Albrech analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "import arff, numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn import preprocessing\n",
    "from sklearn.model_selection import KFold,cross_val_score\n",
    "from sklearn.model_selection import GridSearchCV,RandomizedSearchCV\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset = arff.load(open('albrecht.arff'))\n",
    "data=np.array(dataset['data'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(24, 8)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=data[:,0:6]\n",
    "Y=data[:,7:8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y=Y.reshape(24)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(24, 6)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Albrech n_estimator=500 and max_features= 1 to 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    X, Y, test_size=0.30, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "lab_enc = preprocessing.LabelEncoder()\n",
    "training_scores_encoded = lab_enc.fit_transform(y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "albrecht n_estimators=500 and max_features=1 to 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_feature=7\n",
    "MMRE_list=[]\n",
    "MdMRE_list=[]\n",
    "Pred_list= []\n",
    "for i in np.arange(1,7):   \n",
    "    clf= RandomForestRegressor(n_estimators=500,max_features=i)\n",
    "    clf.fit(X_train, training_scores_encoded)\n",
    "    Y_pred=clf.predict(X_test)\n",
    "    diff=np.absolute(y_test-Y_pred)\n",
    "    MRE=diff/y_test\n",
    "    MMRE=np.mean(MRE)\n",
    "    MdMRE=np.median(MRE)\n",
    "    P=MRE[MRE<.25]\n",
    "    Pred=(P.size/MRE.size) * 100\n",
    "    MMRE_list.append(MMRE)\n",
    "    MdMRE_list.append(MdMRE)\n",
    "    Pred_list.append(Pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.5696435684746409,\n",
       " 0.5432476125553963,\n",
       " 0.5241905397108446,\n",
       " 0.5217940030574177,\n",
       " 0.549832055223801,\n",
       " 0.5367452600329448]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MMRE_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.6106613312680178,\n",
       " 0.5663306226066005,\n",
       " 0.5322111785207178,\n",
       " 0.515310442752033,\n",
       " 0.5239572307559917,\n",
       " 0.525209328342154]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MdMRE_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[25.0, 25.0, 25.0, 25.0, 12.5, 12.5]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pred_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "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": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "x = np.arange(1,7)\n",
    "\n",
    "plt.plot(x, MMRE_list)\n",
    "plt.plot(x, MdMRE_list)\n",
    "\n",
    "plt.legend(['MMRE','MdMRE'], loc='upper right')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "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": [
    "plt.plot(x, Pred_list)\n",
    "plt.legend(['Pred'], loc='upper right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Albrech n_estimator=100 to 1000 and max_features= 5\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "MMRE_list=[]\n",
    "MdMRE_list=[]\n",
    "Pred_list= []\n",
    "for i in np.arange(100,1100,100):   \n",
    "    clf= RandomForestRegressor(n_estimators=i,max_features=5)\n",
    "    clf.fit(X_train, training_scores_encoded)\n",
    "    Y_pred=clf.predict(X_test)\n",
    "    diff=np.absolute(y_test-Y_pred)\n",
    "    MRE=diff/y_test\n",
    "    MMRE=np.mean(MRE)\n",
    "    MdMRE=np.median(MRE)\n",
    "    P=MRE[MRE<.25]\n",
    "    Pred=(P.size/MRE.size) * 100\n",
    "    MMRE_list.append(MMRE)\n",
    "    MdMRE_list.append(MdMRE)\n",
    "    Pred_list.append(Pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.5481462011587654,\n",
       " 0.5389346724512822,\n",
       " 0.539032768359244,\n",
       " 0.5350911707076615,\n",
       " 0.5445490460780971,\n",
       " 0.5309464700812565,\n",
       " 0.5366391507112551,\n",
       " 0.537256885407731,\n",
       " 0.5334994395863559,\n",
       " 0.5340082539632021]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MMRE_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.5226560819241857,\n",
       " 0.531419689342111,\n",
       " 0.5155974355664559,\n",
       " 0.5183818467363711,\n",
       " 0.5249455703282991,\n",
       " 0.5179062145920285,\n",
       " 0.5189683256806014,\n",
       " 0.522874714943419,\n",
       " 0.519703445539253,\n",
       " 0.5204791101931932]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MdMRE_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[12.5, 25.0, 12.5, 12.5, 12.5, 12.5, 12.5, 12.5, 25.0, 12.5]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pred_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "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": [
    "x = np.arange(100,1100,100)\n",
    "plt.plot(x, MMRE_list)\n",
    "plt.plot(x, MdMRE_list)\n",
    "\n",
    "plt.legend(['MMRE','MdMRE'], loc='upper right')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "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": [
    "plt.plot(x, Pred_list)\n",
    "plt.legend(['Pred'], loc='upper right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# GridSearchCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "params_grd={\n",
    " 'max_features': [1,2,3,4,5,6],\n",
    "  'n_estimators': [200, 400, 600, 800, 1000, 1200, 1400, 1600, 1800, 2000]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 10 folds for each of 60 candidates, totalling 600 fits\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done  25 tasks      | elapsed:    3.0s\n",
      "[Parallel(n_jobs=-1)]: Done 146 tasks      | elapsed:   20.9s\n",
      "[Parallel(n_jobs=-1)]: Done 349 tasks      | elapsed:   56.6s\n",
      "[Parallel(n_jobs=-1)]: Done 600 out of 600 | elapsed:  1.8min finished\n",
      "C:\\Users\\Deepak\\Anaconda3\\lib\\site-packages\\sklearn\\model_selection\\_search.py:841: DeprecationWarning: The default of the `iid` parameter will change from True to False in version 0.22 and will be removed in 0.24. This will change numeric results when test-set sizes are unequal.\n",
      "  DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "clf= RandomForestRegressor()\n",
    "grd_search=GridSearchCV(estimator = clf, param_grid = params_grd, \n",
    "                          cv = 10, n_jobs = -1, verbose = 2)\n",
    "grd_search.fit(X_train, training_scores_encoded)\n",
    "best_grid = grd_search.best_estimator_\n",
    "\n",
    "Y_pred=best_grid.predict(X_test)\n",
    "diff=np.absolute(y_test-Y_pred)\n",
    "MRE=diff/y_test\n",
    "MMRE=np.mean(MRE)\n",
    "MdMRE=np.median(MRE)\n",
    "P=MRE[MRE<.25]\n",
    "Pred=(P.size/MRE.size) * 100\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5181951173076893\n",
      "0.5144290559638214\n",
      "25.0\n"
     ]
    }
   ],
   "source": [
    "print(MMRE)\n",
    "print(MdMRE)\n",
    "print(Pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'max_features': 6, 'n_estimators': 200}"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grd_search.best_params_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# Random Hyperparameter Grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "Random_grid={'bootstrap': [True, False],\n",
    " 'max_depth': [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, None],\n",
    " 'max_features': [1,2,3,4,5,6],\n",
    " 'min_samples_leaf': [1, 2, 4],\n",
    " 'min_samples_split': [2, 5, 10],\n",
    " 'n_estimators': [200, 400, 600, 800, 1000, 1200, 1400, 1600, 1800, 2000]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 10 folds for each of 100 candidates, totalling 1000 fits\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.\n",
      "[Parallel(n_jobs=-1)]: Done  34 tasks      | elapsed:    1.4s\n",
      "[Parallel(n_jobs=-1)]: Done 179 tasks      | elapsed:   22.9s\n",
      "[Parallel(n_jobs=-1)]: Done 382 tasks      | elapsed:  1.0min\n",
      "[Parallel(n_jobs=-1)]: Done 665 tasks      | elapsed:  1.9min\n",
      "[Parallel(n_jobs=-1)]: Done 1000 out of 1000 | elapsed:  3.1min finished\n",
      "C:\\Users\\Deepak\\Anaconda3\\lib\\site-packages\\sklearn\\model_selection\\_search.py:841: DeprecationWarning: The default of the `iid` parameter will change from True to False in version 0.22 and will be removed in 0.24. This will change numeric results when test-set sizes are unequal.\n",
      "  DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "clf= RandomForestRegressor()\n",
    "random_grd_search=RandomizedSearchCV(estimator = clf, param_distributions = Random_grid, n_iter = 100, cv = 10, \n",
    "                              verbose=2, random_state=42, n_jobs = -1)\n",
    "random_grd_search.fit(X_train, training_scores_encoded)\n",
    "best_grid = random_grd_search.best_estimator_\n",
    "\n",
    "Y_pred=best_grid.predict(X_test)\n",
    "diff=np.absolute(y_test-Y_pred)\n",
    "MRE=diff/y_test\n",
    "MMRE=np.mean(MRE)\n",
    "MdMRE=np.median(MRE)\n",
    "P=MRE[MRE<.25]\n",
    "Pred=(P.size/MRE.size) * 100\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.49350352629607397\n",
      "0.46553164520495977\n",
      "25.0\n"
     ]
    }
   ],
   "source": [
    "print(MMRE)\n",
    "print(MdMRE)\n",
    "print(Pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'n_estimators': 1200,\n",
       " 'min_samples_split': 10,\n",
       " 'min_samples_leaf': 4,\n",
       " 'max_features': 6,\n",
       " 'max_depth': 30,\n",
       " 'bootstrap': False}"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_grd_search.best_params_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Regression Tree Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "clf= DecisionTreeRegressor(max_depth=30, min_samples_split=20)\n",
    "clf.fit(X_train, y_train)\n",
    "Y_pred=clf.predict(X_test)\n",
    "diff=np.absolute(y_test-Y_pred)\n",
    "MRE=diff/y_test\n",
    "MMRE=np.mean(MRE)\n",
    "MdMRE=np.median(MRE)\n",
    "P=MRE[MRE<.25]\n",
    "Pred=(P.size/MRE.size) * 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8405324382257534\n",
      "0.47200839204309997\n",
      "25.0\n"
     ]
    }
   ],
   "source": [
    "print(MMRE)\n",
    "print(MdMRE)\n",
    "print(Pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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