Week10 - GradBoost.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gradient Boosting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Steps\n",
    "1. Make a first guess for y_train and y_test, using average of y_train\n",
    "$$\n",
    "y_{train_{p_0}} = \\frac{1}{n} \\sum_{i=1}^n y_{train_{i}}  \\\\\n",
    "y_{test_{p_0}} = y_{train_{p_0}} \n",
    "$$\n",
    "2. Calculate the residuals from the training set\n",
    "$$\n",
    "r_0 = y_{train} - y_{train_{p_0}}\n",
    "$$\n",
    "3. Fit a week learner to the residuals minimizing the loss function. Let's call it $f_0$.\n",
    "$$\n",
    "r_0 = f_0(X_{train})\n",
    "$$\n",
    "4. Increment the predicted y's.\n",
    "$$\n",
    "y_{train_{p_1}} = y_{train_{p_0}} + \\alpha f_0(X_{train}) \\\\\n",
    "y_{test_{p_1}} = y_{test_{p_0}} + \\alpha f_0(X_{test}) \\\\\n",
    "$$\n",
    "$\\alpha$ is the learning rate.\n",
    "\n",
    "5. Repeat 2 to 4 until you reach the number of boosting rounds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def GradBoost(model, X_train, y_train, X_test, boosting_rounds, learning_rate: float = 0.1):\n",
    "    #make a first guess of our training target variable using the mean of y_train\n",
    "    y_hat_train = np.repeat(np.mean(y_train), len(y_train))\n",
    "\n",
    "    #Initiate the test prediction with the mean of the training target variable.\n",
    "    y_hat_test = np.repeat(np.mean(y_train), len(y_test))\n",
    "\n",
    "    #Calculate the residuals\n",
    "    residuals = y_train - y_hat_train\n",
    "\n",
    "    #Iterate through the boosting rounds\n",
    "    for i in range(boosting_rounds):\n",
    "        #Fit the model to the residuals\n",
    "        model = model.fit(X_train, residuals)\n",
    "\n",
    "        #Increment the predicted training y with the pseudoresidulas * learning rate\n",
    "        y_hat_train = y_hat_train + learning_rate * model.predict(X_train)\n",
    "\n",
    "        #Increment the predicted test y as well\n",
    "        y_hat_test = y_hat_test + learning_rate * model.predict(X_test)\n",
    "\n",
    "        #Calculate the residuals for the next round\n",
    "        residuals = y_train - y_hat_train\n",
    "\n",
    "    return y_hat_train, y_hat_test\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Demonstration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_regression\n",
    "\n",
    "X, y = make_regression(n_samples = 1000,\n",
    "                        n_features = 20,\n",
    "                        n_informative = 15,\n",
    "                        n_targets = 1,\n",
    "                        bias = 0.0,\n",
    "                        noise = 20,\n",
    "                        shuffle = True,\n",
    "                        random_state = 13)\n",
    "\n",
    "X_train = X[0:800]\n",
    "y_train = y[0:800]\n",
    "\n",
    "X_test = X[800:]\n",
    "y_test = y[800:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "model = DecisionTreeRegressor(criterion='squared_error', max_depth=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "round #: 5, mse: 34533.86849419913\n",
      "round #: 10, mse: 25528.592361427367\n",
      "round #: 15, mse: 19136.599769132084\n",
      "round #: 20, mse: 14648.044507599256\n",
      "round #: 25, mse: 11459.06364248089\n",
      "round #: 30, mse: 9128.094374117594\n",
      "round #: 35, mse: 7310.768003762691\n",
      "round #: 40, mse: 5978.90406036746\n",
      "round #: 45, mse: 4945.0105504213625\n",
      "round #: 50, mse: 4114.202235579171\n",
      "round #: 55, mse: 3504.608724077598\n",
      "round #: 60, mse: 2986.8922224538755\n",
      "round #: 65, mse: 2592.205507526533\n",
      "round #: 70, mse: 2231.005500265884\n",
      "round #: 75, mse: 1942.7838152537684\n",
      "round #: 80, mse: 1721.5043747746472\n",
      "round #: 85, mse: 1538.2240733809201\n",
      "round #: 90, mse: 1386.3457437257232\n",
      "round #: 95, mse: 1240.7055168322297\n",
      "round #: 100, mse: 1117.8412308525265\n"
     ]
    }
   ],
   "source": [
    "mse_train = []\n",
    "n_rounds = np.arange(5, 101, 5)\n",
    "for n_round in n_rounds:\n",
    "    y_hat_train = GradBoost(model,\n",
    "                            X_train,\n",
    "                            y_train,\n",
    "                            X_test,\n",
    "                            boosting_rounds=n_round,\n",
    "                            learning_rate=0.1)[0]\n",
    "\n",
    "    mse_train.append(np.mean((y_train - y_hat_train) **2))\n",
    "    print(\"round #: {0}, mse: {1}\".format(n_round, mse_train[-1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Training Mean squared error')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 8))\n",
    "plt.plot(n_rounds, mse_train)\n",
    "plt.title(\"Training MSE vs Boosting Rounds\", fontsize=20)\n",
    "plt.xlabel('NUmber of Boosting rounds', fontsize=15)\n",
    "plt.ylabel('Training Mean squared error', fontsize=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.10.2 64-bit",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.2"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "369f2c481f4da34e4445cda3fffd2e751bd1c4d706f27375911949ba6bb62e1c"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}