1.Machine_Learning/12.Boosting.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f76fb709",
   "metadata": {},
   "source": [
    "# Boosting\n",
    "\n",
    "\n",
    "__Scenario__: Hypothesis class $\\mathcal H$, whose set of classifiers has large bias and the training error is high.\n",
    "\n",
    "__Famous question__: In his machine learning class project in 1988 Michael Kearns famously asked the question: Can weak learners (H) be combined to generate a strong learner with low bias?\n",
    "\n",
    "__Famous answer:__ Yes! (Robert Schapire in 1990)\n",
    "\n",
    "__Solution:__ Create ensemble classifier $H_T(\\vec x) = \\sum_{t = 1}^{T}\\alpha_t h_t(\\vec{x})$. \n",
    "\n",
    "This ensemble classifier is built in an iterative fashion. \n",
    "1. In iteration t we add the classifier $\\alpha_t h_t (\\vec x)$ to the ensemble. \n",
    "2. At test time we evaluate all classifier and return the weighted sum.\n",
    "\n",
    "The process of constructing such an ensemble in a stage-wise fashion is very similar to gradient descent. \n",
    "\n",
    "However, instead of updating the model parameters in each iteration, we add functions to our ensemble.\n",
    "\n",
    "Let $\\ell$ denote a (convex and differentiable) loss function. With a little abuse of notation we write\n",
    "\n",
    "\n",
    "\\begin{equation}\n",
    "  \\ell (H)=\\frac{1}{n}\\sum_{i=1}^n \\ell (H(\\mathbf{x}_i),y_i).\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0cc96dc5",
   "metadata": {},
   "source": [
    "Assume we have already finished t iterations and already have an ensemble classifier $H_t (\\vec x)$. Now in iteration t+1 we want to add one more weak learner $h_{t+1}to the ensemble. To this end we search for the weak learner that minimizes the loss the most,\n",
    "\n",
    "\\begin{equation}\n",
    "  h_{t+1} = \\textrm{argmin}_{h \\in \\mathbb{H}}\\ell(H_t + \\alpha h_t).\n",
    "\\end{equation}\n",
    "Once $h_{t+1}$ has been found, we add it to our ensemble, i.e,. $H_{t+1} := H_t + \\alpha h_t $"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f037dfc8",
   "metadata": {},
   "source": [
    "# How can we find such $h \\in \\mathcal H$\n",
    "\n",
    "Use gradient descent in function space. In function space, inner product can be defined as \n",
    "\n",
    "\n",
    "$$ < h,g >=\\int\\limits_x h(x)g(x)dx $$ \n",
    "\n",
    "\n",
    "Since we only have training set, we define it as\n",
    "$$ <h,g> = \\sum_i ^n h(x_i) g(x_i) $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab082f03",
   "metadata": {},
   "source": [
    "# Gradient descent in functional space\n",
    "\n",
    "Given $\\mathcal H$, we wan to find the step-size $\\alpha$ and $h$ to minimize the loss $\\ell(H + \\alpha h).$ Use [Taylor Approximation](https://en.wikipedia.org/wiki/Taylor_series) on $\\ell (\\mathcal H + \\alpha h)$.\n",
    "\n",
    "$$ \\ell (\\mathcal H + \\alpha h) \\approx \\ell(H) + \\alpha <\\Delta \\ell(H), h>$$\n",
    "\n",
    "This approximation (of $\\ell$ as a linear function only holds within a small region around $\\ell (H)$, i.e., as long as $\\alpha$ is small."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d7f4eee",
   "metadata": {},
   "source": [
    "\n",
    "### 1. $$ \\begin{equation}\n",
    "\\textrm{argmin}_{h\\in H}\\ell(H+\\alpha h) \\approx \\textrm{argmin}_{h\\in H} \\; \\ell(H) + \\big< \\nabla \\frac{\\partial \\ell}{\\partial H},\\alpha h \\big>\n",
    "\\end{equation}$$\n",
    "\n",
    "The first-order Taylor approximation says that\n",
    "$$ \\ell(a) \\approx \\ell(a) + (b-a) \\frac{\\partial \\ell(a)}{\\partial a}$$\n",
    "+ If $\\alpha$ is small, this appproximation holds. \n",
    "\n",
    "+ The second term denotes the inner product of two functions.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "446ef338",
   "metadata": {},
   "source": [
    "\n",
    "### 2. $$ \\approx \\textrm{argmin}_{h\\in H} \\big< \\nabla \\frac{\\partial \\ell}{\\partial H},\\alpha h \\big>\n",
    "$$\n",
    "\n",
    "+ $\\ell(H)$ dropts as it is not a function of $h$. We need to know\n",
    "__what is the inner product between a function and derivative of a loss function w.r.t. another function__.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aff7850b",
   "metadata": {},
   "source": [
    "### 3 .$$ \\begin{equation}\n",
    "\\textrm{argmin}_{h\\in H}\\ell(H+\\alpha h) \\approx \\textrm{argmin}_{h \\in \\mathbb{H}}\\sum_{i = 1}^{n}\\frac{\\partial \\ell}{\\partial [H(\\mathbf{x}_i)]}h(\\mathbf{x}_i) \\end{equation}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7f8b801",
   "metadata": {},
   "source": [
    "We can write \n",
    "$$ \\ell(H) = \\sum_{i = 1}^{n}\\ell(H(\\mathbf{x}_i)) = \\ell(H(x_1), \\dots , H(x_n)) $$\n",
    "\n",
    "(each prediction is an input to the loss function) $ \\frac{\\partial \\ell}{\\partial H}(\\mathbf{x}_i) = \\frac{\\partial \\ell}{\\partial [H(\\mathbf{x}_i)]} $"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16381720",
   "metadata": {},
   "source": [
    "So we can do boosting if we have an algorithm $\\mathcal A$ to solve\n",
    "\n",
    "$$ h_{t+1} = \\textrm{argmin}_{h \\in \\mathbb{H}} \\sum_{i = 1}^{n} \\underbrace{\\frac{\\partial \\ell}{\\partial [H(\\mathbf{x}_i)]}}_{r_i} h(x) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e224bc4",
   "metadata": {},
   "source": [
    "We need a function $\\mathbb{A}(\\{(\\mathbf{x}_1,r_1),\\dots,(\\mathbf{x}_n,r_n)\\})=\\textrm{argmin}_{h \\in \\mathbb{H}} \\sum_{i = 1}^{n} r_i h(\\mathbf{x}_i)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b44fb321",
   "metadata": {},
   "source": [
    "# Gradient Boosting Regression Tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "fdf60003",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from sklearn.datasets import load_iris,load_diabetes\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from typing import Optional\n",
    "import matplotlib as mpl\n",
    "import copy\n",
    "\n",
    "np.random.seed(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "61edde2e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def avg_squared_difference(y):\n",
    "    return np.mean((y - y.mean()) ** 2)\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",
    "        if isinstance(X,pd.DataFrame) is False:\n",
    "            X=pd.DataFrame(X)\n",
    "        features = list(X.columns)\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",
    "        if isinstance(X, pd.DataFrame) is False:\n",
    "            X = pd.DataFrame(X)\n",
    "            y = pd.Series(y)\n",
    "        features = list(X.columns)\n",
    "\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",
    "\n",
    "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=DecisionRegressionNode):\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",
    "        if isinstance(X, pd.DataFrame) is False:\n",
    "            X = pd.DataFrame(X)\n",
    "\n",
    "        preds = []\n",
    "        for index, x in X.iterrows():\n",
    "            preds.append(self.root.predict(x))\n",
    "        return np.array(preds).flatten()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22673c4e",
   "metadata": {},
   "source": [
    "# Gradient Boosted Decision Tree Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "beab9f5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_bossting_trees_with_fixed_alphas(X,Y,max_depth=1,alpha=.1,n=50):\n",
    "    predf=0 \n",
    "    inputs,outputs=copy.deepcopy(X),copy.deepcopy(Y)\n",
    "    print_count=n//10\n",
    "    for i in range(1,n+1):\n",
    "        # Compute Loss based on original outputs and current predictions\n",
    "        ei = Y - predf\n",
    "        # Update outputs according to loss incurred by our previous prediction\n",
    "        outputs = ei\n",
    "        \n",
    "        # Train mode\n",
    "        reg = DecisionTree(max_depth=max_depth).fit(inputs, outputs,type_of_node=DecisionRegressionNode)\n",
    "\n",
    "        # Update prediction \n",
    "        predf += alpha*reg.predict(inputs)\n",
    "        \n",
    "        if i%print_count==0 or i ==n:\n",
    "            print(f'Epoch: {i}:\\tAvg. Squared Loss:{np.mean((Y-predf)**2)}')\n",
    "    return predf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7420a7b9",
   "metadata": {},
   "outputs": [],
   "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "33ac8bee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred=DecisionTree(max_depth=1).fit(copy.deepcopy(X), copy.deepcopy(Y),type_of_node=DecisionRegressionNode).predict(copy.deepcopy(X))\n",
    "plt.scatter(X,Y)\n",
    "plt.scatter(X,pred)\n",
    "plt.title(f'DT depth 1 Loss: {np.mean((Y-pred)**2):.6f}')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0986dd34",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 100:\tAvg. Squared Loss:0.11559822829282229\n",
      "Epoch: 200:\tAvg. Squared Loss:0.049495112214900355\n",
      "Epoch: 300:\tAvg. Squared Loss:0.040638638215682275\n",
      "Epoch: 400:\tAvg. Squared Loss:0.03945205070887902\n",
      "Epoch: 500:\tAvg. Squared Loss:0.039293072100526995\n",
      "Epoch: 600:\tAvg. Squared Loss:0.039271772198270626\n",
      "Epoch: 700:\tAvg. Squared Loss:0.039268918444291805\n",
      "Epoch: 800:\tAvg. Squared Loss:0.039268536099261606\n",
      "Epoch: 900:\tAvg. Squared Loss:0.03926848487279878\n",
      "Epoch: 1000:\tAvg. Squared Loss:0.039268478009493936\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred=gradient_bossting_trees_with_fixed_alphas(X,Y,alpha=.01,n=1000)\n",
    "plt.scatter(X,Y)\n",
    "plt.scatter(X,pred)\n",
    "plt.title(f'DT depth 1 Loss: {np.mean((Y-pred)**2):.6f}')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e61f3582",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RISIjI8Wdd94pfvzxR4c4AGLMmDEOx7du3SpGjBghNBqNiI6OFrNmzRInT550iPP2c7beU2c/LTcqLC4uFuPHjxc6nU6EhISIiIgIMXz4cLFixQq7je6EEOLw4cNi9OjRIjo6WoSGhoprr71WPPXUU+LMmTN2ce6uDaBNGxgSuSMJ4cMlFUQUMGvXrsX999+PPXv2+KwXhYhIDjjnhYiIiGSFyQsRERHJCoeNiIiISFbY80JERESywuSFiIiIZIXJCxEREcmK4japM5vNqKyshFarDciDzYiIiKj9hBBobGxEfHy8x4d4Ki55qaysRJ8+fTq6GkRERHQFjh8/jt69e7uNUVzyYn3uy/HjxxEZGenTso1GI7Zu3YqMjAyEhIT4tOxgoPT2AcpvI9snf0pvo9LbByi/jf5qX0NDA/r06ePw/DZnFJe8WIeKIiMj/ZK8REREIDIyUrG/kEpuH6D8NrJ98qf0Niq9fYDy2+jv9nkz5YMTdomIiEhWmLwQERGRrDB5ISIiIllh8kJERESywuSFiIiIZIXJCxEREckKkxciIiKSFSYvREREJCtMXoiIiHzIZBYAgM0HDCj+qcb2mnxHcTvsEhERdZTCMgOe3/QdFg4EHvvgWzSbJOijNMjNSkJmsr6jq6cY7HkhIiLygcIyA7Lz96GqocnueFV9E7Lz96GwzNBBNbP0BhX/VINP9p9QRG8Qe16IiIjayWQWyCsoh7OUQACQAOQVlCM9SQe1yvOze3ypsMyAvIJyGOovJ1Vy7w1izwsREVE7lVTU2iUHrQkAhvomlFTUBq5SuNwb1LpuwdAb1B5MXoiIiNqputF14nIlcb7gqTcIsPQGyXEIickLERFRO8VqNT6N84Vg7Q3yBSYvRERE7ZSaGA19lAauZrNIsMwzSU2MDlidgrE3yFeYvBAREbWTWiUhNysJABwSGOvr3KykgE7WDcbeIF9h8kJEROQDmcl6rJwxFHGR9smALkqDlTOGBnxlTzD2BvkKl0oTERH5SGayHmP798SWwk/x4j03IDaqK1ITowO+PBq43BuUnb8PEmA3cbejeoN8hT0vREREPmRNBiZdr0dav54dmhxYe4N0UcHRG+Qr7HkhIiJSsMxkPdKTdCipqEV1YxNitZoO6w3yFSYvREREAWYyi4AmE2qVhLR+Pf1WfqD5ddho586dyMrKQnx8PCRJwscff+zxnB07dmDYsGHQaDS45pprsGrVKn9WkYiIKKAKywz41dLP8Zs3duMP/9iP37yxG79a+vkV7XartGcWecuvPS9nz57FjTfeiPvvvx/33HOPx/iKigpMmjQJc+fORX5+Pr788kvMnz8fV111lVfnExERBTPrdv0SzBihOoRYnEY1umNP/UBk5++zn4diNgFHdwFnTgLd4oCEkYBKbVfWsxsPoM+Zb2zlHO92I/405XrHuSweympbTLHl70eLgWtGOcYEgF+Tl4kTJ2LixIlex69atQpXX301li9fDgAYNGgQ9u7di5deeonJCxERyZp1u/4MVQlyQ9YhXrq8s22liMYzxlnIK9BYHt54qAAoXAw0VF4uIDIeyFwKJE1BYZkBH29YhfdD1iE+tEU5zdF4ZsMsYPq8ywlM+Ua3ZbU55kwtcOPrwIapQLdo+5gACao5L8XFxcjIyLA7NmHCBKxevRpGoxEhISEO5zQ3N6O5udn2uqGhAQBgNBphNBp9Wj9reb4uN1govX2A8tvI9smf0tvYlvaZLl7ED3v/hfOnDQjvrkf/lPFQd2n1tWU2AcdLgLPVQNdYoE+q894CX8R4GWe8YPlOMpZ9Amgvx5RU1GLouX9jWZhlOoRRurwCqKc4h7+FrcLCcyoc3l6F/v/+IwABqFqsEjpTB/zzv2C6S+CLgnL8zU05z2zUYGz/P0L9/afAR79zWRbuujTM1IYY46UYo0pjHzNwkuPn1QZt+Z2XhBABGSCTJAkfffQR7rzzTpcx1113HebMmYMnnnjCdmzXrl0YNWoUKisrodc7LulasmQJ8vLyHI5v2LABERERPqk7ERER+de5c+cwffp01NfXIzIy0m1sUPW8AJYkpyVrbtX6uNXjjz+OhQsX2l43NDSgT58+yMjI8Nj4tjIajSgqKkJ6errTXiC5U3r7AOW3ke2TP6W30Zv2ffuvDUj+6jEAQMsFONa5qGU3v4gbenUHPvodBITdDrICkuX1XX+3HLD2KNi5dIa3MQMnAYc2e12WURWGoutfQfqBRxBibrLF/HJ9NnofWOG0zf5QnvQokspf9nm5RpWmVfsumf4+kJB2xeVaR068EVTJi06nQ1VVld2x6upqdOnSBT17Ol/iFRYWhrCwMIfjISEhfvsP359lBwOltw9QfhvZPvlTehtdtc908SJ6785DiGiyJC6tcgWzAHrtXoIuWg1gPu9063sBCdLWHEvOYD7vogYS4E1M0ePAoIlAUU4byrJUOsTc1OLLXULf79dAMgfuIYixxl/skwsfs28fgPPVQDt+Z9vy+x5UyUtaWhoKCgrsjm3duhUpKSmK/o+YiIgsDn21BYNR4/h0w0tUEqBDLdDougwJAmisdB0AAN7GNJwA9rxhP5H1CsuSztd5iPGt2IRBwOEAXrBbXMAu5dd9Xs6cOYP9+/dj//79ACxLoffv349jx44BsAz5zJo1yxY/b948HD16FAsXLsTBgwfx5ptvYvXq1Vi0aJE/q0lEREHifN2Jjq6Co7ojvisrvEerga7LBCQIbTxOoidcbddiFkAVonFeE+c25ny4DurUuZYVQ+4ezaiNByLj3dbJGuO2nMhelqXVAeLX5GXv3r0YMmQIhgwZAgBYuHAhhgwZgqeffhoAYDAYbIkMACQmJmLz5s3Yvn07brrpJjz77LN45ZVXuEyaiKiTCO/Rq6Or4MDUva/vCrs5+9JDElvN77w0V+f7oU/h6QszAcAhObG+zr0wC8duzoUkSTC3Kt4MyxzR8Ky/AF1CLcuYATgmHpdeT1yK0sE5EEI4vZ4QAqXJOUDmUohL5be+ngCAzBcCut+LX5OXsWPHQgjh8LN27VoAwNq1a7F9+3a7c8aMGYN9+/ahubkZFRUVmDdvnj+rSEREQWTgzRM89jwYEA2DiHYbUymiUR9ylfveCU2cVz0KJT3vRqUX12uO0HksC6MXAfeugxRpv3pWiowH7l2HQz3GYos5FdnGBahCtF1MFXoi27gAW8ypONRjLKR711nOsyunF6R7113edyVpCnDvOqDV9XDpeqaBWZi/r7fL6803LsD8fb2x+eJwZF/4A6pEqxjRE9kX/oBC83AX7faPoJrzQkREnZu6SxdUpuXiql2PwCycrzb6euBiFHxrwMqQ5S5j8oyzoFV3wYt4yXXMxdl4LisZqvdnQ8D+X/NmWNIQKfMFVJ83Y61xlsfrPZiciNSSBXDZy2HtnUiaAgyc7HQ329ifagAAW8ypKGpOQWqLXXhLzANhvlTLWK0G6DcFUqtyJGe74rq5XslPNTDUN8EAN9erb8JTn5Sh1pyKrc0pGBnyPaYCuN/4GHYZr4OACt8UlFs21wvQwx6ZvBARUVAZMmE2SgHEF+chDjW249VSTxjScjExfRaeq/gc8xuBp0PWIR6Xd5itQk88Y5yJPeGjUHvWiEbVAstutq1i8owzsaX5JugN1+HghT9Yymmx422VsJRzp3k4YrWhtt4Ql2WZUzFnwAigbzSw5Wn7BkXGWxKXlrvQqtRA4i0ObU9NjIY+SoOq+iaYocJuc5Ld+xIAXZTlQY7uynHgIq668fJqIWfXs6o9e8EWs8c8AFNhwh7zAJgvJWaG+iaUVNQG7OGPTF6IiCjoDJkwG6bxv8V3X23B+boTCO/RCwNvngDdpR12c7OSkJ3fhKLmFAxv+YygS70FD9zUC6u/POKxB2PNlxU4falHoXWMtUdhx3+Pgz5Kg631zssSUEFvTShUU4B+GUDhFuCO14BIF88IckGtki61bR9arxS39mnkZiX5rIcjVqvxHOSllomQvzF5ISKioKTu0gWDR012+l5msh4rZwxFXkE5dtdf7i3QR2mQm5WEqPBQrP7yCAD3PQqnzxvdxhjqm/D10TpbQiFaxTlNKKyJStIdV7TvScu2GeovJwS6S21zeOhiO7Ts6XE2pUcC0KNrCGrPet6635eJkCdMXoiISJYyk/VIT9KhpKIW1Y1NiNVaej/UKgkms/D4pRwVHmJLXtypbmzCHTf1ClhCAbhvmy9509Pzf+9IxrObDrr9LO2GsgKAyQsREcmWWiU5nWfhzZfy/aP64uXPfvB4DWuPQqASCitXbfM1b3p6VCrJ9lm25I+hLG8weSEiIkXy9KWcnqTDP/Ycb1OPQqASikDzlJi1/Cxrz1x+TIK/ep48YfJCRESK5elLOZCTY4Odp8TM+lnu/rEapw7uxpuzh2PEtbEd8vn4dZM6IiKijmb9Ur7jpl5I69fT7svW2qOgi7KfbKqL0mDljKEB71EIdmqVZOuJ8ueQmSfseSEiooAzmQX2/lQTkLkjngR6Lgu1H5MXIiIKuAnLd+JoXbPttb6D5k5YKXUui1Jx2IiIiALms4MnAQBVDfYbmlXVNyE7fx8KywwdUS2SGSYvREQUECazwAufHnL6nnWybF5BOUyunoBIdAmTFyIiCoiSilqHHpeWBC4/I4fIHSYvREQUEN4++yaQz8gheWLyQkREAeHts28C+YwckicmL0REFBCpidHQRbpOTCTg8tOZidxg8kJERAGhVknImTgQAILmGTkkT0xeiIgoYG4bFAcAiIvkjrZ05bhJHRERBdyWBaNR+ksjd7SlK8LkhYiIAo472lJ7cNiIiIiIZIXJCxEREckKkxciIiKSFSYvREREJCtMXoiIiEhWuNqIiIi8YjILlFTUul3e7E0MUXsxeSEiIo8KywzIKyiHof7yQxP1URrkZiXZNpbzJobIFzhsREREbhWWGZCdv88uKQGAqvomZOfvQ2GZwasYIl9hzwsREblkMgvkFZRDOHlPwPJMoiUbvwMguY3JKyhHepLOjzWlzoQ9L0RE5FJJRa1Db0pLAkBVQzOqGtzHGOqbUFJR6/sKUqfE5IWIiFyqbnSdlHRkWdS5MXkhIiKXYrUaz0EdUBZ1bkxeiIjIpdTEaOijNHC12FkCoIsMgy7SfYw+yrJsmsgXmLwQEZFLapWE3KwkAHBITqyvl0wZjCVT3MfkZiVxvxfyGa42IiKSK7MJOLoLOHMS6BYHJIwEVOori3MTk5msx8oZQ/HsxgPoc+YbxOI0qtEdx7vdiD9Nud62h4s3MXbXq9jtue5ETjB5ISKSo/KNQOFioKHy8rHIeCBzKZA0pW1xXsRkqvZggmYxpAuXY4QmHpJqKQDvY2xWjADqK9zXncgFDhsREclN+UbgvVn2yQYANBgsx8s3eh/XhhipVYzU1hgAOLTZ8mdjq03rWscRucGeFyIiOTGbLL0k7raEK8wBrsv0HPfp4kuTUgIQY63TZ7nANXnu4wZO5hASucXkhYhITo7ucuwlsSOAhhPAnjc8xzW6e9/HMdY6te5xcRZ3dBeQeIuHMqkz47AREZGcnDnpXVzdEb9W44p4Wydv20idFpMXIiI56RbnXVyPvn6txhXxtk7etpE6LSYvRERykjDSsjLH3ZZwkb2A4XM9xgltPE6iJ8zOpqoAMAugCtEQWg/X08Z7Xyet3kVMi7iEkW5iiJi8EBHJi0ptWVIMwOWWcJkvAF1CPcZ9P/QpPH1hJgA4JDDW17kXZuH7oU+5v97Epd7X6bY8z3GcrEseMHkhIpKbpCnAveuAyFa9GJHxluPWvVI8xB3qMRZbzKnINi5AFey37q9CT2QbF2CLORWHeoz1fD1v6zRwkuVPrc59HJEbXG1ERCRHSVMsS4o97ZzrJi72pxoAwBZzKoqaU5CqOmTbGbfEPBDmS/++jdVqgH5eXM/bOgHA/N1A5R7usEtXhMkLEZFcqdTeLSl2EWd96GJVfRPMUGG3OcnufQmAruUDFb25XjvrROQNDhsREXVS3jx0kQ9UpGDE5IWIqBOzPnRRF6WxO66L0mDljKGOD1QkCgIcNiIi6uQyk/VIT9KhpKIW1Y1NiNVahorY40LBiskLEZHCmczCY2KiVklI69ezg2pI1DZMXoiIFKywzIC8gnIY6ptsx/RRGuRmJXFIiGSLc16IiBSqsMyA7Px9dokLAFTVNyE7fx8Ky9w9JJEoeDF5ISJSIJNZIK+gHM52/rceyysoh8nVswGIghiTFyIiBSqpqHXocWlJADDUN6GkojZwlSLyESYvREQKVN3oOnG5kjiiYMLkhYhIgWK1Gs9BbYgjCiZMXoiIFMi69b+rnVokWFYd2bb+J5IRJi9ERDJlMgsU/1SDT/afQPFPNXaTb7n1PykZ93khIpIhb/ZvsW793zpOx31eSOaYvBARyYx1/5bWi5yt+7e0fCYRt/4nJWLyQkQkI572b5Fg2b8lPUlnS1C49T8pDee8EBHJCPdvIWLyQkQkK9y/hYjJCxGRrHD/FiImL0REssL9W4gClLysWLECiYmJ0Gg0GDZsGL744guXsdu3b4ckSQ4/hw4dCkRViYiCGvdvIQpA8vLuu+9iwYIFePLJJ1FaWopbbrkFEydOxLFjx9yed/jwYRgMBttP//79/V1VIqKg4W4DOuv+Lboo+6EhXZTGbpk0kVL5fan0smXL8OCDD+Khhx4CACxfvhxbtmzBypUr8fzzz7s8LzY2Ft27d/d39YiIgtKE5TtxtK7Z9trZBnTcv4U6K78mLxcuXMDXX3+NnJwcu+MZGRnYtWuX23OHDBmCpqYmJCUl4amnnsK4ceOcxjU3N6O5+fJ/4A0NDQAAo9EIo9HYzhbYs5bn63KDhdLbByi/jWyf/BV9VwkAqDtzHmHqy4lI3ZnzWPDO13h52k24bVCc7XjK1ZEAIgEAZtNFmE0BrW6bdYZ7qPQ2+qt9bSlPEkI42+vIJyorK9GrVy98+eWXGDlypO34n//8Z7z11ls4fPiwwzmHDx/Gzp07MWzYMDQ3N2P9+vVYtWoVtm/fjtGjRzvEL1myBHl5eQ7HN2zYgIiICN82iIiIiPzi3LlzmD59Ourr6xEZGek2NiA77EqSfTemEMLhmNWAAQMwYMAA2+u0tDQcP34cL730ktPk5fHHH8fChQttrxsaGtCnTx9kZGR4bHxbGY1GFBUVIT09HSEhIT4tOxgovX2A8tvI9slbSUUtsteX4NkUM/60V4Vms/P/T745e7hsVxMp/R4Cym+jv9pnHTnxhl+Tl5iYGKjValRVVdkdr66uRlxcnIuzHI0YMQL5+flO3wsLC0NYWJjD8ZCQEL/90viz7GCg9PYBym8j2ydPp85dtCUszWYJzSbnycupcxdl336l3sOWlN5GX7evLWX5dbVRaGgohg0bhqKiIrvjRUVFdsNInpSWlkKv5+x5IlI2bkBH5B2/DxstXLgQM2fOREpKCtLS0vD666/j2LFjmDdvHgDLsM+JEyewbt06AJbVSH379sXgwYNx4cIF5Ofn44MPPsAHH3zg76oSEXWo1MRo6CI1AM46fV+CZTm0XIeMiHzF78nLtGnTUFNTg2eeeQYGgwHJycnYvHkzEhISAAAGg8Fuz5cLFy5g0aJFOHHiBMLDwzF48GBs2rQJkyZN8ndViYg6lFolIWfiQFyo+Job0BG5EZAJu/Pnz8f8+fOdvrd27Vq714899hgee+yxANSKiCj43DYoDpsrgLhIjd0+L7pW+7wQdWYBSV6IiKhttiwYjdJfGrkBHZETTF6IiIKQWiUhrV/Pjq4GUVDiU6WJiIhIVtjzQkQUYCaz4DOJiNqByQsRUQAVlhmQV1AOQ32T7Vjrhy4SkXscNiIi8iGTWaD4pxp8sv8Ein+qgcl8+fFxhWUGZOfvs0tcAKCqvgnZ+ftQWGYIdHWJZIk9L0REPuKuVyU9SYe8gnI4exKugGUfl7yCcoztf0ugqkskW0xeiIh8wNqr0jo5sfaqLLitv0OPS0sCgKG+CV8frfNrPYmUgMNGRETtZDILt70qALDmyyNelXXqTLPnIKJOjskLEVE7lVTUeuxVOX3e6FVZMd3CfFQrIuVi8kJE1E7Vja4Tl5a6h4c4PLPISoJlfsywhB4+qxeRUjF5ISJqp1itxqu4+0clAgAfukjUTkxeiIjaKTUxGvoojcdelYdvvRYrZwyFLso+2dFFabByxlDu80LkJa42IiJqJ7VKQm5WErLz90EC7Cbutu5VyUzWIz1Jxx12idqByQsRkQ9kJuuxcsZQh31edE52z+VDF4nah8kLEZGPsFeFKDCYvBAR+RB7VYj8jxN2iYiISFaYvBAREZGsMHkhIiIiWWHyQkRERLLC5IWIiIhkhckLERERyQqXShMReclkFtzDhSgIMHkhIvkym4Cju4AzJ4FucUDCSECl9ktMYZkBz248gD5nvkEsTqMa3XG8243405Tr7Z9J5Ms6Vex2H0PUSTF5ISJ5Kt8IFC4GGiovH4uMBzKXAklTfBpTWGbAxxtW4f2QdYgPrbWFVTZH45kNs4Dp8ywJjK/qBAArRgD1Fe5jiDopJi9EJD+HNgMfzIb9IxABNBiA92YB966zvH5vVrtjTAOzsP3jN7EiZLlDNXSoxYqQ5Xji41CkS8lQv++DOpkuvddocB3DBIY6OSYvRCQ/n+XCIQEALh2TgE8XX3qccztjCnNQoh6OR4z/DwDQenqLSgLMAnjE+P9wcVMo1L6okyoMuCbPbZ0wcDKHkKhTY/JCRPLTulfCjgAaK92834aYhhPodmAN4qVal1EqCYhHLXDOB9drrARUGo91wtFdQOItHsojUi4ulSYiciPG6Cnp6ABnTnZ0DYg6FJMXIiI3YhMGdXQVHHWL6+gaEHUoJi9EJD9aPS5NIHFCArTxltU57Y2J7AV16lycD9fB7GyqCixzXs5r4nxzPW38pba5YqkTEka6iSFSPiYvRCQ/t1kntLZOBC69nrjUsqy4vTGZLwBdQhGe9RdIkgRzqygzAEmSED7lJd9cb+JSz23LfIGTdanTY/JCRPIzcJJlyXBkq16KyPjLS4mTpvgmBgCSpkC6dx2kyHi7MCmyFyRfX2/gJMsxrc59nYg6Ma42IiJ5SppiWTLsbqdaX8VcipNaxUn+vN783UDlHu6wS+QEkxciki+V2vOSYV/FBPp63taJqBPisBERERHJCpMXIiIikhUmL0RERCQrTF6IiIhIVjhhl4g6PZNZoKSiFtWNTYjVapCaGA1166cwElHQYPJCRJ1aYZkBeQXlMNQ32Y7pozTIzUpCZrK73W6JqKNw2IiIOq3CMgOy8/fZJS4AUFXfhOz8fSgsc/f0aiLqKExeiKhTMpkF8grK4eyRRdZjeQXlMLl6qBERdRgmL0TUKZVU1Dr0uLQkABjqm1BSURu4ShGRV5i8EFGnVN3oOnG5kjgiChxO2CUiRXO1kihWq/HqfG/jiChwmLwQkWK5W0mUnqSDPkqDqvomp/NeJAC6KEuyQ0TBhcNGRKRInlYSFZVXITcrCYAlUWnJ+jo3K4n7vRAFISYvRKQ43q4kSk/SYeWModBF2Q8N6aI0WDljKPd5IQpSHDYiIsVpy0qizGQ90pN03GGXSEaYvBCR4rR1JZFaJSGtX09/VomIfIjDRkSkOFxJRKRsTF6ISHFSE6Ohj9I4TMS1kmBZdcSVRETyxOSFiBRHrZK4kohIwZi8EJEiZSbruZKISKE4YZeIFIsriYiUickLESkaVxIRKQ+HjYiIiEhWmLwQERGRrDB5ISIiIllh8kJERESywuSFiIiIZIWrjYgoKJnMwmGJszcxXAZNpHxMXogo6BSWGZBXUG73ZGh9lAZPTx7gMSY3K4kb0BEpXECGjVasWIHExERoNBoMGzYMX3zxhdv4HTt2YNiwYdBoNLjmmmuwatWqQFSTiIJAYZkB2fn77JISAKiqb8Kj7+4HAHx28KTLmOz8fSgsMwSqukTUAfyevLz77rtYsGABnnzySZSWluKWW27BxIkTcezYMafxFRUVmDRpEm655RaUlpbiiSeewCOPPIIPPvjA31Ulog5mMgvkFZRDOHmv5bHnNx9yG5NXUA6T2VkEESmB35OXZcuW4cEHH8RDDz2EQYMGYfny5ejTpw9WrlzpNH7VqlW4+uqrsXz5cgwaNAgPPfQQHnjgAbz00kv+rioRdbCSilqH3pSWrOnIyUb3MYb6JpRU1Pq2ckQUNPw65+XChQv4+uuvkZOTY3c8IyMDu3btcnpOcXExMjIy7I5NmDABq1evhtFoREhIiN17zc3NaG5utr1uaGgAABiNRhiNRl80w8Zanq/LDRZKbx+g/DbKvX3V9WcRpnbdYxKmEnZ/eirLaIz0Wd0CRe730BOltw9Qfhv91b62lOfX5OXUqVMwmUyIi4uzOx4XF4eqqiqn51RVVTmNv3jxIk6dOgW93n4i3vPPP4+8vDyHcrZu3YqIiIh2tsC5oqIiv5QbLJTePkD5bZRz+15M9RzzbIrZc9DxUmw+Xtr+CnUQOd9Dbyi9fYDy2+jr9p07d87r2ICsNpIk+6WLQgiHY57inR0HgMcffxwLFy60vW5oaECfPn2QkZGByEjf/qvLaDSiqKgI6enpDj1ASqD09gHKb6Pc22cyC0xYvhMnG5qczmnRqASeSTHjfw5H4Jf6ZqcxEoC4SA22LBgty2XTcr+Hnii9fYDy2+iv9llHTrzh1+QlJiYGarXaoZelurraoXfFSqfTOY3v0qULevZ0fDJsWFgYwsLCHI6HhIT47ZfGn2UHA6W3D1B+G+XavhAAj08ejOz8fQDsJ+lKl34A4I+ZgzB/wzdOY3CpDE1YqH8r62dyvYfeUnr7AOW30dfta0tZfp2wGxoaimHDhjl0LRUVFWHkyJFOz0lLS3OI37p1K1JSUhT9S0BEFpnJeqycMRS6KI3dcV2UBi9PuwkAcNugOJcxK2cM5T4vRArn92GjhQsXYubMmUhJSUFaWhpef/11HDt2DPPmzQNgGfY5ceIE1q1bBwCYN28eXn31VSxcuBBz585FcXExVq9ejXfeecffVSWiIJGZrEd6ks5h91yz6SI2V7iPkeNQERG1jd+Tl2nTpqGmpgbPPPMMDAYDkpOTsXnzZiQkJAAADAaD3Z4viYmJ2Lx5Mx599FG89tpriI+PxyuvvIJ77rnH31UloiCiVklI62c/VGw2eY4hIuULyITd+fPnY/78+U7fW7t2rcOxMWPGYN++fX6uFREREckRnypNREREssLkhYiIiGSFyQsRERHJSkDmvBARtWQyC64SIqIrxuSFiAKqsMyAvIJyuwcw6qM0yM1K4v4sROQVDhsRUcAUlhmQnb/P4cnRVfVNyM7fh8IyQwfVjIjkhMkLEQWEySyQV1Du9HlE1mN5BeUwmT0/MZqIOjcmL0QUECUVtQ49Li0JAIb6JpRU1AauUkQkS0xeiCggqhtdJy5XEkdEnReTFyIKiFitxnNQG+KIqPNi8kJEAZGaGA19lAauFkRLsKw6Sk2MDmS1iEiGmLwQUUCoVRJys5IAwCGBsb7OzUrifi9E5BGTFyLyGZNZoPinGnyy/wSKf6pxWDmUmazHyhlDoYuyHxrSRWmwcsZQ7vNCRF7hJnVE5BPebj6XmaxHepKOO+wS0RVj8kJE7WbdfK71Di3Wzeda96qoVRLS+vUMbCWJSDE4bERE7cLN54go0Ji8EFG7cPM5Igo0Ji9E1C7cfI6IAo3JCxG1CzefI6JAY/JCRO3CzeeIKNCYvBBRu3DzOSIKNC6VJlI6swk4ugs4cxLoFgckjARUap/GWDefe3bjAfQ58w1icRrV6I7j3W7En6Zc77j53JVej4gITF6IlK18I1C4GGiovHwsMh7IXAokTWlTjChcDKlFjIiMh9QiJlO1BxM0iyFdaBGjiYekWgpgim/qlP5Cez4NIlIIJi9ESlW+EXhvFtB6B5YGg+X4vessr72IEe/NgoCwGxYSDZXAe7MgtShHalWO1LKcpCntr9NHvwNu/HsbPgQiUiImL0RKZDZZei5cbh0nAZ8uvjQpxX3M+YsmhAmB1lNWVADMQqBp4yKEh6rdl1OYA1yX6YM6tWgfQpzEEFFnwOSFSImOl9gPuTgQQKO79y/HhAOOM3EvUUlAeNNJwO0WLgJoOAHsecM3dQIs7bt2tIdYIlIqrjYiUqKz1R1dA0d1R3xXVjC2j4gChskLkRJ1je3oGjjq0dd3ZQVj+4goYJi8EClRn1TL6hx3W8dp4z3GNIfrYBDRcPVMRbMAKkU0miN07q8V2QsYPtcndQJgaR8RdVpMXoiUSKW2LD0G4HLruIlLPcZ0uf1F/C3kIQBwSGCsr18JeQhdJr/o/lqZLwBdQn1SJwCOe8IQUafC5IVIqZKmWJYeR7baIC4y/vLSZQ8x6sF3YOydD2C+cQGqYL+9fxV6Yr5xAcbe+QDUg+/wfC1f1OkuLpMmIq42IlK2pCnAwMnud7P1EJOZrAemz8PUjaMcd8+d2mL3XG+u1d46mczAz5v9/KERUbBj8kKkdCo1kHhLu2Iyk/VIT9KhpGIYqhubEKu1PGjR4XlF3lyrPXUymT2XTUSKx+SFiLyiVklI69ezo6tBRMQ5L0RERCQvTF6IiIhIVpi8EBERkawweSEiIiJZYfJCREREssLkhYiIiGSFyQsRERHJCpMXIiIikhUmL0RERCQrTF6IiIhIVpi8EBERkawweSEiIiJZYfJCREREssLkhYiIiGSFyQsRERHJCpMXIiIikpUuHV0BIvIvk1mgpKIW1Y1NiNVqkJoYDbVK6uhqERFdMSYvRApWWGZAXkE5DPVNtmP6KA1ys5KQmay3HWOCQ0RywuSFSKEKywzIzt8H0ep4VX0TsvP3YeWMochM1nud4BARBQvOeSFSIJNZIK+g3CFxAWA7lldQjs3fWhKclokLcDnBKSwz+L2uRERtxeSFSIG+PlrnkJC0JAAY6pvw1CdlHhMck9lZBBFRx2HyQqRAp840exVXe/aCy/esCU5JRa2PakVE5BtMXogUKKZbmM/Kqm503YNDRNQRmLwQKdCwhB7QR2ngar2QBCC6a4hXZcVqNT6rFxGRLzB5IVIgtUpCblYSADgkMNbX//eOZI8Jjj7KsmyaiCiYMHkhUqjMZD1WzhgKXZR9z4kuSoOVM4Zi0g3xHhOc3Kwk7vdCREGH+7wQKVhmsh7pSTqXG9BZE5zW+7zouM8LEQUxJi9ECqdWSUjr19Pl+54SHCKiYMPkhYg8JjhERMGEc16IiIhIVpi8EBERkaxw2IhIxlo/DXpIb21HV4mIyO/82vNSV1eHmTNnIioqClFRUZg5cyZOnz7t9pw5c+ZAkiS7nxEjRvizmkSyVFhmwK+Wfo7fvLEbf/jHfvzmjd2YsHxnR1eLiMjv/Jq8TJ8+Hfv370dhYSEKCwuxf/9+zJw50+N5mZmZMBgMtp/Nmzf7s5pEslNY5vxp0CcbLK8/O3iyI6pFRBQQfhs2OnjwIAoLC7F7927cfPPNAIA33ngDaWlpOHz4MAYMGODy3LCwMOh0Oq+u09zcjObmyw+ha2hoAAAYjUYYjcZ2tMCRtTxflxsslN4+QBltNJkFnt/0HULVjk97DlVZji3bchDjBsQqbrmzEu6fJ0pvo9LbByi/jf5qX1vKk4QQfnne/ZtvvomFCxc6DBN1794dL7/8Mu6//36n582ZMwcff/wxQkND0b17d4wZMwbPPfccYmNjncYvWbIEeXl5Dsc3bNiAiIiIdreDiIiI/O/cuXOYPn066uvrERkZ6TbWbz0vVVVVThOO2NhYVFVVuTxv4sSJmDp1KhISElBRUYE//elPuPXWW/H1118jLMzxSbmPP/44Fi5caHvd0NCAPn36ICMjw2Pj28poNKKoqAjp6ekICfHuoXZyovT2Acpo4+YDBjz2wbdO3wtTCTybYsaf9qrw7F03YtL1ytohVwn3zxOlt1Hp7QOU30Z/tc86cuKNNicvrno6WtqzZw8AQJIcu6yFEE6PW02bNs329+TkZKSkpCAhIQGbNm3C3Xff7RAfFhbmNKkJCQnx2y+NP8sOBkpvHyDvNsZGdUWzyf1wULNZQmxUV9m20RM53z9vKb2NSm8foPw2+rp9bSmrzcnLww8/jPvuu89tTN++ffHtt9/i5EnHSYP/+c9/EBcX5/X19Ho9EhIS8MMPP7S1qkSKlJoYDX2UBlX1TXA15quL5NOgiUi52py8xMTEICYmxmNcWloa6uvrUVJSgtTUVADAV199hfr6eowcOdLr69XU1OD48ePQ65XV/U10pdQqCblZScjO3wcJsEtgrP0xORMHKm6yLhGRld+WSg8aNAiZmZmYO3cudu/ejd27d2Pu3Lm4/fbb7VYaDRw4EB999BEA4MyZM1i0aBGKi4tx5MgRbN++HVlZWYiJicFdd93lr6oSyY71adC6KI3d8bhIy+vbBnnfu0lEJDd+3WH37bffxiOPPIKMjAwAwJQpU/Dqq6/axRw+fBj19fUAALVajQMHDmDdunU4ffo09Ho9xo0bh3fffRdaLXcOJWrJ2dOgh/TWYkvhpx1dNSIiv/Jr8hIdHY38/Hy3MS1XaoeHh2PLli3+rBKRorR+GrRS95UgImqJD2YkIiIiWWHyQkRERLLC5IWIiIhkhckLERERyQqTFyIiIpIVJi9EREQkK35dKk1EV8ZkFnb7t6QmRnPHXCKiS5i8EAWZwjID8grKYahvsh3TR2mQm5WEzGQ+JoOIiMNGREGksMyA7Px9dokLAFTVNyE7fx8KywwdVDMiouDB5IUoSJjMAnkF5U6fFG09lldQDpPZ1bOkiYg6ByYvRAFmMgsU/1SDT/afQPFPNbZkpKSi1qHHpSUBwFDfhJKK2gDVlIgoOHHOC1EAuZvP0nzR7FUZ1Y2uExwios6APS9EAeJpPsuRU2e9KidWq/FH9YiIZIPJC1EAeDOf5Z2SY9BFauBqQbQESy9NamK0fypJRCQTTF6IAsCb+SxVDc34TerVAOCQwFhf52Ylcb8XIur0mLwQBYC381T6xkRg5Yyh0EXZDw3pojRYOWMo93khIgIn7BIFhLfzVGK1GqT164n0JB132CUicoHJC1EApCZGQx+lQVV9k9N5LxIsvSvW+SxqlYS0fj0DWkciIrlg8kLKZjYBR3cBZ04C3eKA+OHexSWMBFRquxDTxYs49NUWnK87gfAevTDw5glQd+niVTlqlYTcrCRk5++DGmYMVx1CLE6jGt2xxzwQZqjs57N4UZ82tY+ISEGYvJBylW8EChcDDZWXj0UlAtfkeY6LjAcylwJJUwAApVveQnxxHgajxhZysqgnKtNyMWTCbK/KyUzW48NxpxBfnIe4luXgUjnW+Sxe1KdN7SMiUhgmL6RM5RuB92YBrQdpGqssfx7aDFx/h+u4BoPl+L3rUHq8DjfuesRyvMW0k6tEDa7a9QhKAQzp08NjOQAwpPgPEK1iYlGLuOI/AH16WA54KidpivftIyJSICYvpDxmk6VHwt2uKp8tAQZN9BAnQXy6GPGNzQCA1vNlVRJgFoC+eAlEmQaSm3Lw6eJLiY9wsgzaMcZlOYU5wHWZ3rVv8O3Oh5qIiGSOyQspz9Fd9kMpzjRWAnve8BAnIDVWIg5w3HjlEpUE6FALNLq7mLBczy0vYxpOeFFvWMo6ugtIvMVDmURE8sN9Xkh5zpz0Lq7uiF+r4Tfe1tvbz4GISGaYvJDydIvzLq5HX79Ww2+8rbe3nwMRkcwweSHlSRhpWZ3j8ilBALTxwPC5HuIkCG08TqInzM6ml8Ay56UK0RBa9+VAG+/xWl7FRPbyot6wlJUw0vX7REQyxuSFlEeltiwrBuDyKUG3LQG6hHqMkyYuRWVaLgA4JDDW14a0JZAmWsppPR3X9nriUs918iYm8wWv6o3blnCyLhEpFpMXUqakKZZlxZGtngWkvfR64CT3cZHxtmXJQybMxjcjX8F/JPsdb6ulnvhm5CuWfV6SpqA07W+ohv0Tn08iGqVpf7Ncx4treRXTlvYRESkQVxuRciVNAQZOdtyBtnCL57hWO9oOmTAbpvG/xXetdtjVXdpht7DMgOxtMZDwN6S23j13mworexksD1X04lpexbSlfURECsPkhZRNpbZfLmw0ehfnhLpLFwweNdnhuMkskFdQDgFAQIXd5iS79yUAeQXlSE/SWbb/9+JaXsU4i3PVPiIiBeGwEVE7lVTUwlDf5PJ9AcBQ34SSitrAVYqISMGYvBC1U3Wj68TlSuKIiMg9Ji9E7RSr1fg0joiI3GPyQtROqYnR0Edp3O3OAn2UBqmJ0S4iiIioLZi8ELWTWiUhN8sySdfFrivIzUqyTNYlIqJ2Y/JC5AOZyXqsnDEUuij7oSFdlAYrZwy1LJMmIiKf4FJpIh/JTNYjPUmHkopaVDc2IVZrGSpijwsRkW8xeSGCZa8WXyQdapWEtH49PQcSEdEVY/LiJeuXG2DZ12PEtbH8F7VCFJYZkFdQbrdXiz5Kg9ysJA73EBEFIc558UJhmQG/Wvo5HnhrDwDggbf24FdLP0dhmaGDa0btVVhmQHb+PodN5qrqm5Cdv4/3mIgoCDF58YBfbsrVclv/1qzH8grKYWr9OGkiIupQTF7c4JdbxzGZBYp/qsEn+0+g+Kcav3zG3NafiEieOOfFjbZ8uXGSpu8Eag4Kt/UnIpIn9ry4wS+3wAvkMB239ScikicmL27wyy2w/DFM5274idv6ExHJE4eN3LB+uVXVNzn9QpVg2UGVX26+4ethOmfDTwk9wrBwoOXv1m39s/P3QQLs7jG39SciCl7seXGDz6wJLF8O07kafjrZYHn92cGTALitPxGRHLHnxQPrl1teQTlqz5y3HddxEzOf89UwnTfDTy98eggZyb2gVknc1p+ISGaYvHjB+uW2+8dqnDq4G2/OHs4ddv3AV8N0noafAKCqwX74idv6ExHJB4eNvKRWSbYvTf6r3D98NUzHVWJERMrG5IVsK3I2HzDYXncUX8xB4SoxIiJl47BRJ9dyRU6YWuDFVGDC8p14fPLgDpvP0945KJ6GnwBAF8lVYkREcsWel07M3Yqcjn5uk3UOyh039UJav55tGqbzZvgpZ+JADv0REckUk5dOSunPbXI1/BQXaXl926C4jqgWERH5AIeNOqnO8NwmZ8NPQ3prsaXw046uGhERtQOTl06qs6zIab0E2mg0dmBtiIjIF5i8yJjJLK54UitX5BARkVwxeZEpZ8/t0bdh19+WK3IkmJGqOgS9qgFAClQwQ4LafkM4swk4ugs4cxLoFgckjARUaseCvYkLZAwRESkOkxcZsq4Saj2VtqreskrIm/1QrCtyPt6wCk+HrEO8VAujSoPNSMHW0MfwXPM03Jk1z9KTU74RKFwMNFReLiAyHshcCiRNuXysfCNE4WJILeJEZDyklnHelOWrGCIiUiQmLz7UnmGctlzD3SohCZZVQulJOo/XzlTtwYTQv0G0Ki1WqsPK0L9BUg0DygG8NwtofcUGg+X4vessyUL5Roj3ZkFA2C1PFg2VwHuzIN27znLAaYwBkrUseHE9b2KYwBARKRaTFx9p7zCOt3y2SshsAgoXQ2qVSACW9fMSAHy6+NJf3KRKhTnAdZk4X/DfCBMCrfMlFQCzEGjauAjhoWqHxAUApEtHJW+u522dBk7mEBIRkUIxefGW2QQcLbb8/WgxcM0o25ejdRhHghkjVIcQi9OoRnfsqR/oOIzTzrkjLVf/qC7NVbFer8Q8EOZLW/fY4lxd7+gu+yEXBwJodPf+pZiGEzCVvIHw81WOO8JZ6ykB4U0ngSaXIZC8vZ6XdcLRXUDiLR5iiYhIjpi8eMM6v+JMLXDj68CGqUC3aCBzKUwDs5BXUI4MVQlyL80dsaoU0XjGOAt5BRrLMM6hAq/njriKi9WOAgBMcHG9POMsbDGnWlYJuZsXYrrgs4+n+uhBdMyDBNw4c7Kja0BERH7CHXY9Kd9omUfRupfi0vyKH3dswA2NO7EyZDl0qLUL0aEWK0KW44bGnfhxxwbLfI9W5QjrPI3yjV5dL7Xp37iv236X11sZshz3dduP1KZ/uy0HNT9d8UfS2qmQeJ+V5TPduIMuEZFSsefFnUvzQtzNr+jzVR6WhFg2PnOY7yEBZgHkhqxDj69C3M/3uDR3xNP11IU5yA0xAUY31+vyFtRb1G7LwddrLb0wDQYXcRKg1VvGedzFRMbjzPX3o/LAG9Ch1qFOgKVOVYiGBCDOQ0yP8BCEN1V7rJNoMFiGmhxaJ0GKjLcMjxERkSL5teflueeew8iRIxEREYHu3bt7dY4QAkuWLEF8fDzCw8MxduxYfPfdd/6spmtezAuJaDoJveT8CxmwJBTxUi3Cm066n+/RcALY84ZX81DCz590e73wppPezWcZOsdWg9Y1AgBMXGoZYnIXk/kCUvvr8ErIQwAsSUhL1tfL1A9giXGW25g84ywcuznXY51KB+dACOG0HCEESgcv5mRdIiIF82vycuHCBUydOhXZ2dlen/Piiy9i2bJlePXVV7Fnzx7odDqkp6ejsbHRjzV1IcDzJsy1FQG9Hnr2sywrjmw1Y0Wrv7zcOGmK85jIeFuMWiVh7J0PYL5xAaoQbRdWhZ6Yb1yAW+98EN9qR7uN+VY7GteOme72eqaBWZi/rzey3ZQzf19v2T5QkoiIPPPrsFFeXh4AYO3atV7FCyGwfPlyPPnkk7j77rsBAG+99Rbi4uKwYcMG/O53v/NXVZ0L8LyJo+Y4JAbygt3iLCtyBk6+1Mt0EjgCYH4xENbisQBJUy7HuFgllZmsB6bPw9SNo9DnzDe2FVDHu92IP029HpnJeqhUErLzm1DUnILhLVdlXVoltTIrybI3jZvrlfxUA0N9EwxIRVFzivPVVjJ/oCQREbkXVHNeKioqUFVVhYyMDNuxsLAwjBkzBrt27XKavDQ3N6O5udn2uqGhAYDlAXztfghf/HAgKhForAIgYFRZvtCtfwIS0E1nmYPRWOVyDkaT5io0nDfiKtS5nO9RjWh8q78LvaPetl3P0eXrtTtGq7e0z/oZ9R5h+byOFMFoMl8+fonJLPC18TqcMiYgxhiGYUYT1CqzXcz4ATEY+8ex+ProjTh1phkx3cIwLKEH1CoJRqMR4wfEYMX0G/HCp4dQ2jDIdl7vHhrkTByI8QNi7O9Z7xEtKwCYzKiuP4swtbVNEkpxuZwQNWztra4/C6Mx0qHl1vKV+oBGtk/+lN5GpbcPUH4b/dW+tpQnCSH83r++du1aLFiwAKdPn3Ybt2vXLowaNQonTpxAfPzlFSz/9V//haNHj2LLli0O5yxZssTWw9PShg0bEBER0e66ExERkf+dO3cO06dPR319PSIjHf/x2VKbe15cJQst7dmzBykpKW0t2kaS7LsnhBAOx6wef/xxLFy40Pa6oaEBffr0QUZGhsfGe+3QZuCzXBjP1qHo+leQfuARhHSNBm5bAgycZBeDRsPl87TxwG1LYLpuIiYs34nrz3yJxV3egU6qs4VUiWgsvXgfDnQbhS0LRluGTQ5thvgsF1KLsoQ2HpKX12tTTAtGoxFFRUVIT09HSEgIAOCzgyfx6Lv7HfpvrHfj5Wk34bZBgRteM5kFJizfiZMNTa76lBAXqbn8WbbirI1KwvbJn9LbqPT2Acpvo7/aZx058Uabk5eHH34Y9913n9uYvn37trVYAIBOpwMAVFVVQa+/PGGzuroacXHOvyDDwsIQFhbmcDwkJMR3H+r1dwCDbwd+/hL4rg4h961HSIsddu1inMzTCAHw+OTByM5vxqfGoc7ne0weDE1YKACgUErFs+dfRJ+mFnNHutyIP0nXI9PaJjfX86ZO7lg/O5NZ4JlNh9Fkcp44SgCe2XQYGcm9fP4MJ5d1g/Wz3AfAflDMWoPHW3yWLsvx5e9HEGL75E/pbVR6+wDlt9HX7WtLWW1OXmJiYhATE9PW07ySmJgInU6HoqIiDBkyBIBlxdKOHTuwdOlSD2f7mUoNJKQB3222/OksAVCpXW5Jn5msx8oZQ5FXUI7d9Um2462ff9TyidEncDlOajA6PmrAzfW8qZMnPnuOko+1/Cxb1k/nh2dJERFR8PHrhN1jx46htrYWx44dg8lkwv79+wEA1157Lbp16wYAGDhwIJ5//nncddddkCQJCxYswJ///Gf0798f/fv3x5///GdERERg+vTp/qxqQGQm65GepHP55GlfPjHaF1o+R8kXcb7k6bMkIiLl8mvy8vTTT+Ott96yvbb2pmzbtg1jx44FABw+fBj19fW2mMceewznz5/H/PnzUVdXh5tvvhlbt26FVqv1Z1UDRq2SXPZSBFtPR6xW4zmoDXG+5u6zJCIi5fJr8rJ27VqPe7y0XuwkSRKWLFmCJUuW+K9iQSrYejpSE6Ohj9Kgqt715FhdlKXHg4iIKFD4YMYgEmw9HWqVhNwsy7wbF5v1I9e6sRwREVGAMHkJItaeDtfPQLJM8A1kT4d1cqwuyj5h0kVp7CcPExERBUhQ7bDb2Vl7OrLz90GC82XAHdHTwcmxREQUTJi8BJlgXQbMybFERBQsmLwEIfZ0EBERucbkJUj5qqfDZBZMgoiISFGYvChYYZnBYfip9Y6+REREcsPVRgplfcxA603vquqbkJ2/D4VlBhdnEhERBTcmLwrk6TEDgOUxAyazswgiIqLgxuRFgdrymAEiIiK5YfKiQMH2mAEiIiJfYvKiQMH2mAEiIiJfYvKiQMH4mAEiIiJfYfKiQHygIhERKRmTF4XiAxWJiEipuEmdgvExA0REpERMXhSOD1QkIiKl4bARERERyQqTFyIiIpIVJi9EREQkK0xeiIiISFaYvBAREZGsMHkhIiIiWWHyQkRERLLC5IWIiIhkhckLERERyYridtgVQgAAGhoafF620WjEuXPn0NDQgJCQEJ+X39GU3j5A+W1k++RP6W1UevsA5bfRX+2zfm9bv8fdUVzy0tjYCADo06dPB9eEiIiI2qqxsRFRUVFuYyThTYojI2azGZWVldBqtZAk3z6AsKGhAX369MHx48cRGRnp07KDgdLbByi/jWyf/Cm9jUpvH6D8NvqrfUIINDY2Ij4+HiqV+1ktiut5UalU6N27t1+vERkZqchfSCultw9QfhvZPvlTehuV3j5A+W30R/s89bhYccIuERERyQqTFyIiIpIVJi9tEBYWhtzcXISFhXV0VfxC6e0DlN9Gtk/+lN5GpbcPUH4bg6F9ipuwS0RERMrGnhciIiKSFSYvREREJCtMXoiIiEhWmLwQERGRrDB5ISIiIllh8uLGkSNH8OCDDyIxMRHh4eHo168fcnNzceHCBbfnCSGwZMkSxMfHIzw8HGPHjsV3330XoFq3zXPPPYeRI0ciIiIC3bt39+qcOXPmQJIku58RI0b4t6JX6EraJ6f7BwB1dXWYOXMmoqKiEBUVhZkzZ+L06dNuzwnme7hixQokJiZCo9Fg2LBh+OKLL9zG79ixA8OGDYNGo8E111yDVatWBaimV64tbdy+fbvDvZIkCYcOHQpgjb23c+dOZGVlIT4+HpIk4eOPP/Z4jpzuYVvbJ7f79/zzz2P48OHQarWIjY3FnXfeicOHD3s8L9D3kMmLG4cOHYLZbMbf//53fPfdd3j55ZexatUqPPHEE27Pe/HFF7Fs2TK8+uqr2LNnD3Q6HdLT020PjQwmFy5cwNSpU5Gdnd2m8zIzM2EwGGw/mzdv9lMN2+dK2ien+wcA06dPx/79+1FYWIjCwkLs378fM2fO9HheMN7Dd999FwsWLMCTTz6J0tJS3HLLLZg4cSKOHTvmNL6iogKTJk3CLbfcgtLSUjzxxBN45JFH8MEHHwS45t5raxutDh8+bHe/+vfvH6Aat83Zs2dx44034tVXX/UqXm73sK3ts5LL/duxYwf+z//5P9i9ezeKiopw8eJFZGRk4OzZsy7P6ZB7KKhNXnzxRZGYmOjyfbPZLHQ6nXjhhRdsx5qamkRUVJRYtWpVIKp4RdasWSOioqK8ip09e7a44447/FofX/O2fXK7f+Xl5QKA2L17t+1YcXGxACAOHTrk8rxgvYepqali3rx5dscGDhwocnJynMY/9thjYuDAgXbHfve734kRI0b4rY7t1dY2btu2TQAQdXV1AaidbwEQH330kdsYOd5DK2/aJ+f7J4QQ1dXVAoDYsWOHy5iOuIfseWmj+vp6REdHu3y/oqICVVVVyMjIsB0LCwvDmDFjsGvXrkBUMSC2b9+O2NhYXHfddZg7dy6qq6s7uko+Ibf7V1xcjKioKNx88822YyNGjEBUVJTH+gbbPbxw4QK+/vpru88eADIyMly2pbi42CF+woQJ2Lt3L4xGo9/qeqWupI1WQ4YMgV6vx/jx47Ft2zZ/VjOg5HYPr5Rc7199fT0AuP3e64h7yOSlDX766Sf8z//8D+bNm+cypqqqCgAQFxdndzwuLs72ntxNnDgRb7/9Nj7//HP89a9/xZ49e3Drrbeiubm5o6vWbnK7f1VVVYiNjXU4Hhsb67a+wXgPT506BZPJ1KbPvqqqymn8xYsXcerUKb/V9UpdSRv1ej1ef/11fPDBB/jwww8xYMAAjB8/Hjt37gxElf1ObvewreR8/4QQWLhwIX71q18hOTnZZVxH3MNOmbwsWbLE6QSqlj979+61O6eyshKZmZmYOnUqHnroIY/XkCTJ7rUQwuGYv1xJ+9pi2rRpmDx5MpKTk5GVlYVPP/0U33//PTZt2uTDVrjm7/YBHXv/gLa10Vm9PNW3o++hO2397J3FOzseTNrSxgEDBmDu3LkYOnQo0tLSsGLFCkyePBkvvfRSIKoaEHK8h96S8/17+OGH8e233+Kdd97xGBvoe9jFL6UGuYcffhj33Xef25i+ffva/l5ZWYlx48YhLS0Nr7/+utvzdDodAEsmqtfrbcerq6sdMlN/aWv72kuv1yMhIQE//PCDz8p0x5/tC4b7B3jfxm+//RYnT550eO8///lPm+ob6HvoTExMDNRqtUMPhLvPXqfTOY3v0qULevbs6be6XqkraaMzI0aMQH5+vq+r1yHkdg99QQ737/e//z02btyInTt3onfv3m5jO+IedsrkJSYmBjExMV7FnjhxAuPGjcOwYcOwZs0aqFTuO6sSExOh0+lQVFSEIUOGALCMc+/YsQNLly5td9290Zb2+UJNTQ2OHz9u92XvT/5sXzDcP8D7NqalpaG+vh4lJSVITU0FAHz11Veor6/HyJEjvb5eoO+hM6GhoRg2bBiKiopw11132Y4XFRXhjjvucHpOWloaCgoK7I5t3boVKSkpCAkJ8Wt9r8SVtNGZ0tLSDr1XviS3e+gLwXz/hBD4/e9/j48++gjbt29HYmKix3M65B76bSqwApw4cUJce+214tZbbxW//PKLMBgMtp+WBgwYID788EPb6xdeeEFERUWJDz/8UBw4cED85je/EXq9XjQ0NAS6CR4dPXpUlJaWiry8PNGtWzdRWloqSktLRWNjoy2mZfsaGxvFH//4R7Fr1y5RUVEhtm3bJtLS0kSvXr0U0T4h5HX/hBAiMzNT3HDDDaK4uFgUFxeL66+/Xtx+++12MXK5h//4xz9ESEiIWL16tSgvLxcLFiwQXbt2FUeOHBFCCJGTkyNmzpxpi//5559FRESEePTRR0V5eblYvXq1CAkJEf/85z87qgketbWNL7/8svjoo4/E999/L8rKykROTo4AID744IOOaoJbjY2Ntv/OAIhly5aJ0tJScfToUSGE/O9hW9snt/uXnZ0toqKixPbt2+2+886dO2eLCYZ7yOTFjTVr1ggATn9aAiDWrFlje202m0Vubq7Q6XQiLCxMjB49Whw4cCDAtffO7NmznbZv27ZttpiW7Tt37pzIyMgQV111lQgJCRFXX321mD17tjh27FjHNMCDtrZPCHndPyGEqKmpEb/97W+FVqsVWq1W/Pa3v3VYlimne/jaa6+JhIQEERoaKoYOHWq3RHP27NlizJgxdvHbt28XQ4YMEaGhoaJv375i5cqVAa5x27WljUuXLhX9+vUTGo1G9OjRQ/zqV78SmzZt6oBae8e6NLj1z+zZs4UQ8r+HbW2f3O6fq++8lv+PDIZ7KF2qLBEREZEsdMrVRkRERCRfTF6IiIhIVpi8EBERkawweSEiIiJZYfJCREREssLkhYiIiGSFyQsRERHJCpMXIiIikhUmL0RERCQrTF6IiIhIVpi8EBERkaz8f3AmnWgPd4lCAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred=DecisionTree(max_depth=2).fit(copy.deepcopy(X), copy.deepcopy(Y),type_of_node=DecisionRegressionNode).predict(copy.deepcopy(X))\n",
    "plt.scatter(X,Y)\n",
    "plt.scatter(X,pred)\n",
    "plt.title(f'DT depth 1 Loss: {np.mean((Y-pred)**2):.6f}')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "62d66e29",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 10:\tAvg. Squared Loss:0.08422045053463774\n",
      "Epoch: 20:\tAvg. Squared Loss:0.020421952093401318\n",
      "Epoch: 30:\tAvg. Squared Loss:0.012665544085014142\n",
      "Epoch: 40:\tAvg. Squared Loss:0.011722545947714925\n",
      "Epoch: 50:\tAvg. Squared Loss:0.011607899388896949\n",
      "Epoch: 60:\tAvg. Squared Loss:0.011593961043815541\n",
      "Epoch: 70:\tAvg. Squared Loss:0.01159226646645001\n",
      "Epoch: 80:\tAvg. Squared Loss:0.01159206044540297\n",
      "Epoch: 90:\tAvg. Squared Loss:0.011592035398053292\n",
      "Epoch: 100:\tAvg. Squared Loss:0.01159203235288031\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred=gradient_bossting_trees_with_fixed_alphas(X,Y,max_depth=2,alpha=.1,n=100)\n",
    "plt.scatter(X,Y)\n",
    "plt.scatter(X,pred)\n",
    "plt.title(f'DT depth 2 Loss: {np.mean((Y-pred)**2):.6f}')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd63e0d4",
   "metadata": {},
   "source": [
    "# The tast is very easy. Hence Not much of an improvement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "704ecb28",
   "metadata": {},
   "outputs": [],
   "source": [
    "X,y=load_diabetes(return_X_y=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5dc23112",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DT depth 1 Loss: 3622.711742\n"
     ]
    }
   ],
   "source": [
    "pred=DecisionTree(max_depth=1).fit(copy.deepcopy(X), copy.deepcopy(y),type_of_node=DecisionRegressionNode).predict(copy.deepcopy(X))\n",
    "print(f'DT depth 1 Loss: {np.mean((y-pred)**2):.6f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c58eb0e6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DT depth 3 Loss: 2910.822660\n"
     ]
    }
   ],
   "source": [
    "pred=DecisionTree(max_depth=3).fit(copy.deepcopy(X), copy.deepcopy(y),type_of_node=DecisionRegressionNode).predict(copy.deepcopy(X))\n",
    "print(f'DT depth 3 Loss: {np.mean((y-pred)**2):.6f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9f6fd82f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DT depth 5 Loss: 1958.249684\n"
     ]
    }
   ],
   "source": [
    "pred=DecisionTree(max_depth=5).fit(copy.deepcopy(X), copy.deepcopy(y),type_of_node=DecisionRegressionNode).predict(copy.deepcopy(X))\n",
    "print(f'DT depth 5 Loss: {np.mean((y-pred)**2):.6f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0d97313",
   "metadata": {},
   "source": [
    "# Gradient Boosting 100 Decision Regression Trees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "90221eee",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 10:\tAvg. Squared Loss:6528.515326754847\n",
      "Epoch: 20:\tAvg. Squared Loss:3550.7706206881967\n",
      "Epoch: 30:\tAvg. Squared Loss:3037.013201090766\n",
      "Epoch: 40:\tAvg. Squared Loss:2899.9725653829983\n",
      "Epoch: 50:\tAvg. Squared Loss:2814.4763218153034\n",
      "Epoch: 60:\tAvg. Squared Loss:2762.824730987714\n",
      "Epoch: 70:\tAvg. Squared Loss:2714.410076870103\n",
      "Epoch: 80:\tAvg. Squared Loss:2688.795392899784\n",
      "Epoch: 90:\tAvg. Squared Loss:2667.0049001020743\n",
      "Epoch: 100:\tAvg. Squared Loss:2650.1621649684607\n",
      "DT depth 1 Loss: 2650.162165\n"
     ]
    }
   ],
   "source": [
    "pred=gradient_bossting_trees_with_fixed_alphas(X,y,max_depth=1,alpha=.1,n=100)\n",
    "print(f'DT depth 1 Loss: {np.mean((y-pred)**2):.6f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c4b530ce",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 10:\tAvg. Squared Loss:6197.372825358515\n",
      "Epoch: 20:\tAvg. Squared Loss:3161.5394368802663\n",
      "Epoch: 30:\tAvg. Squared Loss:2641.2705432817843\n",
      "Epoch: 40:\tAvg. Squared Loss:2416.66771964921\n",
      "Epoch: 50:\tAvg. Squared Loss:2319.014488512071\n",
      "Epoch: 60:\tAvg. Squared Loss:2243.3377088434463\n",
      "Epoch: 70:\tAvg. Squared Loss:2148.6632183897964\n",
      "Epoch: 80:\tAvg. Squared Loss:2069.1684148661143\n",
      "Epoch: 90:\tAvg. Squared Loss:2002.0033899260352\n",
      "Epoch: 100:\tAvg. Squared Loss:1952.844146476107\n",
      "DT depth 2 Loss: 1952.844146\n"
     ]
    }
   ],
   "source": [
    "pred=gradient_bossting_trees_with_fixed_alphas(X,y,max_depth=2,alpha=.1,n=100)\n",
    "print(f'DT depth 2 Loss: {np.mean((y-pred)**2):.6f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23ca17ae",
   "metadata": {},
   "source": [
    "# Adaptive Boosting\n",
    "\n",
    "+ $y_i \\in \\{+1,-1\\}$\n",
    "+ $h \\in \\mathcal H$ are binary funcs,i.e,. $h(x) \\in \\{+1,-1\\}$\n",
    "+ Step-size: Line-search to obtain best $\\alpha$\n",
    "+ Loss func: $\\ell (H) = \\sum_i ^n e^{- y_i H(x_I)} $\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02e19b74",
   "metadata": {},
   "source": [
    "### 1 .$$ \\begin{equation}\n",
    "\\textrm{argmin}_{h\\in H}\\ell(H+\\alpha h) \\approx \\textrm{argmin}_{h \\in \\mathbb{H}}\\sum_{i = 1}^{n}\\frac{\\partial \\ell}{\\partial [H(\\mathbf{x}_i)]}h(\\mathbf{x}_i) \\end{equation}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71a81c26",
   "metadata": {},
   "source": [
    "### 2. $$ r_i=\\frac{\\partial \\ell}{\\partial H(\\mathbf{x}_i)}=-y_i {e^{-y_i H(\\mathbf{x}_i)}} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ee5e621",
   "metadata": {},
   "source": [
    "## 3. $$ h(\\mathbf{x}_i)=\\textrm{argmin}_{h \\in \\mathbb{H}}\\sum_{i=1}^{n}r_ih(\\mathbf{x}_i) \\;\\; \\Big(\\textrm{substitute in: } r_i=e^{-H(\\mathbf{x}_i)y_i}\\Big)$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "299a6972",
   "metadata": {},
   "source": [
    "## 4. $$ =\\textrm{argmin}_{h \\in \\mathbb{H}} -\\sum_{i=1}^n y_i e^{-H(\\mathbf{x}_i) y_i} h(\\mathbf{x}_i) \\Big(\\textrm{substitute in: } w_i=\\frac{1}{Z}e^{-H(\\mathbf{x}_i)y_i}\\Big)$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83674eab",
   "metadata": {},
   "source": [
    "### 5. $$=\\textrm{argmin}_{h \\in \\mathbb{H}}-\\sum_{i=1}^{n} w_i y_i h(\\mathbf{x}_i)\n",
    "\\;\\; \\Big(y_ih(\\mathbf{x}_i)\\in \\{+1,-1\\} \\textrm{ with } h(\\mathbf{x}_i)y_i=1 \\iff h(\\mathbf{x}_i)=y_i \\Big)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "446fad79",
   "metadata": {},
   "source": [
    "### 6. $$ =\\textrm{argmin}_{h \\in \\mathbb{H}}-\\sum_{i=1}^{n} w_i y_i h(\\mathbf{x}_i) \\Big(y_ih(\\mathbf{x}_i)\\in \\{+1,-1\\} \\textrm{ with } h(\\mathbf{x}_i)y_i=1 \\iff h(\\mathbf{x}_i)=y_i \\Big)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2fc13cae",
   "metadata": {},
   "source": [
    "### 7. $$ =\\textrm{argmin}_{h \\in \\mathbb{H}}\\sum_{i: h(\\mathbf{x}_i)\\neq y_i} w_i - \\sum_{i: h(\\mathbf{x}_i)= y_i} w_i \n",
    " \\Big(\\sum_{i: h(\\mathbf{x}_i)= y_i} w_i=1-\\sum_{i: h(\\mathbf{x}_i)\\neq y_i} w_i\\Big)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c536c13",
   "metadata": {},
   "source": [
    "## 8. $$ =\\textrm{argmin}_{h \\in \\mathbb{H}}\\sum_{i: h(\\mathbf{x}_i)\\neq y_i} w_i  \n",
    "\\;\\; \\Big(\\textrm{This is the weighted classification error.}\\Big) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdd95bea",
   "metadata": {},
   "source": [
    "# Implementation of AdaBoost\n",
    "1. https://geoffruddock.com/adaboost-from-scratch-in-python/\n",
    "2. https://xavierbourretsicotte.github.io/AdaBoost.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "39e5bd2d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_adaboost(X: np.ndarray,\n",
    "                  y: np.ndarray,\n",
    "                  clf=None,\n",
    "                  sample_weights: Optional[np.ndarray] = None,\n",
    "                  annotate: bool = False,\n",
    "                  ax: Optional[mpl.axes.Axes] = None) -> None:\n",
    "    \"\"\" Plot ± samples in 2D, optionally with decision boundary \"\"\"\n",
    "\n",
    "    assert set(y) == {-1, 1}, 'Expecting response labels to be ±1'\n",
    "\n",
    "    if not ax:\n",
    "        fig, ax = plt.subplots(figsize=(5, 5), dpi=100)\n",
    "        fig.set_facecolor('white')\n",
    "\n",
    "    pad = 1\n",
    "    x_min, x_max = X[:, 0].min() - pad, X[:, 0].max() + pad\n",
    "    y_min, y_max = X[:, 1].min() - pad, X[:, 1].max() + pad\n",
    "\n",
    "    if sample_weights is not None:\n",
    "        sizes = np.array(sample_weights) * X.shape[0] * 100\n",
    "    else:\n",
    "        sizes = np.ones(shape=X.shape[0]) * 100\n",
    "\n",
    "    X_pos = X[y == 1]\n",
    "    sizes_pos = sizes[y == 1]\n",
    "    ax.scatter(*X_pos.T, s=sizes_pos, marker='+', color='red')\n",
    "\n",
    "    X_neg = X[y == -1]\n",
    "    sizes_neg = sizes[y == -1]\n",
    "    ax.scatter(*X_neg.T, s=sizes_neg, marker='.', c='blue')\n",
    "\n",
    "    if clf:\n",
    "        plot_step = 0.01\n",
    "        xx, yy = np.meshgrid(np.arange(x_min, x_max, plot_step),\n",
    "                             np.arange(y_min, y_max, plot_step))\n",
    "\n",
    "        Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "        Z = Z.reshape(xx.shape)\n",
    "        \n",
    "        # If all predictions are positive class, adjust color map acordingly\n",
    "        if list(np.unique(Z)) == [1]:\n",
    "            fill_colors = ['r']\n",
    "        else:\n",
    "            fill_colors = ['b', 'r']\n",
    "\n",
    "        ax.contourf(xx, yy, Z, colors=fill_colors, alpha=0.2)\n",
    "\n",
    "    if annotate:\n",
    "        for i, (x, y) in enumerate(X):\n",
    "            offset = 0.05\n",
    "            ax.annotate(f'$x_{i + 1}$', (x + offset, y - offset))\n",
    "\n",
    "    ax.set_xlim(x_min+0.5, x_max-0.5)\n",
    "    ax.set_ylim(y_min+0.5, y_max-0.5)\n",
    "    ax.set_xlabel('$x_1$')\n",
    "    ax.set_ylabel('$x_2$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f7daeb2f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import make_gaussian_quantiles\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "def make_toy_dataset(n: int = 100, random_seed: int = None):\n",
    "    \"\"\" Generate a toy dataset for evaluating AdaBoost classifiers \"\"\"\n",
    "    \n",
    "    n_per_class = int(n/2)\n",
    "    \n",
    "    if random_seed:\n",
    "        np.random.seed(random_seed)\n",
    "\n",
    "    X, y = make_gaussian_quantiles(n_samples=n, n_features=2, n_classes=2)\n",
    "    \n",
    "    return X, y*2-1\n",
    "\n",
    "X, y = make_toy_dataset(n=10, random_seed=10)\n",
    "plot_adaboost(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "4d223b66",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train error: 0.0%\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.ensemble import AdaBoostClassifier\n",
    "\n",
    "bench = AdaBoostClassifier(n_estimators=10, algorithm='SAMME').fit(X, y)\n",
    "plot_adaboost(X, y, bench)\n",
    "\n",
    "train_err = (bench.predict(X) != y).mean()\n",
    "print(f'Train error: {train_err:.1%}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "cb802291",
   "metadata": {},
   "outputs": [],
   "source": [
    "class AdaBoost:\n",
    "    \"\"\" AdaBoost enemble classifier from scratch \"\"\"\n",
    "\n",
    "    def __init__(self):\n",
    "        self.stumps = None\n",
    "        self.stump_weights = None\n",
    "        self.errors = None\n",
    "        self.sample_weights = None\n",
    "\n",
    "    def _check_X_y(self, X, y):\n",
    "        \"\"\" Validate assumptions about format of input data\"\"\"\n",
    "        assert set(y) == {-1, 1}, 'Response variable must be ±1'\n",
    "        return X, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "f303e59f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.tree import DecisionTreeClassifier\n",
    "\n",
    "def fit(self, X: np.ndarray, y: np.ndarray, iters: int):\n",
    "    \"\"\" Fit the model using training data \"\"\"\n",
    "\n",
    "    X, y = self._check_X_y(X, y)\n",
    "    n = X.shape[0]\n",
    "\n",
    "    # init numpy arrays\n",
    "    self.sample_weights = np.zeros(shape=(iters, n))\n",
    "    self.stumps = np.zeros(shape=iters, dtype=object)\n",
    "    self.stump_weights = np.zeros(shape=iters)\n",
    "    self.errors = np.zeros(shape=iters)\n",
    "\n",
    "    # initialize weights uniformly\n",
    "    self.sample_weights[0] = np.ones(shape=n) / n\n",
    "\n",
    "    for t in range(iters):\n",
    "        # fit  weak learner\n",
    "        curr_sample_weights = self.sample_weights[t]\n",
    "        stump = DecisionTreeClassifier(max_depth=1, max_leaf_nodes=2)\n",
    "        stump = stump.fit(X, y, sample_weight=curr_sample_weights)\n",
    "\n",
    "        # calculate error and stump weight from weak learner prediction\n",
    "        stump_pred = stump.predict(X)\n",
    "        err = curr_sample_weights[(stump_pred != y)].sum()# / n\n",
    "        stump_weight = np.log((1 - err) / err) / 2\n",
    "\n",
    "        # update sample weights\n",
    "        new_sample_weights = (\n",
    "            curr_sample_weights * np.exp(-stump_weight * y * stump_pred)\n",
    "        )\n",
    "        \n",
    "        new_sample_weights /= new_sample_weights.sum()\n",
    "\n",
    "        # If not final iteration, update sample weights for t+1\n",
    "        if t+1 < iters:\n",
    "            self.sample_weights[t+1] = new_sample_weights\n",
    "\n",
    "        # save results of iteration\n",
    "        self.stumps[t] = stump\n",
    "        self.stump_weights[t] = stump_weight\n",
    "        self.errors[t] = err\n",
    "\n",
    "    return self"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "4bf43797",
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(self, X):\n",
    "    \"\"\" Make predictions using already fitted model \"\"\"\n",
    "    stump_preds = np.array([stump.predict(X) for stump in self.stumps])\n",
    "    return np.sign(np.dot(self.stump_weights, stump_preds))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "720b2226",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train error: 0.0%\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# assign our individually defined functions as methods of our classifier\n",
    "AdaBoost.fit = fit\n",
    "AdaBoost.predict = predict\n",
    "\n",
    "clf = AdaBoost().fit(X, y, iters=10)\n",
    "plot_adaboost(X, y, clf)\n",
    "\n",
    "train_err = (clf.predict(X) != y).mean()\n",
    "print(f'Train error: {train_err:.1%}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "98f08bf7",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x3000 with 20 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def truncate_adaboost(clf, t: int):\n",
    "    \"\"\" Truncate a fitted AdaBoost up to (and including) a particular iteration \"\"\"\n",
    "    assert t > 0, 't must be a positive integer'\n",
    "    from copy import deepcopy\n",
    "    new_clf = deepcopy(clf)\n",
    "    new_clf.stumps = clf.stumps[:t]\n",
    "    new_clf.stump_weights = clf.stump_weights[:t]\n",
    "    return new_clf\n",
    "\n",
    "\n",
    "def plot_staged_adaboost(X, y, clf, iters=10):\n",
    "    \"\"\" Plot weak learner and cumulaive strong learner at each iteration. \"\"\"\n",
    "\n",
    "    # larger grid\n",
    "    fig, axes = plt.subplots(figsize=(8, iters*3),\n",
    "                             nrows=iters,\n",
    "                             ncols=2,\n",
    "                             sharex=True,\n",
    "                             dpi=100)\n",
    "    \n",
    "    fig.set_facecolor('white')\n",
    "\n",
    "    _ = fig.suptitle('Decision boundaries by iteration')\n",
    "    for i in range(iters):\n",
    "        ax1, ax2 = axes[i]\n",
    "\n",
    "        # Plot weak learner\n",
    "        _ = ax1.set_title(f'Weak learner at t={i + 1}')\n",
    "        plot_adaboost(X, y, clf.stumps[i],\n",
    "                      sample_weights=clf.sample_weights[i],\n",
    "                      annotate=False, ax=ax1)\n",
    "\n",
    "        # Plot strong learner\n",
    "        trunc_clf = truncate_adaboost(clf, t=i + 1)\n",
    "        _ = ax2.set_title(f'Strong learner at t={i + 1}')\n",
    "        plot_adaboost(X, y, trunc_clf,\n",
    "                      sample_weights=clf.sample_weights[i],\n",
    "                      annotate=False, ax=ax2)\n",
    "\n",
    "    plt.tight_layout()\n",
    "    plt.subplots_adjust(top=0.95)\n",
    "    plt.show()\n",
    "\n",
    "clf = AdaBoost().fit(X, y, iters=10)\n",
    "plot_staged_adaboost(X, y, clf)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "pDL",
   "language": "python",
   "name": "pdl"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}