02_Imputing_missing_value_strategies.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Imputing Missing Values through Various Strategies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd \n",
    "import numpy as np \n",
    "\n",
    "from sklearn import datasets as d \n",
    "\n",
    "iris = d.load_iris()\n",
    "iris_X = iris.data \n",
    "masking_array = np.random.binomial(1,.25,iris_X.shape).astype(bool)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "iris_X[masking_array] = np.nan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True, False, False, False],\n",
       "       [False, False, False, False],\n",
       "       [ True, False,  True,  True],\n",
       "       [False, False, False, False],\n",
       "       [False, False, False, False]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "masking_array[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[nan, 3.5, 1.4, 0.2],\n",
       "       [4.9, 3. , 1.4, 0.2],\n",
       "       [nan, 3.2, nan, nan],\n",
       "       [4.6, 3.1, 1.5, 0.2],\n",
       "       [5. , 3.6, 1.4, 0.2]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris_X[:5]"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Imputing strategies: \n",
    "##### `mean (default)` <br>\n",
    "##### `median` <br>\n",
    "##### `most_frequent (mode)` "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5.78018868, 3.5       , 1.4       , 0.2       ],\n",
       "       [4.9       , 3.        , 1.4       , 0.2       ],\n",
       "       [5.78018868, 3.2       , 3.74642857, 1.15929204],\n",
       "       [4.6       , 3.1       , 1.5       , 0.2       ],\n",
       "       [5.        , 3.6       , 1.4       , 0.2       ]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import impute \n",
    "imp = impute.SimpleImputer()\n",
    "iris_X_prime = imp.fit_transform(iris_X)\n",
    "iris_X_prime[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Notice the difference in the position [1,2]\n",
    "\n",
    "iris_X_prime[1,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris_X[1,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5.7 , 3.5 , 1.4 , 0.2 ],\n",
       "       [4.9 , 3.  , 1.4 , 0.2 ],\n",
       "       [5.7 , 3.2 , 4.25, 1.3 ],\n",
       "       [4.6 , 3.1 , 1.5 , 0.2 ],\n",
       "       [5.  , 3.6 , 1.4 , 0.2 ]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#MEADIAN \n",
    "\n",
    "imp = impute.SimpleImputer(strategy='median')\n",
    "iris_X_prime = imp.fit_transform(iris_X)\n",
    "iris_X_prime[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1. ,  3.5,  1.4,  0.2],\n",
       "       [ 4.9,  3. ,  1.4,  0.2],\n",
       "       [-1. ,  3.2, -1. , -1. ],\n",
       "       [ 4.6,  3.1,  1.5,  0.2],\n",
       "       [ 5. ,  3.6,  1.4,  0.2]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#If missing values are -1, as it is possible \n",
    "\n",
    "iris_X[np.isnan(iris_X)] = -1 \n",
    "iris_X[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5.78018868, 3.5       , 1.4       , 0.2       ],\n",
       "       [4.9       , 3.        , 1.4       , 0.2       ],\n",
       "       [5.78018868, 3.2       , 3.74642857, 1.15929204],\n",
       "       [4.6       , 3.1       , 1.5       , 0.2       ],\n",
       "       [5.        , 3.6       , 1.4       , 0.2       ]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#The using it with imputer will be as follows: \n",
    "\n",
    "imp = impute.SimpleImputer(missing_values=-1)\n",
    "iris_X_prime = imp.fit_transform(iris_X)\n",
    "iris_X_prime[:5]"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Pandas functionality to fill missing value is bit less reusable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1. ,  3.5,  1.4,  0.2],\n",
       "       [ 4.9,  3. ,  1.4,  0.2],\n",
       "       [-1. ,  3.2, -1. , -1. ],\n",
       "       [ 4.6,  3.1,  1.5,  0.2],\n",
       "       [ 5. ,  3.6,  1.4,  0.2]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris_X_prime = np.where(pd.DataFrame(iris_X).isnull(),-1,iris_X)\n",
    "iris_X_prime[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1. ,  3.5,  1.4,  0.2],\n",
       "       [ 4.9,  3. ,  1.4,  0.2],\n",
       "       [-1. ,  3.2, -1. , -1. ],\n",
       "       [ 4.6,  3.1,  1.5,  0.2],\n",
       "       [ 5. ,  3.6,  1.4,  0.2]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(iris_X).fillna(-1)[:5].values"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Modelling when we have Outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1e0797f7ac0>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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0WVLLVeVSyLnA2UA7M9sC3Eng6piGwFvBrzF/c8njmcDdZlYKVAA3u3tBNdUuEtPKyiuY/dF6Hn5rNQ3q1eGBK4byg+Ruah0gVVKVq2UmHWF49lGWTQVSQy1KJN6tzN1HSmo66Vv2ckFSR+69bDAdW6jRl1SdvqEqUosUl5XzxDs5PPneWlo2rs/jPxrOJUPU6EuOn8JdpJb4ctNuUualsyZ/P5cN68Lv1ehLQqBwF4mwopIyHnpzNc9+vJ5OLRrx3HUnc86ADpEuS6Kcwl0kgj7O2cmU+elsLjjIT8YkkDJ2AM3V6EvCQOEuEgF7D5Zy32sreSltMz3bNeWlyWMY3UuNviR8FO4iNezNrO1MW5jJrgMl3HRWoNFXo/pq9CXhpXAXqSE7CouZ/koWr6XnMrBzC2ZfezJDurWMdFkSoxTuItXM3Vnw1VbufnUFRcXl/OaCftx8dm/q11WjL6k+CneRarR1z0FuX5DBe6t2MCIh0OirTwc1+pLqp3AXqQYVFc4LSzcy8/VsKhzuHJfENaeo0ZfUHIW7SJit27GfKakZfL6hgDP6tuO+CUPo3kaNvqRmKdxFwqSsvIJnPlzPI0tW06heHf44cSgTR6rRl0SGwl0kDLK27SUlNZ3MrfsYO6gTd182iA7N1ehLIkfhLhKCQ6XlPP5ODk+/v5ZWTRrw1I9HcNGQzpEuS0ThLnKilm0sICU1g5z8/Vwxoht3XDqQVk3U6EtqB4W7yHE6UFzGH99YxfOfbqBLy8Y8f/0ozurXPtJlifyHKoW7mT1L4H6p+e4+ODjWBngJSAQ2AFe6+24L/PXoUeBioAi4zt2/DH/pIjXvwzU7mDo/g617DnLNmB78buwAmjXUMZLUPlX9itzfgLGHjU0B3nb3vsDbwWmAiwjcO7UvMBl4KvQyRSJrb1Epv/3Xcq6e/TkN6tXhnzedwl3jByvYpdaq0m+mu39gZomHDY8ncG9VgOeB94CU4Pgcd3fgMzNrZWad3T03LBWL1LB/Z+Zyx8tZFBwo4b/O7s0vzuurRl9S64Vy2NGxUmBvBzoGn3cFNldabktw7D/C3cwmEziyJyEhIYQyRKpHfuEh7nw5i9czt5PUuQXPXXcyg7uq0ZdEh7B8pnR3NzM/ztfMAmYBJCcnH9drRaqTu5P65VbueXUFB0vLuXVsf248o5cafUlUCSXc87453WJmnYH84PhWoHul5boFx0Rqvc0FRdy2IIMP1+wkuUdr7p84lN7tm0W6LJHjFkq4LwKuBWYGH1+uNP5zM3sRGA3s1fl2qe0qKpw5n27ggTdWYcDd4wfxk9E9qKNGXxKlqnop5FwCfzxtZ2ZbgDsJhPo/zewGYCNwZXDxxQQug8whcCnkT8Ncs0hY5eQXkpKawbKNuzmzX3vumzCYbq3V6EuiW1Wvlpl0lFnnHWFZB24JpSiRmlBaXsGsD9bx6JI1NGlYl4evPIkJw7uq0ZfEBF2kK3Epc+tefjcvnZW5+7h4SCfu+v5g2jdvGOmyRMJG4S5x5VBpOX9asoZnPlxHm6YNePonIxk7uFOkyxIJO4W7xI3P1xcwJTWddTsP8IOR3Zh2SRItm9SPdFki1ULhLjFvf3EZD/w7mzmfbqRb68b8/YZRnNFXjb4ktincJaa9uyqf2+dnkLvvED89LZHffq8/TdUPRuKAfsslJu0+UMI9r65g/ldb6dOhGfNuPpWRPVpHuiyRGqNwl5ji7izO2M6dizLZU1TKf5/bh5+f24eG9dToS+KLwl1iRv6+Q0xbmMmbK/IY0rUlc64fTVKXFpEuSyQiFO4S9dydf6Vt4Z7XVlBSVsGUiwbws9N7Uk+NviSOKdwlqm3aFWj09VHOTkb1bMP9VwylZ7umkS5LJOIU7hKVyiucv32ygQffWEXdOsa9lw3mR6MS1OhLJEjhLlFnTV4ht6am89WmPZzTvz1/mDCELq0aR7oskVpF4S5Ro6SsgqffX8vj7+TQtGFd/vTDYYwf1kWNvkSOQOEuUSF9yx5unZdO9vZCxp3UhTvHJdGumRp9iRyNwl1qtUOl5Tzy1mqe+XAd7Zs35JlrkrkgqeOxXygS5xTuUmt9tm4XU+dnsH7nASaN6s7UiwfSopEafYlUxQmHu5n1B16qNNQL+D3QCrgR2BEcv83dF5/oeiT+FB4qZebr2bywdBPd2zTmHz8bzal92kW6LJGocsLh7u6rgGEAZlaXwE2wFxC4rd4j7v5gOAqU+PJudj63Lcggb98hfnZ6T379vX40aaAPmCLHK1z/as4D1rr7Rl25ICei4EAJd7+SxcKvt9GvYzOe/PGpDE9Qoy+RExWucL8KmFtp+udmdg2QBvzG3Xcf/gIzmwxMBkhISAhTGRJt3J1X0nOZviiLwkOl/PK8vtxyTh8a1FPrAJFQWOB+1iG8gVkDYBswyN3zzKwjsBNw4B6gs7tf/13vkZyc7GlpaSHVIdFn+95Ao68lK/M4qVtL7p84lAGd1OhLpKrMbJm7Jx9pXjiO3C8CvnT3PIBvHoMrfgZ4NQzrkBji7rz4xWbue20lpRUVTLtkID89rSd11TpAJGzCEe6TqHRKxsw6u3tucHICkBmGdUiM2LjrAFNSM/h03S7G9GrDzMuHkqhGXyJhF1K4m1lT4ALgpkrDD5jZMAKnZTYcNk/iVHmF89zH63nwzVXUr1OHGZcP4aqTu6t1gEg1CSnc3f0A0PawsatDqkhizqrtgUZfyzfv4fyBHbj3siF0atko0mWJxDRdQCzVpqSsgiffy+GJd3No3qg+j00azrihnXW0LlIDFO5SLb7evIeUeemsyitk/LAu/P7SJNqq0ZdIjVG4S1gdLCnn4bdWMfuj9XRo3ohnr0vm3AFq9CVS0xTuEjafrN3JlNQMNhUUMWlUAlMvHqBGXyIRonCXkO07VMqMxdnM/XwTPdo2Ye6NYzild9tjv1BEqo3CXUKyZEUety/MYEdhMZPP7MWvzu9H4wZ1I12WSNxTuMsJ2bW/mLteWcGi5dsY0Kk5z1yTzNBurSJdlogEKdzluLg7i5ZvY/qiLPYXl/HrC/px81m91ehLpJZRuEuVbdtzkGkLM3knO5/hCa24/4qh9OvYPNJlicgRKNzlmCoqnH98vomZr2dTXuHccWkS152aqEZfIrWYwl2+0/qdB5iSms7S9QWc1qctMyYMJaFtk0iXJSLHoHCXIyorr2D2R+t5+K3VNKhXh/uvGMKVyWr0JRItFO7yLStz95GSmk76lr1ckNSRey8bTMcWavQlEk0U7vL/FJeV88Q7OTz53lpaNanPEz8awcVDOuloXSQKKdwFgC837SZlXjpr8vdz+fCu3HFpEq2bNoh0WSJyghTuca6opIwH31jNc5+sp3OLRjx33cmcM6BDpMsSkRCFHO5mtgEoBMqBMndPNrM2wEtAIoG7MV3p7rtDXZeE18c5O5kyP53NBQe5ekwPUi4aQLOG+v+9SCwI17/kc9x9Z6XpKcDb7j7TzKYEp1PCtC4J0d6Dpdz32kpeSttMz3ZNeWnyGEb3UqMvkVhSXYdp44Gzg8+fB95D4V4rvJm1nWkLM9l1oISbz+rN/5zfl0b11ehLJNaEI9wdeNPMHPiLu88COrp7bnD+duBbd2sws8nAZICEhIQwlCHfZUdhMdNfyeK19FwGdm7B7GtPZki3lpEuS0SqSTjC/XR332pmHYC3zCy78kx392Dwc9j4LGAWQHJy8rfmS3i4Owu+2srdr66gqLic313Yn8ln9qJ+XTX6EollIYe7u28NPuab2QJgFJBnZp3dPdfMOgP5oa5Hjt/WPQe5bX4G76/ewYiEVjwwcSh9OqjRl0g8CCnczawpUMfdC4PPvwfcDSwCrgVmBh9fDrVQqbqKCud/l27k/tezcWD6uCSuPkWNvkTiSahH7h2BBcFvMNYD/uHu/zazL4B/mtkNwEbgyhDXI1W0dsd+pqSm88WG3ZzRtx33TRhC9zZq9CUSb0IKd3dfB5x0hPFdwHmhvLccn9LyCp75cB1/WrKGRvXq8MeJQ5k4sptaB4jEKX1jJQZkbt1LSmo6Wdv2MXZQJ+6+bBAdmqvRl0g8U7hHsUOl5fz5nTU8/f46WjdpwFM/HsFFQzpHuiwRqQUU7lEqbUMBt6ams27HASaO7Ma0SwbSqokafYlIgMI9yhwoLuOBf2cz57ONdGnZmDnXj+LMfu0jXZaI1DIK9yjy/uod3DY/g217D3LtKYn87sL+NFWjLxE5AiVDFNhTVMI9r64k9cst9G7flH/ddArJiW0iXZaI1GIK91ru9Yxc7ng5i91FJdxyTm/++1w1+hKRY1O411L5hYe48+UsXs/czqAuLXj++pMZ1EWNvkSkahTutYy7M2/ZFu59bSUHS8tJGTuAG8/oST01+hKR46Bwr0U2FxRx24IMPlyzk1GJbZhxxRB6t28W6bJEJAop3GuBigpnzqcbeOCNVRhwz/hB/Hh0D+qo0ZeInCCFe4Tl5BeSkprBso27Oatfe+67fAhdWzWOdFkiEuUU7hFSWl7BX95fy2Nv59CkYV0evvIkJgzvqkZfIhIWCvcIyNy6l9/NS2dl7j4uGdqZ6eMG0b55w0iXJSIxROFegw6VlvOnJWt45sN1tGnagL9cPZILB3WKdFkiEoMU7jXk8/UFTElNZ93OA/wwuTu3XTyQlk3qR7osEYlRJxzuZtYdmEPgbkwOzHL3R81sOnAjsCO46G3uvjjUQqPV/uIy7n89m79/tpHubRrzvzeM5vS+7SJdlojEuFCO3MuA37j7l2bWHFhmZm8F5z3i7g+GXl50e3dVPtMWZLJt70GuP60nv72wH00a6MOSiFS/E04ad88FcoPPC81sJdA1XIVFs90HSrjn1RXM/2orfTo0Y97NpzKyR+tIlyUicSQsh5FmlggMB5YCpwE/N7NrgDQCR/e7j/CaycBkgISEhHCUEXHuzmsZuUxflMWeolJ+cW4fbjm3Dw3rqdGXiNQsc/fQ3sCsGfA+8Ad3n29mHYGdBM7D3wN0dvfrv+s9kpOTPS0tLaQ6Ii1v3yHuWJjJmyvyGNK1JQ9MHMrAzi0iXZaIxDAzW+buyUeaF9KRu5nVB1KBF9x9PoC751Wa/wzwaijrqO3cnX+mbebe11ZSUlbB1IsGcMPpavQlIpEVytUyBswGVrr7w5XGOwfPxwNMADJDK7H22rSriKkL0vk4Zxejerbh/iuG0rNd00iXJSIS0pH7acDVQIaZfR0cuw2YZGbDCJyW2QDcFMI6aqXyCudvn2zgwTdWUbeO8YcJg5l0coIafYlIrRHK1TIfAUdKs5i+pn1NXiG3pqbz1aY9nNO/PX+YMIQuavQlIrWMLrquopKyCp5+fy1/fmcNzRrW49GrhvH9k7qo0ZeI1EoK9ypYvnkPKanpZG8vZNxJXZg+Lom2zdToS0RqL4X7dzhYUs6flqzmmQ/X0b55Q565JpkLkjpGuiwRkWNSuB/Fp2t3MXV+Oht2FTFpVHemXDSQlo3V6EtEooPC/TD7DpUy8/Vs/rF0Ez3aNuEfN47m1N5q9CUi0UXhXsk72XncNj+T/MJD3HhGT359QX8aN1DrABGJPgp3YNf+Yu5+dQUvf72N/h2b8/TVIxnWvVWkyxIROWFxHe7uzivpgUZfhYdK+eV5fbnlnD40qKfWASIS3eI23HP3HuSOhVksWZnHSd1acv/E0QzopEZfIhIb4i7cKyqcF7/YzIzFKymtqOD2iwdy/ek9qavWASISQ+Iq3DfuOkBKajqfrSvglF5tmXnFEHq0VaMvEYk9cRHu5RXOsx+t56G3VlG/Th1mXD6Eq07urtYBIhKzYj7cs7fvI2VeOsu37OX8gR2497IhdGrZKNJliYhUq5gN9+Kycp54dy1PvptDi8b1eWzScMYN7ayjdRGJCzEZ7l9t2k1Kajqr8/Zz2bAu/H7cINo0bRDpskREakxMhXtRSRkPvbmaZz9eT6cWjXj2umTOHaBGXyISf6ot3M1sLPAoUBf4q7vPrK51AXySs5Mp8zPYVFDET8YkkDJ2AM0bqdGXiMSnagl3M6sLPAFcAGwBvjCzRe6+Itzr2nuwlBmLV/LiF5tJbNuEFyePYUyvtuFejYhIVKmuI/dRQI67rwMwsxeB8UBYwz19yx5unJPGjsJibjqrF786vx+N6qvRl4hIdYV7V2BzpektwOjKC5jZZGAyQEJCwgmtJKFNE/p1bM4z1yQztFurE6tURCQGRewPqu4+C5gFkJyc7CfyHq2aNODvN4w+9oIiInGmutofbgW6V5ruFhwTEZEaUF3h/gXQ18x6mlkD4CpgUTWtS0REDlMtp2XcvczMfg68QeBSyGfdPas61iUiIt9Wbefc3X0xsLi63l9ERI5OtxwSEYlBCncRkRikcBcRiUEKdxGRGGTuJ/T9ofAWYbYD2BjCW7QDdoapnGgRj9sM8bnd2ub4cbzb3cPd2x9pRq0I91CZWZq7J0e6jpoUj9sM8bnd2ub4Ec7t1mkZEZEYpHAXEYlBsRLusyJdQATE4zZDfG63tjl+hG27Y+Kcu4iI/KdYOXIXEZFKFO4iIjEoqsPdzMaa2SozyzGzKZGupzqYWXcze9fMVphZlpn9MjjexszeMrM1wcfWka61OphZXTP7ysxeDU73NLOlwX3+UrCldMwws1ZmNs/Mss1spZmdEg/72sx+Ffz9zjSzuWbWKBb3tZk9a2b5ZpZZaeyI+9cCHgtuf7qZjTiedUVtuFe6CfdFQBIwycySIltVtSgDfuPuScAY4Jbgdk4B3nb3vsDbwelY9EtgZaXp+4FH3L0PsBu4ISJVVZ9HgX+7+wDgJALbHtP72sy6Ar8Akt19MIE24VcRm/v6b8DYw8aOtn8vAvoGfyYDTx3PiqI23Kl0E253LwG+uQl3THH3XHf/Mvi8kMA/9q4EtvX54GLPA5dFpMBqZGbdgEuAvwanDTgXmBdcJKa228xaAmcCswHcvcTd9xAH+5pA+/HGZlYPaALkEoP72t0/AAoOGz7a/h0PzPGAz4BWZta5quuK5nA/0k24u0aolhphZonAcGAp0NHdc4OztgMdI1VXNfoTcCtQEZxuC+xx97LgdKzt857ADuC54Kmov5pZU2J8X7v7VuBBYBOBUN8LLCO293VlR9u/IWVcNId7XDGzZkAq8D/uvq/yPA9czxpT17Sa2aVAvrsvi3QtNageMAJ4yt2HAwc47BRMjO7r1gSOUnsCXYCmfPvURVwI5/6N5nCPm5twm1l9AsH+grvPDw7nffMRLfiYH6n6qslpwPfNbAOBU27nEjgf3Sr40R1ib59vAba4+9Lg9DwCYR/r+/p8YL2773D3UmA+gf0fy/u6sqPt35AyLprDPS5uwh08zzwbWOnuD1eatQi4Nvj8WuDlmq6tOrn7VHfv5u6JBPbtO+7+Y+BdYGJwsZjabnffDmw2s/7BofOAFcT4viZwOmaMmTUJ/r5/s90xu68Pc7T9uwi4JnjVzBhgb6XTN8fm7lH7A1wMrAbWArdHup5q2sbTCXxMSwe+Dv5cTOD889vAGmAJ0CbStVbjf4OzgVeDz3sBnwM5wL+AhpGuL8zbOgxIC+7vhUDreNjXwF1ANpAJ/B1oGIv7GphL4O8KpQQ+qd1wtP0LGIErAtcCGQSuJqryutR+QEQkBkXzaRkRETkKhbuISAxSuIuIxCCFu4hIDFK4i4jEIIW7iEgMUriLiMSg/wvAo+ld7RsBXAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt \n",
    "%matplotlib inline \n",
    "\n",
    "num_points = 100 \n",
    "x_vals = np.arange(num_points)\n",
    "y_truth = 2 * x_vals \n",
    "plt.plot(x_vals, y_truth)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Adding noise to that data and label it as `y_noisy`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[     0      2      4      6      8     10     12     14     16     18\n",
      "     20     22     24     26     28     30     32     34     36     38\n",
      "  -3300  -3628  -3972  -4332  -4708  -5100  -5508  -5932  -6372  -6828\n",
      "  -7300  -7788  -8292  -8812  -9348  -9900 -10468 -11052 -11652 -12268\n",
      "     80     82     84     86     88     90     92     94     96     98\n",
      "    100    102    104    106    108    110    112    114    116    118\n",
      "    120    122    124    126    128    130    132    134    136    138\n",
      "    140    142    144    146    148    150    152    154    156    158\n",
      "    160    162    164    166    168    170    172    174    176    178\n",
      "    180    182    184    186    188    190    192    194    196    198]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1e07b8f0b50>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_noisy = y_truth.copy()\n",
    "#changing y-values of some points in the line \n",
    "y_noisy[20:40] = y_noisy[20:40] * (-4 * x_vals[20:40]) - 100 \n",
    "\n",
    "print(y_noisy)\n",
    "\n",
    "plt.title(\"Noise in y-direction\")\n",
    "plt.xlim([0,100])\n",
    "plt.scatter(x_vals, y_noisy, marker='x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Import both LinearRegression and TheilSenRegressor \n",
    "\n",
    "from sklearn.linear_model import LinearRegression, TheilSenRegressor \n",
    "from sklearn.metrics import r2_score, mean_absolute_error "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OLS R-Squared:  -904.7565621836717 Mean Absolute Error:  1480.9397011701171\n",
      "TSR R-Squared:  0.9999999999265342 Mean Absolute Error:  0.0004425033844090672\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1e07b968fd0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "named_estimators = [('OLS',LinearRegression()),('TSR',TheilSenRegressor())]\n",
    "\n",
    "for num_index, est in enumerate(named_estimators):\n",
    "    y_pred = est[1].fit(x_vals.reshape(-1,1),y_noisy).predict(x_vals.reshape(-1,1))\n",
    "    print(est[0],\"R-Squared: \",r2_score(y_truth,y_pred),\"Mean Absolute Error: \",mean_absolute_error(y_truth,y_pred))\n",
    "    plt.plot(x_vals,y_pred,label=est[0])\n",
    "plt.plot(x_vals, y_truth, label='True Line')\n",
    "plt.legend(loc='upper left')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Theil-Sen overlaps the real line"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Next, plotting the dataset and the estimated lines "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1e07ba01340>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for num_index, est in enumerate(named_estimators):\n",
    "    y_pred = est[1].fit(x_vals.reshape(-1,1),y_noisy).predict(x_vals.reshape(-1,1))\n",
    "    plt.plot(x_vals, y_pred, label = est[0])\n",
    "\n",
    "plt.legend(loc='upper right')\n",
    "plt.title(\"Noise in y-direction\")\n",
    "plt.xlim([0,100])\n",
    "plt.scatter(x_vals, y_noisy, marker='x',color='red')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`TheilSenRegressor` is a robust estimator - performs well in the presence of outliers. OLS regression, can decrease good results"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Trying other estimators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import Ridge, LinearRegression, TheilSenRegressor, RANSACRegressor, ElasticNet, HuberRegressor \n",
    "from sklearn.metrics import r2_score, mean_absolute_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "named_estimators = [('OLS', LinearRegression()),('Ridge',Ridge()), ('TSR',TheilSenRegressor()),\n",
    "                    ('RANSAC',RANSACRegressor()),('Elastic Net',ElasticNet()),('Huber',HuberRegressor())]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OLS R-Squared:  -904.7565621836717 Mean Absolute Error:  1480.9397011701171\n",
      "Ridge R-Squared:  -904.7501604538695 Mean Absolute Error:  1480.9385250222022\n",
      "TSR R-Squared:  0.9999999999265342 Mean Absolute Error:  0.0004425033844090672\n",
      "RANSAC R-Squared:  1.0 Mean Absolute Error:  0.0\n",
      "Elastic Net R-Squared:  -904.4272711687513 Mean Absolute Error:  1480.8791832083955\n",
      "Huber R-Squared:  0.9999999867470167 Mean Absolute Error:  0.006644972890123926\n"
     ]
    }
   ],
   "source": [
    "for num_index, est in enumerate(named_estimators):\n",
    "    y_pred = est[1].fit(x_vals.reshape(-1,1),y_noisy).predict(x_vals.reshape(-1,1))\n",
    "    print(est[0],\"R-Squared: \", r2_score(y_truth,y_pred),\"Mean Absolute Error: \",mean_absolute_error(y_truth,y_pred))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Putting it all together with PipeLine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5.1, 3.5, 1.4, 0.2],\n",
       "       [4.9, 3. , 1.4, 0.2],\n",
       "       [4.7, nan, 1.3, 0.2],\n",
       "       [4.6, 3.1, 1.5, 0.2],\n",
       "       [5. , nan, nan, 0.2]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris \n",
    "import numpy as np \n",
    "iris = load_iris()\n",
    "iris_data = iris.data \n",
    "mask = np.random.binomial(1,.25, iris_data.shape).astype(bool)\n",
    "iris_data[mask] = np.nan \n",
    "iris_data[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Next, imputing first for the missing values,\n",
    "#and then PCA \n",
    "\n",
    "from sklearn import pipeline, preprocessing, decomposition, impute \n",
    "\n",
    "#creating IMPUTER and PCA classes\n",
    "pca = decomposition.PCA() \n",
    "imputer = impute.SimpleImputer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.63732384,  0.18440746, -0.16205286,  0.23616388],\n",
       "       [-2.6663669 , -0.13723681, -0.12539919, -0.1932054 ],\n",
       "       [-2.82224298, -0.28006933, -0.07577852, -0.13367274],\n",
       "       [-2.68253483, -0.41274729, -0.1287365 , -0.00929935],\n",
       "       [-0.57970608, -0.76260092, -0.83825711,  0.15075786]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Loading them in PIPELINE \n",
    "\n",
    "pipe = pipeline.Pipeline([('imputer',imputer),('pca',pca)])\n",
    "iris_data_transformed = pipe.fit_transform(iris_data)\n",
    "iris_data_transformed[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.63732384,  0.18440746, -0.16205286,  0.23616388],\n",
       "       [-2.6663669 , -0.13723681, -0.12539919, -0.1932054 ],\n",
       "       [-2.82224298, -0.28006933, -0.07577852, -0.13367274],\n",
       "       [-2.68253483, -0.41274729, -0.1287365 , -0.00929935],\n",
       "       [-0.57970608, -0.76260092, -0.83825711,  0.15075786]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pipe2 = pipeline.make_pipeline(imputer, pca) \n",
    "pipe2.steps \n",
    "[('imputer', impute.SimpleImputer(copy=True, missing_values='NaN',strategy='mean',verbose=0)),\n",
    " ('pca',decomposition.PCA(copy=True, iterated_power='auto',n_components=None,random_state=None, svd_solver='auto',tol=0.0,whiten=False))]\n",
    "\n",
    "iris_data_transformed2 = pipe2.fit_transform(iris_data)\n",
    "iris_data_transformed2[:5]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(steps=[('simpleimputer', SimpleImputer()),\n",
       "                ('pca', PCA(n_components=2))])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Accessing the attributes of each object in a pipeline\n",
    "\n",
    "pipe2.set_params(pca__n_components=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.63732384,  0.18440746],\n",
       "       [-2.6663669 , -0.13723681],\n",
       "       [-2.82224298, -0.28006933],\n",
       "       [-2.68253483, -0.41274729],\n",
       "       [-0.57970608, -0.76260092]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris_data_transformed3 = pipe2.fit_transform(iris_data)\n",
    "iris_data_transformed3[:5]"
   ]
  }
 ],
 "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",
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