From Quantile Regression to Quantile Random Forests.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## From Quantile Regression to Quantile Random Forests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "\n",
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       "    }\n",
       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   \n",
       "2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0  242.0   \n",
       "3  0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0  222.0   \n",
       "4  0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0  222.0   \n",
       "\n",
       "   PTRATIO       B  LSTAT  \n",
       "0     15.3  396.90   4.98  \n",
       "1     17.8  396.90   9.14  \n",
       "2     17.8  392.83   4.03  \n",
       "3     18.7  394.63   2.94  \n",
       "4     18.7  396.90   5.33  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "\n",
    "import pandas as pd  \n",
    "import seaborn as sns \n",
    "from sklearn import metrics\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "from sklearn.datasets import load_boston\n",
    "boston_dataset = load_boston()\n",
    "boston = pd.DataFrame(boston_dataset.data, columns=boston_dataset.feature_names)\n",
    "boston.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20, 5))\n",
    "\n",
    "features = ['LSTAT', 'RM','CRIM','DIS']\n",
    "target = boston_dataset.target\n",
    "\n",
    "for i, col in enumerate(features):\n",
    "    plt.subplot(1, len(features) , i+1)\n",
    "    x = boston[col]\n",
    "    y = target\n",
    "    plt.scatter(x, y, marker='o')\n",
    "    plt.title(col)\n",
    "    plt.xlabel(col)\n",
    "    plt.ylabel('MEDV')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import preprocessing\n",
    "boston = pd.DataFrame(boston_dataset.data, columns=boston_dataset.feature_names)\n",
    "\n",
    "# Standardize the variables\n",
    "# It is not necessary to standardize the target. I do it just for convenience.\n",
    "X_scaled = pd.DataFrame(preprocessing.scale(boston))\n",
    "Y_scaled = preprocessing.scale(boston_dataset.target)\n",
    "X_scaled.columns = boston.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### OLS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2 score is 0.73\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error\n",
    "X_train, X_test, Y_train, Y_test = train_test_split(X_scaled, Y_scaled, test_size = 0.2, random_state=5)\n",
    "\n",
    "OLS = LinearRegression()\n",
    "OLS.fit(X_train, Y_train)\n",
    "\n",
    "# model evaluation for testing set\n",
    "y_test_predict = OLS.predict(X_test)\n",
    "r2 = metrics.r2_score(Y_test, y_test_predict).round(2)\n",
    "print('R2 score is {}'.format(r2) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the coefficients in descending order\n",
    "w = pd.DataFrame()\n",
    "w['Var'] = X_train.columns\n",
    "w = w.set_index('Var') # Set the variable names as the index\n",
    "w['beta'] = OLS.coef_\n",
    "w['beta_abs'] = np.abs(w['beta']) # Get the absolute value for ranking\n",
    "w = w.sort_values(by='beta_abs')\n",
    "w['beta'].plot.barh()\n",
    "plt.title('OLS')\n",
    "#fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantile Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.regression.quantile_regression as Q_reg\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "quantiles = [0.01, 0.05, 0.50, 0.95 , 0.99]\n",
    "\n",
    "# Get the model, the cofficients and the predictions in (a) - (c)\n",
    "def Qreg(q):\n",
    "   # (a) Modeling \n",
    "   mod = Q_reg.QuantReg(Y_train, X_train).fit(q=q)\n",
    "    \n",
    "   # (b) Get the coefficients and the lower and upper bounds\n",
    "   coefs = pd.DataFrame()\n",
    "   coefs['param'] = mod.params\n",
    "   coefs = pd.concat([coefs,mod.conf_int()],axis=1) # \"mod.conf_int\" will give the lower and upper bounds\n",
    "   coefs['q'] = q\n",
    "   coefs.columns = ['beta','beta_lower','beta_upper','quantile']\n",
    "    \n",
    "   return coefs\n",
    "\n",
    "Qreg_coefs = pd.DataFrame()\n",
    "\n",
    "# Get the actual and quantile predictions\n",
    "for q in quantiles:\n",
    "    coefs = Qreg(q)\n",
    "    Qreg_coefs = pd.concat([Qreg_coefs,coefs])\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2 score is 0.7536284701070339\n"
     ]
    }
   ],
   "source": [
    "q = 0.5\n",
    "Y_test_pred = Q_reg.QuantReg(Y_train, X_train).fit(q=q).predict(X_test)\n",
    "r2 = metrics.r2_score(Y_test,Y_test_pred)\n",
    "print('R2 score is {}'.format(r2) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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>0.01</th>\n",
       "      <th>0.05</th>\n",
       "      <th>0.5</th>\n",
       "      <th>0.95</th>\n",
       "      <th>0.99</th>\n",
       "      <th>actual</th>\n",
       "      <th>interval</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.09</td>\n",
       "      <td>2.09</td>\n",
       "      <td>1.78</td>\n",
       "      <td>1.62</td>\n",
       "      <td>1.62</td>\n",
       "      <td>2.989460</td>\n",
       "      <td>-0.47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.70</td>\n",
       "      <td>-1.69</td>\n",
       "      <td>-1.91</td>\n",
       "      <td>-1.99</td>\n",
       "      <td>-1.99</td>\n",
       "      <td>-1.570830</td>\n",
       "      <td>-0.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1.29</td>\n",
       "      <td>-1.28</td>\n",
       "      <td>-1.49</td>\n",
       "      <td>-1.56</td>\n",
       "      <td>-1.57</td>\n",
       "      <td>-1.690551</td>\n",
       "      <td>-0.28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.47</td>\n",
       "      <td>1.47</td>\n",
       "      <td>1.31</td>\n",
       "      <td>1.22</td>\n",
       "      <td>1.23</td>\n",
       "      <td>1.378665</td>\n",
       "      <td>-0.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.59</td>\n",
       "      <td>-0.59</td>\n",
       "      <td>-0.75</td>\n",
       "      <td>-0.82</td>\n",
       "      <td>-0.82</td>\n",
       "      <td>-0.928689</td>\n",
       "      <td>-0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>-1.28</td>\n",
       "      <td>-1.27</td>\n",
       "      <td>-1.15</td>\n",
       "      <td>-1.08</td>\n",
       "      <td>-1.08</td>\n",
       "      <td>-1.549063</td>\n",
       "      <td>0.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>-1.64</td>\n",
       "      <td>-1.64</td>\n",
       "      <td>-1.50</td>\n",
       "      <td>-1.43</td>\n",
       "      <td>-1.43</td>\n",
       "      <td>-0.819852</td>\n",
       "      <td>0.21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>0.22</td>\n",
       "      <td>0.23</td>\n",
       "      <td>0.40</td>\n",
       "      <td>0.48</td>\n",
       "      <td>0.48</td>\n",
       "      <td>-0.340967</td>\n",
       "      <td>0.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>0.92</td>\n",
       "      <td>0.92</td>\n",
       "      <td>1.10</td>\n",
       "      <td>1.18</td>\n",
       "      <td>1.19</td>\n",
       "      <td>0.584152</td>\n",
       "      <td>0.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>101</th>\n",
       "      <td>-0.70</td>\n",
       "      <td>-0.69</td>\n",
       "      <td>-0.52</td>\n",
       "      <td>-0.43</td>\n",
       "      <td>-0.43</td>\n",
       "      <td>0.584152</td>\n",
       "      <td>0.27</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>102 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     0.01  0.05   0.5  0.95  0.99    actual  interval\n",
       "0    2.09  2.09  1.78  1.62  1.62  2.989460     -0.47\n",
       "1   -1.70 -1.69 -1.91 -1.99 -1.99 -1.570830     -0.29\n",
       "2   -1.29 -1.28 -1.49 -1.56 -1.57 -1.690551     -0.28\n",
       "3    1.47  1.47  1.31  1.22  1.23  1.378665     -0.24\n",
       "4   -0.59 -0.59 -0.75 -0.82 -0.82 -0.928689     -0.23\n",
       "..    ...   ...   ...   ...   ...       ...       ...\n",
       "97  -1.28 -1.27 -1.15 -1.08 -1.08 -1.549063      0.20\n",
       "98  -1.64 -1.64 -1.50 -1.43 -1.43 -0.819852      0.21\n",
       "99   0.22  0.23  0.40  0.48  0.48 -0.340967      0.26\n",
       "100  0.92  0.92  1.10  1.18  1.19  0.584152      0.27\n",
       "101 -0.70 -0.69 -0.52 -0.43 -0.43  0.584152      0.27\n",
       "\n",
       "[102 rows x 7 columns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.regression.quantile_regression as Q_reg\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "quantiles = [0.01, 0.05, 0.50, 0.95 , 0.99]\n",
    "\n",
    "# Get the model, the cofficients and the predictions in (a) - (c)\n",
    "def Qreg(q):\n",
    "   # (a) Modeling \n",
    "   mod = Q_reg.QuantReg(Y_train, X_train).fit(q=q)\n",
    "    \n",
    "   # (b) Get the coefficients and the lower and upper bounds\n",
    "   coefs = pd.DataFrame()\n",
    "   coefs['param'] = mod.params\n",
    "   coefs = pd.concat([coefs,mod.conf_int()],axis=1) # \"mod.conf_int\" will give the lower and upper bounds\n",
    "   coefs['q'] = q\n",
    "   coefs.columns = ['beta','beta_lower','beta_upper','quantile']\n",
    "    \n",
    "   # (c) Predictions\n",
    "   pred = pd.Series(mod.predict(X_test).round(2))\n",
    "   return coefs, pred\n",
    "\n",
    "Qreg_coefs = pd.DataFrame()\n",
    "Qreg_actual_pred = pd.DataFrame()\n",
    "\n",
    "# Get the actual and quantile predictions\n",
    "for q in quantiles:\n",
    "    coefs, pred = Qreg(q)\n",
    "    Qreg_coefs = pd.concat([Qreg_coefs,coefs])\n",
    "    Qreg_actual_pred = pd.concat([Qreg_actual_pred,pred],axis=1)\n",
    "\n",
    "Qreg_actual_pred.columns=quantiles\n",
    "Qreg_actual_pred['actual'] = Y_test\n",
    "Qreg_actual_pred['interval'] = Qreg_actual_pred[0.99] - Qreg_actual_pred[0.01]\n",
    "Qreg_actual_pred = Qreg_actual_pred.sort_values('interval').reset_index(drop=True)\n",
    "Qreg_actual_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2 score is 0.75\n"
     ]
    }
   ],
   "source": [
    "r2 = metrics.r2_score(Qreg_actual_pred['actual'], Qreg_actual_pred[0.5]).round(2)\n",
    "print('R2 score is {}'.format(r2) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Get the absolute value of the coefficients for ranking\n",
    "Qreg_coefs['beta_abs'] = np.abs(Qreg_coefs['beta'] ) \n",
    "Qreg_coefs = Qreg_coefs.sort_values(by=['quantile','beta_abs'])\n",
    "\n",
    "fig = plt.figure(figsize=(12, 5))\n",
    "\n",
    "n = len(quantiles)\n",
    "\n",
    "for i in range(n):\n",
    "    plt.subplot(1, n, i+1)\n",
    "    w = Qreg_coefs[Qreg_coefs['quantile']==quantiles[i]]\n",
    "    w['beta'].plot.barh()\n",
    "    plt.title('Quantile = ' + str(quantiles[i] ))\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantile Gradient Boosting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.ensemble import GradientBoostingRegressor\n",
    "quantiles = [0.01, 0.05, 0.50, 0.95 , 0.99]\n",
    "\n",
    "# Get the model and the predictions in (a) - (b)\n",
    "def GBM(q):\n",
    "    \n",
    "   # (a) Modeling  \n",
    "   mod = GradientBoostingRegressor(loss='quantile', alpha=q,\n",
    "                                n_estimators=500, max_depth=8,\n",
    "                                learning_rate=.01, min_samples_leaf=20,\n",
    "                                min_samples_split=20)\n",
    "   mod.fit(X_train, Y_train)\n",
    "\n",
    "   # (b) Predictions\n",
    "   pred = pd.Series(mod.predict(X_test).round(2))\n",
    "   return pred, mod\n",
    "\n",
    "GBM_models=[]\n",
    "GBM_actual_pred = pd.DataFrame()\n",
    "\n",
    "for q in quantiles:\n",
    "    pred , model = GBM(q)\n",
    "    GBM_models.append(model)\n",
    "    GBM_actual_pred = pd.concat([GBM_actual_pred,pred],axis=1)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12, 5))\n",
    "\n",
    "n = len(quantiles)\n",
    "\n",
    "for i in range(n):\n",
    "    plt.subplot(1, n, i+1)\n",
    "    feature_importance = GBM_models[i].feature_importances_\n",
    "    sorted_idx = np.argsort(feature_importance)\n",
    "    pos = np.arange(sorted_idx.shape[0]) + .5\n",
    "    plt.barh(pos, feature_importance[sorted_idx], align='center')\n",
    "    plt.yticks(pos, np.array(boston.columns)[sorted_idx])\n",
    "    plt.title('Quantile = ' + str(quantiles[i] ))\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2 score is 0.89\n"
     ]
    }
   ],
   "source": [
    "GBM_actual_pred.columns=quantiles\n",
    "GBM_actual_pred['actual'] = Y_test\n",
    "GBM_actual_pred['interval'] = GBM_actual_pred[np.max(quantiles)] - GBM_actual_pred[np.min(quantiles)]\n",
    "GBM_actual_pred = GBM_actual_pred.sort_values('interval')\n",
    "GBM_actual_pred\n",
    "\n",
    "r2 = metrics.r2_score(GBM_actual_pred['actual'], GBM_actual_pred[0.5]).round(2)\n",
    "print('R2 score is {}'.format(r2) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def showIntervals(df):  \n",
    "    df = df.reset_index(drop='index')\n",
    "    plt.plot(df['actual'],'go',markersize=3,label='Actual')\n",
    "    plt.fill_between(\n",
    "        np.arange(df.shape[0]), df[0.01], df[0.99], alpha=0.5, color=\"r\",\n",
    "        label=\"Predicted interval\")\n",
    "    plt.xlabel(\"Ordered samples.\")\n",
    "    plt.ylabel(\"Values and prediction intervals.\")\n",
    "    plt.xlim([0, 100])\n",
    "    plt.ylim([-4, 6])\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "    \n",
    "showIntervals(GBM_actual_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9607843137254902\n"
     ]
    }
   ],
   "source": [
    "def correctPcnt(df):\n",
    "    correct = 0\n",
    "    obs = df.shape[0]\n",
    "    for i in range(obs):\n",
    "        if df.loc[i,0.01] <= df.loc[i,'actual'] <= df.loc[i,0.99]:\n",
    "            correct += 1\n",
    "    print(correct/obs)\n",
    "    \n",
    "    \n",
    "correctPcnt(GBM_actual_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quantile Random Forests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>0</th>\n",
       "      <td>2.87</td>\n",
       "      <td>2.99</td>\n",
       "      <td>2.39</td>\n",
       "      <td>2.40</td>\n",
       "      <td>2.91</td>\n",
       "      <td>2.76</td>\n",
       "      <td>2.52</td>\n",
       "      <td>2.80</td>\n",
       "      <td>2.56</td>\n",
       "      <td>2.60</td>\n",
       "      <td>...</td>\n",
       "      <td>2.20</td>\n",
       "      <td>2.24</td>\n",
       "      <td>2.28</td>\n",
       "      <td>2.56</td>\n",
       "      <td>2.99</td>\n",
       "      <td>1.96</td>\n",
       "      <td>2.99</td>\n",
       "      <td>2.90</td>\n",
       "      <td>2.44</td>\n",
       "      <td>2.61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.48</td>\n",
       "      <td>0.39</td>\n",
       "      <td>0.16</td>\n",
       "      <td>1.04</td>\n",
       "      <td>0.39</td>\n",
       "      <td>0.56</td>\n",
       "      <td>0.42</td>\n",
       "      <td>0.65</td>\n",
       "      <td>1.38</td>\n",
       "      <td>0.93</td>\n",
       "      <td>...</td>\n",
       "      <td>0.86</td>\n",
       "      <td>0.38</td>\n",
       "      <td>0.86</td>\n",
       "      <td>0.70</td>\n",
       "      <td>1.06</td>\n",
       "      <td>0.73</td>\n",
       "      <td>0.71</td>\n",
       "      <td>0.62</td>\n",
       "      <td>1.08</td>\n",
       "      <td>0.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.02</td>\n",
       "      <td>0.02</td>\n",
       "      <td>0.11</td>\n",
       "      <td>-0.08</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.11</td>\n",
       "      <td>-0.07</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>0.29</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.22</td>\n",
       "      <td>-0.03</td>\n",
       "      <td>0.31</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.18</td>\n",
       "      <td>-0.95</td>\n",
       "      <td>-1.29</td>\n",
       "      <td>-1.23</td>\n",
       "      <td>-1.31</td>\n",
       "      <td>-0.95</td>\n",
       "      <td>-1.04</td>\n",
       "      <td>-1.05</td>\n",
       "      <td>-1.36</td>\n",
       "      <td>-1.56</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.98</td>\n",
       "      <td>-0.72</td>\n",
       "      <td>-1.74</td>\n",
       "      <td>-1.68</td>\n",
       "      <td>-1.10</td>\n",
       "      <td>-1.20</td>\n",
       "      <td>-1.62</td>\n",
       "      <td>-1.03</td>\n",
       "      <td>-1.01</td>\n",
       "      <td>-1.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.47</td>\n",
       "      <td>1.31</td>\n",
       "      <td>2.08</td>\n",
       "      <td>2.40</td>\n",
       "      <td>2.32</td>\n",
       "      <td>2.34</td>\n",
       "      <td>2.00</td>\n",
       "      <td>1.84</td>\n",
       "      <td>0.99</td>\n",
       "      <td>2.96</td>\n",
       "      <td>...</td>\n",
       "      <td>2.20</td>\n",
       "      <td>1.36</td>\n",
       "      <td>2.28</td>\n",
       "      <td>2.56</td>\n",
       "      <td>1.18</td>\n",
       "      <td>2.52</td>\n",
       "      <td>1.05</td>\n",
       "      <td>2.25</td>\n",
       "      <td>2.44</td>\n",
       "      <td>2.61</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 200 columns</p>\n",
       "</div>"
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       "      0     0     0     0     0     0     0     0     0     0  ...     0  \\\n",
       "0  2.87  2.99  2.39  2.40  2.91  2.76  2.52  2.80  2.56  2.60  ...  2.20   \n",
       "1  0.48  0.39  0.16  1.04  0.39  0.56  0.42  0.65  1.38  0.93  ...  0.86   \n",
       "2 -0.02  0.02  0.11 -0.08  0.06  0.10  0.12  0.11 -0.07 -0.06  ... -0.02   \n",
       "3 -1.18 -0.95 -1.29 -1.23 -1.31 -0.95 -1.04 -1.05 -1.36 -1.56  ... -0.98   \n",
       "4  2.47  1.31  2.08  2.40  2.32  2.34  2.00  1.84  0.99  2.96  ...  2.20   \n",
       "\n",
       "      0     0     0     0     0     0     0     0     0  \n",
       "0  2.24  2.28  2.56  2.99  1.96  2.99  2.90  2.44  2.61  \n",
       "1  0.38  0.86  0.70  1.06  0.73  0.71  0.62  1.08  0.09  \n",
       "2  0.29 -0.01  0.06  0.10  0.22 -0.03  0.31  0.09  0.14  \n",
       "3 -0.72 -1.74 -1.68 -1.10 -1.20 -1.62 -1.03 -1.01 -1.09  \n",
       "4  1.36  2.28  2.56  1.18  2.52  1.05  2.25  2.44  2.61  \n",
       "\n",
       "[5 rows x 200 columns]"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# random forest\n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "rf = RandomForestRegressor(n_estimators=200, random_state=0,min_samples_split=10)\n",
    "rf.fit(X_train, Y_train)\n",
    "\n",
    "# Get the predictions of all trees for all observations\n",
    "# Each observation has N predictions from the N trees\n",
    "pred_Q = pd.DataFrame()\n",
    "for pred in rf.estimators_:\n",
    "    temp = pd.Series(pred.predict(X_test).round(2))\n",
    "    pred_Q = pd.concat([pred_Q,temp],axis=1)\n",
    "pred_Q.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0.01</th>\n",
       "      <th>0.05</th>\n",
       "      <th>0.50</th>\n",
       "      <th>0.95</th>\n",
       "      <th>0.99</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.0491</td>\n",
       "      <td>2.1395</td>\n",
       "      <td>2.670</td>\n",
       "      <td>2.9900</td>\n",
       "      <td>2.9900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0593</td>\n",
       "      <td>0.1295</td>\n",
       "      <td>0.620</td>\n",
       "      <td>0.9700</td>\n",
       "      <td>1.1400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.2314</td>\n",
       "      <td>-0.1800</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.3115</td>\n",
       "      <td>0.7104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.7701</td>\n",
       "      <td>-1.6705</td>\n",
       "      <td>-1.105</td>\n",
       "      <td>-0.8290</td>\n",
       "      <td>-0.5992</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.1892</td>\n",
       "      <td>0.9680</td>\n",
       "      <td>2.250</td>\n",
       "      <td>2.8130</td>\n",
       "      <td>2.9600</td>\n",
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       "     0.01    0.05   0.50    0.95    0.99\n",
       "0  2.0491  2.1395  2.670  2.9900  2.9900\n",
       "1  0.0593  0.1295  0.620  0.9700  1.1400\n",
       "2 -0.2314 -0.1800  0.005  0.3115  0.7104\n",
       "3 -1.7701 -1.6705 -1.105 -0.8290 -0.5992\n",
       "4  0.1892  0.9680  2.250  2.8130  2.9600"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RF_actual_pred = pd.DataFrame()\n",
    "\n",
    "for q in quantiles:\n",
    "    s = pred_Q.quantile(q=q, axis=1)\n",
    "    RF_actual_pred = pd.concat([RF_actual_pred,s],axis=1,sort=False)\n",
    "RF_actual_pred.head()   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>0.01</th>\n",
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       "      <th>0.5</th>\n",
       "      <th>0.95</th>\n",
       "      <th>0.99</th>\n",
       "      <th>actual</th>\n",
       "      <th>interval</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>-0.46</td>\n",
       "      <td>-0.40</td>\n",
       "      <td>-0.28</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.15</td>\n",
       "      <td>-0.38</td>\n",
       "      <td>0.61</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>-0.46</td>\n",
       "      <td>-0.41</td>\n",
       "      <td>-0.18</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.17</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>-0.50</td>\n",
       "      <td>-0.44</td>\n",
       "      <td>-0.32</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.13</td>\n",
       "      <td>-0.15</td>\n",
       "      <td>0.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-1.80</td>\n",
       "      <td>-1.75</td>\n",
       "      <td>-1.61</td>\n",
       "      <td>-1.39</td>\n",
       "      <td>-1.15</td>\n",
       "      <td>-1.32</td>\n",
       "      <td>0.65</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>-0.06</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.31</td>\n",
       "      <td>0.61</td>\n",
       "      <td>0.06</td>\n",
       "      <td>0.67</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>-1.05</td>\n",
       "      <td>-0.84</td>\n",
       "      <td>2.99</td>\n",
       "      <td>2.99</td>\n",
       "      <td>2.99</td>\n",
       "      <td>0.58</td>\n",
       "      <td>4.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>-1.32</td>\n",
       "      <td>-1.07</td>\n",
       "      <td>-0.72</td>\n",
       "      <td>2.99</td>\n",
       "      <td>2.99</td>\n",
       "      <td>-0.52</td>\n",
       "      <td>4.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>-1.33</td>\n",
       "      <td>-0.83</td>\n",
       "      <td>-0.21</td>\n",
       "      <td>0.00</td>\n",
       "      <td>2.99</td>\n",
       "      <td>-0.12</td>\n",
       "      <td>4.32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>-1.34</td>\n",
       "      <td>-1.17</td>\n",
       "      <td>-0.00</td>\n",
       "      <td>2.99</td>\n",
       "      <td>2.99</td>\n",
       "      <td>-0.82</td>\n",
       "      <td>4.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>-1.50</td>\n",
       "      <td>-1.36</td>\n",
       "      <td>-0.82</td>\n",
       "      <td>2.99</td>\n",
       "      <td>2.99</td>\n",
       "      <td>0.54</td>\n",
       "      <td>4.49</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>102 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     0.01  0.05   0.5  0.95  0.99  actual  interval\n",
       "11  -0.46 -0.40 -0.28  0.00  0.15   -0.38      0.61\n",
       "100 -0.46 -0.41 -0.18  0.00  0.17    0.05      0.63\n",
       "27  -0.50 -0.44 -0.32  0.01  0.13   -0.15      0.63\n",
       "5   -1.80 -1.75 -1.61 -1.39 -1.15   -1.32      0.65\n",
       "26  -0.06  0.01  0.16  0.31  0.61    0.06      0.67\n",
       "..    ...   ...   ...   ...   ...     ...       ...\n",
       "74  -1.05 -0.84  2.99  2.99  2.99    0.58      4.04\n",
       "33  -1.32 -1.07 -0.72  2.99  2.99   -0.52      4.31\n",
       "92  -1.33 -0.83 -0.21  0.00  2.99   -0.12      4.32\n",
       "19  -1.34 -1.17 -0.00  2.99  2.99   -0.82      4.33\n",
       "73  -1.50 -1.36 -0.82  2.99  2.99    0.54      4.49\n",
       "\n",
       "[102 rows x 7 columns]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RF_actual_pred = pd.DataFrame()\n",
    "\n",
    "for q in quantiles:\n",
    "    s = pred_Q.quantile(q=q, axis=1)\n",
    "    RF_actual_pred = pd.concat([RF_actual_pred,s],axis=1,sort=False)\n",
    "   \n",
    "RF_actual_pred.columns=quantiles\n",
    "RF_actual_pred['actual'] = Y_test\n",
    "RF_actual_pred['interval'] = RF_actual_pred[np.max(quantiles)] - RF_actual_pred[np.min(quantiles)]\n",
    "RF_actual_pred = RF_actual_pred.sort_values('interval')\n",
    "RF_actual_pred = RF_actual_pred.round(2)\n",
    "RF_actual_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2 score is 0.81\n"
     ]
    }
   ],
   "source": [
    "r2 = metrics.r2_score(RF_actual_pred['actual'], RF_actual_pred[0.5]).round(2)\n",
    "print('R2 score is {}'.format(r2) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9509803921568627\n"
     ]
    }
   ],
   "source": [
    "correctPcnt(RF_actual_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "showIntervals(RF_actual_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.2"
  }
 },
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