dDg8T3MbKiSHqLg5RERGFKB6kSUrGBIeIKER5epAmUTBhgkNEFKIsy7udzX4RYF5NxaXbFIyY4BARhSi5B2lyAjAFIyY4REQhjEu3Sam4ioqIKMS5OkiTKFgxwSEiIi7dJsXhEBUREREpDhMcIiIiUhwmOERERKQ4THCIiIhIcTjJmIgoSPHQSiLnmOAQEQWhslodikrrbA7L1IgqFOZouXcNEThERUQUdMpqdchfXW13Erje0IL81dUoq9X1UM2IAgcTHCKiINJhklBUWgfJwWuWa0WldegwOYogCh1McIiIgkhVfZNdz01nEgCdoQVV9U3+qxRRAOIcHCIiP+vO5ODGZufJzcXEESkVExwiIj/q7uTg+CiV2xhP4oiUikNURER+4o3JwWlJMdCIKjjr7xFgTpjSkmK6X2GiIMYEh4jID7w1OTg8TEBhjhYA7JIcy/PCHC33w6GQxwSHiMgPvDk5ODtZgxUzU6AWbYeh1KIKK2amcB8cInAODhGRX3h7cnB2sgYTtGq3k5W52zGFKiY4RER+4IvJweFhAjIGxTp9nbsdUyhjgkNEymbqAH7YAZw9AVyWAAzIBMLCfRPjIs4yOVhvaIEAE9LCDiAeZ9CIvqgyDYGEMKg7Tw7uZp0sE5oFmJDe6bO+NgxB/upq+6Esf35P3vy+iZzwS4KzfPly/PWvf4VOp8OwYcPw/PPPY8yYMQ5jt27dinHjxtld379/P4YMGWJ9vm7dOjz55JM4fPgwBg0ahKeffhp33HGHz9pAREGobgNQthAwNly4Fp0IZJcA2inejXETF66dgsIcLT569xU81fttJAoX5to0SDFY0j4LU3PmmYePulmnjiE5KCqtQ1ZYFQqdfFZRqQoTtGqvfF6PxBC5IUiS5NP9vNeuXYvc3FwsX74cN910E1599VX84x//QF1dHa666iq7eEuCc/DgQURHR1uvX3755QgPN2fvFRUVGDNmDP7yl7/gjjvuwPr16/HUU0/hq6++wqhRo9zWyWg0QhRFGAwGm88gIgWp2wC8PwuwW7f06/yT6W+b/9MbMdopsj9Pen8WJEg2KzxMAAQIELxUp4O/exnPln+HFb2fBwB0nnJjWaSV316AOXPnI6P1//z3PXkrhklOyPLk99vnCc6oUaOQkpKCFStWWK8NHToUU6dORXFxsV28JcE5ffo0+vbt67DMGTNmwGg0YtOmTdZr2dnZ6NevH9asWeO2TkxwiBTO1AE8n2zbA2BDAKI05t/M7sZEJwLz9wDLRvjn82TE/KKKh+FcOxLQBEfziU0SoEcsvr79c9y+9daAqbfs77vgWw5XhShPfr99uky8ra0Nu3fvRlZWls31rKws7Nixw+V7R44cCY1Gg5tvvhlffPGFzWsVFRV2ZU6cONFpma2trTAajTYPIlKwH3a4+JEEAAlobvBOjPE48PXr/vs8GTGXtJyARnCc3ADmHp1E4RSuO/5BQNVb9vf9g+vfDyLAxwnOyZMn0dHRgYSEBJvrCQkJ0Ov1Dt+j0Wjw2muvYd26dfjwww8xePBg3Hzzzdi+fbs1Rq/Xe1RmcXExRFG0Pvr379/NlhFRQDt7wr+fd/qIfz/PSwaE+fl78hZ/318KSn6ZZCwItn9GSJJkd81i8ODBGDx4sPV5RkYGjh07hr/97W/47W9/e1FlLlq0CAsWLLA+NxqNTHKIlOyyBPcx3tRvoH8/z0vCYpJ6ugoXx9/3l4KST3tw4uLiEB4ebtez0tjYaNcD40p6ejoOHTpkfa5Wqz0qMzIyEtHR0TYPIlKwAZnmuRquTmyKSvROTPQVwI15XilLikrECcTC2WkN5rkzMZCi5H2W5CRG8nK9/RoTfYX5/hK54dMEJyIiAqmpqSgvL7e5Xl5ejsxM+f8DrampgUZzYb+GjIwMuzI/++wzj8okIgULCzcvKQbg9MSmSSXeicl+BugV4ZWyvkt5Ak+15QKAXZJjeV7YNgvfpTwh67MEwC7JkSCYr3ix3n6NyX6GE4xJFp+fRbVgwQL84x//wBtvvIH9+/fj4YcfxtGjRzFv3jwA5uGjWbNmWeOff/55fPTRRzh06BD27duHRYsWYd26dXjwwQetMQ899BA+++wzlJSU4MCBAygpKcHmzZtRUFDg6+YQUbDQTjEvKY7usmNvdOKFpcbeivHS5x3oNxafmtKQ314APWxPA9cjFvntBfjUlIYD/cbK/iyhS4zgg3r7PYZIBp8vEwfMG/0tXboUOp0OycnJeO6556zzaebMmYMjR45g69atAIClS5fitddew/Hjx9GnTx8MGzYMixYtwq233mpT5gcffIAnnngC33//vXWjvzvvvFNWfbhMnCiEBMhOxnJiKg6fwt2vVwIAwhzsdmz69W/SNXnp5iMaAqTePfp9U0gJqH1wAhETHCIKRB0mCaNLtkBvaLHb5g4wD9KoRRW+WjieB2ZSSAqYfXCIiEi+8DABhTlaAE5noKAwR8vkhkgGJjhERAEkO1mDFTNToBZtTxVXiyr7AzKJyCmeJk5EFGCykzWYoFWjqr4Jjc0tiI8ynzLOnhsi+ZjgEBEFoPAwwTyRmIguCoeoiIiISHGY4BAREZHiMMEhIiIixWGCQ0RERIrDBIeIiIgUhwkOERERKQ4THCIiIlIcJjhERESkOExwiIiISHGY4BAREZHiMMEhIiIixWGCQ0RERIrDBIeIiIgUhwkOERERKQ4THCIiIlIcJjhERESkOExwiIiISHGY4BAREZHiMMEhIiIixWGCQ0RERIrDBIeIiIgUhwkOERERKQ4THCIiIlIcJjhERESkOExwiIiISHGY4BAREZHi+CXBWb58OZKSkqBSqZCamoovv/zSaeyHH36ICRMm4PLLL0d0dDQyMjLw6aef2sSsWrUKgiDYPVpaWnzdFCIiIgoCPk9w1q5di4KCAjz++OOoqanBmDFjMGnSJBw9etRh/Pbt2zFhwgRs3LgRu3fvxrhx45CTk4OamhqbuOjoaOh0OpuHSqXydXOIiIgoCAiSJEm+/IBRo0YhJSUFK1assF4bOnQopk6diuLiYlllDBs2DDNmzMBTTz0FwNyDU1BQgDNnzlxUnYxGI0RRhMFgQHR09EWVQURERP7lye+3T3tw2trasHv3bmRlZdlcz8rKwo4dO2SVYTKZ0NzcjJiYGJvrZ8+exYABA3DllVdi8uTJdj08nbW2tsJoNNo8iIh8ocMkoeLwKXy85zgqDp9Ch8mnf0MSkRO9fFn4yZMn0dHRgYSEBJvrCQkJ0Ov1ssr4+9//jp9//hnTp0+3XhsyZAhWrVqF4cOHw2g04oUXXsBNN92EvXv34pprrrEro7i4GEVFRd1rDBGRG2W1OhSV1kFnuDAfUCOqUJijRXaypgdrRhR6/DLJWBAEm+eSJNldc2TNmjVYvHgx1q5di/j4eOv19PR0zJw5EyNGjMCYMWPw/vvv49prr8WLL77osJxFixbBYDBYH8eOHeteg4iIuiir1SF/dbVNcgMAekML8ldXo6xW10M1IwpNPu3BiYuLQ3h4uF1vTWNjo12vTldr167F3Llz8a9//Qu33HKLy9iwsDDceOONOHTokMPXIyMjERkZ6VnliYhk6jBJKCqtg6PBKAmAAKCotA4TtGqEh7n/446Ius+nPTgRERFITU1FeXm5zfXy8nJkZmY6fd+aNWswZ84cvPvuu7jtttvcfo4kSdizZw80GnYBE5H/VdU32fXcdCYB0BlaUFXf5L9KEYU4n/bgAMCCBQuQm5uLG264ARkZGXjttddw9OhRzJs3D4B5+Oj48eN4++23AZiTm1mzZuGFF15Aenq6tfenT58+EEURAFBUVIT09HRcc801MBqNWLZsGfbs2YOXX37Z180hIrLT2CxvDy65cUTUfT5PcGbMmIFTp05hyZIl0Ol0SE5OxsaNGzFgwAAAgE6ns9kT59VXX8X58+fxwAMP4IEHHrBenz17NlatWgUAOHPmDO6//37o9XqIooiRI0di+/btSEtL83VziIjsxEfJ24NLbhwRdZ/P98EJRNwHh4i8qcMkYXTJFugNLQ7n4QgA1KIKXy0czzk4RN0QMPvgEBGFgvAwAYU5WgDmZKYzy/PCHC2TGyI/YoJDROQF2ckarJiZArVoOwylFlVYMTOF++AQ+ZnP5+AQESlBh0lCVX0TGptbEB+lQlpSjF2PTHayBhO0ardxROR7THCIiNzwZIfi8DABGYNi/V1FIuqCQ1REpGjdPRuKOxQTBSf24BCRYnX3bCjuUEwUvNiDQ0SK5I2eF+5QTBS8mOAQkeK463kBzD0v7oaruEMxUfBigkNEiuOtnhfuUEwUvJjgEJHieKvnJS0pBhpRZbd5n4UA85yetKQYzypIRD7HBIeIFMdbPS/coZgoeDHBISLF8WbPC3coJgpOXCZORIpj6XnJX10NAbCZbHwxPS/coZgo+PA0cZ4mTqRY3d0Hh4gCiye/3+zBISLFYs8LUehigkNEisazoYhCEycZExERkeIwwSEiIiLFYYJDREREisMEh4iIiBSHCQ4REREpDhMcIiIiUhwmOERERKQ4THCIiIhIcZjgEBERkeJwJ2MiCnkdJonHORApDBMcIgppPJCTSJk4REVEIausVof81dU2yQ0A6A0tyF9djbJaXQ/VjIi6iwkOEYWkDpOEotI6SA5es1wrKq1Dh8lRBBEFOiY4RBSSquqb7HpuOpMA6AwtqKpv8l+liMhr/JLgLF++HElJSVCpVEhNTcWXX37pMn7btm1ITU2FSqXC1VdfjVdeecUuZt26ddBqtYiMjIRWq8X69et9VX0iUqDGZufJzcXEEVFg8XmCs3btWhQUFODxxx9HTU0NxowZg0mTJuHo0aMO4+vr63HrrbdizJgxqKmpwWOPPYb58+dj3bp11piKigrMmDEDubm52Lt3L3JzczF9+nTs3LnT180hIoWIj1J5NY6IAosgSZJPB5hHjRqFlJQUrFixwnpt6NChmDp1KoqLi+3iFy5ciA0bNmD//v3Wa/PmzcPevXtRUVEBAJgxYwaMRiM2bdpkjcnOzka/fv2wZs0at3UyGo0QRREGgwHR0dHdaR4RBakOk4TRJVugN7Q4nIcjAFCLKny1cDyXjBMFCE9+v33ag9PW1obdu3cjKyvL5npWVhZ27Njh8D0VFRV28RMnTsSuXbvQ3t7uMsZZma2trTAajTYPIgpt4WECCnO0AMzJTGeW54U5WiY3REHKpwnOyZMn0dHRgYSEBJvrCQkJ0Ov1Dt+j1+sdxp8/fx4nT550GeOszOLiYoiiaH3079//YptERAqSnazBipkpUIu2w1BqUYUVM1O4Dw5REPPLRn+CYPsXkCRJdtfcxXe97kmZixYtwoIFC6zPjUYjkxwiAmBOciZo1dzJmEhhfJrgxMXFITw83K5npbGx0a4HxkKtVjuM79WrF2JjY13GOCszMjISkZGRF9sMIgpQ3jpiITxMQMagWB/UkIh6ik+HqCIiIpCamory8nKb6+Xl5cjMzHT4noyMDLv4zz77DDfccAN69+7tMsZZmUSkPGW1Oowu2YK7X6/EQ+/twd2vV2J0yRbuPkxEAPywTHzBggX4xz/+gTfeeAP79+/Hww8/jKNHj2LevHkAzMNHs2bNssbPmzcPP/zwAxYsWID9+/fjjTfewMqVK/HII49YYx566CF89tlnKCkpwYEDB1BSUoLNmzejoKDA180hogDAIxaIyB2fz8GZMWMGTp06hSVLlkCn0yE5ORkbN27EgAEDAAA6nc5mT5ykpCRs3LgRDz/8MF5++WUkJiZi2bJl+P3vf2+NyczMxHvvvYcnnngCTz75JAYNGoS1a9di1KhRvm4OEfUwd0csCDAfsTBBq+Y8GqIQ5vN9cAIR98EhCl4Vh0/h7tcr3catyUvnvBoihQmYfXCIiLyNRywQkRxMcIgoqPCIBSKSgwkOEQWVtKQYaESV3e7DFgIAjWheMk5EoYsJDhEFFR6xQERyMMEhoqDDIxaIyB2/HNVAROQpd7sU84gFInKFCQ4RBZyyWh2KSutsNvLTiCoU5mhtemd4xAIROcMhKiIKKNylmIi8gQkOEQUMd7sUA+ZdijtMIbc/KRF5iAkOEQWMqvomu56bziQAOkMLquqb/FcpIgpKTHCIKGBwl2Ii8hYmOEQUMLhLMRF5CxMcIgoY3KWYiLyFCQ4RBQzuUkxE3sIEh4gCCncpJiJv4EZ/RBRwuEsxEXUXExwiCkjcpZiIuoNDVERERKQ4THCIiIhIcZjgEBERkeIwwSEiIiLFYYJDREREisMEh4iIiBSHCQ4REREpDhMcIiIiUhxu9EdEXtNhktzuPiwnhoiou5jgEJFXlNXqUFRaB52hxXpNI6pQmKO1nh8lJ4aIyBsESZKknq6EvxmNRoiiCIPBgOjo6J6uDlHQK6vVIX91Nbr+Y2Lpl1kxMwUA3MYwySEiVzz5/WYPDhF1S4dJQlFpnV3iAgASzAnM4g37AAguY4pK6zBBq+ZwFRF5BScZE1G3VNU32Qw5dSUB0BtboTe6jtEZWlBV3+T9ChJRSPJpgnP69Gnk5uZCFEWIoojc3FycOXPGaXx7ezsWLlyI4cOH49JLL0ViYiJmzZqFhoYGm7ixY8dCEASbx1133eXLphCRE43NzhOXniyLiEKbTxOce+65B3v27EFZWRnKysqwZ88e5ObmOo3/5ZdfUF1djSeffBLV1dX48MMP8d1332HKlCl2sXl5edDpdNbHq6++6sumEJET8VGqgCyLiEKbz+bg7N+/H2VlZaisrMSoUaMAAK+//joyMjJw8OBBDB482O49oiiivLzc5tqLL76ItLQ0HD16FFdddZX1+iWXXAK1Wu2r6hORTGlJMdCIKugNLQ7n2AgAEqIjAQg4YXQeoxbNS8aJiLzBZz04FRUVEEXRmtwAQHp6OkRRxI4dO2SXYzAYIAgC+vbta3P9nXfeQVxcHIYNG4ZHHnkEzc3NTstobW2F0Wi0eRCRd4SHCSjM0QK4sCLKwvJ88ZRhWDzFdUxhjpYTjInIa3yW4Oj1esTHx9tdj4+Ph16vl1VGS0sLHn30Udxzzz02y8HuvfderFmzBlu3bsWTTz6JdevW4c4773RaTnFxsXUekCiK6N+/v+cNIiKnspM1WDEzBWrRdohJLaqsy7/lxBAReYvHQ1SLFy9GUVGRy5ivv/4aACAI9n+NSZLk8HpX7e3tuOuuu2AymbB8+XKb1/Ly8qz/PTk5Gddccw1uuOEGVFdXIyUlxa6sRYsWYcGCBdbnRqORSQ6Rl2UnazBBq3a5S7GcGCIib/A4wXnwwQfdrlgaOHAgvvnmG5w4ccLutZ9++gkJCQku39/e3o7p06ejvr4eW7ZscbuZT0pKCnr37o1Dhw45THAiIyMRGRnpsgwi6r7wMAEZg2K7HUNE1F0eJzhxcXGIi4tzG5eRkQGDwYCqqiqkpaUBAHbu3AmDwYDMzEyn77MkN4cOHcIXX3yB2Fj3/xDu27cP7e3t0GjYxU1EREQ+nIMzdOhQZGdnIy8vD5WVlaisrEReXh4mT55ss4JqyJAhWL9+PQDg/Pnz+I//+A/s2rUL77zzDjo6OqDX66HX69HW1gYAOHz4MJYsWYJdu3bhyJEj2LhxI6ZNm4aRI0fipptu8lVziIiIKIj4dB+cd955B8OHD0dWVhaysrJw3XXX4Z///KdNzMGDB2EwGAAAP/74IzZs2IAff/wR119/PTQajfVhWXkVERGBzz//HBMnTsTgwYMxf/58ZGVlYfPmzQgPD/dlc4iIiChI8LBNHrZJREQUFDz5/eZZVERERKQ4THCIiIhIcZjgEBERkeIwwSEiIiLFYYJDREREisMEh4iIiBSHCQ4REREpDhMcIiIiUhwmOERERKQ4THCIiIhIcZjgEBERkeIwwSEiIiLFYYJDREREisMEh4iIiBSHCQ4REREpDhMcIiIiUhwmOERERKQ4THCIiIhIcZjgEBERkeL06ukKEFFw6DBJqKpvQmNzC+KjVEhLikF4mNDT1SIicogJDhG5VVarQ1FpHXSGFus1jahCYY4W2cmaHqwZEZFjHKIiIpfKanXIX11tk9wAgN7QgvzV1Sir1fVQzYiInGOCQ0ROdZgkFJXWQXLwmuVaUWkdOkyOIoiIeg4THCJyqqq+ya7npjMJgM7Qgqr6Jv9ViohIBiY4RORUY7Pz5OZi4oiI/IUJDhE5FR+l8mocEZG/MMEhIqfSkmKgEVVwthhcgHk1VVpSjD+rRUTkFhMcInIqPExAYY4WAOySHMvzwhwt98MhooDDBIeIXMpO1mDFzBSoRdthKLWowoqZKdwHh4gCEjf6IzJ1AD/sAM6eAC5LAAZkAmHhFxcXaDFeKis7WYMJQy7HgZ2f4tzp4+jT7woMGfU7hPfq5fXP8klZRBRyfJrgnD59GvPnz8eGDRsAAFOmTMGLL76Ivn37On3PnDlz8NZbb9lcGzVqFCorK63PW1tb8cgjj2DNmjU4d+4cbr75ZixfvhxXXnmlT9pBCla3AShbCBgbLlyLTgSySwDtFM/iAi3Gg7KksoUQOsVI0YkQusSEly3EsM7l7Oz5essqi4hCkiBJks926Jo0aRJ+/PFHvPbaawCA+++/HwMHDkRpaanT98yZMwcnTpzAm2++ab0WERGBmJgLkxjz8/NRWlqKVatWITY2Fn/605/Q1NSE3bt3Izzc/V9vRqMRoijCYDAgOjq6Gy2koFa3AXh/FmC3jd2v80mmv23+oZQTBwRWjAf1lt6fBQmSzXi1CYAAAUIA11tWWUSkKJ78fvsswdm/fz+0Wi0qKysxatQoAEBlZSUyMjJw4MABDB482OH75syZgzNnzuCjjz5y+LrBYMDll1+Of/7zn5gxYwYAoKGhAf3798fGjRsxceJEt3VjgkMwdQDPJ9v+9W9DMPcGzN8DLBvhOi5KY/5dDZQYD+p97nwHIn85AUdzhE0S0NonAX0iwgOu3rLKKviWw1VECuPJ77fPJhlXVFRAFEVrcgMA6enpEEURO3bscPnerVu3Ij4+Htdeey3y8vLQ2NhofW337t1ob29HVlaW9VpiYiKSk5Pdlktk9cMOFz+QACABxuPA16+7j2tuCKwYD+rd55zj5AYAwgSgT8uJgKy3rLJ+4L8HRKHMZ3Nw9Ho94uPj7a7Hx8dDr9c7fd+kSZMwbdo0DBgwAPX19XjyyScxfvx47N69G5GRkdDr9YiIiEC/fv1s3peQkOC03NbWVrS2tlqfG43Gi2wVKcbZE/LiTh/xaTV8hvWWf4+JSJE87sFZvHgxBEFw+di1axcAQBDs/zSUJMnhdYsZM2bgtttuQ3JyMnJycrBp0yZ89913+OSTT1zWy1W5xcXFEEXR+ujfv78HLSZFuixBXly/gT6ths+w3vLvMREpkscJzoMPPoj9+/e7fCQnJ0OtVuPECfu/oH766SckJMj/h0ej0WDAgAE4dOgQAECtVqOtrQ2nT5+2iWtsbHRa7qJFi2AwGKyPY8eOedBiUqQBmeZ5Gq726I2+Argxz31cVGJgxcisd2sfNXRSDJwdBG6SgAYpBq2XqAOq3rLLGpDp5HUiCgUeJzhxcXEYMmSIy4dKpUJGRgYMBgOqqqqs7925cycMBgMyM+X/w3Pq1CkcO3YMGo15M7HU1FT07t0b5eXl1hidTofa2lqn5UZGRiI6OtrmQSEuLNy8nBiA0z16s58BekW4j5tU0iMxUpcYycN695q8FC/0vg8A7JIcy/Nlve9Dr9uW+qdt3vy+s5/hBGOiEOezScZDhw5FdnY28vLyUFlZicrKSuTl5WHy5Mk2K6iGDBmC9evXAwDOnj2LRx55BBUVFThy5Ai2bt2KnJwcxMXF4Y477gAAiKKIuXPn4k9/+hM+//xz1NTUYObMmRg+fDhuueUWXzWHlEg7xbycOLrLTrzRibbLjOXE+TmmJuMFNML2/KcTiEFNxguy6x0+7HaMnfpf+EN7AfRdytIjFn9oL8DYqf+F8GG3+69t3vy+iSik+XQfnKamJruN/l566SWbjf4EQcCbb76JOXPm4Ny5c5g6dSpqampw5swZaDQajBs3Dn/5y19s5s20tLTgf/7nf/Duu+/abPQnd24Nl4mTjSDbybisVof81dUQYEJa2AHE4wwa0Rdfm4bAhDD74xPcfF5ZrQ5/2fAt+p/day3r2GUj8OSU4R6V49UYb5dFRIoQEPvgBDImOBSsOkwSRpdsgc7Q4vB1AeYzor5aON56AGaHSUJVfRMam1sQH2U++bvr4ZhyYoiIeponv988i4ooiFTVNzlNbgDzvr46Qwuq6puQMSgWZbU6FJXW2bxHI6pQmKO16Z0JDxOQMSjWl1UnIvIrniZOFEQam50nN13jLENZXRMivaEF+aurUVar80UViYgCAhMcoiASH6WSFRd3aSSKSuvsTmoCLpzeVFRahw5na8SJiIIcExyiIJKWFAONqHK1Aww0ogoQIHsoi4hIiZjgEAWR8DABhTlaAE53gEFhjhYnz7ZCDrlDXkREwYYJDlGQyU7WYMXMFKhF2+EqtaiyLhGXO5QlN46IKNhwFRVREMpO1mCCVu10abdlKEtvaHE4D8eynDwtKcbBq0REwY8JDlGQcrW02zKUZd4QEDZJTuehLO51Q0RKxSEqIoWSM5RFRKRU7MEhUjB3Q1lERErFBIdI4bhLMRGFIg5RERERkeIwwSEiIiLFYYJDREREisMEh4iIiBSHCQ4REREpDhMcIiIiUhwmOERERKQ4THCIiIhIcZjgEBERkeJwJ2MiP+swSTw6gYjIx5jgEPlRWa0ORaV10BlarNc0ogqFOVoefklE5EUcoiLyk7JaHfJXV9skNwCgN7Qgf3U1ymp1PVQzIiLlYYJD5AcdJglFpXWQHLxmuVZUWocOk6MIIiLyFBMcIj+oqm+y67npTAKgM7Sgqr7Jf5UiIlIwJjhEftDY7Dy5uZg4IiJyjQkOkR/ER6m8GkdERK5xFRWRH6QlxUAjqqA3tDichyMAUIvmJeMAl5ITEXUXExwiPwgPE1CYo0X+6moIgE2SY0lbCnO0CA8TuJSciMgLOERF5CfZyRqsmJkCtWg7DKUWVVgxMwXZyRouJSci8hKfJjinT59Gbm4uRFGEKIrIzc3FmTNnXL5HEASHj7/+9a/WmLFjx9q9ftddd/myKURekZ2swVcLx2NNXjpeuOt6rMlLx1cLxyM7WcOl5EREXuTTIap77rkHP/74I8rKygAA999/P3Jzc1FaWur0PTqd7V+omzZtwty5c/H73//e5npeXh6WLFlifd6nTx8v1pzInpx5MXJiwsMEZAyKtSvfk6Xkjt5PREQX+CzB2b9/P8rKylBZWYlRo0YBAF5//XVkZGTg4MGDGDx4sMP3qdVqm+cff/wxxo0bh6uvvtrm+iWXXGIXS+QrcubFdHfuDJeSExF5j8+GqCoqKiCKojW5AYD09HSIoogdO3bIKuPEiRP45JNPMHfuXLvX3nnnHcTFxWHYsGF45JFH0Nzc7LW6E3UmZ16MN+bOcCk5EZH3+KwHR6/XIz4+3u56fHw89Hq9rDLeeustREVF4c4777S5fu+99yIpKQlqtRq1tbVYtGgR9u7di/LycofltLa2orW11frcaDR60BIKZe7mxQgAFm/YB0BwGVNUWocJWrXLpd6eLiUnIiLnPO7BWbx4sdOJwJbHrl27AJgnDHclSZLD64688cYbuPfee6FS2f7FmpeXh1tuuQXJycm466678MEHH2Dz5s2orq52WE5xcbF1orMoiujfv7+HraZQJWdejN7YCr2x+8cwWJaSAxeWjlt0XUpORESuedyD8+CDD7pdsTRw4EB88803OHHihN1rP/30ExISEtx+zpdffomDBw9i7dq1bmNTUlLQu3dvHDp0CCkpKXavL1q0CAsWLLA+NxqNTHJIFm/Od5FTlmUpede5PGrug0NE5BGPE5y4uDjExcW5jcvIyIDBYEBVVRXS0tIAADt37oTBYEBmZqbb969cuRKpqakYMWKE29h9+/ahvb0dGo3jf/wjIyMRGRnpthyirrw530VuWdnJGkzQqrmTMRFRN/hskvHQoUORnZ2NvLw8VFZWorKyEnl5eZg8ebLNCqohQ4Zg/fr1Nu81Go3417/+hfvuu8+u3MOHD2PJkiXYtWsXjhw5go0bN2LatGkYOXIkbrrpJl81h0KUZV6Ms9RCAKCOjoQ62nWMxsO5M5al5LdffwUyBsUyuSEi8pBPN/p75513MHz4cGRlZSErKwvXXXcd/vnPf9rEHDx4EAaDwebae++9B0mScPfdd9uVGRERgc8//xwTJ07E4MGDMX/+fGRlZWHz5s0IDw/3ZXMoBMmZF7N4yjAsnsK5M0REgUSQJCnktkU1Go0QRREGgwHR0dE9XR0KAv7YB4eIiFzz5PebCQ4THJLJWzsZExHRxfHk95uniRPJ5OyIBU9jiIjI93iaOBERESkOExwiIiJSHCY4REREpDhMcIiIiEhxmOAQERGR4jDBISIiIsXhMnEKedy7hohIeZjgUEjj7sNERMrEISoKWWW1OuSvrrZJbgBAb2hB/upqlNXqeqhmRETUXUxwSNE6TBIqDp/Cx3uOo+LwKXSYJOv1otI6ODqnxHKtqLTOGk9ERMGFQ1QUtNzNnXE1/CT2ibDruelMAqAztKCqvolHLxARBSEmOBSU3M2dsQw/de1/sQw//ddNA2V9TmOz8ySIiIgCF4eoKOi4mzuz8ZsGt8NP6/ccl/VZ8VGq7lWWiIh6BBMcCipy5s488XGt2+Gnpp/bEXNpBJwtBhdg7hFKS4rpXoWJiKhHMMGhoFJV3yQreZFj6vWJAGCX5FieF+ZouR8OEVGQYoLjZ85W9ZA83pwTM0GrxoqZKVCLtsNQalGFFTNTuA8OEVEQ4yRjP/LmpnKhuvuu3DkxMZdG4PTPbQ6HsgSYkxjLdzZBqw7J75KISMmY4PiJu1U9nvQYhPLuu2lJMdCIKugNLS6Tlydv0+KBd6shADZxjoafwsMELgUnIlIYDlH5gTc3lQv13XfDwwQU5mgBuJ47c+t1Gg4/ERGFMPbg+IGcibFyNpVzlygJMCdKE7TqgB5i6e7wWnayOXnp2oul7tKLlZ2s4fATEVGIYoLjRc5+uOVOjHUX561EqSd5a3hNbvLC4SciotDEBMdLXP1wy50Y6y7OW4lST/HmPCSAyQsRETnHBMcLLD/cAkxIDzuAeJxBI/ria8MQ5K+uxsv3jLROjBVgQlqnmCrTEEgIs67qAYCO8+dxYOenOHf6OPr0uwJDRk1EeK9eNglQmINyTL9OqbJJlEwdwA87gLMngMsSgAGZQFi4bQP8ENN5eM1R3SWE2Q6v+bPeRESkOExwusnyw50VVoXC3m8jUWiyvtYgxWBJ+yz85RPzqp4N772Cp5zETM2Zh/AwATWfvoXEiiIMwylrzInyWDRkFCJtwixoRBVGNG93Ws7eqN9e2H23bgNQthAwNlyocHQikF0CaKf4NcYyvDbRyfdU1D4LnxrSzMNrrf/nv3oTEZEiCZIkhdxOc0ajEaIowmAwIDo6ultlVRw+hVUrl2FF7+cBAJ2ngFgWReW3F2DBhGtx7bYHIEGyWbpmAiBAgDD9bdQcO40RO+Y7LWdv5jIAcBszcuJs84/7+7MAuwGhX980/W3zf/op5uO2VGx8/zW339Pc0UlIqyrwT72Z5BARBRVPfr+Z4HQzwfm45ihu/Oh3UKMJjhbnmCRAjxj069MbfVpOOClFgBSlQWNzKy6XTjktp1GIQUKUCmhucHiGkgQBQnQiMH8PsGyEbc9Fl89DlMb8W++PmOhEVNz2OQa8m+n2e4q9NAKRv+j9UicUfMvhKiKiIOLJ7zeHqLrpN798azPc0lWYACSiCXA571eC0NyABMB+c5dO5ajRBDQ7L0WABBiPA1+/7uLH3fx5aHb1updjjMeRdupDhMv5nn7xX53www4gaYybWCIiCkbc6K+bhka5/EXuGaeP9HQN7ISfOdLTVbB31lmPGhERBTsmON0UFqXu6SrY6eg7sKerYK/fwJ6ugb3LEnq6BkRE5CM+TXCefvppZGZm4pJLLkHfvn1lvUeSJCxevBiJiYno06cPxo4di3379tnEtLa24o9//CPi4uJw6aWXYsqUKfjxxx990AIZBmQC0YmQnIwtSRCAqETznA9n408QIEUl4gRi4ey0BsscFSnKdTmIvgJVsXeiQYpxWVaDFIPWS9Suy5JRb1kx0VcAN+bJKutcnwSX9T6nSvBenQZkOnmdiIiCnU8TnLa2NkybNg35+fmy37N06VI8++yzeOmll/D1119DrVZjwoQJaG6+MPmkoKAA69evx3vvvYevvvoKZ8+exeTJk9HR0eGLZrgWFg5kl/x6qKPtD6oEwXxlUol5aTIAZycoCZNK0JBRCAB2P/CW57qMxRAmuS4H2c+g8ZwJRe2zXJZV1D4Le5MXuS7r13pLMK/2sikHv65PktE2ZD8D9IpwG9eR/QyK2me7rvf52eiY+IyserutEycYExEplk8TnKKiIjz88MMYPny4rHhJkvD888/j8ccfx5133onk5GS89dZb+OWXX/Duu+8CAAwGA1auXIm///3vuOWWWzBy5EisXr0a3377LTZv3uzL5jinnQJMfxtCtO0uvEJ04oXlyL/GoEsMOsWMnDgbezOX4SfBdnfeRiH2wvJvGeXER6nwqSkN+e0F0CPGJkyPWOS3F+BTUxo6Bue4LavMdCPy2x6CXupSjhSL/LaHUGa6UVadOn9PzuKqVKPx3tnrXdb7vbPXo0o12v3nya0TEREpkl+Wia9atQoFBQU4c+aMy7jvv/8egwYNQnV1NUaOHGm9fvvtt6Nv37546623sGXLFtx8881oampCv379rDEjRozA1KlTUVRUZFdua2srWltbrc+NRiP69+/vlWXiNry0s66znYzlltNhkjC6ZIvbnZO/Wjje5a7BlnJ0hhanuw/LKUfu9/TxnuN46L09AFzv1PzCXdfj9uuv4E7GREQhJmiXiev15v1PEhJsJ38mJCTghx9+sMZERETYJDeWGMv7uyouLnaY+HhdWLj7ZccyYsJ79cKwm2676HLCwwQU5mh/PfcpDJUmrfU1y4BNYY72wsGUTsrqfLinqUs5FjaHe8ppv4vP63zEhLPPs4nz0vdNRETK4/EQ1eLFiyEIgsvHrl27ulUpQegyl0WS7K515Spm0aJFMBgM1sexY8e6Vb9gkJ2swYqZKVCLtgd4qkWV7EMt/X24Z1pSDDSiytXUYGg6ndlFRETkjMc9OA8++CDuuusulzEDBw68qMqo1eYl13q9HhrNhR/gxsZGa6+OWq1GW1sbTp8+bdOL09jYiMxMx6tiIiMjERkZeVF1CmbZyRpM0KpRVd+ExuYWxEeZk4PwLlsJd5gkhzGenoLurBy5Ovc8mSdtX+Cw54mIiMgJjxOcuLg4xMXF+aIuSEpKglqtRnl5uXUOTltbG7Zt24aSEvOqmNTUVPTu3Rvl5eWYPn06AECn06G2thZLly71Sb2CWXiYYB4+cqKsVoei0jrrUBRg7iUpzNFiglZtPQXd0UQtAbCegu6qHDm9RRaWnqeuZakvoiwiIgpdPp1kfPToUTQ1NWHDhg3461//ii+//BIA8Jvf/AaXXXYZAGDIkCEoLi7GHXfcAQAoKSlBcXEx3nzzTVxzzTX43//9X2zduhUHDx5EVFQUACA/Px//7//9P6xatQoxMTF45JFHcOrUKezevRvh4e4nkHrzLKpgVlar+3Weji1L/8iKmSkAgPzV1QAc96h0jnFVjqeJSXd7g4iISHkCZpLxU089hbfeesv63NIr88UXX2Ds2LEAgIMHD8JgMFhj/vznP+PcuXP4wx/+gNOnT2PUqFH47LPPrMkNADz33HPo1asXpk+fjnPnzuHmm2/GqlWrZCU3ZNZhklBUWuewZ0aCOTkpKq3DVwvHu+xRmaBVY3TJFrflTNCqPR6uctXzRERE5ApPEw/RHpyKw6dw9+uVbuPW5KUjY1Cs0x4VT8shIiK6WAHTg0OBy9MVUs56VPy90oqIiEgOHrYZojxdIeXrcoiIiLyJCU6I8taeM9y7hoiIAhETnBBl2XMGcHocpaw9Z7xVDhERkTcxwQlh3tjt2JvlEBEReQtXUYXoKqrOvLXnDPeuISIiX+IqKvKIt/ac4d41REQUKDhERURERIrDBIeIiIgUhwkOERERKQ4THCIiIlIcJjhERESkOExwiIiISHGY4BAREZHiMMEhIiIixWGCQ0RERIoTkjsZW06nMBqNPVwTIiIiksvyuy3nlKmQTHCam5sBAP379+/hmhAREZGnmpubIYqiy5iQPGzTZDKhoaEBUVFREATvHgZpNBrRv39/HDt2TJEHeSq9fYDy28j2BT+lt5HtC36+aqMkSWhubkZiYiLCwlzPsgnJHpywsDBceeWVPv2M6Ohoxf4PF1B++wDlt5HtC35KbyPbF/x80UZ3PTcWnGRMREREisMEh4iIiBSHCY6XRUZGorCwEJGRkT1dFZ9QevsA5beR7Qt+Sm8j2xf8AqGNITnJmIiIiJSNPThERESkOExwiIiISHGY4BAREZHiMMEhIiIixWGC001HjhzB3LlzkZSUhD59+mDQoEEoLCxEW1uby/dJkoTFixcjMTERffr0wdixY7Fv3z4/1dozTz/9NDIzM3HJJZegb9++st4zZ84cCIJg80hPT/dtRS/SxbQvmO4fAJw+fRq5ubkQRRGiKCI3Nxdnzpxx+Z5AvofLly9HUlISVCoVUlNT8eWXX7qM37ZtG1JTU6FSqXD11VfjlVde8VNNL54nbdy6davdvRIEAQcOHPBjjeXbvn07cnJykJiYCEEQ8NFHH7l9TzDdQ0/bF2z3r7i4GDfeeCOioqIQHx+PqVOn4uDBg27f5+97yASnmw4cOACTyYRXX30V+/btw3PPPYdXXnkFjz32mMv3LV26FM8++yxeeuklfP3111Cr1ZgwYYL1nKxA0tbWhmnTpiE/P9+j92VnZ0On01kfGzdu9FENu+di2hdM9w8A7rnnHuzZswdlZWUoKyvDnj17kJub6/Z9gXgP165di4KCAjz++OOoqanBmDFjMGnSJBw9etRhfH19PW699VaMGTMGNTU1eOyxxzB//nysW7fOzzWXz9M2Whw8eNDmfl1zzTV+qrFnfv75Z4wYMQIvvfSSrPhgu4eets8iWO7ftm3b8MADD6CyshLl5eU4f/48srKy8PPPPzt9T4/cQ4m8bunSpVJSUpLT100mk6RWq6VnnnnGeq2lpUUSRVF65ZVX/FHFi/Lmm29KoijKip09e7Z0++23+7Q+3ia3fcF2/+rq6iQAUmVlpfVaRUWFBEA6cOCA0/cF6j1MS0uT5s2bZ3NtyJAh0qOPPuow/s9//rM0ZMgQm2v//d//LaWnp/usjt3laRu/+OILCYB0+vRpP9TOuwBI69evdxkTjPfQQk77gvn+SZIkNTY2SgCkbdu2OY3piXvIHhwfMBgMiImJcfp6fX099Ho9srKyrNciIyPxu9/9Djt27PBHFf1i69atiI+Px7XXXou8vDw0Njb2dJW8ItjuX0VFBURRxKhRo6zX0tPTIYqi2/oG2j1sa2vD7t27bb57AMjKynLaloqKCrv4iRMnYteuXWhvb/dZXS/WxbTRYuTIkdBoNLj55pvxxRdf+LKafhVs9/BiBev9MxgMAODyd68n7iETHC87fPgwXnzxRcybN89pjF6vBwAkJCTYXE9ISLC+FuwmTZqEd955B1u2bMHf//53fP311xg/fjxaW1t7umrdFmz3T6/XIz4+3u56fHy8y/oG4j08efIkOjo6PPru9Xq9w/jz58/j5MmTPqvrxbqYNmo0Grz22mtYt24dPvzwQwwePBg333wztm/f7o8q+1yw3UNPBfP9kyQJCxYswOjRo5GcnOw0rifuIRMcJxYvXuxw0lfnx65du2ze09DQgOzsbEybNg333Xef288QBMHmuSRJdtd85WLa54kZM2bgtttuQ3JyMnJycrBp0yZ89913+OSTT7zYCud83T6gZ+8f4FkbHdXLXX17+h664ul37yje0fVA4kkbBw8ejLy8PKSkpCAjIwPLly/Hbbfdhr/97W/+qKpfBOM9lCuY79+DDz6Ib775BmvWrHEb6+972MsnpSrAgw8+iLvuustlzMCBA63/vaGhAePGjUNGRgZee+01l+9Tq9UAzBmtRqOxXm9sbLTLcH3F0/Z1l0ajwYABA3Do0CGvlemKL9sXCPcPkN/Gb775BidOnLB77aeffvKovv6+h47ExcUhPDzcrifD1XevVqsdxvfq1QuxsbE+q+vFupg2OpKeno7Vq1d7u3o9ItjuoTcEw/374x//iA0bNmD79u248sorXcb2xD1kguNEXFwc4uLiZMUeP34c48aNQ2pqKt58802EhbnuGEtKSoJarUZ5eTlGjhwJwDzuvm3bNpSUlHS77nJ40j5vOHXqFI4dO2aTEPiSL9sXCPcPkN/GjIwMGAwGVFVVIS0tDQCwc+dOGAwGZGZmyv48f99DRyIiIpCamory8nLccccd1uvl5eW4/fbbHb4nIyMDpaWlNtc+++wz3HDDDejdu7dP63sxLqaNjtTU1PTovfKmYLuH3hDI90+SJPzxj3/E+vXrsXXrViQlJbl9T4/cQ59NXw4Rx48fl37zm99I48ePl3788UdJp9NZH50NHjxY+vDDD63Pn3nmGUkURenDDz+Uvv32W+nuu++WNBqNZDQa/d0Et3744QeppqZGKioqki677DKppqZGqqmpkZqbm60xndvX3Nws/elPf5J27Ngh1dfXS1988YWUkZEhXXHFFYponyQF1/2TJEnKzs6WrrvuOqmiokKqqKiQhg8fLk2ePNkmJlju4XvvvSf17t1bWrlypVRXVycVFBRIl156qXTkyBFJkiTp0UcflXJzc63x33//vXTJJZdIDz/8sFRXVyetXLlS6t27t/TBBx/0VBPc8rSNzz33nLR+/Xrpu+++k2pra6VHH31UAiCtW7eup5rgUnNzs/X/ZwCkZ599VqqpqZF++OEHSZKC/x562r5gu3/5+fmSKIrS1q1bbX7zfvnlF2tMINxDJjjd9Oabb0oAHD46AyC9+eab1ucmk0kqLCyU1Gq1FBkZKf32t7+Vvv32Wz/XXp7Zs2c7bN8XX3xhjencvl9++UXKysqSLr/8cql3797SVVddJc2ePVs6evRozzTADU/bJ0nBdf8kSZJOnTol3XvvvVJUVJQUFRUl3XvvvXZLUoPpHr788svSgAEDpIiICCklJcVmeers2bOl3/3udzbxW7dulUaOHClFRERIAwcOlFasWOHnGnvOkzaWlJRIgwYNklQqldSvXz9p9OjR0ieffNIDtZbHsiy662P27NmSJAX/PfS0fcF2/5z95nX+NzIQ7qHwa2WJiIiIFIOrqIiIiEhxmOAQERGR4jDBISIiIsVhgkNERESKwwSHiIiIFIcJDhERESkOExwiIiJSHCY4REREpDhMcIiIiEhxmOAQERGR4jDBISIiIsVhgkNERESK8/8BRm5xMFPGx9sAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_X,df_Y=pd.DataFrame(X), pd.Series(Y)\n",
    "model=DecisionTree(max_depth=1).fit(df_X,df_Y,type_of_node=DecisionRegressionNode)\n",
    "plt.scatter(X,Y)\n",
    "plt.scatter(X, model.predict(df_X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "a7939754",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f7f9f8357c0>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_X,df_Y=pd.DataFrame(X), pd.Series(Y)\n",
    "model=DecisionTree(max_depth=3).fit(df_X,df_Y,type_of_node=DecisionRegressionNode)\n",
    "plt.scatter(X,Y)\n",
    "plt.scatter(X, model.predict(df_X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "9e383932",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>sex</th>\n",
       "      <th>bmi</th>\n",
       "      <th>bp</th>\n",
       "      <th>s1</th>\n",
       "      <th>s2</th>\n",
       "      <th>s3</th>\n",
       "      <th>s4</th>\n",
       "      <th>s5</th>\n",
       "      <th>s6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.038076</td>\n",
       "      <td>0.050680</td>\n",
       "      <td>0.061696</td>\n",
       "      <td>0.021872</td>\n",
       "      <td>-0.044223</td>\n",
       "      <td>-0.034821</td>\n",
       "      <td>-0.043401</td>\n",
       "      <td>-0.002592</td>\n",
       "      <td>0.019908</td>\n",
       "      <td>-0.017646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.001882</td>\n",
       "      <td>-0.044642</td>\n",
       "      <td>-0.051474</td>\n",
       "      <td>-0.026328</td>\n",
       "      <td>-0.008449</td>\n",
       "      <td>-0.019163</td>\n",
       "      <td>0.074412</td>\n",
       "      <td>-0.039493</td>\n",
       "      <td>-0.068330</td>\n",
       "      <td>-0.092204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.085299</td>\n",
       "      <td>0.050680</td>\n",
       "      <td>0.044451</td>\n",
       "      <td>-0.005671</td>\n",
       "      <td>-0.045599</td>\n",
       "      <td>-0.034194</td>\n",
       "      <td>-0.032356</td>\n",
       "      <td>-0.002592</td>\n",
       "      <td>0.002864</td>\n",
       "      <td>-0.025930</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.089063</td>\n",
       "      <td>-0.044642</td>\n",
       "      <td>-0.011595</td>\n",
       "      <td>-0.036656</td>\n",
       "      <td>0.012191</td>\n",
       "      <td>0.024991</td>\n",
       "      <td>-0.036038</td>\n",
       "      <td>0.034309</td>\n",
       "      <td>0.022692</td>\n",
       "      <td>-0.009362</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.005383</td>\n",
       "      <td>-0.044642</td>\n",
       "      <td>-0.036385</td>\n",
       "      <td>0.021872</td>\n",
       "      <td>0.003935</td>\n",
       "      <td>0.015596</td>\n",
       "      <td>0.008142</td>\n",
       "      <td>-0.002592</td>\n",
       "      <td>-0.031991</td>\n",
       "      <td>-0.046641</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        age       sex       bmi        bp        s1        s2        s3  \\\n",
       "0  0.038076  0.050680  0.061696  0.021872 -0.044223 -0.034821 -0.043401   \n",
       "1 -0.001882 -0.044642 -0.051474 -0.026328 -0.008449 -0.019163  0.074412   \n",
       "2  0.085299  0.050680  0.044451 -0.005671 -0.045599 -0.034194 -0.032356   \n",
       "3 -0.089063 -0.044642 -0.011595 -0.036656  0.012191  0.024991 -0.036038   \n",
       "4  0.005383 -0.044642 -0.036385  0.021872  0.003935  0.015596  0.008142   \n",
       "\n",
       "         s4        s5        s6  \n",
       "0 -0.002592  0.019908 -0.017646  \n",
       "1 -0.039493 -0.068330 -0.092204  \n",
       "2 -0.002592  0.002864 -0.025930  \n",
       "3  0.034309  0.022692 -0.009362  \n",
       "4 -0.002592 -0.031991 -0.046641  "
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = load_diabetes()\n",
    "data.keys()\n",
    "X = pd.DataFrame(data['data'], columns=data['feature_names'])\n",
    "y = pd.Series(data['target'])\n",
    "del data\n",
    "X.columns = pd.Index(rename_columns(x) for x in X.columns)\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "da7ff9c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      151.0\n",
       "1       75.0\n",
       "2      141.0\n",
       "3      206.0\n",
       "4      135.0\n",
       "       ...  \n",
       "437    178.0\n",
       "438    104.0\n",
       "439    132.0\n",
       "440    220.0\n",
       "441     57.0\n",
       "Length: 442, dtype: float64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17bad8bd",
   "metadata": {},
   "source": [
    "#### Max depth = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "af0739ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3622.711742378153"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = DecisionTree(max_depth=1).fit(X, y,type_of_node=DecisionRegressionNode).predict(X)\n",
    "avg_squared_difference(y-preds)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13e82667",
   "metadata": {},
   "source": [
    "#### Max depth = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "05903353",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2910.8226603045914"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = DecisionTree(max_depth=3).fit(X, y,type_of_node=DecisionRegressionNode).predict(X)\n",
    "avg_squared_difference(y-preds)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6259b629",
   "metadata": {},
   "source": [
    "#### Max depth = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "9ac41f0b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1958.2496839949893"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = DecisionTree(max_depth=5).fit(X, y,type_of_node=DecisionRegressionNode).predict(X)\n",
    "avg_squared_difference(y-preds)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4376152",
   "metadata": {},
   "source": [
    "#### Max depth = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "15d2c21c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.1006787330316743"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = DecisionTree(max_depth=10).fit(X, y,type_of_node=DecisionRegressionNode).predict(X)\n",
    "avg_squared_difference(y-preds)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3afd18a8",
   "metadata": {},
   "source": [
    "#### Max depth = 15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "68207b59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = DecisionTree(max_depth=15).fit(X, y,type_of_node=DecisionRegressionNode).predict(X)\n",
    "avg_squared_difference(y-preds)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64cc7783",
   "metadata": {},
   "source": [
    "# Bias-Variance Decomposition\n",
    "\n",
    "\n",
    "\n",
    "Increasing max depth in Decision Trees should ring bells for overfitting, i.e,. __increasing the variance part of bias-variance decomposition__.\n",
    "\n",
    "\n",
    "1- Predictions of decision trees are neither __smooth__ nor __continuous__, but piecewise constant approximations\n",
    "2. There are concepts that are hard to learn because decision trees do not express them easily, such as XOR, parity or multiplexer problems"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28c57544",
   "metadata": {},
   "source": [
    "# Bagging (Bootstraph Aggregating)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8deeca9",
   "metadata": {},
   "source": [
    "### Recall The Bias-Variance Decomposition\n",
    "\n",
    "$$\n",
    "\\begin{equation*}\n",
    "    \\underbrace{\\mathbb{E}[(h_D(x) - y)^2]}_\\mathrm{Error} = \\underbrace{\\mathbb{E}[(h_D(x)-\\bar{h}(x))^2]}_\\mathrm{Variance} + \\underbrace{\\mathbb{E}[(\\bar{h}(x)-\\bar{y}(x))^2]}_\\mathrm{Bias} + \\underbrace{\\mathbb{E}[(\\bar{y}(x)-y(x))^2]}_\\mathrm{Noise}\n",
    "\\end{equation*}\n",
    "$$\n",
    "\n",
    "Our goal is to reduce the variance term: $\\mathbb{E}[(h_D(x)-\\bar{h}(x))^2]$. Hence, $ h_D \\to \\bar{h}$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13382d9e",
   "metadata": {},
   "source": [
    "### Weak law of large numbers\n",
    "\n",
    "the weak law of large numbers says (roughly) for i.i.d. random variables $x_i$ with mean  $\\bar{x}$\n",
    "$$ \\frac{1}{m}\\sum_{i = 1}^{m}x_i \\rightarrow \\bar{x} \\textrm{ as }  m\\rightarrow \\infty$$\n",
    "\n",
    "Assume that we have $\\mathcal D_i, \\dots \\mathcal D_n$ drawn from $\\mathbb P ^n(\\mathcal X, \\mathcal Y)$\n",
    "\n",
    "$$ \\hat{h} = \\frac{1}{m}\\sum_{i = 1}^m h_{D_i} \\to \\bar{h} \\qquad as\\  m \\to \\infty $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a2acf9b",
   "metadata": {},
   "source": [
    "### Prediction: Averaging m classifiers\n",
    "\n",
    "\n",
    "$$ \\hat{h}_D(x) = \\frac{1}{m}\\sum_{i = 1}^{m}h_{D_i}(x) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a112bd2a",
   "metadata": {},
   "source": [
    "## Creating bootstraph dataset\n",
    "\n",
    "Create them by drawing uniformly with replacement from the origially given set $\\mathcal D$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0454bd46",
   "metadata": {},
   "source": [
    "\n",
    "1. Reduces variance, so has a strong beneficial effect on high variance classifiers.\n",
    "2. As the prediction is an average of many classifiers, you obtain a mean score and variance.\n",
    "3. Bagging provides an unbiased estimate of the test error, which we refer to as the __out-of-bag error__. \n",
    "\n",
    "\n",
    "\n",
    "### Out-of-Bag Error\n",
    "$$ \\forall (\\mathbf{x}_i,y_i)\\in D \\\\ \\tilde \n",
    "S_i=\\{k| (\\mathbf{x}_i,y_i)\\notin D_k\\}$$\n",
    "\n",
    "\n",
    "$S_i$ is a set of all the training sets $D_k$ not containing $(x_k ,y_k)$\n",
    "\n",
    "$$ \\\\\n",
    "h_i(\\mathbf{x})=\\frac{1}{|S_i|}\\sum_{k\\in S_i}h_k(\\mathbf{x}). $$\n",
    "\n",
    "$$ \\\\ \\epsilon_\\mathrm{OOB}=\\frac{1}{n}\\sum_{(\\mathbf{x}_i, y_i) \\in D}l(\\tilde h_i(\\mathbf{x_i}),y_i) $$\n",
    "The idea is that each training point was not picked and all the data sets Dk. If we average the classifiers hk of all such data sets, we obtain a classifier (with a slightly smaller m) that was not trained on (xi,yi) ever and it is therefore equivalent to a test sample. If we compute the error of all these classifiers, we obtain an estimate of the true test error. The beauty is that we can do this without reducing the training set. We just run bagging as it is intended and obtain this so called out-of-bag error for free\n",
    "\n",
    "### Feature Selection\n",
    "\n",
    "1. Train Random Forest.\n",
    "2. Look at whenever you split a feature how much impurity goes down.\n",
    "3. Rank those splits.\n",
    "4. You got the most important features."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11b3fa85",
   "metadata": {},
   "source": [
    "# Random Forest\n",
    "\n",
    "https://link.springer.com/article/10.1023/A:1010933404324"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "457fa496",
   "metadata": {},
   "source": [
    "1. Create m datasest with replacement\n",
    "2. Train $m$ decision tree. Perform each split by considering only $k=\\sqrt{d}$ randomly selected features\n",
    "3. Final classifier : $ h(\\mathbf{x})=\\frac{1}{m}\\sum_{j=1}^m h_j(\\mathbf{x})$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b4fe96d",
   "metadata": {},
   "source": [
    "Set m as big as you can store in your machine."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d88a8473",
   "metadata": {},
   "source": [
    "## [Kilian Weinberger](https://www.youtube.com/watch?v=4EOCQJgqAOY&list=PLl8OlHZGYOQ7bkVbuRthEsaLr7bONzbXS&index=31) $$ \\text{Most of the time RF is the second best algorithm}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d994f465",
   "metadata": {},
   "source": [
    "# TODOs\n",
    "Intread key messages from scikit learn blogs\n",
    "\n",
    "1. https://scikit-learn.org/stable/auto_examples/release_highlights/plot_release_highlights_0_24_0.html#individual-conditional-expectation-plots\n",
    "\n",
    "2. https://scikit-learn.org/stable/auto_examples/calibration/plot_compare_calibration.html#sphx-glr-auto-examples-calibration-plot-compare-calibration-py\n",
    "\n",
    "3. https://scikit-learn.org/stable/auto_examples/ensemble/plot_ensemble_oob.html#sphx-glr-auto-examples-ensemble-plot-ensemble-oob-py\n",
    "\n",
    "4. https://scikit-learn.org/stable/auto_examples/inspection/plot_permutation_importance_multicollinear.html#sphx-glr-auto-examples-inspection-plot-permutation-importance-multicollinear-py\n",
    "\n",
    "5. https://scikit-learn.org/stable/common_pitfalls.html#common-pitfalls"
   ]
  }
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