15.1_Equal_frequency_discretisation.ipynb

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    "## Discretisation\n",
    "\n",
    "Discretisation is the process of transforming continuous variables into discrete variables by creating a set of contiguous intervals that spans the range of the variable's values.\n",
    "\n",
    "### Discretisation helps handle outliers and highly skewed variables\n",
    "\n",
    "Discretisation helps handle outliers by placing these values into the lower or higher intervals together with the remaining inlier values of the distribution. Thus, these outlier observations no longer differ from the rest of the values at the tails of the distribution, as they are now all together in the same interval / bucket. In addition, by creating appropriate bins or intervals, discretisation can help spread the values of a skewed variable across a set of bins with equal number of observations.\n",
    "\n",
    "\n",
    "### Discretisation approaches\n",
    "\n",
    "There are several approaches to transform continuous variables into discrete ones. This process is also known as **binning**, with each bin being each  interval. Discretisation methods fall into 2 categories: **supervised and unsupervised**. Unsupervised methods do not use any information, other than the variable distribution, to create the contiguous bins in which the values will be placed. Supervised methods typically use target information in order to create the bins or intervals.\n",
    "\n",
    "####  Unsupervised discretisation methods\n",
    "\n",
    "- Equal width binning\n",
    "- Equal frequency binning\n",
    "\n",
    "\n",
    "#### Supervised discretisation methods\n",
    "\n",
    "- Discretisation using decision trees\n",
    "\n",
    "\n",
    "In this lecture, I will describe **equal frequency discretisation**, and in the following sections I will expand on the other methods to make variables discrete.\n",
    "\n",
    "## Equal frequency discretisation\n",
    "\n",
    "Equal frequency binning divides the scope of possible values of the variable into N bins, where each bin carries the same amount of observations. This is particularly useful for skewed variables as it spreads the observations over the different bins equally. Typically, we find the interval boundaries by determining the quantiles.\n",
    "\n",
    "Equal frequency discretisation using quantiles consists of dividing the continuous variable into N quantiles, N to be defined by the user. There is no rule of thumb to define N. However, if we think of the discrete variable as a categorical variable, where each bin is a category, we would like to keep N (the number of categories) low (typically no more than 10).\n",
    "\n",
    "Equal frequency binning is straightforward to implement and by spreading the values of the observations more evenly it may help boost the algorithm's performance. On the other hand, this arbitrary binning may also disrupt the relationship with the target on occasions. Therefore, whenever possible, it will bring value to examine whether this type of binning is the right strategy, and it will depend on the variable and the algorithm that we want to use to make the predictions.\n",
    "\n",
    "I will demonstrate how to perform equal frequency binning using the Titanic dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Titanic dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "% matplotlib inline\n",
    "\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\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>Survived</th>\n",
       "      <th>Age</th>\n",
       "      <th>Fare</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>7.2500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>38.0</td>\n",
       "      <td>71.2833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>26.0</td>\n",
       "      <td>7.9250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>35.0</td>\n",
       "      <td>53.1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>8.0500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Survived   Age     Fare\n",
       "0         0  22.0   7.2500\n",
       "1         1  38.0  71.2833\n",
       "2         1  26.0   7.9250\n",
       "3         1  35.0  53.1000\n",
       "4         0  35.0   8.0500"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# load the numerical variables of the Titanic Dataset\n",
    "\n",
    "data = pd.read_csv('titanic.csv', usecols = ['Age', 'Fare', 'Survived'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((623, 3), (268, 3))"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's separate into train and test set\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(data[['Age', 'Fare', 'Survived']],\n",
    "                                                    data.Survived, test_size=0.3,\n",
    "                                                    random_state=0)\n",
    "X_train.shape, X_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variable Age contains missing data, that I will fill by extracting a random sample of the variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def impute_na(data, variable):\n",
    "    # function to fill NA with a random sample\n",
    "    \n",
    "    df = data.copy()\n",
    "    \n",
    "    # random sampling\n",
    "    df[variable+'_random'] = df[variable]\n",
    "    \n",
    "    # extract the random sample to fill the na\n",
    "    random_sample = X_train[variable].dropna().sample(df[variable].isnull().sum(), random_state=0)\n",
    "    \n",
    "    # pandas needs to have the same index in order to merge datasets\n",
    "    random_sample.index = df[df[variable].isnull()].index\n",
    "    df.loc[df[variable].isnull(), variable+'_random'] = random_sample\n",
    "    \n",
    "    return df[variable+'_random']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# replace NA in both train and test sets\n",
    "\n",
    "X_train['Age'] = impute_na(data, 'Age')\n",
    "X_test['Age'] = impute_na(data, 'Age')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Age\n",
    "#### Original distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x4c102bf4e0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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pXqqruaC72c7XXFObNtTabvnfZBd1NVuTXLOzswcyc3rQeo2KPiJ+DNgHfC4zf3+VxyeB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\nPtQLY00AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x4c0f8a53c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's remind ourselves of the original distribution\n",
    "\n",
    "data.Age.hist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**How does survival correlate with Age?**\n",
    "\n",
    "We can determine the relation between survival and Age by plotting the mean survival per Age. In this case, I will calculate the Survival rate per each year of Age. See below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x4c11768978>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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A36zZmIrxMrpBo0U/akCmmMLnJBusrGlQhkEhKlIHGsRwrc4rDRvFHJ8UdY1A\ntDsT5RY8A5F5EB7GC0bshBmNYgL4Cugpe8Zij9fvekwN243NgQDiE+VCFFNWjynDgFBpOCjJGoR3\n7w6dSN1w/K53APcidmMU08JKFZMFI5Yh6RQjayDGcgY2YybMaARGGvS7HlPDae1B5AwNhkZNpTbc\nkAYxXA9nhp0JxljTMySCK+pDFuZaiYzT1GhX5kEslis9j2ACRthAjOeN2BV1teGi0K6B6HPJ77rl\nxgrUArztaLwHkWkQGQaBmuWCsSA3BwjyIIbNg4gm9JmGtisbBi2Uqz3PgQBG2ECM5Vt4EA27iWJK\nQr8pprrjxoa4CpQUBsJlzE8MzDSIDIOA3KVNwA9zHSID4bgMDdsNh7Rr2q4Lc2WMYbHc2z4QAiMr\nUo/nDV+YkSHc43YNhN9Vrl8Uk53sQZRyRhPF5LiMd5uznMyDyNASp9dq+JNbHg5lO+dNDf/lJRdj\nbjx9j2K/AJ4izHWY6jGJPCjZkOV02nWJcsubddQsty8U08gaiLgopobjwmXhmzsNBiNSJ1BMpu7X\ntxdwXAZdI4zl4kX5DBkA4NYHl/CRrz+B+ck8dCI4jOHMeh1XHZzGa595OPVx5J7uAsMY5ho0NQqm\nMUPffRTTYpnnQPQ6xBUYYQMxnjeVE2atwW+Odj2IsZwBjfrXE6JuOy1FakDddtRxGQydN0PJopgy\ntIJYUX/hV16I6VIOluPikrf9k9LTboVKo3llPoxhrn5TI+lZN3XadR3lRJnvXoe4AiOsQYzndWWF\n04oVbpWYFppGmCj0r+R3UpgrwMesqsWkkedBZBRThhYQBqIgZRbvnyr6K8y0UFFMw6hBqAyZqWu7\nrqOc+H37oUGMrIEYyxtgrDnzWG432i6m+lhuIynMFRAUU3OYq64BpXyz8ciQQUa0DwrAaQexwkwL\nUVFYzqQ2NIJGwxXmKp6HQqjuGoUi/3YDFssV7BnPhX6vXmGkDQTQnDwWXUW1g8mi0VcNIlmk1n0P\nSMBhDIamoZSLD+vNkAEIEkTlfgCHZko9oZiICAVzuPpSqymm3adBLKxUcbAP9BIwwgZi3DMQG5FJ\ns2Y1u8dpMVkw+1byu55QagPgYltTwyCXQdP4+WYeRIZWUEXvHZ4p4cx6vS1xuRLjhRdMfaiquQbh\nuFImtbYLDUS50tM2ozJG1kDEehCeSN1uJjXQZ4opRRRTrEitaSjl4mtPZcgAcAE56jmLyJaTbegQ\nVYUHAQA3+GgHAAAgAElEQVQFQxvKMNdiKFGOdlUehOMyPLna+z4QAiNsIPhNEU2W80PfOqGYCv3r\nKpdUrA/wEuUsJyS8Oy6DRshE6gyJ4I2ywveYiGxZaMNABBRTmNPOmzpqQ6hBlCKJcrspD+LMeg2W\nw/qSRQ2MsIGYyPO8hWioa7caRL+imNJRTDoYCwuBIg+ilNezhkEZWqIWqcAKBB7EYhs6RLVhgwhN\nxiZvaMOpQUSjmHaRBxGEuGYUUwjCg4jSLt1oEFNFEzXL7UsyUCoPQtFVznYZdE3zPYhoWG+GDAIq\nDWJ+ogBTJ7+hTBqIJjyy2A1g+ERqFcWk067SIIIkuRH0IIjoZUT0IBEdJ6K3xuxzHRF9m4juJaIv\npz22EKmjFJMqsiEt/IquPU6WY4yh4STnQQRNg4LvdxkPcx3LG3DZcIUZtosvP7SMf7nvzLaOgTGG\n933peFsr6lFBtBc7wPN7Dk4X24pkiitVkze0obr/Kg0bukah6EBT13ZVmOtCuQIi4MB0oS/H75uB\nICIdwPsAvBzA5QBeR0SXR/aZBvCnAL6fMXYFgB9Je/z4MFcvk7rDKCag9/WY/H7UKSgmINwTwhEe\nRIzHNEp43y3H8Z5/fWhbx1CuWPiDLzyIm+94YlvH0Q/ULFc5sR+eLbWVLBdtFiRQMHXUh8iDED0r\nZE/H0ClUi2qnY2GlivmJQuLis1P004N4FoDjjLFHGGMNAB8F8OrIPj8O4JOMsScAgDG2lPbgpZwO\nIpUHwV8nTcYq9KseUz2hH7WA4FIrUQNBgXcxyvWYViqNvpUySQshYN775Pq2jqMfqCk8CIAL1Ytt\nJMtFS2gLFEytJ6U2bMfFF+893TVdWm04TWX9c7q2qzrK8T4Q/dEfgP4aiIMAFqTXi957Mi4GMENE\ntxLRXUT006oDEdENRHQnEd25vLws3lM2DVIlC6WFX9G1xwZCrGiSyn0XFRpEUKzP8yBGOJKpvNXo\nW5RYWgj6YScaiGpDTQ0dni3i3FYjtfdZsZxQATyBgqn3RJ+77eFl3PA3d+GB0xtdHUdlyAx9d4W5\nLvapD4TAdovUBoBrALwSwEsB/AYRXRzdiTH2IcbYtYyxa/fu3eu/r6roWrXU7nEaBBRTbyfhRkoP\nwqeYpGzqIIqpWZ8YJbguw2rVwkbNCnXJGzREt7HljTqWNmrbNo5+IO7eF6GuJ1fT0UzVhq3U8HgU\nU/er8w3v+dro8jmrKAyisYsS5SzHxam1at8imIAEA0FEG0S0Hvcv4dgnAcg1hg9578lYBPAFxtgW\nY+wsgNsAPC3t4HlXuWgtJjUPmwb9oph8A5GYByGMgORBMG4gxn0NYjQppo2aDcdlcBmwuY1GTqYf\ndpoXoRKpAfhZtmlrMsVTTL3JpBaRUN1GRFUtu2mcuV3UUe7J1SpcBhzqUwQTkGAgGGMTjLFJAO8B\n8FZwiugQgF8H8EcJx/4GgIuI6ClElAPwYwA+E9nnHwA8n4gMIioBeDaA+9MOflzRVa5q2Z17EMX+\ntB2tpzYQcRSTpoxwGiWUKw3/735lq6eBHOFy3w4yEK7orhYjUgPpDUQrkboXYa7CC+n2WNyQhakw\nYxf1pPZDXIeAYvp+xtifMsY2GGPrjLH3o1lwDoExZgN4I4AvgE/6H2OM3UtENxLRjd4+9wP4ZwB3\nA7gDwJ8zxr6bdvBjir7UcTxsGuQNDTld630Uk9AgUpT7BsIPjhCpx3IirHc0PYgVyUBspw4hTx73\nPrm2bePoNcTKPprcBgBzYzkUTT11JFOcByHCXLsVl30PostoI5UhE2GuuyFfqN9JckD6hkFbRPQT\n4JFIDMDrAGwlfYgx9nkAn4+894HI6z8A8AcpxxHCWN7AylZ4VdRJu1EBIsJkH+oxNRz+QHTuQfBM\nar5tRD2ILdmD2H6KqWBqO4pi8svcKyZ2IsKhmfS5EJWGrSwdXTB5pn+anJ5W6JUHUbWaDZmp8+AU\ny2HIGe0HqowSFsoV6Bph/1R/ciCA9B7EjwN4LYAz3r8f8d7bVqgpJrcp9K0dTBaNnk9gacNcC0ar\nKKbRDnMtVwKj269yJmkgKKYrD07h8XOVbR1LL5FUYubwbCl1NnWc2C1Cx7sVqoW3021OhcrTMb1n\nbDeEui6WqzgwXYCRMK90g1RHZow9xhh7NWNsD2NsL2PsBxhjj/VtVCmhimKqeckznWKyD13l0moQ\nmkZNfamFSF0wNWi0MzyIYaCYrjo0DQC4f4d4Eao+0jIOzRRTZY9bjgvLYcrj9KovtfB2ujU0nE6O\naBDeZGnZu4Ni6qf+AKQ0EER0MRH9KxF913t9FRG9ra8jS4ExRRRTpQuRGuCRTP2KYkqTvBct+e16\nIrXI+xhVD2JlaERq/ls87TA3EDuFZqom9GI/PFPCes1OvLeFJxKnQQDouuS3MDDVLjwIxphHhUUT\n5TyKaRd4EAvl/oa4Aukppj8D8F8BWADAGLsbPCppWzGRN9Bw3FBqfbXRXBO/HfRFg2jDQBQibUdt\nT6QGRNvR0fQgVisN7BnPgWh7DYTjUUwHpgrYM57fMQYiEKnjKKZ0oa6ttIxe9aXuhQZRt124rHmc\nvgexw0Nda5aD5Y36cHgQAEqMsTsi7237TKWqx1TrQqQGgMmC0fNEubQUE9DsQfCOctxCqDLHRwUr\nWw3MjeUxnu/99W0HgmLSNcIVByZ3TCRTMLGr7zGRLJdEM6l6LAgEBqJLDcLqnmKK6z1veM/KTg91\n7XcVV4G0BuIsER0Fj2ACEb0GwKm+jSolxiIVXRljysiGdiAopl6GyaVNlANEX+qwgRA3PfcgRpNi\nKlcsTJfMvlB47UCI1Kau4YoDkzi+tNmX8u6DRqJI7RuI1kJ10HBLFcXkUUxdXq8gzLXz41RiqDDx\njDV2uAchItKGhWL6RQAfBHApEZ0E8CsAbuzbqFIiWvLbchgcl3WlQUwWTTgu6+lE3PAehDShgcWc\nWqQGeKb1qFZzLW81MDuW40EA2ypS84mDexBTsF2Gh05vbtt4eoUkkXqqZGKiYKSmmNQaRK88iO4p\nJvGMNFFMmhfFlHkQPUFaA/E4Y+wlAPYCuJQx9nzG2ON9HFcqRCkmcXN3pUH0oeS3WM2k8yAMhUjN\nDcR43hhhD6KBmbHcEHkQnGICdkbCXCvtQODQTCmx9WhrikmEuXbpQfhhrp0bmri2qEEexM72IBZX\nKsgZGvaO5/v6PWkNxKNE9CEAzwEwNMut8Uhf6mrCKioN+lGPSTwISXkQgOdBWFGRWngQ+khWc2WM\noVyxMFMy+9rWNQ1EFJOuaTgyW8J43tgRQrWYtAstvNTDKUJdKylE6m6bBvXCg4gzZOYuEakXyhUc\nmi76+mS/kNZAXArg/4JTTY8S0XuJ6Pn9G1Y6jEf6UgctCDtPHAlKfvduIm44LoiC1U0rlCJRTG5E\npB5FimndK9Q3UxoCD8KjHgyNoGmEy/fvDKE6TaMskSzXSl8TlYRVmdRBolx3HkS9BxqEqt0oICfK\n7WyKaWGl2tcifQJpE+UqjLGPMcZ+CMDVACYBpG4P2i9Eu6wFkQ1pK4g0Y6oPBfsatoucrqXqURGN\nYrKjIvUI5kGIJLmZktAgtrPUhmcgPGN9+YFJ3H9qww9/HVWICbNVKPWhmSKqloNzUtJiFJWY6CBA\nimLqlUjdgygmVT8IALB2eFe5xXLFr9LbT6ReahPRi4joTwHcBaAAXnpjWxEVqeNWFe1AaBA9pZhs\nN5X+AADFnBFuOcoiHkTDHrlCZKKS66ynQVQtZ9vaQgoDIXSdpx6cQtVy8OjZxNJiQw0R3t1qEZIm\nkqllHkSvRGq7hxSTGdUgPIppxA1+K2zWbZQrlh+63E+kzaR+DDxy6SsArmSMvZYx9ol+DiwNomGu\ncbHR7cAv+d1Dnrxuu6lboJZyOhqO60fbuBEPwmXdc8CDhjAQM2O5vlzfdiCuq+lFu+wUoTquRLeM\nNGW/W0Yx9TrMtQdRTIUInWzuAg9C/H79bDUqkNaDuIox9oOMsZsZY0Oz1DJ1DTlDCyimHojUk4V4\nDeIrDy/j43cttn3Mhp2++qXfdtQ7F1mkHlckBm4Xzm3W8Xv//EAqaqa8xY3BjJcHAfSOwvune07h\nDR++C2/48F344JdPJO4vxqt7E8mxfePIGaNf2bVmOSgkLEJEzHyrqq4Vy4Gpk78SlxFXrO+vvvoo\nvvVE2X/9r/efwefvUadJiVwl1XFk3HzHE7jzsZX4ccZEMflhrju41MYg+kAItCTriegtjLHfB/Au\nImqaCRhjb+rbyFJCrujaC5Ha0DWM5XQlxfSh2x7BI8tbeM01h9o6ZsNJTzHJoYTj3s2vSXkQAH84\n5toaQe9x28PLeP+tJ/BDVx/ERfMTLfcNexD8HHpB4d2zuIY3ffRbmB3LwXIYbnlgCTe88MKWNIsf\n5upNJKau4cBUAafXRrv9aNVyEqsYj+UNTJdMnFqNP9fViuXTrFEQEe8JIa38a5aDd3zuPvz4s4/g\n6iMzAIC/+upjWKtaeMWV+5uO0XBcCIa0lSfyh194EC+6ZC+uvWBWuT1OKxElvhs7OA8i8CC22UAg\n6O52Z78H0inkiq41nz/tXKQGvHpMCgrkZLmKc1t1MMZSCc4CDdtJFeIKSFEYDgsEVV+DCIf1bidE\ntcw0DeJXthowNMJE3uhZ3++tuo03ffRb2DOexz/98gvw8bsW8c5/vB9rVQvTpVzs5+REOQHeZGa0\nV5xpS8zsm8i37MW9vFHDvsn4/gIFUw9RnI8sb8Fl4cS0huPG1gwTXgNRaw+i0nBCWlwUVctB3tBC\nvyMgJ8qN9u/ZCgvlCko5HTMltSHvJVrOpIyxz3p/3sMY+2bfR9MBxvOm32UtKBPQOcUE8EimKAXi\nugyL5ap38zu+/pEG7YjUhmQgXG+p5XsQ+eFpOyqqZaaZWHmZjRyIqGd5Jr/1mXvx2Lkt3PyfnoPp\nUg7neU1TTq/XWhuIiNEF+DVPY+iGGWkbZc1PFrC0UY/dfma9jn0T8clXeUMLaQcPndkAEF4o2I4b\nO7kL72OyYMYudFyX01CtkkJVlVwBwDR2fh7EYrmKwzOlthapnSItF/NuIrqfiN5BRE/t64jaxLjk\nQfix4F0aiMlCc6z+0kbdz4g+txkfJqhCow2RWohsDceN9SCGoeS3EAHTPIi8zAY3DL3o+/2Z7zyJ\nj9+1iF968TE850JOtp3nrXqTqCLbYdAIoQQjU6eRn1DSiNQAsHcij6X1eAOxtFHD/GS8gYj2pRYG\nQl4oWA4L1ROTIbyG6RIvaaO67iKMtpUHoepHDQCmFnSU26lYWKkMRKAG0udBvBjAiwEsA/ggEd0z\nDP0gAK8nRCOsQaSdjOPAs33Dqxs5A/XcVvwDpkKjDQ9C7oglBFXNWymMDZEHIYxXKoqp0vBX9d16\nEAsrFfz3T96Da86fwZu+9yL//XnPQJxZTzAQLmvqwGXq2sjX7qla6crc75soYGmjpgyVdlyGs5sN\n7JtoRTFpIWoo8CBkAxHvQYjJX9wPqkgm8dlW/SJqMV3vAop2tA1+HBjjTMYgQlyBNvIgGGOnGWN/\nDF6k79sAfrNvo2oDY3kDm95kLnjYbtPPVT0h5MiPtj2INkRqWYNwIzH7w9R2VBiGNBPraqWBWW9C\nyBsacrrWcZjrf/3kPQABf/SjTw9N9MJAnEr0INwQvQRwD23UPYi65aQyEPOTeVgOC7WAFTi3VYfj\nskQPQhaXHzrDK++EKCaXoW67ygg3YRAEf67SIQS11GohpGo3CkiJciNu8OOwVrWwWbf7XsVVIG0e\nxGVE9HYiugfAnwD4dwDthfL0CeNSj4S0bnYSVBVH5X6+7XoQdctNLVIbLSimUl70rN5+D0JMqGkm\n1pUtCzMexUREXTVluv/UOl511YGmCI6coWHPeC6VBxEVNnOG1rWB2O7kRa5BJN9jwjtQCdWCetrb\nwoPgGgS/VpWGjSe8iJqoByHGFIVPMRWFgVB4EFY6iklFJQeJcqNt8OMg5qFBRDAB6T2IvwRQBvBS\nxth1jLH3M8aW+jiu1OBtR/mEGXfTtIvJoomNuh1aAS2sVHx65GwHHkQ+5bhyLURq4UFsRjyIn/8/\nd/KV9QBhpzQQjDGsVhqYkYTjyaLRcbmNhhOv58xPJoer2q7bFONvaNRV7Z6a5eB5v3sLPvudJ2P3\n+V9ffBCv/eDtHX9HEtKL1Nw7OKPQIYTR2JekQXgexMNngrqddkik5n+rFjLCIAiKSRXq6nsQLSim\naowHYe7wntSD6gMhkGggiEgH8Chj7D2MsfgnYJswntex1XDguownC6VYRSVBGIJNSYdYLFdxbN84\nxnJ6RyJ1ag/CF9maPYiCqUGj8INnOy7+7fgy/u34cltj6hYizjzJld+o27BdhtmxwEBMxYQRp4HV\ngq47b7KA0y0EWIDz7FEPwtS1lqU/Tixv4g+/8KBP+UVx36l1nFqr4fFz8TmkXz1xDvee7F+2drWR\nnAcBSB6EwtMSHsR8izDXvKH71YmF/rBvIh9q0CP+VnkAwkBMFVtRTMGCLw6Vhrr3vK4RNNq5iXKD\nzIEAUhgIxpgD4DARxccObiPGvczniuXwVVRPKKbmZK6FcgWHZoqYG89jpV2KyXbaDnO1HNefkIRI\nTUReRdfgwXnk7BZqlouFlSo2Bli+QngQSQ+iKNQnh56qosTSwnJYbFXc+akCTq+17ndgO8yPdBHg\neRDxhu7zd5/Ce790HCeW1ZXu71nkE39cchZjDA+f2cBWw+m6EqoKrsf5p8qD8LwDVair8Cpa9Rgo\nmJrvQTx0ZgM5Q8PRveMhUVj8rZrgRR2m6VILisn7XCNGxxD7xBXlNHRtx3aUWyxXMVU0Y5MZe43U\n/SAAfJWIfoOIflX86+fA0kJuGlRtOE3FuzpBtF6Q7bg4tVbD4ZkS5sZzLathqtBOLaacbyBYUBZC\nmtB429HAg/iutCp94PRGW+PqBoJaSiq6J8RQEeYKqPNM0sB1+TVRlYEAuAdRrlgtJ2HbZX6ZDYGk\nMFdxDt96YlW5/W7PQMQdY2mj7kfFrbR576SBSFxLI1IXTB2TBUPtQWzUMDuWa7mYCXsQmzi2dxwF\nM5xHYvkUU7wHMZ1CpOZ/q6nISovWwqZGIx+VFgexUB0U0hqIEwA+5+0/If3bdoj6RBs1O1W5gTSI\n1gs6tVaD4zIcni1ibizfvgbRhoEQIrUtUUyygeAVXYMH6J6Ta/72+wZYT0hUy0zi7pUeRNHoyIMQ\nwmOsgZgS9Em8h2e7zC+zIWAkhLmueqVCvrVQVm6/e5EbjrgCcTJX3w8D0W4NsvnJQowG0TpJDhBh\nroEHcfH8uJdoqBCpWxmIYnKYa9wxgPgoJoAny416VFocFlYqA6nBJJBquc0Y+x/9HkinCEI/uQfR\nKkQvLaIlv4UwdHimhD3jOX9CSAPGWEdhrg3H9UXqqAchF+u79+Q6nnZoCo+c3cL9pwZoIFImyokJ\ncTZCMa3X7LZLloiVaRzF5CfLrddwZE79ENmOq9AgqCUlIWpJqTyIrbqN48si1FN9DMHVA8NhIPZN\nqsttLK23LrMBBKU21msWTq3VcPF5E7j35HpooWD5FFO8SD0lPAilSG1Lfzdvd1yGhu3G0smGNvqZ\n8SqIHIjrL903sO9MZSCI6EsAVMX6ru/5iNpEiGJKGcmRBL+rnEcxLXqhZYdmSpgdy2Flq5F6crMc\nBsbStRsFgsnPdlio+5lASeoq57oM9z65htdccwh5Qx+ogUibKCcX6hOYKvIs2q2G43uAaSCMUpIH\ncbpFqGt8olwyxfTgmQ1s1u3QmO99ct0vPhenQTy81GcPQvRiT+k975so4BuKSqlLG/XEwoui1MbD\nntG7ZH4CD57e8I2C4zIIW5EuzFVBMVkyxRRvQOI8iJxOOzJRbnmzjrrtDkygBlIaCABvlv4uAPhh\nANsfjI9w0yAuUnevQUSzfRfLFWgE7J8uYG48D9tlWK/a/iqoFcTKNJ8yukrOpPbDXEmmmHSf4nrs\n3Ba2Gg6uODgFQ9fwka8/rozS6QfEhJD0IJYrDega+cI/EC630ZaBcFobiHm/3Ea8UK1OlGu94uRh\nuibKFQt3L6ziecf2+NuEN1k09VgP4uEzG3wiPbPRtn6VBrVOPIj1cNFJ12VYTkUx6bBd5tOZF89P\nhDLR5WsQRzHpGvm/u4piqskUU4s8ibhnPUp57RQs+AvVIdMgGGN3Sf++yhj7VQDX9Xdo6SCimLYa\nNmo9yoMYyxnQKOgJsVCuYv9UEabOk7EA4GzKSCYh4rafKKcWqeXSIt/1HtKnHpjCZfsnUbPcgXVG\nS5soV65YmCmZIW+r03IbQveIu5aTBQOlnI7Ta601CCMqUhvJIvULL94LAPjWQphmuufkGvZPFbwM\n5eZjMMbw8NImnnH+DHSN2oqAK281Uq2ExSSbNsR730QBDccNXf+VSgO2y1qGuMrfcc/JNZRyOg5O\nF0MUnUw1qUVqFwVD8/OCVAaikqBB+E2NYp51U6cd2VFuUaK6B4W0mdSz0r89RPQyAFN9HlsqiL7U\nm3UHFcvpqheEgKYRJgpBrP7CShA5MDfGV1hpcyF8A5GyYVBOqiUTJ1KLvtTfPbmGnKHhovlxXLaf\nUwP3DYhmslPmQZS3Gk3VVf2S3+0aCO9aRid4ASLCeZOFltnUtsOaPAhTiw9zdVyG9ZqF82dLOLp3\nrEmHuGdxDVcenIIZs2pd3qhjrWrhkvlxzJTM1BRTteHgRX/wJXz4a48n79u2SN2cLCeE/TQeBMAj\nty7aNw5NoxBFJxs0JcVk81D0YisDEaKYmomKoFlQnIHQdmRHOdEoaFB1mID0UUx3gfeEuBO8zMav\nAvi5pA8R0cuI6EEiOk5Eb22x3zOJyCai16Qcjw/hqq5uNeC4rCceBMBXubJILXi/Oc+DOLeZbiUo\nMkU7yoOIE6mFB3FyDZedx138Y/vGYWjUMx3iiXOVlq0pGyk9iJWtRkigBqQosTZ7QiRRTICXTd3C\nQMQlyjkuUybCrVUtMMajsK4+MoNvL5T9shprVQuPnN3CVYemvGS75s8L/eHi+QnMjuVSLyzufHwF\n6zW7ZWluAV+DSEsxKcptnPGzqFt7ECIa7+GlTVzs6RUyRSeL/XEidd7QYeo8oU2lQVQTKCa/WVAL\nA9FNZvywYmGlgj3juZ7keqVFy1nLm7jPY4w9hTF2IYD/AeAB7999CZ/VAbwPwMsBXA7gdUR0ecx+\nvwfgi52cQNHUoREXcID0D0kSeDkIC3XbwZn1uu/WzXlia1ouWXgQ7Zb7tiSRuinMtc4jgL57cg1X\nHJzyjq/j2L7xnhmIN//9d/ALH4lvASLGlvQgrlaCOkwCnXaVa6QwEOcldIezVKU2xDVXJP0FIruJ\npx+extnNhr+SE5nRVx6ajg2tFBFMx+bHMTuW84+XhNtPnAOQnGcCyJx85x7EcpsehOMyXHIeNxAy\nRSeHC6soprrlomBqIKKm0uHB52x/EaE6RlLveWMHlG9XYZBVXAWSFMIPAngJABDRCwH8DoBfAvB0\nAB8C0GrF/ywAxxljj3if/yiAV6PZsPwSgE8AeGa7g/eOi7GcgbOegVDViO8EIhTzpOj/6tVfF9E4\naVeCdZ9iSmkgNIUHQWEPwmXA8aVNrNdsPPVAwPRdvn8SXz1xNtX3JOGJlQpOr9diQx/TJsqtVBq4\nujQdei+uL/XxpQ387E3fCK0qc7qGP37d1bjm/Bl/8hFtJVU4b6qAk6tVPPNd/9d/byJv4KM3PAf7\nJgtKD0JOToxq5qteBNN0KYeL5/nk+c0nyjg8W8LdwkAcnOKRMwoD8/DSJqZLJvaO5zE3lsf9p9MZ\n8H/3DESaia5tkVrlQXhe194EAyH3VhcRT6amKTWpOJFaGBm5rpOMSsPB3FgOa1UrIYpJ/azL49lJ\nWChXcNWh6eQde4ikWUtnjIl4uB8F8CHG2CcYY78B4FjCZw8CWJBeL3rv+SCigwB+EMD7Wx2IiG4g\nojuJ6M7l5eaaQ2N5A2c3+ITdCw0CCCimhQjvZ+oapktm6oquYtWb1kBoopaMJFLLnLug1L72KP9Z\nnnpw0t922f5JnFmvp6a/4uC4zPfIbn1IXeMpSJSLfxAZYyhvNUIhrgAwUVCL1A+e3sTCShXPumAW\nL7lsHi84tgcnV6u+riIeekOLv5Y/cs0h/ORzjuAll83jJZfN48qDPEfksXOcLuMahNqDUAnCIklu\nppTDJfMTKJq6r0Pcs7iGw7NFzI7lPN5bQTGd2cBF+8ZBRH6IdBI26zbuOSnKd6TwINqkmIo5HRN5\nI5RQuLRRx3TJTDyGHI13iaCYdILLeCSUleBB1GzJQBhaLMUkandVFTRVksfEPZqdRTE5LsOTq9WB\nRjAByR6ETkQGY8wG8L0Abmjjs2nwRwB+nTHmtsopYIx9CNxjwbXXXtv0y4/ldd+D6JUGIUp++5ED\nUgenuTa4ZFGWIJ8yigmAL3hGGwYBwarpjkdXYGjk88AANxAAcP+pDTz/os4TBs9u1v3v/vKDy3jt\ntYeb9vET5VpUzdz0CvVFe+fqXn/qaMG+hsMf/De/9BI8Zc8Y1ioWPvmtk76XkoZiunDvON75A1f6\nr+94dAW3PLDkH8N2FWGuUnJiFCIHYqZkwtA1XHVoyo9kuvvkKq46OO2PqdIInw9jDA+d2cQrr9oP\nAJgdy2G1YvFQ2xbn8I1HV/zrr9I1ohD1jdq596PJcksbtUR6CQAKngcxUTB8qkousW2FNIiYKCbP\nyMRTTA72TxWgaxTjQbQWqQ1Ng+0MRRR+z3B6vQbLYQONYAKSPYibAXyZiP4BQBXAVwCAiI4BSCpN\neRKAPLMc8t6TcS2AjxLRY+B01Z8S0Q+kG3qA8YKJ5Y0+aBA1CwsrVZg6YV6qkT83nvcNUhLazYMA\nhIGICXP1HoqvP3IOF89PhM5XRDJ1q0OIpjv7JvK47eFl5cpaeA6t6u6Xt8Tk2lzncbLYXLCvEaHj\nxMCwsLMAACAASURBVP8NP2s7mWKKwj+GZ3xUYa45KTkxCuFBiEisq4/M4L4n13B6rYaFlSquPMQp\nPlU9p+VNHsF00b5xAPBXxapmPTL+/cRZ5HQNB6YKbXkQ7XRS3DdRCHkQZ9briSGuQBDmesn8hB+6\nrNLNAKBqqUVqYWTypq72ILyimyVT78hAmLoWm7Q4qlhcaV6oDgIt7yjG2LsA/BqAmwA8nwVdUTRw\n7aAVvgHgIiJ6ilcJ9scAfCZy/Kcwxi5gjF0A4OMAfoEx9ul2T2I8r2PDyy7uZRRTzXJxYnkTB6eL\noS51cympAkDOg0g/LtPjs1VhriWPYlraqIfoJYAbrn0T+a4NhBB5f+TaQ9io2fimosREmjBXIcjO\njjUbiIlCc0+IaM5Ik4FIyKRWQRzL9yAUYa6GpPuozkFO9Lv6yDQsh+HmO54AAFx1UBiIZt77uFeD\n6aJ93HAHBqL1vXP7I+dw9ZFpTBTMVOGaosx9O50U5yfzfuQSwMNxk/QHIFiAXXxe4LnKbT4bCR5E\nNaRBaDH9IGyUcjqKObWHUUuimHZgJnWU6h4U0pT7/hpj7FOMsS3pvYcYY/EhLnwfG8AbAXwBwP0A\nPsYYu5eIbiSiG7sduIwxSazqmUjtCan3PbnelNreTkXXdsNcgSATVBXmOiY9FE892JyKcvmBya5z\nIYRg+ZprDsPQCF96sLk3lJ8Y1eJBXKk0F+oTUFV0jQr6ukbQNZJW/x0YCO9Y4tiOqtSGEYjUUZQr\nFqaLQaLf1Yc5pfS3noG4ImQgwp8XEUwXz3MPYi5FgMNqpYF7n1zHc4/OIWekK1vdSYmZfZMFP5ua\nMeZRTMkehFi1X+x5RUCYohP3w0TeUIrUdcv1vemCoTYAvBkQT3qME6l1jWITJndimOvCSgVEwIHp\n5N+ol+iNohsDxtjnGWMXM8aOet4IGGMfYIx9QLHvzzDGPt7J98jlGnopUgPAydXm0LK5sTzKlXRZ\nrlHaJA1yEYrJiGRSC1xxoNlAXLZ/EseXNpUrs7Q4tVaDqRPOny3hmvNn8KUHmg1EKg9iK96DmFQ0\nDfIpJOnBz0nNfARtEFesT4V8E03VrEGI/hAqD2K10vBLUwN8Yj04XcTyRh0X7hnz7xNV06GHlzYx\nWTD8lfmsl0PTyvv8+qMrYAx47oVziWXIBaqNdP2oZeybyPOie1Ub5YoFy2ndi1rgyGwJ7/rBp+KH\nrwk6DssUnfgNJ4tmTC2msAfRimIq5oxYiqlk6rG10AydUoUHjxIWy1WcN1kIRZENAn01EIOCPGn2\nTIOQGnJEeb894zkwlswlA+3nQQBBHLdKpBbekkaB5iDjsv2TsF2G40vq5jZpcGadryY1jfDiS/fh\ngdMbTbkFaUptyAJvFFMpNAhAcPueMeqAYjL1sHfgqEptSG1em85hy2rSUK4+wr0IoT/wMTdP5g+f\n4clkYiIThrJVuY3bT5xDwdTw9CPTyBma7/m0Qi1lsyAZInR5aaPme4xpPAgiwk88+3w/Eg0IU3RC\nk5osmrH9IIQGoRKpLceF5TCUTB2lnK7UMZJ6z+d0bcd1lFsoD7bMt8COMxA9i2IqBsds8iC8jltp\nQl3bDXMFRHXR+IZBAHB077iSTrvcF6o5vbFZt/Gb//BdXP/uW1N3nDu9VvMro153Ca9BdGuEZvIT\no1qK1A1oBGX3KxElJqPhOD6tJJAzdH+STJNJHUWgYzj+MeLCXOMS5aIU2dVHZgDw/AeBqAbBGMND\nSxu4aD6gYoShaUVP3n7iHK49f9bLNk4Xz9+pBwFwcVpka3daKl+m6ISRnSyoKaaaHYliini6cpZ0\nPMXU2kAY+s4Lc11cGWyjIIEdYSDG88HN0isNQlAHAHA48sP4K8EUoa4izLUtDULjxc/UUUz8/K5U\n6A8A8JQ9vMPX/afW8eWHlvHS/30b/vr2x/HI8lao7HQrnF6v+b0VLpmfwP6pAm59MJwPEazq4x/E\nlUoDM6WcUjydKprYajghmk7VuztvaCF6COjQQEjlqGMT5RSr9VWv2KCMF160B0VTx/dIVV2jGsTZ\nzQZWK5YvUIt9JgtGLMV0brOOB89s4LlH5wCEz70Vah202p2XPIilNjwIFQRFZ0thrtyDsBHEtcD3\nimWKqdoIn59fiC9noGjqSiNTSSjKaeywRLmG7eL0eg2HBljmW2CHGIjAKLRD5bRCmGIK/zBBRddk\nA+GHubajQRi8+JmjEKkLpoaXXLYPr3rafuVndY1wyfwEPnrHE3j9X96BYk7H7//wVQDQsraSAGMs\n5EEQEa67ZC/+7fjZ0GSVJsw1yt/LCHpuBBRCw25urCQLtSqNIglNUUwKikmIrCphs1xpTvS7aH4C\n97/jZX7eCSBCK4Nr8fDShrfveOizvKe5+r752iM8+VEYCJWuoUJHIrXCg9jXoQfh1w+zWWAgCiZc\nhhBFFs34Lpg66lbUg/CiEXMaijEeRNWyY0NcAX7P7CQDcWqtCpc1L1QHgR1hIATF1G6oXyuIKKai\nqfvRJwJBRddkiqkeCd1MA0Mj2K6aYiIi/Pnrn4nrL52P/fwzzp9B3XbxS9cfwz++6fn4/qcfAMAL\n8CVh3Wvdep4UE3/dJfuwWbdx1+O85SZjgRjZ6kFc2WooBWpAXW6j4TT3m+YidUAPAfHVXFUQgnbI\nQDQlyokS682r2brthrzJOOQigrJoM3pxpAFPq2zqfz9xFmM53fcO0050nVBMY3kD43nD9yAmC0bH\n+p0pUXSBSG34YxMQgnQqislsFcXktGQKjB3Wk3phZXtCXIHeZENvO4QH0Sv9AeA3b87QcGim2BQt\nMVU0oWuUKpta0CbttNY0vJWjbyDa+CwAvOWll+IN1x0NUQbnTRbwRAoPQojRwoMAgO85tgemTrj1\nwSU89+hcaKXdupezFdv9KtrWFVD37pbLJnRCMRHxcMi644IxbnSjGkQuRqQuS2U2kmDqGhgLKKyH\nlzYwUTCaspNnx3Kxntztj5zDs54y659fWg+Cl69of623byKPpY06HIclVnFtBVOi6ARl6BfbsxzM\niHF63oLoBVEwdD9aTyyCRORTKaejaBrqUhsNB3vG470dEebabkvbYYWqmsOgsKM8iF4aCIBPYqoJ\nTtN4XZ00InXddtrSHwARhaH2INKgmNOb+OQjs6V0BmK92UCM5w0884JZX4eQV7Wt4vRVpb4FRDc+\nOdRV1bu72zBXwFuJ28w3bHEeRHS1vtoiCisKuUw70BzBJDA3ps6hObNewyPLWz69JMadJiO400ZZ\nvLNcDUsbta56uZsSRSdTTEC4lpIIvZY1CCDcE0LOki7ldFQsJ6RjiH1aUUxyZvdOwEK5AkOjkFc/\nKOwsA9HjOuk/87zz8dprDym3pa3HpFoVJyEa5tqLFqKHUxqIM8KDiNyMVxyYxOMrPFdSfvDiPIgn\nV6tY2qjjwr1jyu1qD8JpouJyklBrOy5MndpeFfKJ1pGKHzb3pAZUBiI+0S8KM0JTLW/WQ0ZWYHYs\nh7LX01zGvU/yyjXPODLjvyfTa61Q7UCkBrxyGxtcg+hUoAbCFJ24N1Tlun2KyQgoJv6+3EFOaBA8\nk5pFdAyAn29rAxG07d0JWFipYv90oWX9rn5hZ1FMPTYQb7z+othtabOpVcJrEvxaTAqRulMcmS3h\nk9+qhRKVVPDrMEVWlAWTh5syxkKRR3HJgiL7+vpL9ym3+yJ1NUmk1n0jogpRTQPhhQTVYJs7yvHj\nRykmz4MYS6FBGAHNAnh9DxRJTbNjOd7TvGaHtA2Rt3JMylDmGkTyKrgTkRrgFNOZ9Rpc1rlADYQp\nOjmKCYhqEDEehGQAAorJ8I1AVGOpNhwUzRYahCSaI9m2Dz0WtykHAtgxHgS/eXpNMbXC3Fg+lUit\nok2SYPbBgzgyVwRjPDO8FU6v1zA3lmvK2CyYfDVnSdmyRIilQL70wBIOzRRDE54MVV/qhuchyJAp\nJsthbdNLQOCFqMqnA1znAJqNXbsahBgjwFe9qgKNQbJceHFxfGkTe8ZzIW8lpyeX2nBd5lVIbf/e\nn58soGa5aNhuTzwIS2qTK2sQAtUmA9HsQUQppugxGGN+raY45FrktYwiFsrVzEB0g4k8vxl7lUWd\nBnPj6SimutUc258E0eO3U5FahSOelpJEM51eqyqregqarG47/iqxZOpKN75mOfjq8XO4/tJ9sXRQ\n0dRhaBTSICybKTyIIDqoE2MLcIMr0x9pi/UFFFOyBxGlqeq2o6QW47Kpjy9t4ujesDEVrVAdRfit\ngKBfOrn3Za8hTanvOMjXTxjzNFFMYhESppiCRLliThxD1jFcuKw1WxDVg0YZNcvB8kZ9W5LkgB1i\nILbHg8hho24n1jxqOOqVZCuIHr+91iCA5FyI0+t17Fdw54GBCKiaYs5QJpd97ZFzqFoOXhxDLwE8\nuihabqPuuMhFPJeQB2E3twtNg5yho2GzWA0ip8dTTKWcnqr+TVSDqNuu8nNBiHSwuGCMl0aJels+\nbdViogtyCzqJYgp+5zSlvuMgU0y260LXyE/orKShmKR6TEGYKy/3HT1GUrtRoHXplFFDEMGUeRAd\nw9A15A2tpdvZa4hyG0llv1XZwUkQq2bHZdAIPQnV2zueR8HUEnMhzqzXMK80EPza1u2ARijmNL+z\nnIxbHlhC0dTx3AvnmrbJmIxUdFVdq5BI7TbnSaSBSLYTE23U4Pod5dxmiikNvQTIRsaF6zI0pJIS\nMlQF+5Y361iv2U0GImp0VGi3H7WMnnkQMsXk0YBFXz8IVv++gTDCFFM9QjGZOsHUNf8YsoGoSGGw\ncUhz3UYFC5GWx4PGjjAQALBnPJ8q2qRXSFO6GegszNXQvDBX1lwWolMQUWKoa81ysLLVwH4VxSSF\nJIoJu2QaTatbxhhueWAJ33NsLpH24BVdZZG6mZaRM6kbjttWkpw/di8aSFUdF2jWDwRWK1Yqeil0\nDJtJ2fMKkVpRj0klUPPPh7PAVYjy+u1A9hq6EamDjnL83E1N81f4IQ/CDlNMvgZhh6OYxGeLkkgt\nb5e3qSAorx3hQYhGQdukQeyIKCYAuOlnnxmbtdsPCA8iqbNcw3Yx1abh4v2NXWXdoG6QZCBEh7GW\nHoQlexB6KDkM4JPdYrmKN1x3NHE8kwWjSaRuzoPQQxRTu94YwI1MpWEHeRBNYa7qPIh2PAhRsK7h\nuEGbWcXCoJjTUTR1vxQ6AJxY5uHDKg0CSDAQKSiXOIzneaSQTtRVDTP/+tncgzB0UhqIejRRLoZi\nEmMpqTwIqVZT4nh2iAeRM7SWiYH9xI7xIC6an/An7UFA1GNK9iDaz4MwdYLlegaih5mgh2dLWFip\nNMXgC/hJci08iJBI7T3A8oN4i9c74sWXxOsPAlNFExvVsEjdFMUUKdbXDcUkKKSoB0HEK8iqEuXS\nexDBpCR0qTjtKVpu48TSJsZyepP2044G0WmAxr6JPPZ24T0A4bwD8RtpGvFifFazBuF7CKooJinH\noWQKHSPwMpPajcrj2QkGYrHMq7j2qoRQu9gxHsSgEReuGEUnkTeiXLHjsp7eGEdmS9hqcBpJZUxP\nrXG+M0mkFp3uZAMhJqhbHljCpedN4MB0Mmca7Uut9iB4BJKo/9RJmKvpNZCxY6KYxD6qUhupPQhJ\nGBWRRXHidjSH5vjSJo7uG2/SmtJ4EGL13WkO0EXzE10vQgwpc9mS6mmVckZocq9ZLjQKjKm4Z6qR\nKCZxLuL/miJUttX5ypndo46Fle0LcQUyA9ExxvMGcoaGswnlNuqWi3wHYa6OyyNCVJNZp5BDXVUG\nQjSOSRKpxYhEGKLg7tcqFu58vIz//MILU41nshDuKsdF6kgUk9RroHMPgtf8sWPyIACeLCeLmo7L\nsFZtLvUdB3nV6nsQMQuD2UgW/vGlTTzvaLOgHy1VrkLV6pxiAoD3/NjTQejuHjPlhkFSLkvR1Jui\nmApSJ7iCH+YqU0xBjoOKYqqm8CAMifIadSyUK7jqkLq0/yCwYyimQYOIsCdFuY1OwlzFZFOz3J5r\nEEB8LsTptTpKOR0T+eZ1g+9BWOE8CCBIMLvt4WU4LsP3XpZMLwH8Ibek7Nu4ct8A/CikjgyEX/xQ\nUEzNxzANLeRBrFctMJauzAYQjpwJ4v3Vk5hMMW3ULJxer+GoIqEwWqpchW5EasDru9Bl9J+mBRSd\n7bq+xlPKhTvG8aKCwXflFbWYqpbrLzxUOoZPMbXIpJZF81HGRs1qWfByEMgMRBeYG0/Opu4kzFVM\nNjXL6amBEOWC43IhTq9Xcd5UQRlWK5dFEB6DmFjEg/ilB5YwUzLx9MMzTZ9XQeagGWOxxfoAeKUy\nOs+krtvxiXLiPZmzLreRJCePM40HMScZCCFQqzLOZe8pDrVGMuUyCIgS2w1bppiiHoTr12EC+PUh\nCoe5Vhu2v/BQ6RhpopjMHeJBLIoQ14xiGk2kqcfUSS0mscKt225PRWpe5TXfwoOoxVaMDKKYHJ+Q\n8DUIL+Lq1oeW8aKL96Y2aoVcwEGL4+eaRGr+vqil1IkHwTuzxRfrA5o7wq1WRSXX9jQIKyGKCQBm\nxnKoWg6qDSc2xBWQ26Wm8CB61CirU+S862e7EsUUMRDVSB0wIkLe0EK1mKKVWqM6Rjsi9agX6xML\nue3KogYyD6IrRLlkFTrJgxAhkzXL6Xn0QqtQ1zPr9XgDYQZGSzx4wgOwXRdPrFSwstXA847uUX5e\nhYJPW7mxvbvl6CDLcf1r0w6CUhvqRDmxj+xBtFNmA5D6MtuSSB1D+/g5NFt1HF/ahKmTT/+Fx9RG\nJvV2exDe9ZONeCkX7ktdt5yma1Iw9aZSG/K5RHUM8XcrSi2g+0abYvI9iIxiGk3sGc/j3FY9NmzU\ndnjdmDSlGmSIHr91q7ciNcANhOhQJcN1Gc6s15QlqoGwSC36UIsHuWEzbNX5Km8q5YQqf74qJd+p\nMqn973VYx3kQcukSFU3Fm8xIFNNWux5EoEEki9RBFv6J5U2cPzem9IzEuUbLXcsIPIjtNRDi+llO\n0LGPT+7hKKZodnnB0JuK9cmCezEX7kvNvU2tpZcaJMqNuAdRrmAsp6cOlOgHMgPRBebGcqhZLrYU\nbRGBIHO0/TwIwff3wYOYK+HJtWoTbXF2qw7bZS0MhJQH4Yo8CM5Q2q7bFOOeBmLfakMyEJGJTs4m\n5uW+O9AgdB2OV/4CUHsQRoRiaqeSK/+OYLVfS6CYZseCbOoTS5s4tldd8TZnJCd8iQlzu+LkBXj3\nO14KXhj16ORes5wmQ1YwNf96uS5r6vUQ1TGSKrkCkjc36gZipYpDM6Vt7YqXGYgu4NdjiqGZRLZs\ntOl9EgxJpO6HB6Eq+306plGQQF6ig4T4J+dBpOGGo5BF6sBAJEQxdUAxiWOIMSqjmJooJgsaAROF\ndDKdKsw1jgYRFNOZtRoeX6nElkQXIb8t8yAanTUL6jVMnZo8CNERTkDVGlWmmETJjaKUJV00w0Ym\nqR81EHjgo95RbrFc2bYaTAKZgegCc142dVwuhCjDIbKu00KmFrQerx7iQl1VvahlEBFyhoaa7YRK\nbQD8Qewk3DIvJUoJDaK5H0QwSXYSEQbIBoLTHco8CD0c5lquNDBdyqVemcv1nOoJnqMo2PfNJ8pw\nXBZrIMyUHsR200uA8MA8L08PPIimKKbI/ZE3dd/TVi0ySjm9KRs7ySDuhExqxhgWy1U/8nC7kBmI\nLiBWgnEehBCwRYnntBAPWK/DXAHJQJzbCr1/pkWZDYGCoYUEZdmDSJPAFIXKg1AV6xPfwau5dhbm\nCsgehDrMtRHxINIK1ICkQdhSFFOMsZzIGzB1wjceKwNQRzABUohvS5HaHRIPQvNzWsS4S6YRatSk\n6mZYMDTfg6gqQnZVUUxJ95hfnXeEPYjVioXNur2tAjWQGYiuICimczEehHh/rk0PIqCYei9S753I\nI29oTR7EqbUaDI1a1rPKe21HxYMnHlRb8iDamaxCInVCFJOvQXSUKMePIbQi1TFyhhYSNdspswFw\nD8vQOM2SJFITEWZKOTx6lhvpuL7dpqS/xCEaOrpd4KVKuBEX92+QCc0neKVIbep+HoTKg4jqGFER\nWz0WkSg3uh7EQnn7Q1yBzEB0BeFBnI3zILY68yBykgfRa/Exruz36fUa9k3kW3oseUND3XZgOy6I\ngsimkAbRIsM1CrmaZxDFpC61wYsEdt4PAgiSrOIT5WSKKX2ZDQGxiubUoPp7BIRQfXC6GMupp/Mg\nnI6aBfUa4vrJTZ3kBQDAw1yjxqxo6r5IHfSjjojUkTDYRJFa7kk9ohiGJDkgMxBdoWDqGM8bsbkQ\n5zYbKOX0tikAMbHU7d57EP+vvTOPleSq7vB3qqu63zaLZ8Z4xmMb2/GWsTEGT8zmADaE2CjBWfyH\nrUAQwnEcQYAoEiGJhIRQpESKIpKIgBAhC0SgAE5iWU6IcVAkggiMwYDHxtgCwxvGy3jezLy915s/\nqm7V7XpV3dXVVa+rJ/eTRn6vl3rH1dX31Dm/c84F3QvRL1KnbRRk0gg6kltdhec4fXn3cKpoPfsl\nlVzF1P9+fRe+1vSPH2+ky4J2OoNSTF6QQ9ecDjSIUdBDATeDxr9B1Sc6qkxLL/l2Z4ggKiNSBxqE\nkQbUC7mOAOKjNoC+TmkdacwaNxlxHcOvYhp8E1JzBEemu1EubJI7m0VqEblFRJ4QkadE5AMJz/+G\niHxXRL4nIl8TkZeWaU8Z+N3UKSmm1ebI6SWgr1KnaJEaksd+P3NmM3GKq0nDrfn7QQQb9+iFoNPz\nNQhHtvYxDMKc5tkeIlLrxWO8CGJQFVO/g/BTTKNFEH6/RY9mym5yJroXIr4HhInjyJYRIHE22sNT\nLtuBZ4jU5qgN8B1zt+dPet1a5lrbokH0RRAxHWOjlS2l5tacqd5RbvHUOrtmPXbOTK4HAkp0ECJS\nAz4K3AocAu4UkUOxl/0IeJ1S6iXAh4FPlGVPWcRn+5ucXGuNnF6CaDomFLMfdZyL9syx2uxwaj2a\npPr8crNvj+IkZjwn3A/Cq0URRKvTC8sPR6nZ1rN4NtvdsPInrcxV6wfjOIi1gVVMElZnbba7bLZ7\nOSIIJxy1Maw5UqcnB0UQ+pjDNIg0MXw70eev01WhA5419qWO9q1IL3NdTxCpZ+v9FWjmfhED7XG2\njm+fJo6d2ph4iSuUG0HcADyllPqhUqoFfA64zXyBUuprSqlTwa9fBy4o0Z5S2DvfSNUgXlhtjVzi\nClF5I5TnICAqde10e6w2O0OrdnQEodMI5tz9PGKpiISdtNE2nckite7UzrsfBEQLUGqjXLAQj9ok\nF/0drUF0h07w1cce5iB0F3gazXavEhGEGziyVrcXXr9mCjGtDLrhRbOYknbH005GP5elign8KHya\ny1wXl9Ynrj9AuQ7iILBo/H4seCyNdwL/nvSEiNwtIkdE5MiJEycKNHF89i3UUye6Lq01c0UQbskR\nxMGgMuJ40Cyn784XEsZ8mzR0BBEIkeZm9RsZOlyTmA3q3IeJ1KvN/CmmRqzMNekY/i5+/kJ8el2P\n2RhVpJZg1MbwXQSvOG+BHQ2XK8/bMeSYztBRG1VwEPWaE0QQvTACNquYUiMI199SttdTYZTQn2Lq\nT1O1OtnKel1nsGOtMlEPxOQjiEpMcxWRm/AdxI1JzyulPkGQfjp8+HClPvW9C36KqRfb/U0pxcnV\nVtgUNQpmHr8MkXrnrL/wrW76X0h9dz4/zEEEIrUuZTRF6rwLld8p2xvaSb02hoPQTkffhSadUr9R\nrj+CGGWulD5GOyjHHZZiuuWa/dx01YuGRl2NIXfCVRGp3ZrQ7HTpqegzMquY0vbI0L83O72wWskU\noU0dI8mBpFGvDdZuqsyJ1SbNTm/iPRBQbgTxU+BC4/cLgsf6EJFrgU8CtymlTpZoTynsnW/Q6am+\nndEAljc6dHoqzDWPgpkjL0OkXgi+gCvNfgcxNIJwa0EVk9YgoghiPedC5c/iGSRSxzSIMUZtbLS7\neDVJ1EnMO84oghixA94QqYdFECKSKSVn7skdR6l8qb0y8GoOG61gQ6YtfRCRBhF3nDPGpkEbrS4i\n/VGG6WSiXpvh97VuzZnaYX16mObZnmL6JnC5iFwiInXgDuA+8wUichFwL/A2pdQPSrSlNHSVUnxf\nCD1+Y9+AxrM0zLvkMlJM8w3/S6cdw2pmB+HQbHfDNII5NXMzZwShRcq0CEJEqNec0NZcZa5GFJJ2\nPj03uuPMq0HoXgC/iqmYRTs+I8pEp56GVUxtB15Nwj6TsMzVi0TqaD7VVpEa/BJY3QRnOvA5Q4MI\nq5wynFszZThtHKtIkxyU6CCUUh3g3cCXgMeBf1ZKHRWRe0TknuBlHwT2An8jIo+IyJGy7CkLrTHE\neyHCMRt5ROpauSK1W3OY8ZzQMegeg2Eppplgbk6nq/rKXFs6xZRHg/BqAzup9WPrzfQS1WGYZa5p\n7/ecKJWjI4hRRm1AUHEUDOsbdYJvGoMiiDwTdMvCdZwwRbQlxdTqDEgxRc2SSQK0qWOMMhDSM4oO\npo1oo6DJRxClahBKqQeAB2KPfdz4+S7grjJtKJswgogJ1Ut6zEYekbrkCAJgoeGFDmI11CCG58Ob\nwWLu1ZxovMQYKabZeo3VZicqc00RkEOROueGQeCXuWr9ZetrHHoKuj3FqbUWs15t5Cig7vqRTrM9\n+j7kaWink8RGhRyEV3PQbTX6+q27Dq4jgQaRXMWk+yI2g9fEryEzxZRUBjvIns7URhAb7FtoVEJb\nmnxsOuVEE11jKaYKRxDgj7GOi9TZqpj8CELbqL+Imxlm5CQxE4xa0JNak/SBuusYjXKjn49GIFL3\nVLrob1Zk5Rmz4dsWjdoYdZOoNOoD+iCShttNCvNzMdOAuhM6iiBSUkxtX4SOj2oxdYyokS6LBjG9\nIvViBcZ8a6yDGJM9c8kRhE4xjZrHhlijXEmbhcw3alGKqZW1iqnmO4NON0wjuMF4iawNTHG0Wwjw\nPgAAFkRJREFUBuE33yX/v9Zdh9Vw1Eb+FBOkp6j0cTs9xZmNdmqkMQitF2y2C04xDYkgqiJSa8xz\nPBcM2wsjiPiGULEUU9zZmTpGNIojY4ppWh3E0uTHfGusgxgTt+awe87b0k19cq3Jrllv5P2owR+x\noCOH8lJM7pYUUxaRGvyII0wjBFtNbuSMIGY9J5zFlHauTJE61zRXd3jKLowgOj2WN9rsyuUgnLAP\noqhFuz5goUtL20wCs/LOTAPqPaWjzYC2DusDX6ROuob0bK+NVmekicG+s56+FFO3pzh+eoMLKyBQ\ng3UQhbB3vp4oUudJL2nc0h2EF6aYVjf96p5hd716IVrd7IRpBLcmNNv+ojiWSD3IQbjRpjF5Ukw1\nw+GmvV87nnavx/JmPgehF/MiRepBozZ02qYqGkT4s2OmmNz+FFPCLCbwd8ZLEqnrNX//6fVWdySR\n2nWms8z12eVNOj1ViR4IsA6iEPYuNMLd4zQn15rsyyFQa3TKozwHYaSYmh3m64Onj0IUQaw0O2Ea\nwas5rGxmD/3jzNSjURvpEYSZ3853yWrHkHY+66EGoVjOnWLyF/MsfRBZGTRqI2k0xaQwHa/pLPwd\n4aJO6rh4b5a5JlXCiQhzQRQyahVTawojiKiCyUYQZw37Fupb+iBOrrbCmf95cIcsaOOyMOMafRDd\noekliL7ca81OmEbwak7YJJhLgwia7zbb3dTF33QceTqpIXIsae83ezrO5E0xuf6drlLpu8mNfMxB\nInWYcpn819jUHcx001woUneDPUTiDsLUIJLHtcwGNxGbI6aYpjGCqMo+EJrJX1lnAXvmt85jOrk2\nXopJL2TlidRuXyf1wkwGB+FG1UCekbLRDiJPLlx/2Vc2O6mLd5+DyHlnXg9sT2+UixaqtVY315hl\nrxb1lvy/E6mN/1/T0fujVLqhcB+PUs0yVz0ROI52MustPxWaJYqc1jLXxaV1ROD83TaCOGvYO9/g\n9EY7vGPp9hSn1lsDt+8chldyimlHw5+z3+r0WGt1hlYwQf+ip+8SXcdheSNIMeXUIACWN9upi2o9\nJb89CvrYaSK3Pq7e22Pn7OgtQmYvQGEOIqgSS6JKIrX5ubixFJPWIJLsjMpce6lzpbSOsd7qMucN\nT4X6NqSftyqzeGqd/TtnchW3lEE1rJhy9i3UUYpwf4VT6y2UIteob82wnPm46JTSWrPDarOTLcVk\nCIxemLIRVsZIMWkHcWajPUCkLiDFpB1EWgQRHFcXG+SrYoqOXVSKSc93SqJaGkRyiikSqbtbBGqI\nHOlqs02npxLHaGgdY5TBhLq6bto4dmqjMuklsA6iEHSkoO8+wzEbY4jUbskRhI4YVpudQKQe7iDM\nJifPyOkvByJ1njtZrWsMdhCGY8qbYhpyPvWiplOFeVNMmu0ZtZE8vmISuCmFBHNaP0jZZc9xhLrr\nsLTm32QkOYAoxZS918ad0jLXY0vrE99m1MQ6iALQE1u1Y9CLzFgidcllrjsCzWFls8Nas5sxxWRG\nEFGZq94OMkuHa5wwxbTRTs0t91fI5DsfehOb1Ga84G/rfpa8VUyaojqpdS69l5BP32h3qbtOadfI\nKNRTIgh/cfermNIc2YzrcDoYkJh0DWkdw2+ky3aNTWOjXKvT45nlzco0yYF1EIUQjtsIHIMeuzFO\niknfTZcpUoPfRe2nmIYvaGaJoptQFZSrUa5uCN8pDsK8G/dyDOsDM4JIqWIKntefXd4+CE1Rs5j0\ndZAkVPtpm2p8hU3dwfwcZ7waPeXfAKSl3Wa8WuiYkyqy9LiOjXaH2YzndRodxPHTGyhFZZrkwDqI\nQtCpJH2R6whiHJFaRxBOyRrEymbbTzGNKFJ7CQ4i76gNzaBOavCjqbznQx87TeTekmLKJVIbGkRh\nInW6g/jxyTUO7KrGYtIX5Tlbr4lT661UZzbj1cIR67PeoCqm5CqnJNwp3JM6LHGtSJMcWAdRCLtm\nPWqOhCmmpbUWjsDuHHehmnDWUckppqU1XxwcOcWU0Jmcq8w1i4MIey7yn4thZa71mEidS4Mw7C9s\nWF9wzKTR1UePL3P1+TsL+Tvj0tdJ7fanmMC/zlJTTF6kQST2QXiuP2pjBJFap+aUmh4nsRjsA2Ed\nxFmG44jfCxGI1C+sttgz3xjr7r/sMlftEJ5b3gSGz2GCWASRUDaab0e56D2pZa7u1mhlVIY2yukI\nYq2F60iuaKg/tVLcqA3YGkGcWGny/EqTQxVxEOaNjNk0pzWDU+ut1BTkrBFBJJ33uXqN9fZoIrVn\ndMZPC4tL67iOsH/nzKRNCbEOoiD2ztfDEd8nV5u5tho12a4y12fP+A4iSwRhLuZ6QYg3RY2K6VTS\nRWpn4PNZqLuDz6f+Gy+sNtk562Wqtd/yN0oQqfUx253+he7o8TMAXH3+rkL+zrikNcrpstVuT6U6\nzYZXCwsdkvsgaigFp9dbIziI4LxNkQ5x7NQG5++erUTRgcY6iILYuxB1U4/bRQ3bUOYa3Nk9G0YQ\n2fZH1sRTYHmraWYy9DiEPQzjpJhqg4+h8+Yrm51cAjWUU+bqhSJ1t+/xo8eXASoTQXgDRm1o0lNM\n0eNpndQAy5udRI0iCf39mSYdokr7QGisgyiIvfONPpF6HIEaogXNKamKyXGE+XrNSDENXxRrTrTN\naChSBwtYnpQMxCKIISL1WCmmYY1yRt58Z4axI0m4fY1yBYvUsQjisePLXLhnNrczKxrz/HkpacdB\nZa6atBTToOeTCIcvTlGz3OLSBhfsro7+ANZBFIYfQQQOYq01doopGmVRXri5MOMaKaZsXzydOtH2\nabE6bzev2V2b5iD03fh4KabBozbMvHmeHggoKcXk6n2/+xe6o8fPcPWBaqSXoP/8eX0RRORs05ym\n6TjSRm0Mej7RnilLMW22u7yw2rQRxNnKvoUGK80OK5ttVjY7Y/VAQHQXVlaZK/i6g+7dyCJSw9bF\nWn8R82576Rj7UAyvYhpHpA4c25AqJsjvIErppA7sNhe6lc02T59cr0wFE/SXIpv6TV+KKcVpmtpE\n4qgNb/QIwpuyFNOxClYwgXUQhaEjhh88twrAnjHGbIDRqVyig9jRcNENullEaoju9txYqmmceUD6\nmMNEajONMSreEJHaTA/lKXGFcvog9DHNcRuPP7MCwNUHq+Mgouuh//xmSjEZn39ShGc6hazXWXje\npiSCWFzyeyCqsg+ExjqIgtgTOgj/yzu2SO2UK1IDfSO+szqIRuxuXn8Rx3EQ+r3DIoi0/aSz0Bii\nY3h9EUQ+DULrMUljrfOS1EldtQomMK6H2GdkXhdpVUzaQaQ+Xx+cgkoi2t9jyiKICo3ZAOsgCkOL\n0tpBFJZiKkmkBvoG9M1nFf9iTWvemCkm872pGwYVUuY62OGad755hV9tX1HRAxh9EB3TQSyzb6HO\ni3aMF6UWSXg9uIMcxGCROq1Lul+kzjqLSfdBTEkEcWqDhutwboU+U7AOojC0Q3gySDGNM8kVtifF\npCOIGS85tE9Cz9PRd2huARHETMYIYpwU07BRGyLRvtX5U0yBgyhwuqp2NnEHcej8XYVFKUWgr5/4\n9eo4EkYGg/ogIF1fmDNKW8/WPojFpXUOnjNbqc8UrIMoDB1BPFFQimk7ROodQVopq0ANW1NM+q45\nb5krRAtHuSK1jiDSj6Gdcn6R2n9/kRFEOGojWOianS5PPrdSKYEatkaUJvquP12k9h9Pi0Jnc6SY\nIgcxLSmmau0DobEOoiDm6zUarsOJlSb1mjPSopvEdpS5at0hq/4ApoPot2+sFNMQkTrulPJQj5Xn\nJqHz5+M2ypWZYnryuVU6PVU9B+H0Xxcms6HGMLiKKTWCyNEHoT/nadmXuopNcmAdRGGISFjJtHeh\nPnaouB0RhE4xZdksSKO/5PFGuawdrknoBSRtM6C4IJ6HLCk7/ffzNsrpu/0iN/CJRxBVFKjBv079\nRsr0KqTUPghXRxDJ591MX85lvM7CCGIK9qVe2Wxzer1tI4izHZ1mGje9BMYsphJzkjrKWRhhQYz2\ndtaNclqkzn8p6SqVRppIXUgEMbhRDiLnkTeC0O8vI4JodrSDWGah4fLiitXLg///P6hMNXVYX/B8\nUg8E9OsY2VNMgUg9BftSRyWu1ftMrYMoEO0YxhWoofxx32A4iJFSTP3pIC0cjyVS62OWOGojdGyD\nIojg+Lk1iLDMtXiRWufSjx5f5mcP7Cg1ssxLveaEIy5M9KKeN8XkP+cOfY1J2Cg3BaM2oiY5m2I6\nq9GOoYgIwt2OFFMeDcLrvxN3wwhijBRTfRtE6gwD/0KROmcVU1jmWtAcJt+mSIPo9hSPP7NcufSS\nxq2lRRC6Wi6tzHWwSA3RDcjojXLVTzEt6o2CbARxdqNLXfeNOagPomFj2xNBZL/jjYvU29kol3R3\nmpVhozbAX4xnvVqqHcMoQ6SuBbn9drfH0yfXWG91KydQa7yak3h+Z4c0wjUyLP6zQRFI1humaNRG\n9SOIxaV15us1ds9VY/CiSakOQkRuEZEnROQpEflAwvMiIn8VPP9dEXl5mfaUje6m3jPmoD6I7syr\nJlLr9El8y9FxylyHVTHF5z7lIdpfY4AGUXNyd1H7xxYcKTbFBL7trW4vHPFd1QjCqzmJzjVMMQ2Z\nxTQ4xVQb6RqbpmF9x05tcOGeucr1QECJDkJEasBHgVuBQ8CdInIo9rJbgcuDf3cDHyvLnu0gFKmL\ncBDbIFLnKXPVX2Z9p6i/iONU7jRilVFxikwxDaqE8mqSO70UHcMpbDc5Tb3m0Or0OHr8DPWaw+Xn\nLRR6/KJwa5IYQcwN1SAGVzGBfxORtYsaoobIaeiDOHZqvZICNcB4xfqDuQF4Sin1QwAR+RxwG/CY\n8ZrbgH9U/saxXxeR3SJyQCn1TIl2lUYoUhegQZjTMcsiX6Ncf0lqmGIqIIJI3XK0Nn6KqTFkT2rw\nF3dvdrzFvZ5yFz3WMV2He791DKXgiv0LYznKMvFqTqJt+tpI+3xnh3RS6+dGuca0HR/58pP8w9ee\nzvy+SfDDF9Z45aV7J21GImU6iIPAovH7MeAVGV5zEOhzECJyN36EwUUXXVS4oUXxikv28Fs/f0kh\nH/arL9vHb7/uUq7cv6MAy5I5d0eD973xcm65Zn/m99x6zX56SoXO5eUXncPdr72Un7v4nNx2/OI1\n+1nebKfOoXFrDn/05qu46coX5f4bV5y3wD2v+xluvGxf6mvufu2lY8++ev+tV3HtwWJTQL/z+st4\n+MdLAPzytecXeuwi+d2bL0us4PvVlx3k3IX0PdoP7JrhPTdfxpuuPi/12O94zSXhvtVZ2D3ncdeN\nl3D8zEbm90yKK/bv4PbrL5i0GYmIf/NewoFFbgduUUrdFfz+NuAVSql3G6+5H/hTpdRXg98fAv5A\nKXUk7biHDx9WR46kPm2xWCyWBETkYaXU4VHeU2as+lPgQuP3C4LHRn2NxWKxWCZAmQ7im8DlInKJ\niNSBO4D7Yq+5D/jNoJrplcCZadUfLBaL5WyjNA1CKdURkXcDXwJqwKeUUkdF5J7g+Y8DDwBvBp4C\n1oF3lGWPxWKxWEajTJEapdQD+E7AfOzjxs8KeFeZNlgsFoslH9Wsl7NYLBbLxLEOwmKxWCyJWAdh\nsVgslkSsg7BYLBZLIqU1ypWFiJwAfjxpO4awD3hh0kZkwNpZLNbOYrF2FsuVSqmRRjOUWsVUBkqp\ncydtwzBE5MioHYuTwNpZLNbOYrF2FouIjDyCwqaYLBaLxZKIdRAWi8ViScQ6iHL4xKQNyIi1s1is\nncVi7SyWke2cOpHaYrFYLNuDjSAsFovFkoh1EBaLxWJJxDqIMRCRT4nI8yLyqPHYHhF5UESeDP6b\nf6u1ghCRC0XkKyLymIgcFZH3VtFWEZkRkW+IyHcCOz9URTs1IlITkW8HG19V0k4ReVpEvicij+gy\nx4rauVtEviAi3xeRx0XkVVWzU0SuDM6j/rcsIu+rmp2Brb8XfIceFZHPBt+tke20DmI8/h64JfbY\nB4CHlFKXAw8Fv0+aDvD7SqlDwCuBd4nIIapnaxO4WSn1UuA64JZgn5Cq2al5L/C48XtV7bxJKXWd\nUatfRTv/EvgPpdRVwEvxz2ul7FRKPRGcx+uA6/G3KPgXKmaniBwE3gMcVkpdg7/dwh3ksVMpZf+N\n8Q+4GHjU+P0J4EDw8wHgiUnbmGDzvwG/UGVbgTngW/j7mFfOTvzdDx8Cbgbur+pnDzwN7Is9Vik7\ngV3AjwiKZqpqZ8y2NwH/U0U7gYPAIrAHvxn6/sDeke20EUTxnKeiXfGeBdJ3Yp8AInIx8DLgf6mg\nrUHa5hHgeeBBpVQl7QQ+Arwf6BmPVdFOBXxZRB4WkbuDx6pm5yXACeDvgpTdJ0VknurZaXIH8Nng\n50rZqZT6KfDnwE+AZ/B36vxPcthpHUSJKN9VV6aOWEQWgC8C71NKLZvPVcVWpVRX+SH8BcANInJN\n7PmJ2ykivwQ8r5R6OO01VbAz4MbgfN6Kn1p8rflkRex0gZcDH1NKvQxYI5b+qIidAARbKL8F+Hz8\nuSrYGWgLt+E73vOBeRF5q/marHZaB1E8z4nIAYDgv89P2B4ARMTDdw7/pJS6N3i4krYCKKVOA1/B\n13iqZudrgLeIyNPA54CbReQzVM9OfTeJUup5/Hz5DVTPzmPAsSBaBPgCvsOomp2aW4FvKaWeC36v\nmp1vBH6klDqhlGoD9wKvJoed1kEUz33A24Of346f758oIiLA3wKPK6X+wniqUraKyLkisjv4eRZf\nJ/k+FbNTKfWHSqkLlFIX46ca/ksp9VYqZqeIzIvIDv0zfh76USpmp1LqWWBRRK4MHnoD8BgVs9Pg\nTqL0ElTPzp8ArxSRueC7/wZ80X90Oyct9kzzP/yL5BmgjX8X9E5gL754+STwZWBPBey8ET+c/C7w\nSPDvzVWzFbgW+HZg56PAB4PHK2VnzObXE4nUlbITuBT4TvDvKPDHVbQzsOk64Ejw2f8rcE5F7ZwH\nTgK7jMeqaOeH8G+uHgU+DTTy2GlHbVgsFoslEZtislgsFksi1kFYLBaLJRHrICwWi8WSiHUQFovF\nYknEOgiLxWKxJGIdhMUyAiLyKyKiROSqSdtisZSNdRAWy2jcCXw1+K/FclZjHYTFkpFgltWN+A2R\ndwSPOSLyN8E+Bg+KyAMicnvw3PUi8t/BoLwv6TEHFsu0YB2ExZKd2/D3LPgBcFJErgd+DX/k+yHg\nbcCrIJx99dfA7Uqp64FPAX8yCaMtlry4kzbAYpki7sTf2Ab8IX134n+HPq+U6gHPishXguevBK4B\nHvTH4VDDH8tisUwN1kFYLBkQkT34mwO9REQU/oKv8CekJr4FOKqUetU2mWixFI5NMVks2bgd+LRS\n6sVKqYuVUhfi74K2BPx6oEWchz+8D/zdu84VkTDlJCJXT8JwiyUv1kFYLNm4k63RwheB/fiTfB8D\nPoO/TeoZpVQL36n8mYh8B3+C7qu3z1yLZXzsNFeLZUxEZEEptSoie4FvAK9R/h4HFstUYzUIi2V8\n7g82OqoDH7bOwXK2YCMIi8VisSRiNQiLxWKxJGIdhMVisVgSsQ7CYrFYLIlYB2GxWCyWRKyDsFgs\nFksi/wd7GFwzqxLsNgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x4c0d503240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "fig = data.groupby(['Age'])['Survived'].mean().plot()\n",
    "fig.set_title('Normal relationship between variable and target')\n",
    "fig.set_ylabel('Survived')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By looking at the plot, we get an intuition that younger people (children) were more likely to survive (see higher survival rates at ages below 10 and 10-15). However, it looks like children of 10 years of age, had a very low survival chance. This does not make a lot of sense and most likely indicates that our 10 year old sample is not big enough and then the survival rate is underestimated. Let's see below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x4c11768320>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZIzENQ2sKGo2CuJpCjoh+iohMIjKI6KcA5Fp5Y5po+NQ1M1QbEKiE5lrzFIDq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\nEZKFuDioXGxkajAEimNoIamx3ThjZ+JOmtRp3TTONO40cTJ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      "text/plain": [
       "<matplotlib.figure.Figure at 0x4c118077f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# here I plot the number of passengers within each 1 year age bucket / bin\n",
    "fig = plt.figure()\n",
    "fig = data.groupby(['Age'])['Survived'].count().plot()\n",
    "fig.set_title('Number of people per year age bin')\n",
    "fig.set_ylabel('Survived')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we suspected, there were very few children at the age of 10 on the Titanic. If none of them or only half of the 10 year old children survived, we would be led to think that being 10 years old decreased your chances of survival, when in reality, there were only 2 children of the age that were not lucky enough  to survive, therefore leading to underestimation of survival rate.\n",
    "\n",
    "By grouping Age into bins, we can get a better view of the survival rate depending on the Age of the passenger. Let's see below.\n",
    "\n",
    "### Discretisation with quantiles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(20.125, 28.0]</td>\n",
       "      <td>22.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(28.0, 38.0]</td>\n",
       "      <td>38.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(20.125, 28.0]</td>\n",
       "      <td>26.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>(28.0, 38.0]</td>\n",
       "      <td>35.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(28.0, 38.0]</td>\n",
       "      <td>35.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>(38.0, 80.0]</td>\n",
       "      <td>54.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>(0.419, 20.125]</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>(20.125, 28.0]</td>\n",
       "      <td>27.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>(0.419, 20.125]</td>\n",
       "      <td>14.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Age   Age\n",
       "0   (20.125, 28.0]  22.0\n",
       "1     (28.0, 38.0]  38.0\n",
       "2   (20.125, 28.0]  26.0\n",
       "3     (28.0, 38.0]  35.0\n",
       "4     (28.0, 38.0]  35.0\n",
       "5              NaN   NaN\n",
       "6     (38.0, 80.0]  54.0\n",
       "7  (0.419, 20.125]   2.0\n",
       "8   (20.125, 28.0]  27.0\n",
       "9  (0.419, 20.125]  14.0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# I will divide Age in 5 bins. I use the qcut (quantile cut) function from pandas and I indicate that I want 4 cutting points, thus 5 bins.\n",
    "# retbins= True indicates that I want to capture the limits of each interval (so I can then use them to cut the test set)\n",
    "\n",
    "Age_disccretised, intervals = pd.qcut(data.Age, 4, labels=None, retbins=True, precision=3, duplicates='raise')\n",
    "pd.concat([Age_disccretised, data.Age], axis=1).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see in the above output how by discretising using quantiles, we placed each Age observation within one interval. For example, age 22 was placed in the 20-28 interval, whereas age 38 was placed into the 28-28 interval. We can visualise the interval cut points below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.42 ,  20.125,  28.   ,  38.   ,  80.   ])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "intervals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And because we generated the bins using the quantile cut method, we should have roughly the same amount of observations per bin. See below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Age_discretised\n",
       "(0.419, 20.125]    179\n",
       "(20.125, 28.0]     183\n",
       "(28.0, 38.0]       175\n",
       "(38.0, 80.0]       177\n",
       "Name: Age, dtype: int64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate number of passengers per bin\n",
    "temp = pd.concat([Age_disccretised, data.Age], axis=1)\n",
    "temp.columns = ['Age_discretised', 'Age']\n",
    "temp.groupby('Age_discretised')['Age'].count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    Q2\n",
       "1    Q3\n",
       "2    Q2\n",
       "3    Q3\n",
       "4    Q3\n",
       "Name: Age, dtype: category\n",
       "Categories (4, object): [Q1 < Q2 < Q3 < Q4]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we can also add labels instead of having the interval boundaries, to the bins, as follows:\n",
    "\n",
    "Age_disccretised, intervals = pd.qcut(data.Age, 4, labels=['Q1', 'Q2', 'Q3', 'Q4'], retbins=True, precision=3, duplicates='raise')\n",
    "Age_disccretised.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Q1', 'Q2', 'Q3', 'Q4', 'Q5', 'Q6', 'Q7', 'Q8', 'Q9', 'Q10']\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Fare</th>\n",
       "      <th>Survived</th>\n",
       "      <th>Age_disc_label</th>\n",
       "      <th>Age_disc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>857</th>\n",
       "      <td>51.0</td>\n",
       "      <td>26.5500</td>\n",
       "      <td>1</td>\n",
       "      <td>Q10</td>\n",
       "      <td>(49.0, 80.0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>49.0</td>\n",
       "      <td>76.7292</td>\n",
       "      <td>1</td>\n",
       "      <td>Q9</td>\n",
       "      <td>(41.6, 49.0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>386</th>\n",
       "      <td>1.0</td>\n",
       "      <td>46.9000</td>\n",
       "      <td>0</td>\n",
       "      <td>Q1</td>\n",
       "      <td>(0.669, 13.2]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>124</th>\n",
       "      <td>54.0</td>\n",
       "      <td>77.2875</td>\n",
       "      <td>0</td>\n",
       "      <td>Q10</td>\n",
       "      <td>(49.0, 80.0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>578</th>\n",
       "      <td>14.5</td>\n",
       "      <td>14.4583</td>\n",
       "      <td>0</td>\n",
       "      <td>Q2</td>\n",
       "      <td>(13.2, 19.0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>549</th>\n",
       "      <td>8.0</td>\n",
       "      <td>36.7500</td>\n",
       "      <td>1</td>\n",
       "      <td>Q1</td>\n",
       "      <td>(0.669, 13.2]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>118</th>\n",
       "      <td>24.0</td>\n",
       "      <td>247.5208</td>\n",
       "      <td>0</td>\n",
       "      <td>Q4</td>\n",
       "      <td>(22.0, 26.0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>20.0</td>\n",
       "      <td>8.0500</td>\n",
       "      <td>0</td>\n",
       "      <td>Q3</td>\n",
       "      <td>(19.0, 22.0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>157</th>\n",
       "      <td>30.0</td>\n",
       "      <td>8.0500</td>\n",
       "      <td>0</td>\n",
       "      <td>Q6</td>\n",
       "      <td>(29.0, 32.0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127</th>\n",
       "      <td>24.0</td>\n",
       "      <td>7.1417</td>\n",
       "      <td>1</td>\n",
       "      <td>Q4</td>\n",
       "      <td>(22.0, 26.0]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Age      Fare  Survived Age_disc_label       Age_disc\n",
       "857  51.0   26.5500         1            Q10   (49.0, 80.0]\n",
       "52   49.0   76.7292         1             Q9   (41.6, 49.0]\n",
       "386   1.0   46.9000         0             Q1  (0.669, 13.2]\n",
       "124  54.0   77.2875         0            Q10   (49.0, 80.0]\n",
       "578  14.5   14.4583         0             Q2   (13.2, 19.0]\n",
       "549   8.0   36.7500         1             Q1  (0.669, 13.2]\n",
       "118  24.0  247.5208         0             Q4   (22.0, 26.0]\n",
       "12   20.0    8.0500         0             Q3   (19.0, 22.0]\n",
       "157  30.0    8.0500         0             Q6   (29.0, 32.0]\n",
       "127  24.0    7.1417         1             Q4   (22.0, 26.0]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# and now, I will divide into 10 quantiles for the rest of the exercise. I will leave the quantile\n",
    "# boundary and generate labels as well for comparison\n",
    "\n",
    "# create 10 labels, one for each quantile\n",
    "labels = ['Q'+str(i+1) for i in range(0,10)]\n",
    "print(labels)\n",
    "\n",
    "# bins with labels\n",
    "X_train['Age_disc_label'], bins = pd.qcut(x=X_train.Age, q=10, labels=labels, retbins=True, precision=3, duplicates='raise')\n",
    "\n",
    "# bins with boundaries\n",
    "X_train['Age_disc'], bins = pd.qcut(x=X_train.Age, q=10, retbins=True, precision=3, duplicates='raise')\n",
    "\n",
    "\n",
    "X_train.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Age 51 was placed into the 49-80 bucket, which is also the last bucket (Q10) in our distribution, as it contains the majority of the elder people. The age of 8 was placed into the 0-13 bucket, which is the first interval (Q1) of the discretised variable. And below the interval limits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.67,  13.2 ,  19.  ,  22.  ,  26.  ,  29.  ,  32.  ,  36.  ,\n",
       "        41.6 ,  49.  ,  80.  ])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bins"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To divide the test set, we will use the cut method of pandas, and we will pass the interval edges above. \n",
    "\n",
    "As with all feature engineering methods, the limits of the intervals should be set on the training set, and then propagated to the test set. We should not calculate the quantiles in the test set. We should use the limits estimated using the train set data. If the distributions are similar, we should expect to have roughly the same amount of observations in each age bucket in the test set as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Fare</th>\n",
       "      <th>Survived</th>\n",
       "      <th>Age_disc_label</th>\n",
       "      <th>Age_disc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>495</th>\n",
       "      <td>42.0</td>\n",
       "      <td>14.4583</td>\n",
       "      <td>0</td>\n",
       "      <td>Q9</td>\n",
       "      <td>(41.6, 49.0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>648</th>\n",
       "      <td>18.0</td>\n",
       "      <td>7.5500</td>\n",
       "      <td>0</td>\n",
       "      <td>Q2</td>\n",
       "      <td>(13.2, 19.0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>278</th>\n",
       "      <td>7.0</td>\n",
       "      <td>29.1250</td>\n",
       "      <td>0</td>\n",
       "      <td>Q1</td>\n",
       "      <td>(0.67, 13.2]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>35.0</td>\n",
       "      <td>146.5208</td>\n",
       "      <td>1</td>\n",
       "      <td>Q7</td>\n",
       "      <td>(32.0, 36.0]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>255</th>\n",
       "      <td>29.0</td>\n",
       "      <td>15.2458</td>\n",
       "      <td>1</td>\n",
       "      <td>Q5</td>\n",
       "      <td>(26.0, 29.0]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Age      Fare  Survived Age_disc_label      Age_disc\n",
       "495  42.0   14.4583         0             Q9  (41.6, 49.0]\n",
       "648  18.0    7.5500         0             Q2  (13.2, 19.0]\n",
       "278   7.0   29.1250         0             Q1  (0.67, 13.2]\n",
       "31   35.0  146.5208         1             Q7  (32.0, 36.0]\n",
       "255  29.0   15.2458         1             Q5  (26.0, 29.0]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we use pandas cut method and pass the quantile edges calculated in the training set\n",
    "X_test['Age_disc_label'] = pd.cut(x = X_test.Age, bins=bins, labels=labels)\n",
    "X_test['Age_disc'] = pd.cut(x = X_test.Age, bins=bins)\n",
    "\n",
    "X_test.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Age_disc\n",
       "(0.67, 13.2]    26\n",
       "(13.2, 19.0]    38\n",
       "(19.0, 22.0]    24\n",
       "(22.0, 26.0]    33\n",
       "(26.0, 29.0]    21\n",
       "(29.0, 32.0]    25\n",
       "(32.0, 36.0]    22\n",
       "(36.0, 41.6]    22\n",
       "(41.6, 49.0]    23\n",
       "(49.0, 80.0]    32\n",
       "Name: Age, dtype: int64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's check that we have equal frequency (equal number of observations per bin)\n",
    "X_test.groupby('Age_disc')['Age'].count()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discretisation by quantiles guarantees same number of observations in each partition/bin/interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Age_disc\n",
       "(0.669, 13.2]    0.101124\n",
       "(13.2, 19.0]     0.115570\n",
       "(19.0, 22.0]     0.088283\n",
       "(22.0, 26.0]     0.113965\n",
       "(26.0, 29.0]     0.099518\n",
       "(29.0, 32.0]     0.088283\n",
       "(32.0, 36.0]     0.109149\n",
       "(36.0, 41.6]     0.083467\n",
       "(41.6, 49.0]     0.105939\n",
       "(49.0, 80.0]     0.094703\n",
       "Name: Survived, dtype: float64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t1 = X_train.groupby(['Age_disc'])['Survived'].count() / np.float(len(X_train))\n",
    "t1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Age_disc\n",
       "(0.67, 13.2]    0.097015\n",
       "(13.2, 19.0]    0.141791\n",
       "(19.0, 22.0]    0.089552\n",
       "(22.0, 26.0]    0.123134\n",
       "(26.0, 29.0]    0.078358\n",
       "(29.0, 32.0]    0.093284\n",
       "(32.0, 36.0]    0.082090\n",
       "(36.0, 41.6]    0.082090\n",
       "(41.6, 49.0]    0.085821\n",
       "(49.0, 80.0]    0.119403\n",
       "Name: Survived, dtype: float64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t2 = X_test.groupby(['Age_disc'])['Survived'].count() / np.float(len(X_test))\n",
    "t2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
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       "    <tr>\n",
       "      <th>Age_disc</th>\n",
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       "      <th>(0.669, 13.2]</th>\n",
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       "      <td>0.097015</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>(32.0, 36.0]</th>\n",
       "      <td>0.109149</td>\n",
       "      <td>0.082090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(36.0, 41.6]</th>\n",
       "      <td>0.083467</td>\n",
       "      <td>0.082090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(41.6, 49.0]</th>\n",
       "      <td>0.105939</td>\n",
       "      <td>0.085821</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(49.0, 80.0]</th>\n",
       "      <td>0.094703</td>\n",
       "      <td>0.119403</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>(0.67, 13.2]</th>\n",
       "      <td>0.101124</td>\n",
       "      <td>0.097015</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  train      test\n",
       "Age_disc                         \n",
       "(0.669, 13.2]  0.101124  0.097015\n",
       "(13.2, 19.0]   0.115570  0.141791\n",
       "(19.0, 22.0]   0.088283  0.089552\n",
       "(22.0, 26.0]   0.113965  0.123134\n",
       "(26.0, 29.0]   0.099518  0.078358\n",
       "(29.0, 32.0]   0.088283  0.093284\n",
       "(32.0, 36.0]   0.109149  0.082090\n",
       "(36.0, 41.6]   0.083467  0.082090\n",
       "(41.6, 49.0]   0.105939  0.085821\n",
       "(49.0, 80.0]   0.094703  0.119403\n",
       "(0.67, 13.2]   0.101124  0.097015"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "temp = pd.concat([t1,t2], axis=1)\n",
    "temp.columns = ['train', 'test']\n",
    "temp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x4c11895be0>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NzBLjwm9mlpiaCr+kaZLWSFon6dJu5kvS3Hz+/ZImV81vk3SfpNvr1XAzM+ufXgu/pDbg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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x4c1189cf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "temp.plot.bar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed, we see roughly the same frequency per interval in both training and testing set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x4c11a1c208>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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dWjdmWH47npteyOqte/2OIyIiIiISElFb0APceV4nEuNj+e0EjbEUERERkegU1QV9RmoD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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x4c119b2a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# and now let's observe the relationship between age and survival again, using the discrete Age transformed \n",
    "# variable\n",
    "\n",
    "fig = plt.figure()\n",
    "fig = X_train.groupby(['Age_disc'])['Survived'].mean().plot(figsize=(12,6))\n",
    "fig.set_title('Normal relationship between variable and target')\n",
    "fig.set_ylabel('Survived')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using discretisation we capture more clearly the survival rate according to the age of the passenger. We can see that children (<18) were the most likely to survive, and people in the early 30s as well, potentially mother with children, whereas people between 20-30 and older than 35 were the less likely to survive the tragedy.\n",
    "\n",
    "Now that we have a discrete variable, we can go ahead and preprocess it as categorical variable, to squeeze a bit more performance out of the machine learning algorithm. Why not ordering the bins according to survival rate?\n",
    "\n",
    "\n",
    "### Combine discretisation with label ordering according to target\n",
    "\n",
    "You can revise the lectures on engineering categorical variables to re-cap on how to preprocess labels.\n",
    "\n",
    "For this demonstration I will assign ordinal numbers to the different bins, according to the survival rate per bin."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Fare</th>\n",
       "      <th>Survived</th>\n",
       "      <th>Age_disc_label</th>\n",
       "      <th>Age_disc</th>\n",
       "      <th>Age_disc_ordered</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>857</th>\n",
       "      <td>51.0</td>\n",
       "      <td>26.5500</td>\n",
       "      <td>1</td>\n",
       "      <td>Q10</td>\n",
       "      <td>(49.0, 80.0]</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>49.0</td>\n",
       "      <td>76.7292</td>\n",
       "      <td>1</td>\n",
       "      <td>Q9</td>\n",
       "      <td>(41.6, 49.0]</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>386</th>\n",
       "      <td>1.0</td>\n",
       "      <td>46.9000</td>\n",
       "      <td>0</td>\n",
       "      <td>Q1</td>\n",
       "      <td>(0.669, 13.2]</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>124</th>\n",
       "      <td>54.0</td>\n",
       "      <td>77.2875</td>\n",
       "      <td>0</td>\n",
       "      <td>Q10</td>\n",
       "      <td>(49.0, 80.0]</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>578</th>\n",
       "      <td>14.5</td>\n",
       "      <td>14.4583</td>\n",
       "      <td>0</td>\n",
       "      <td>Q2</td>\n",
       "      <td>(13.2, 19.0]</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Age     Fare  Survived Age_disc_label       Age_disc  Age_disc_ordered\n",
       "857  51.0  26.5500         1            Q10   (49.0, 80.0]                 3\n",
       "52   49.0  76.7292         1             Q9   (41.6, 49.0]                 2\n",
       "386   1.0  46.9000         0             Q1  (0.669, 13.2]                 9\n",
       "124  54.0  77.2875         0            Q10   (49.0, 80.0]                 3\n",
       "578  14.5  14.4583         0             Q2   (13.2, 19.0]                 6"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# order the intervals according to survival rate\n",
    "ordered_labels = X_train.groupby(['Age_disc_label'])['Survived'].mean().sort_values().index\n",
    "\n",
    "# number the intervals according to survival rate\n",
    "ordinal_label = {k:i for i, k in enumerate(ordered_labels, 0)} \n",
    "\n",
    "# remap the intervals to the encoded variable\n",
    "X_train['Age_disc_ordered'] = X_train.Age_disc_label.map(ordinal_label)\n",
    "X_test['Age_disc_ordered'] = X_test.Age_disc_label.map(ordinal_label)\n",
    "\n",
    "X_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x4c11a817b8>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LUjIREWmkbp48v9aWpWQiItIIvTZvLS/PruzJ1/tHyUREpJHZuGMP//PSFwzr3q7qiROk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\nf+dNxPbdRbz0+WomfrqKBev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      "text/plain": [
       "<matplotlib.figure.Figure at 0x4c11aa7b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the monotonic relationship\n",
    "fig = plt.figure()\n",
    "fig = X_train.groupby(['Age_disc_ordered'])['Survived'].mean().plot()\n",
    "fig.set_title('Monotonic relationship between discretised Age and target')\n",
    "fig.set_ylabel('Survived')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Go ahead and compare the performance machine learning algorithms using the original distribution of Age, Age discretised using quantiles and Age in quantiles followed by ordering according to Survival rate. Enjoy!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fare\n",
    "\n",
    "Let's look at the benefit that can be bought forward by equal frequency discretisation on highly skewed variables like Fare."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x4c11af6470>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NzMwMPIcHHt7D/Yfe+A/5Hr9z5g0/59zcHMO8V8vJJNUKk1XvJNUK46930LtuTiVZBdA9\nn+7aTwBre/qt6dokSWMyaNDvBbZ221uBPT3tW5JcnuRaYD1wYLgpSpKGsej1jiRfAGaAa5I8D/w5\ncB+wO8ldwPeBOwCq6nCS3cAR4Axwd1W9MqK5S5L6sGjQV9X7z3PoPefpvwPYMcykJElLx0/GSlLj\nDHpJapxBL0mNM+glqXEGvSQ1zqCXpMYZ9JLUOINekhpn0EtS4wx6SWqcQS9JjTPoJalxBr0kNc6g\nl6TGGfSS1DiDXpIaZ9BLUuMW/YWpC0lyHPg58Apwpqqmk1wN/HdgHXAcuKOqfjLcNCVJg1qKFf3G\nqrqxqqa7/e3A/qpaD+zv9iVJYzLUiv48NrPwY+IAu4A54N+P4Dxjt277VwYee/y+25ZwJpJ0fsOu\n6Av4WpKDSbZ1bVNVdbLb/iEwNeQ5JElDSFUNPjhZXVUnkvwKsA/4MLC3qq7s6fOTqrrqHGO3AdsA\npqambpqdnR14HqdfeJFTLw08fCxuWP22gcbNz8+zcuXKJZ7NpWmSaoXJqneSaoXR1btx48aDPZfN\nz2uoSzdVdaJ7Pp3kEeBm4FSSVVV1Mskq4PR5xu4EdgJMT0/XzMzMwPN44OE93H9oFFehRuf4nTMD\njZubm2OY92o5maRaYbLqnaRaYfz1DnzpJslbkrz11W3gd4Cngb3A1q7bVmDPsJOUJA1umGXwFPBI\nkldf56+r6n8k+Ttgd5K7gO8Ddww/TUnSoAYO+qr638BvnKP9x8B7hpmUJGnp+MlYSWqcQS9JjTPo\nJalxBr0kNc6gl6TGGfSS1DiDXpIat7y+N6Ahg37z5T03nHntq0ElqR+u6CWpcQa9JDXOoJekxhn0\nktQ4g16SGmfQS1LjDHpJapz30U+gQe/hBzh+321LOBNJbwSDfhkaJqglTR4v3UhS40a2ok+yCfjP\nwArgc1V136jOpfYN+/9ivOSkSTaSFX2SFcB/AX4X2AC8P8mGUZxLknRho1rR3wwc635AnCSzwGbg\nyIjOJ42Mf7zWcjeqoF8N/KBn/3ngt0Z0Lr2Blmvo+QdsjdJi//u654Yz/OF5+rwR/12kqpb+RZN/\nA2yqqn/X7X8A+K2q+qOePtuAbd3urwNHhzjlNcCPhhi/nFhruyap3kmqFUZX77+oqrcv1mlUK/oT\nwNqe/TVd22uqaiewcylOluTbVTW9FK91qbPWdk1SvZNUK4y/3lHdXvl3wPok1yb5ZWALsHdE55Ik\nXcBIVvRVdSbJHwF/w8LtlZ+vqsOjOJck6cJGdh99VX0V+OqoXv8sS3IJaJmw1nZNUr2TVCuMud6R\n/DFWknTp8CsQJKlxyzrok2xKcjTJsSTbxz2fpZDk80lOJ3m6p+3qJPuSPNs9X9Vz7N6u/qNJbhnP\nrAeTZG2Sx5McSXI4yUe69ubqTfLmJAeSPNnV+vGuvblaX5VkRZLvJnm022+51uNJDiV5Ism3u7ZL\np96qWpYPFv7I+/fAvwR+GXgS2DDueS1BXf8a+E3g6Z62/wRs77a3A/+x297Q1X05cG33fqwYdw0X\nUesq4De77bcC/6urqbl6gQAru+3LgG8B72yx1p6a/xj4a+DRbr/lWo8D15zVdsnUu5xX9K99zUJV\n/V/g1a9ZWNaq6uvAC2c1bwZ2ddu7gNt72mer6uWqeg44xsL7sixU1cmq+k63/XPgGRY+Vd1cvbVg\nvtu9rHsUDdYKkGQNcBvwuZ7mJmu9gEum3uUc9Of6moXVY5rLqE1V1clu+4fAVLfdzHuQZB3wDhZW\nuk3W213KeAI4DeyrqmZrBf4S+BPgH3raWq0VFv7R/lqSg92n/uESqtcfHllmqqqSNHWrVJKVwJeA\nj1bVz5K8dqyleqvqFeDGJFcCjyS5/qzjTdSa5PeA01V1MMnMufq0UmuP366qE0l+BdiX5Hu9B8dd\n73Je0S/6NQsNOZVkFUD3fLprX/bvQZLLWAj5h6vqy11zs/UCVNVPgceBTbRZ67uA309ynIVLqu9O\n8hBt1gpAVZ3onk8Dj7BwKeaSqXc5B/0kfc3CXmBrt70V2NPTviXJ5UmuBdYDB8Ywv4FkYen+IPBM\nVX2y51Bz9SZ5e7eSJ8kVwHuB79FgrVV1b1Wtqap1LPx3+bdV9Qc0WCtAkrckeeur28DvAE9zKdU7\n7r9WD/mX7ltZuFPj74E/G/d8lqimLwAngf/HwrW7u4B/DuwHngW+Blzd0//PuvqPAr877vlfZK2/\nzcK1zaeAJ7rHrS3WC/wr4LtdrU8D/6Frb67Ws+qe4R/vummyVhbu/Huyexx+NYsupXr9ZKwkNW45\nX7qRJPXBoJekxhn0ktQ4g16SGmfQS1LjDHpJapxBL0mNM+glqXH/H+tV6FfpfjTEAAAAAElFTkSu\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x4c11ac9208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's plot the hist, to remind us of the skewness of Fare\n",
    "X_train.Fare.hist(bins=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x4c11bcacc0>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ofOxAc2OMwVSGwaQVllqvduQhH03hgOnjaW9tKkEoDDLdx58Ae4ej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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x4c11bea780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's plot survival rate per ticket price\n",
    "fig = plt.figure()\n",
    "fig = data.groupby(['Fare'])['Survived'].mean().plot()\n",
    "fig.set_title('Normal relationship between variable and target')\n",
    "fig.set_ylabel('Survived')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The relationship between Fare and survival is not very clear from this plot. It looks very noisy for the lowest fares, and the survival rate was highest for highest fares, however, there were very few people that paid > 500 dollars, so most likely that survival rate is inflated.\n",
    "\n",
    "Let's go ahead and discretise Fare using equal frequency intervals, and plot again the survival rate and the number of observations within bins."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x4c11a37978>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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F8mDg1xFxQHH0+L8RsVfm+EYCRMTqnHF0J+cVxZJ+RTo6vFlpysoDSY21zgXe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\n2Un05xd7A2EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x4c118acd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# calculate quantile boundaries on train set and create the discrete variable\n",
    "X_train['Fare_disc'], bins = pd.qcut(x=X_train.Fare, q=8, retbins=True, precision=3, duplicates='raise')\n",
    "\n",
    "# cut test set using bin boundaries estimated above\n",
    "X_test['Fare_disc'] = pd.cut(x = X_test.Fare, bins=bins)\n",
    "\n",
    "# if the distributions in train and test set are similar, we should expect similar distribution of \n",
    "# observations in the different intervals in the train and test set\n",
    "t1 = X_train.groupby(['Fare_disc'])['Survived'].count() / np.float(len(X_train))\n",
    "t2 = X_test.groupby(['Fare_disc'])['Survived'].count() / np.float(len(X_test))\n",
    "temp = pd.concat([t1,t2], axis=1)\n",
    "temp.columns = ['train', 'test']\n",
    "temp.plot.bar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed, we have now spread the observations evenly for all the intervals in both train and test set. Let's go ahead and plot the survival rate per Fare once again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x4c11e11da0>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ORXWNbn0tV20T4/S78QO8jhM0tPEAAAAg4jzy/mqt3Fai//xgmFJaxnkdJ2gY2QcAAEBE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\nH5pZS/xbYWabckxzSGKaFjN718z+MY671sw2JMZ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      "text/plain": [
       "<matplotlib.figure.Figure at 0x4c11c29b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's plot survival rate per ticket price bin\n",
    "fig = plt.figure()\n",
    "fig = X_train.groupby(['Fare_disc'])['Survived'].mean().plot(figsize=(12,6))\n",
    "fig.set_title('Normal relationship between variable and target')\n",
    "fig.set_ylabel('Survived')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we get a much clearer view and as we have similar amount of passengers within each bucket, we can be confident that the conclusions are fair. We can see, clearly, that people that paid the highest Fares (>68 dollars) were the most likely to survive, and people who paid the lowest Fares (<10 dollars) were the less likely to survive. Sad but true.\n",
    "\n",
    "**That is all for this demonstration. I hope you enjoyed the notebook, and see you in the next one.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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