08.06-Discretisation-using-Decision-Trees-and-Feature-Engine.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discretisation with Decision Trees using Feature-Engine\n",
    "\n",
    "\n",
    "feature Engine allows you to implement decision tree discretisation on all your numerical variables very easily, including search over the multiple parameters of the decision tree, to find the best one.\n",
    "\n",
    "## In this demo\n",
    "\n",
    "We will learn how to perform discretisation with decision trees and Feature-Engine using the Titanic dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Titanic dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "from feature_engine.discretisers import DecisionTreeDiscretiser"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<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>1</td>\n",
       "      <td>29.0000</td>\n",
       "      <td>211.3375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.9167</td>\n",
       "      <td>151.5500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>2.0000</td>\n",
       "      <td>151.5500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>30.0000</td>\n",
       "      <td>151.5500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>25.0000</td>\n",
       "      <td>151.5500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   survived      age      fare\n",
       "0         1  29.0000  211.3375\n",
       "1         1   0.9167  151.5500\n",
       "2         0   2.0000  151.5500\n",
       "3         0  30.0000  151.5500\n",
       "4         0  25.0000  151.5500"
      ]
     },
     "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',\n",
    "                   usecols = ['age', 'fare', 'survived'])\n",
    "\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((916, 2), (393, 2))"
      ]
     },
     "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(\n",
    "    data[['age', 'fare']],\n",
    "    data['survived'],\n",
    "    test_size=0.3,\n",
    "    random_state=0)\n",
    "\n",
    "X_train.shape, X_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variables Age and Fare contain missing data, that I will fill by extracting a random sample of the variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def impute_na(data, variable):\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(\n",
    "        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": {},
   "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')\n",
    "\n",
    "X_train['fare'] = impute_na(data, 'fare')\n",
    "X_test['fare'] = impute_na(data, 'fare')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
       "    .dataframe thead th {\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>age</th>\n",
       "      <th>fare</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>501</th>\n",
       "      <td>13.0</td>\n",
       "      <td>19.5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>588</th>\n",
       "      <td>4.0</td>\n",
       "      <td>23.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>402</th>\n",
       "      <td>30.0</td>\n",
       "      <td>13.8583</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1193</th>\n",
       "      <td>21.0</td>\n",
       "      <td>7.7250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>686</th>\n",
       "      <td>22.0</td>\n",
       "      <td>7.7250</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       age     fare\n",
       "501   13.0  19.5000\n",
       "588    4.0  23.0000\n",
       "402   30.0  13.8583\n",
       "1193  21.0   7.7250\n",
       "686   22.0   7.7250"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeDiscretiser(cv=10,\n",
       "                        param_grid={'max_depth': [1, 2, 3],\n",
       "                                    'min_samples_leaf': [10, 4]},\n",
       "                        random_state=None, regression=False, scoring='accuracy',\n",
       "                        variables=['age', 'fare'])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# set up the decision tree discretiser indicating:\n",
    "# cross-validation number (cv)\n",
    "# how to evaluate model performance (scoring)\n",
    "# the variables we want to discretise (variables)\n",
    "# whether it is a target for regression or classification\n",
    "# and the grid with the parameters we want to test\n",
    "\n",
    "treeDisc = DecisionTreeDiscretiser(cv=10, scoring='accuracy',\n",
    "                                   variables=['age', 'fare'],\n",
    "                                   regression=False,\n",
    "                                   param_grid={'max_depth': [1, 2, 3],\n",
    "                                              'min_samples_leaf':[10,4]})\n",
    "\n",
    "treeDisc.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'max_depth': 2, 'min_samples_leaf': 4}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we can inspect the tree for age\n",
    "treeDisc.binner_dict_['age'].best_params_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.618995633187773"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# and the performance obtained on the train set while fitting\n",
    "\n",
    "treeDisc.scores_dict_['age']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'max_depth': 3, 'min_samples_leaf': 10}"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# and the best parameters for fare\n",
    "treeDisc.binner_dict_['fare'].best_params_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6888646288209607"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# and the performance obtained on the train set while fitting\n",
    "\n",
    "treeDisc.scores_dict_['fare']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By comparing the accuracy of the decision trees for age and fare, we can derive that fare is a better indicator of the outcome survived."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# let's transform the data\n",
    "\n",
    "train_t = treeDisc.transform(X_train)\n",
    "test_t = treeDisc.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.38011696, 0.53846154, 0.        ])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's inspect how many bins we found\n",
    "\n",
    "train_t['age'].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Survived')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# monotonic relationship with target: train set\n",
    "\n",
    "pd.concat([train_t, y_train], axis=1).groupby(['age'])['survived'].mean().plot()\n",
    "plt.title('Monotonic relationship between discretised Age and target')\n",
    "plt.ylabel('Survived')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Survived')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# monotonic relationship with target: test set\n",
    "\n",
    "pd.concat([test_t, y_test], axis=1).groupby(['age'])['survived'].mean().plot()\n",
    "plt.title('Monotonic relationship between discretised Age and target')\n",
    "plt.ylabel('Survived')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our tree kept the monotonic relationship between bins and target. I have to say that I needed to play quite a bit with the parameters of the tree to find the optimal tree, to keep the monotonic relationship. But, it is the trade off, like from anything else in life :)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Survived')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's explore the monotonic relationship for fare\n",
    "pd.concat([train_t, y_train], axis=1).groupby(['fare'])['survived'].mean().plot()\n",
    "plt.title('Monotonic relationship between discretised Age and target')\n",
    "plt.ylabel('Survived')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Survived')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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42OsiQr929Rg79Hg+uuVE+rRO45Upyzjpye944KN5rN6y16fEFcPLHeE5QNOA5034/ean64ABAKr6XxFJBtKAjR7mMsaYEu0vKOSTOes4s2NDUpMTi23XvWktXrvqWJZt2s2oqcsZPyObMT+v5pyujRnWrxWdGteswNQVw8s1jRlAWxFpKSJJODu6JwW1WQ2cBgdvAJ+Mc5tGY4zxzeRFm9ixL59BPYO3qIfWul51nry4Kz/ecyo39G3F5EUbOecfP3LVv3/mp2WbK9Xhup4VDfdG7sOBr4BfcY6SWiAij4jIeW6zkcANIjIHGAtco5Vp7BpjotKHs3NIq16Fk9qklel9DWokc9/ZxzDt3lO566z2/LpuF5e//jMXvDyNL+evo7Ao+mdvUXeP8IyMDLWbMBljvLJtTx69HvuGq09owQPnBp8lUDa5+YV8MDuHUd8vZ9WWvbRKq8bQk1txYc90qiTEl1Pi8IjILFXNONr+2BnhxhgT4NO5a8kvVC4Mc9NUSZIT47mid3O+G3kKL13eg6pV4rn3w3n0fXIy/5y6jF25+eWQuGJZ0TDGmAAfzF5Dh4apdGxUo/TGYYqPE87t2phPhp/EO9f1om2D6jz+xSL6PPEdT365iI27csvts7wWdfcIN8YYryzftJus7O3cN7ADIuV/qRARoW/bevRtW4+5Odt5beoyXpu6jH//uIKLj23C0L6taJFWrdw/tzxZ0TDGGNfEzDXECVzQ4+g3TZWma5NavHLFsazYvIdR3y/n/Zk5jPtlNQO7NOKmfq3pnB6Zh+ta0TDGGKCoSJmYuYYT26TRoEZyhX1uy7RqPD6oC3ec3pY3pq1k9PRVfDZ3HX3bpjGsX2v6tK7ryVrPkbJ9GsYYA8xYuZWcbfvCPjejvNWvkcy9Azsw7b5TuWdABxat38UV//qZ816axmdzI+dwXSsaxhiDs2mqalI8Z3VqWHpjD9VITuSmU1rzw939eXxQF3bl5nPLmNmc9swUxvy8mtz8Ql/zWdEwxsS83PxCPpu7jgGdG1I1KTK22icnxjOkVzO+HXkKr1zRk9TkRO6fOI++T03m1SnL2OnT4bqRMXaMMcZH3/y6gV37C7jIvaJtJImPE87u0oiBnRvy07ItvDZ1GU9+uYhXJi/l8uObcd2JLalfgftgrGgYY2Leh7PX0LBGMse3qut3lGKJCCe2SePENmnMX7ODV6cu4/Xvl/N/P67komPTGXpya1pWwOG6VjSMMTFt0679TF2yiRv6tiI+Sm7j2jm9Ji9f3pOVm/fw+g/LeW9WDuNmZDOwc0OG9WtN1ya1PPtsKxrGmJj2yZy1FBapb0dNHY0WadX4+4VduO30trw5bSXvTF/F5/PW06d1XW46pTUntUkr98N1bUe4MSamfZiZQ+f0GrRrkOp3lCNWPzWZuwd04Kd7T+W+gR1YunE3V/37F8598ceDRbG8WNEwxsSsJRt2MX/NTgb1iLwd4EciNTmRG/u15od7+vPEoC7syyvk1rGZnPrMlHL7DNs8ZYyJWR/OXkN8nHBe98Z+RylXVRLiGdyrGZdkNOXrhet5derycuu3rWkYY2JSYZHycdYa+rWrR1r1Kn7H8UR8nDCgcyM+urlPufXTioYxJiZNX76FdTtyubACLk7ot/LcGW5FwxgTkz6YnUNqlQTO6NjA7yhRxYqGMSbm7M0r4Mv56zm7SyOSEyv2tqvRzoqGMSbmfLVgPXvzCqPy3Ay/WdEwxsScD2evIb1WCse1qON3lKhjRcMYE1M27Mxl2tLNDOqZTlyUXDYkkljRMMbElI+z1lCkxMRRU17wtGiIyAARWSwiS0Xk3hDdnxORLPdviYhs9zKPMcZ8OHsN3ZvWolW96n5HiUqenREuIvHAy8AZQA4wQ0QmqerCA21U9Y6A9rcCPbzKY4wxC9fuZNH6XTx6fie/o0QtL9c0egFLVXW5quYB44DzS2g/BBjrYR5jTAzbvHs/j366kMR44dyuleuyIRXJy2tPpQPZAc9zgN6hGopIc6Al8F0x3YcCQwGaNWtWvimNMZXetKWbuX18Fjv25fO3CzpTu1qS35GilpdFI9RhCcVdn3cw8L6qhrxjuqqOAkYBZGRklN81fo0xlVp+YRHPf7OEV6Yso2VaNd76Yy86Nq7hd6yo5mXRyAGaBjxvAqwtpu1g4BYPsxhjYkz21r3cNi6T2au3c2lGEx4+rxNVk+zC3kfLyzE4A2grIi2BNTiF4fLgRiLSHqgN/NfDLMaYGPLFvHXc/cFcVOGFwd05v7sdXltePCsaqlogIsOBr4B44A1VXSAijwAzVXWS23QIME5VbbOTMeao5OYX8sinCxnz82q6NanJP4b0oHndan7HqlQ8XVdT1c+Bz4NeezDo+cNeZjDGxIYlG3Zx65hMFm/YxY0nt2Lkme1JSrDzl8ubbeAzxkQ1VWXsL9k88ukCqldJ4K1re9GvXT2/Y1VaVjSMMVFrx7587v9wHp/NW8dJbdJ49rJu1E9N9jtWpWZFwxgTlWat2saIsZls2JnLPQM6cOPJrewChBXAioYxJqoUFSmvTl3Gs18voVHNZCYMO4GezWr7HStmWNEwxkSNjTtzuWNCFtOWbuGcro147MIu1ExJ9DtWTLGiYYyJClMWb2TkhDnsySvgiUFduOy4pojY5qiKZkXDGBPR8gqKePqrRbz+wwraN0hl3OXH07ZBqt+xYpYVDWNMxFq1ZQ+3js1kbs4OrujdjL+c25HkxHi/Y8U0KxrGmIj0cdYa/jxxPnECr17Rk4FdGvkdyWBFwxgTYfbmFfDQxwt4b1YOxzavzQuDu9OkdlW/YxmXFQ1jTMRYsHYHt47NZMXmPQzv34bbT29LQrxdCiSSWNEwxvhOVXn7v6v4+2e/UqtqIqOv602fNml+xzIhWNEwxvhq25487v5gLl8v3ED/9vX430u6Ubd6Fb9jmWJY0TDG+Obn5Vu4fXwWm3fv54FzjuG6k1rauRcRzoqGMabCFRYpL373G//49jea1anKhzedSJcmNf2OZcJgRcMYU6HW7djHbeOy+GXFVgb1SOeRCzpTvYrNiqKFfVPGmArz9cIN3PX+HPIKinjmkm5cdGwTvyOZMrKiYYzxXG5+IU98sYg3f1pJp8Y1eHFID1rVq+53LHMErGgYYzy1bNNubh2TycJ1O/njiS24d2AHqiTYpUCilRUNY4wnVJX3Z+Xw0KQFVEmI499XZ3DaMQ38jmWOkhUNY0y525WbzwMfzefjrLX0blmHFwb3oGFNuw1rZWBFwxhTrubmbOfWsZlkb93Ln85oxy392xBvt2GtNDy9qIuIDBCRxSKyVETuLabNpSKyUEQWiMgYL/MYY7xTVKS8/v1yLnr1J/ILihh/4wmMOK2tFYxKxrM1DRGJB14GzgBygBkiMklVFwa0aQvcB5yoqttEpL5XeYwx3tm8ez8jJ8xh6pJNnNmxAU9d3JVaVZP8jmU84OXmqV7AUlVdDiAi44DzgYUBbW4AXlbVbQCqutHDPMYYD0xbupnbx2exY18+j57fiSuPb26XAqnEvCwa6UB2wPMcoHdQm3YAIjINiAceVtUvg3skIkOBoQDNmjXzJKwxpmzyC4t47uslvDp1Ga3rVefta3txTKMafscyHvOyaIRa1NAQn98WOAVoAvwgIp1Vdfthb1IdBYwCyMjICO6HMaaCZW/dy23jMpm9ejuXZTTlofM6UjXJjquJBV5+yzlA04DnTYC1IdpMV9V8YIWILMYpIjM8zGWMOQqfz1vHPR/MBYUXh/TgD90a+x3JVCAvj56aAbQVkZYikgQMBiYFtfkI6A8gImk4m6uWe5jJGHOEcvMLuX/iPG4ePZtW9arz2Yi+VjBikGdrGqpaICLDga9w9le8oaoLROQRYKaqTnK7nSkiC4FC4C5V3eJVJmPMkVmyYRfDx8xmyYbd3NivFSPPaE9Sgt2GNRaJanTtIsjIyNCZM2f6HcOYmKCqjPllNY98spDU5ASeubQ7/drV8zuWOQIiMktVM462P7bnyhgT0o59+dz34Vw+n7eevm3TeObSbtRPtUuBxDorGsaY35m1ahsjxmayYWcu9w7swNC+rYizM7sNVjSMMQEKi5TXpi7j2a+X0KhmMu8NO4EezWr7HctEECsaxhgANu7M5Y4JWUxbuoVzuzbisUFdqJGc6HcsE2GsaBhjmLx4I3dOmMOevAKevKgLl2Y0tUuBmJCsaBgTw/IKinj6q0W8/sMKOjRMZdyQ42nbINXvWCaCWdEwJkat3LyHEeMymZuzg6uOb86fzzmG5ES7DaspmRUNY2LQx1lr+PPE+cQJvHblsQzo3NDvSCZKWNEwJobs2V/AQ5MW8P6sHDKa1+aFIT1Ir5XidywTRUosGiKyi99fmfYgVbXrIBsTJRas3cGtYzNZsXkPI05tw4jT2pIQb5cCMWVTYtFQ1VQA93pR64F3cC55fgVge8uMiQKqyls/reSxzxdRu1oio6/vTZ/WaX7HMlEq3M1TZ6lq4A2UXhWRn4GnPMhkjCkn2/bkcdf7c/nm1w2c2qE+T1/clbrVq/gdy0SxcItGoYhcAYzD2Vw1BOeqtMaYCDV9+RZuH5fFlj37+cu5Hbn2xBZ27oU5auEWjcuBF9w/Baa5rxljIkxBYREvfreUF7/7jeZ1qzHx6hPpnF7T71imkgiraKjqSuB8b6MYY47W2u37uH1cFr+s3MqgHuk8ckFnqlexgyRN+QlrahKRdsCrQANV7SwiXYHzVPVvnqYzxoTt64UbuOv9OeQVFPHspd0Y1LOJ35FMJRTu8XavA/cB+QCqOhfn9q3GGJ/l5hfy8KQF3PD2TJrUTuGzEX2tYBjPhLveWlVVfwnaiVbgQR5jTBks27Sb4WMy+XXdTq49sSX3DGxPlQS7FIjxTrhFY7OItMY90U9ELgbWeZbKGFMiVeW9WTk89PECUpLieeOaDE7t0MDvWCYGhFs0bgFGAR1EZA2wAucEP2NMBduVm88DH83n46y1nNCqLs8P7k6DGnYbVlMxwi0aq1T1dBGpBsSp6i4vQxljQpuTvZ0R4zLJ3rqXkWe04+b+bYi327CaChRu0VghIl8C44HvPMxjjAmhqEj514/LeerLxdRPrcL4G0/guBZ1/I5lYlC4RaM98AeczVT/FpFPgXGq+qNnyYwxAGzevZ+RE+YwdckmzurUgCcv6kqtqkl+xzIxKqxDblV1n6pOUNVBQA+gBjC1tPeJyAARWSwiS0Xk3hDdrxGRTSKS5f5dX+YhMKYS+2XFVga+8AP/Xb6FRy/ozGtXHmsFw/gq7FNFRaQfcBkwEJgBXFpK+3jgZeAMIAeYISKTVHVhUNPxqjq8TKmNiQHZW/dy/VszSKtehbev7cUxjexOBMZ/4Z4RvgLIAiYAd6nqnjDe1gtYqqrL3X6Mw7kUSXDRMMYE2V9QyC1jZqPAW9f2ommdqn5HMgYIf02jm6ruLGO/04HsgOc5QO8Q7S4SkZOBJcAdqpod3EBEhgJDAZo1a1bGGMZEn8c++5W5OTsYddWxVjBMRCntzn13q+pTwN9F5Hd38FPVESW9PcRrwf34BBirqvtFZBjwFnBqiM8ZhXOeCBkZGcXeSdCYyuCTOWt567+ruKFvS87sZPfuNpGltDWNX93/M4+g3zlA04DnTYC1gQ1UdUvA09eBJ4/gc4ypNJZv2s29H8ylZ7Na3D2gg99xjPmd0m73+on7cK6qZpax3zOAtiLSEliDc4HDw+7BISKNVPXA5UjO41CRMibm5OYXcvPo2SQlxPHS5T1JtPt3mwgU7j6NZ0WkEfAezvkZC0p7g6oWiMhw4CsgHnhDVRe49xufqaqTgBEich7OxQ+3AtccyUAYUxk89PECFq3fxZt/PI7GtVL8jmNMSKIa3i4CEWmIc5jtZTjnaYz3434aGRkZOnPmkWwtMyZyvT8rhzvfm8Pw/m2486z2fscxlZCIzFLVjKPtT9jrv6q6XlX/AQzDOfz2waP9cGMMLF6/iwc+msfxrepw++lt/Y5jTInCKhoicoyIPCwi84GXgJ9wdmwbY47Cnv0F3Dx6FtWrJPKPwT1IsP0YJsKFu0/j/4CxwJmqura0xsaY0qkq90+cx4rNe3j3+t7JxVqrAAAVHElEQVTUt8ubmyhQatFwLweyTFVfqIA8xsSMsb9k83HWWkae0Y4+rdP8jmNMWEpdF1bVQqCuiNhV0owpJ/PX7ODhTxZwcrt63NK/jd9xjAlb2DdhAqaJyCTg4HWnVPVZT1IZU4ntzM3nljGzqVM1iecu7Uac3UTJRJFwi8Za9y8OSPUujjGVm6pyz/tzydm2j/FDj6du9Sp+RzKmTMIqGqr6V6+DGBML3vxpJV/MX8/9Z3cgw+68Z6JQuJdGn8zvLzaIqv7u4oLGmNAyV2/jsc9/5fRj6nND31Z+xzHmiIS7eerOgMfJwEU4l/4wxoRh+948ho/JpEGNZJ65pDsith/DRKdwN0/NCnppmoiUertXYwwUFSkjJ8xh0679vH/TCdSsmuh3JGOOWLibpwI3vsYBGYBd6N+YMIz6YTnfLtrII+d3omuTWn7HMeaohLt5ahaH9mkUACuB67wIZExl8suKrTz91WLO6dqIq45v7nccY45aaXfuOw7IVtWW7vOrcfZnrMTu9W1MiTbv3s+tY2fTrE5VnhjUxfZjmEqhtDPC/wnkAbj38X4c55asO3Bvv2qM+b3CIuX2cVls35vPy5f3JDXZ9mOYyqG0zVPxqrrVfXwZMEpVPwA+EJEsb6MZE71e+m4pPy7dzJMXdaFj4xp+xzGm3JS2phEvIgcKy2nAdwHdwt0fYkxMmbZ0M89/u4RBPdO5NKOp33GMKVelzfjHAlNFZDOwD/gBQETa4GyiMsYE2LAzl9vGZdKmXnX+dkFn249hKp0Si4aq/l1EvgUaAf/RQ/eGjQNu9TqcMdGkoLCIW8dmsmd/IeOG9qRqkq2Mm8qn1KlaVaeHeG2JN3GMiV7Pfr2EX1Zs5bnLutGmvl3X01ROdm9JY8rB5EUbeWXKMob0asaFPexOyKbysqJhzFFas30fd0zIomOjGjz0h45+xzHGU54WDREZICKLRWSpiNxbQruLRURFJMPLPMaUt7yCIoaPmU1BofLKFT1JToz3O5IxnvKsaLj3Fn8ZGAh0BIaIyO8Ww0QkFRgB/OxVFmO88sQXi8hcvZ2nLu5Ki7RqfscxxnNermn0Apaq6nJVzQPGAeeHaPco8BSQ62EWY8rdl/PX8ca0FVzTpwVnd2nkdxxjKoSXRSMdyA54nuO+dpCI9ACaquqnJfVIRIaKyEwRmblp06byT2pMGa3asoe73ptLt6a1uP/sY/yOY0yF8bJohDqr6eDd/0QkDngOGFlaj1R1lKpmqGpGvXr1yjGiMWWXm1/IzaNnExcnvDSkB0kJdjyJiR1eTu05QOA1FJoAawOepwKdgSkishI4HphkO8NNpHv004UsWLuTZy/tRtM6Vf2OY0yF8rJozADaikhLEUkCBgOTDnRU1R2qmqaqLVS1BTAdOE9VZ3qYyZij8nHWGkb/vJob+7XitGMa+B3HmArnWdFQ1QJgOPAV8CswQVUXiMgjInKeV59rjFeWbtzNfR/O47gWtbnzzPZ+xzHGF55eHEdVPwc+D3rtwWLanuJlFmOOxr68Qm4ePYvkxHheHNKTxHjbj2Fik11RzZgw/OXj+fy2cTdv/bEXDWsm+x3HGN/Y4pIxpZgwM5v3Z+Vw66ltObmdHb1nYpsVDWNK8Ou6nfzlo/n0aV2X205r63ccY3xnRcOYYuzeX8Ato2dTIyWRFwb3ID7ObqhkjBUNY0JQVe77cB4rt+zhxSE9qJdaxe9IxkQEKxrGhPDuz6v5ZM5a7jyrPce3qut3HGMihhUNY4LMy9nBo58spH/7egw7ubXfcYyJKFY0jAmwY18+N4+ZRVr1JJ69tDtxth/DmMPYeRrGuFSVu96bw7rtuUwYdgK1qyX5HcmYiGNrGsa4/v3jCv6zcAP3nX0MPZvV9juOMRHJioYxwKxV23jii0Wc1akB157Ywu84xkQsKxom5m3dk8fwMbNpXCuFpy7uhojtxzCmOLZPw8S0oiLlTxOy2LI7jw9v7kPNlES/IxkT0WxNw8S0V6cuY8riTTz4h450Tq/pdxxjIp4VDROzpi/fwjP/Wcx53RpzRe9mfscxJipY0TAxadOu/dw6NpMWadV4bFAX249hTJhsn4aJOYVFym3jMtmVm8871/WiehX7GRgTLvu1mJjzwre/8dOyLTx9cVc6NKzhdxxjooptnjIx5fslm3jxu9+45NgmXJLR1O84xkQdKxomZqzfkcvt47NoVz+VR87v7HccY6KSFQ0TE/ILixg+Zjb78wt55cqepCTF+x3JmKhk+zRMTPjfrxYzc9U2Xhjcndb1qvsdx5ioZWsaptL7euEG/vn9cq48vhnnd0/3O44xUc3ToiEiA0RksYgsFZF7Q3QfJiLzRCRLRH4UkY5e5jGxJ3vrXkZOyKJzeg0eOMcmL2OOlmdFQ0TigZeBgUBHYEiIojBGVbuoanfgKeBZr/KY2LO/oJDhY2ajwCuXH0tyou3HMOZoebmm0QtYqqrLVTUPGAecH9hAVXcGPK0GqId5TIx5/PNFzMnZwdMXd6NZ3ap+xzGmUvByR3g6kB3wPAfoHdxIRG4B/gQkAaeG6pGIDAWGAjRrZtcIMqX7bO463vxpJded1JIBnRv6HceYSsPLNY1QF/P53ZqEqr6sqq2Be4AHQvVIVUepaoaqZtSrV6+cY5rKZsXmPdzzwVx6NKvFPQM6+B3HmErFy6KRAwSectsEWFtC+3HABR7mMTEgN7+Qm0fPJiFeeOnyniQl2AGCxpQnL39RM4C2ItJSRJKAwcCkwAYi0jbg6TnAbx7mMTHgr58s4Nd1O3nu0u6k10rxO44xlY5n+zRUtUBEhgNfAfHAG6q6QEQeAWaq6iRguIicDuQD24CrvcpjKr8PZ+cw9pdsbj6lNf071Pc7jjGVkqdnhKvq58DnQa89GPD4Ni8/38SO3zbs4s8T59O7ZR3+dEY7v+MYU2nZBl8T9fbmFXDT6NlUqxLPi0N6kBBvk7UxXrFrT5mopqo8MHE+yzbtZvR1valfI9nvSMZUarZIZqLa+BnZfJi5hjtOb0efNml+xzGm0rOiYaLWgrU7eHDSAvq2TWN4/zZ+xzEmJljRMFFpV24+t4yeTZ2qSTx/WXfi4kKdS2qMKW+2T8NEHVXl3g/mkb1tH+OGHk/d6lX8jmRMzLA1DRN13v7vKj6bt467z2rPcS3q+B3HmJhiRcNElTnZ2/nbZws5/Zj63NC3ld9xjIk5VjRM1NixN5+bR8+mfmoy/3tJN9uPYYwPbJ+GiQqqysj3sti4K5f3hvWhVtUkvyMZE5NsTcNEhdd/WM43v27kz2cfQ/emtfyOY0zMsqJhIt7MlVt58svFnN2lIVf3aeF3HGNimhUNE9G27N7P8DGZNK2dwhMXdUXE9mMY4yfbp2EiVlGRcvv4LLbuzWPizX2okZzodyRjYp4VjXKSV1DEztx8du7LZ8e+fBrVTKFhTbt43tF4efJSfvhtM48P6kKnxjX9jmOMwYrGQUVFyq79BQdn+k4BcJ7vzHVf25fPztyCg48D2+3LLzysfw1qVGHKnf1JSYr3aYii209LN/PcN0u4sEc6g49rWvobjDEVotIUDVUlN//wpf1DM/uC0K8FFINd+wtQLb7/IlAjOZEaKQnUTEmkRnIiretVdx4feM19fVduPn/5eAHvTF/J0JNbV9xIqCQ27sxlxLhMWtWrzt8u6Gz7MYyJIFFXNNZs38etYzMDlvzd//sKyCssKvG9VZPiD5vxN6yRTPsGqe7MPsH5n5J4sCgEFoPqSQllOpnsPws38OqUZVzeuznVq0TdaPZNQWERt47NZM/+Qsbe0JNqNu6MiShR94vcsS+f+Wt2HJzJp9dO+f1MPjkxYMnfeS01OZGkhIo7WOzOM9tz/svTeOPHFYw4rW2FfW60e+6bJfy8YivPXtqNtg1S/Y5jjAkSdUWjY6MaTL7zFL9jlKpb01qc2bEBr3+/nP85obmdwRyGyYs38vLkZQw+rimDejbxO44xJgQ7T8NDI89sz+68Av75/XK/o0S8tdv3ccf4LDo0TOXh8zr5HccYU4yoW9OIJu0bpnJet8a8OW0lfzyxBfVT7RDcA/IKili7fR/Z2/aSs20fY35eTUGh8soVPUlOtCPOjIlUnhYNERkAvADEA/9S1SeCuv8JuB4oADYB16rqKi8zVbTbT2/Hp3PX8crkZTG1BF1QWMS6HbkHi0LOVuf/gefrd+YedrRacmIcz1/WnVb1qvsX2hhTKs+KhojEAy8DZwA5wAwRmaSqCwOaZQIZqrpXRG4CngIu8yqTH1qmVePink0Y8/Nqbji5Fem1UvyOVC4Ki5QNO3OdQnBYQdhL9lanKBQWHaoKcQKNaqaQXjuFPq3TaFI7haZ1qh783yC1CgnxtrXUmEjn5ZpGL2Cpqi4HEJFxwPnAwaKhqpMD2k8HrvQwj29GnN6WiZlrePHb33jioq5+xwmLqrJp136yt+0jx107CCwOa7fvI7/w8BNbGtSoQpPaVTmuRW2a1K5K0zopzv/aVWlYM7lCj14zxnjDy6KRDmQHPM8BepfQ/jrgi1AdRGQoMBSgWbNm5ZWvwqTXSuHy3s14Z/oqbuzXmpZp1fyOhKqydU9esUVhzbZ97C84/LyXtOpJpNeuSpf0mgzs3CigKKTQuFaK7YswJgZ4WTRCnQkX8pxrEbkSyAD6hequqqOAUQAZGRklnLcduW7u35pxM1bz/DdLeGFwD88/T1XZua/gsE1GOdv2HlYk9uYdfumTWlUTaVq7Ku0bpHL6MQ2cTUe1nU1I6bVTqJpkx00YE+u8nAvkAIEXDWoCrA1uJCKnA38G+qnqfg/z+Kp+ajLX9GnJP79fxs2ntKF9w6M/cW33/oJDawdBO5pztu5l1/6Cw9qnVkmgSZ2qNK9bjZPa1Dtsv0KT2imk2lVkjTGl8LJozADaikhLYA0wGLg8sIGI9AD+CQxQ1Y0eZokIw/q1YvT0VTzzn8WM+p+MUtvvzStgTUAhOFAYDhSH7XvzD2ufkhhP0zrO2kGvEPsVaqQk2HWcjDFHxbOioaoFIjIc+ArnkNs3VHWBiDwCzFTVScDTQHXgPXdmtlpVz/Mqk99qVU3i+r6teO6bJczN2U67BqnuuQr7frcJac22vWzenXfY+5MS4g5uMurapOaho4/cTUh1qiVZUTDGeEq0pEu7RqCMjAydOXOm3zGO2K7cfE5+ajJ78wp/t6M5MV5oXOtQETi06cjZ2ZxWvUqZLppojDEHiMgsVS19E0cpbM9mBUtNTuTJi7ry9cINNAkqDg1qJBNvRcEYE8GsaPjgzE4NObNTQ79jGGNMmdnZVsYYY8JmRcMYY0zYrGgYY4wJmxUNY4wxYbOiYYwxJmxWNIwxxoTNioYxxpiwWdEwxhgTtqi7jIiI7AIW+50jDGnAZr9DhMFyli/LWb4sZ/lprqr1jrYn0XhG+OLyuH6K10RkpuUsP5azfFnO8hUtOcuDbZ4yxhgTNisaxhhjwhaNRWOU3wHCZDnLl+UsX5azfEVLzqMWdTvCjTHG+Cca1zSMMcb4xIqGMcaYsEVs0RCRASKyWESWisi9IbpXEZHxbvefRaRFxacMK+fJIjJbRApE5GI/Mro5Ssv5JxFZKCJzReRbEWkeoTmHicg8EckSkR9FpGMk5gxod7GIqIj4cjhmGOPzGhHZ5I7PLBG5PhJzum0udafRBSIypqIzuhlKG5/PBYzLJSKy3Y+cnlLViPsD4oFlQCsgCZgDdAxqczPwmvt4MDA+QnO2ALoCbwMXR/D47A9UdR/fFMHjs0bA4/OALyMxp9suFfgemA5kRGJO4BrgpYrOdgQ52wKZQG33ef1IzBnU/lbgDT/HrRd/kbqm0QtYqqrLVTUPGAecH9TmfOAt9/H7wGkiUtE32C41p6quVNW5QFEFZwsUTs7JqrrXfTodaFLBGSG8nDsDnlYD/DiSI5zpE+BR4CkgtyLDBQg3p9/CyXkD8LKqbgNQ1Y0VnBHKPj6HAGMrJFkFitSikQ5kBzzPcV8L2UZVC4AdQN0KSRcigytUzkhQ1pzXAV94mii0sHKKyC0isgxnhjyigrIFKjWniPQAmqrqpxUZLEi43/tF7mbJ90WkacVEO0w4OdsB7URkmohMF5EBFZbukLB/R+7m3ZbAdxWQq0JFatEItcYQvEQZThuvRUKGcISdU0SuBDKApz1NFFpYOVX1ZVVtDdwDPOB5qt8rMaeIxAHPASMrLFFo4YzPT4AWqtoV+IZDa+8VKZycCTibqE7BWYL/l4jU8jhXsLL83gcD76tqoYd5fBGpRSMHCFziaQKsLa6NiCQANYGtFZIuRAZXqJyRIKycInI68GfgPFXdX0HZApV1fI4DLvA0UWil5UwFOgNTRGQlcDwwyYed4aWOT1XdEvBdvw4cW0HZAoX7e/9YVfNVdQXORUvbVlC+wAzhTp+DqYSbpoCI3RGeACzHWb07sMOpU1CbWzh8R/iESMwZ0PZN/NsRHs747IGzk69thH/vbQMe/wGYGYk5g9pPwZ8d4eGMz0YBjy8EpkdozgHAW+7jNJzNRHUjLafbrj2wEvfk6cr253uAEr6gs4El7ozsz+5rj+AsBQMkA+8BS4FfgFYRmvM4nCWUPcAWYEGE5vwG2ABkuX+TIjTnC8ACN+PkkmbWfuYMautL0QhzfD7ujs857vjsEKE5BXgWWAjMAwZHYk73+cPAE37kq4g/u4yIMcaYsEXqPg1jjDERyIqGMcaYsFnRMMYYEzYrGsYYY8JmRcMYY0zYrGgYEyYRGSEiv4rIaL+zGOMXO+TWmDCJyCJgoDpnJJfWNkGda6IZU6kk+B3AmGggIq/hXBJ7koi8i3N10xRgH/BHVV0sItcA5+CceFoNOFVE7gIuBaoAE1X1IT/yG1NerGgYEwZVHeZeWbU/kAc8o6oF7vW6HgMucpueAHRV1a0icibO9ZF64ZzRPElETlbV730YBGPKhRUNY8quJvCWiLTFucppYkC3r1X1wIUzz3T/Mt3n1XGKiBUNE7WsaBhTdo8Ck1X1Qvc2w1MCuu0JeCzA46r6z4qLZoy37OgpY8quJrDGfXxNCe2+Aq4VkeoAIpIuIvU9zmaMp6xoGFN2TwGPi8g0nPtGh6Sq/wHGAP8VkXk4tyVOrZiIxnjDDrk1xhgTNlvTMMYYEzYrGsYYY8JmRcMYY0zYrGgYY4wJmxUNY4wxYbOiYYwxJmxWNIwxxoTt/wHHG9SNa2x5ywAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# monotonic relationship with target: test set\n",
    "\n",
    "pd.concat([test_t, y_test], axis=1).groupby(['fare'])['survived'].mean().plot()\n",
    "plt.title('Monotonic relationship between discretised Age and target')\n",
    "plt.ylabel('Survived')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For fare, the monotonic relationship was preserved, almost entirely, except at the edges, which suggests that the tree could be overfitting to the train set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Number of observations per bin')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LkhqL4m0MPDavJ877O18CbAc0ACMkDY2IsU2u6wEcCzzZor/AzMwWmua6j/5vAZ97Y2BcLpOBpOuA3YCxTa47EzgHOHEBX8/MzBbQXLuPIuLBxh/gJaBH/nkxn5uXlYE3q44b8rkKSRsAq0TE3+Y7cjMzW+iKzD7aB3gK+B6wD/BkLp89z4fO4VxUPW8H4ALgpwViGChppKSREyZMKPDSZmbWEkVmH/038PWIeA9A0rLAvcBN83hcA2lQulEfYHzVcQ9gHeABSQArAEMl7RoRI6ufKCIuJ5Xvpn///oGZmdVEkdlHHRoTQjax4ONGAKtL6idpMdIWnkMb74yISRHROyL6RkRf4AngCwnBzMzqp0hL4W5J9wB/zcf7AsPm9aCImCnpaOAeoCMwJCLGSDoDGBkRQ5t/BjMzq7ciZS5OkrQnsDlpnODyomUuImIYTRJIRJw6l2u3KvKcZmZWO0VaCkTELcAtNY7FzMxKVmRswMzMFhFOCmZmVjHXpCDpH/n3r+sXjpmZlam5MYUVJW0J7JpLVHxuMVpEPF3TyMzMrO6aSwqnAoNIi87Ob3JfANvUKigzMyvHXJNCRNwE3CTpFxFxZh1jMjOzkhRZp3CmpF2BLfKpB1zAzsysfSpSEO9XwHGkktdjgePyOTMza2eKLF7bBVg/ImZDZTvOZ4DBtQzMzMzqr+g6haWqbvesRSBmZla+Ii2FXwHPSLqfNC11C9xKMDNrl4oMNP9V0gPA10lJ4eSIeKfWgZmZWf0VLYj3NlV7IZiZWfvk2kdmZlbhpGBmZhXNJgVJHSS9UK9gzMysXM0mhbw24VlJX6pTPGZmVqIiA80rAmMkPQVMbTwZEbvWLCozMytFkaRwes2jMDOzVqHIOoUHJX0ZWD0i7pXUFehY+9DMzKzeihTEOwy4Cfh9PrUycFstgzIzs3IUmZJ6FLAZMBkgIl4BlqtlUGZmVo4iSWF6RHzaeCCpE2nnNTMza2eKJIUHJf0cWELSdsCNwB21DcvMzMpQJCkMAiYAzwOHA8OAU2oZlJmZlaPI7KPZeWOdJ0ndRi9HhLuPzMzaoXkmBUm7AJcBr5JKZ/eTdHhE3FXr4MzMrL6KLF47D9g6IsYBSFoVuBNwUjAza2eKjCm815gQsteA92oUj5mZlWiuLQVJe+abYyQNA24gjSl8DxhRh9jMzKzOmus++m7V7XeBLfPtCcDSNYvIzMxKM9ekEBGH1DMQMzMrX5HZR/2AY4C+1de7dLaZWftTZPbRbcCVpFXMs2sbjpmZlalIUpgWERfXPBIzMytdkSmpF0n6paRNJW3Y+FPkySXtKOllSeMkDZrD/SdIGivpOUn/yPs2mJlZSYq0FNYFDgS24bPuo8jHcyWpI3AJsB3QAIyQNDQixlZd9gzQPyI+lnQEcA6w7/z9CWZmtrAUSQp7AF+pLp9d0MbAuIh4DUDSdcBuQCUpRMT9Vdc/AQyYz9cwM7OFqEj30bPAUi147pWBN6uOG/K5uTkUl84wMytVkZbC8sBLkkYA0xtPFpiSqjmcm2N1VUkDgP58tkCu6f0DgYEAX/rSlwqEbGZmLVEkKfyyhc/dAKxSddwHGN/0IknbAv8NbBkR05veDxARlwOXA/Tv399lu83MaqTIfgoPtvC5RwCr58VvbwH7AQdUXyBpA+D3wI4R4SJ7ZmYlK7KieQqfdfssBnQGpkbEks09LiJmSjoauAfoCAyJiDGSzgBGRsRQ4FygO3CjJIB/e6W0mVl5irQUelQfS9qdNLNoniJiGGn7zupzp1bd3rZYmGZmVg9FZh99TkTcxjzWKJiZWdtUpPtoz6rDDqRZQh7sNTNrh4rMPqreV2Em8AZpEZqZmbUzRcYUvK+CmdkiorntOE+d231ARMSZNYjHzMxK1FxLYeocznUjlaPoBTgpmJm1M81tx3le421JPYDjgEOA64Dz5vY4MzNru5odU5C0DHAC8H3gamDDiPigHoGZmVn9NTemcC6wJ6nm0LoR8VHdojIzs1I0t3jtp8BKwCnAeEmT888USZPrE56ZmdVTc2MK873a2czM2jZ/8JuZWYWTgpmZVTgpmJlZhZOCmZlVOCmYmVmFk4KZmVU4KZiZWYWTgpmZVTgpmJlZRZGd18zM2r/Tetb59SbV9/UKckvBzMwqnBTMzKzCScHMzCqcFMzMrMJJwczMKjz7yMxapb6D7qzr673Rpa4v12q5pWBmZhVOCmZmVuGkYGZmFU4KZmZW4aRgZmYVTgpmZlbhpGBmZhVOCmZmVlHTxWuSdgQuAjoCV0TE2U3uXxz4E7ARMBHYNyLeqGVMrZ7L95pZiWrWUpDUEbgE2AlYG9hf0tpNLjsU+CAiVgMuAH5dq3jMzGzeatlS2BgYFxGvAUi6DtgNGFt1zW7Aafn2TcBvJSkiooZxzRcvtTezRUktxxRWBt6sOm7I5+Z4TUTMBCYBvWoYk5mZNaOWLQXN4VzTFkCRa5A0EBiYDz+S9PICxtZqCXoD/6nbC54+p7fAWsLvXdu2CLx/Xy5yUS2TQgOwStVxH2D8XK5pkNQJ6Am83/SJIuJy4PIaxdmqSBoZEf3LjsPmn9+7ts3vX1LL7qMRwOqS+klaDNgPGNrkmqHAQfn23sB9rWk8wcxsUVOzlkJEzJR0NHAPaUrqkIgYI+kMYGREDAWuBP4saRyphbBfreIxM7N5k7+Yty6SBubuMmtj/N61bX7/EicFMzOrcJkLMzOrcFIwM7MKJwWzdk6S/5+3MZJKW4RS04J4Nn8krQ9MB4iIF0sOx9o4Sd8C3omIV8qOxYqRtBkQEfFYWSV//A2ilZC0E3AHcCRwo6RDSg7J2jBJ3wGuAFYvOxabNyXLA38E/ippy4iIfL6urQa3FEqW3/BuwDHAURExVNImwDWSFo+Iy8qN0NoaScsAvwB+FBEPS+oMEBEzyo3M5ia3CN6VdA3QHfiNpJMj4q56x+KkULL8j+EjSSOBJSV1jognJO1HajF8EhFXlxymtS0dgCk5ISwHnAP0lHQn8I+IeL3c8KypnLhnAV2A0cBjwFmS1gJmRsTF9epOcvdR6/EO8G1gCYCIGAkcCBwjqV+ZgVnbEhH/AcblQpJ/AB4GrgI2I+1vYq2EpN755syImA3cBvSJiNuAu4H/BZaqZ0xOCiVr7C+MiEuBrsBlknrmFsMjwHPMoXKsWTVJO0k6qOrU48DXgFkRcWVE3A5cDewhqXspQdrnSNoFuFbStcA3G08Dq+X79gJ+CxwiaZt6DTo7KZRA0pqSNs1Nxsp7EBH75uMLgR9KOgrYEphZTqTWFuRtbX8M/F7SHvn0TcBbwAqSDs/negBT8ZeM0uVxw/OBM0l7yhwOEBFPkt6ja4HBEXEicDLwr7rF5jIX9SVpT1KT8K38MxK4KiImV13zQ2Al0je90yJiTBmxWtsh6TBS9+PGwFkRcWVuEexF2gO9L+nf1I8iYnRpgRoAko4BVo2In0jqS9q6eDTwBKm76OlcQLTu01KdFOootwyuAS6OiEcl7QVsQlqbcG5ETGpy/eIRMb2EUK0NyF2MM/Lt3YDFgFeB60ll6WcAp+bfawPvRcSEksK1KrmlcAVpGvpA4DfAbNLMozERcbWkTnlHyrpy91H9Lclnc8dvBf5G+s+8P4CkjSVtmO//tP7hWVsgaXPgR1WnngX2jIingd+Tpjj3jIhPIxnjhFAuSV+XtI2kTSLiCeBo4F3grog4LSLOIHUTbQWVLYrrzkmhjvK3uvOBPSV9K882eITUbNxC0hKkGSLj8/VuxtkXSNoRGAYcV3X6A2CCpH2BHwKnA/vkqc1Wsvye/QnYArgv//9/gDQrrLOkLfKlHwDdJHUtJVC8TqEMDwNrAgfm/sKHgL/k6YMrRcQF5YZnrZmk7wKnkD5cTpB0TkT8LCImSZpEmmH0/Yi4WdLDfHELXKuzXL7mAuCIiHhA0gxgCUmrRMSbkp4DfprHEr8BfC8iPi4tXn8ZrT9JSwMHAN8hdSFNB34GbBMR75YZm7VekpYC/kwak/q7pB1IA8mDIuL9/O9q2Yj4p6SOETGr1IANAEnrAItFxNOSVgZeJs0OW5806eRWUg/BusCwiHi1tGBxUihN3rd6M9JUtGnARRHxTLlRWWsnqWfjhARJK5IGKq+KiN82ua6UYmr2GUlrAuMjYko+7kT6MrhYRFyRi9/dDWyZx4JaBSeFkknqSBo+mF12LNY65e6HzqRVr8/kUtgd8j7o25C6k45yZd3WIxe4PA/YNSLGVZ3vERFTGpO2pEtI+9ePKi3YJjzQXLKImOWEYHOTP1z+AgwAhknaPSJm54Qg4AXgReArZcZpn5G0LWlCyY8jYlxuIQCQE0KHnBD2J/UWtKpZYR5oNmulJH2N9OHyo7yu5X7gIEn3ANPzl4n3JL0LnCHpLlKr083/kkjqBhwGPBQRDymVwz4+TwKYHBGXpMt0EHAisF9E/LvEkL/ALQWzVqaqfv4SwBk5IXQAxpKLo0XE7Nz1SJ7f/p3cgnBCKFFETCXNNOog6UzgfuATUqmajXI57FnA+6SupVZXrcAtBbPWZxlgYi6h/gKkJAD8U9J0oGO+bnk+W9PydimRGgCSekXERID8vgEMAn4bEZfmpL4/aYYREXFHacHOg1sKZq1InmZ6u6TfSDozIj7K5zvkxY0rA50kHQwMldS9qmVhJVDa5e4eSQc2nssrlo8ELs/Hs4GlgVUkLdaa3zO3FMxaiTxAeR7pG+YsUpnrDrlbaLakaaRB5ZNI1XMPaUwaVg5JXwV+B1wH7JonFV0DEBHjq647DDiUtLCwVZevcVIwK1n+1tgN2B44JiLuz4PMW5JWLXeOiF/lGStLkbohdvEU1PJFxEuSjiVVKvgWae8DGhMDQK6CegAwICLGlhLofPA6BbOSVc1Z7xURE6tWLj8PPAAcBHwaEYdIOgL4e/Xcd6u/XJBwsYi4r+pcV1JiPxS4ISL+LKlfRLwuqWuZpSvmh5OCWYkkbU3qez4wIqblAUkB6zcuaJK0EWla6hElhmpZLlN+Bqm8yF1N7luStK/FPqQJASuRZoZ9WPdAW8gDzWYlqBpo3BPYkVQUsVsekIyIGFV1zUZAH0ldW/MA5aJAUk9SddojIuIuSZ2Vdr4DICImR8StwEfA5qSV5m0mIYDHFMzKdj2pQNpypE3bt6u6r3Ne5HQEaYCyTXQ/tHMdSJ+bz0laAbgYWFzSs8BvImJCrmm0HbBDRDxfYqwt4paCWQmqFpnNBHYhbdD+vKSngEfzt8/VgJ1oIwOUi4KI+IC0IO07pNXmfyfVnlof+Em+5lFg87aYEMBJwayuJO0i6YDG4zyffUxEvEdqKawJdI6I6TkRDGiNq14XJZK2l3Rq1anxpJLlHYFb8of/kcA3JS0LEBEN9Y904XBSMKsTSTuTvl023Xe7o6SrgCtJ+/WOlHRLHnT+pL5RWiMlXYCDgdNy2Qoi4vfAM0BfYAdJ3YENSXsst/kuPs8+MquD/AF/LXB1RNydZ6n0zDtvbUfaPvOciLgtT23s6dIVrYPSVprrkPbEvi8ijszn9yF1G60JrEAaVB5dWqALiQeazWoszxjqAHQH3s7fLG8GQtJLpPUI38/z2ZUHlNv8N862rnE1OdAT6AJsDDwt6Q7go4jYX9LdpFpVH+cuwDbP3UdmNRbJTNIuW0eQ6uFcRZrL/jrwNaBdfKC0B5LWkLQS0Cufug1YISImk8pdb0uqY9Q4BfWN9pIQwEnBrGbyAOWJko7MrYMbgA+A1YGX8vz1S4CvAqvA52YlWQkkfZe0qdElwGH5fesGdJU0mLSn8uHAxpL+t7xIa8dJwawGJG1JKpQWpEHIJ4DFSJu0/ws4QmkP3+2BrqRkYSXKxe3OBg4hffh/HVg8It4H7gGOBU6LiD8BawBDyoq1ljzQbFYDkk4CekXEoHz8K9IK131IieJ7pITQEfh5exigbOskbQEMjoidJPUAHiFVpX01//57RLybCxTOKDPWWnJSMKsBSduTFjj9IiIm5XNnAzsDm0bE1FwyYYZXKrcOeSe7x4APgQ2A/yMlho1ICwn/mzSg3K73VHf3kdlCIqlP/oYJ8CywNqlFAEBuNYwAds/Hk5wQyiXp25KOl/TTvE3m5qS9FyHgAAAMcUlEQVSuo3si4pyIeAy4j7QmoVN7TwjgpGC2UEjalVTu+rI8ILkCcDTwE0k/ktQ4k+UD0hRHK1leTHgR8B9gsKRTImJGRDwITJP0s3zpV0izjTqXFGpdufvIbAFJ+jJwB2kjlVmkLqLdSdU0pwIXAm+Q1gVtAezhWkblkvQl4CbSeM69OUFsAIyIiOFK26IeQ5oEsCxpHclz5UVcP04KZgtI0rrABRGxbT7+JmlLzQB+BkwmfdtcHxgeEa+UFasluXzFyhHxaq52Ooa0oHA14GnSCnOR1pC8Wr21ZnvnpGDWQpJWiIh38u1bgbeBE4BfkKafvgNMyFMYrRWQ9A2gQ0Q8XrXj3XrAahFxSy4x8jAwJCIuKTfacnhMwawFcvfC7yQtn0/9DFgZ+BOwVkScRPr2uUue1WIly+/Z1cCn8LmFgmNyQuiQB/5vYhEuM+LaR2bzSdIupBr6P4+IdwFyl9BuudDd1HzpCqQduLxbWsnynspDSKXIR+Vd7qZK6tK4DWpEzJZ0ILBv/lkkOSmYzYdcL/+vwMURcX+ukbMu0Dsirs31cZA0EDiKtPfyzPIitlyhdkPSmoP38iDz2ZImA8tIGhQRr0lqnBwwICJeLjHkUnlMwayAxv7nfHs/0syUP5NWKD9NWp38IPDTiPhU0sHA44vyh0trImkp4CDgv0izw84BniRtm7kZabbYKqTqp++UFWdr4KRgVoCkPqSB5MUj4mNJ+5KSwn9HxLl5gPJ+0n4Jl5YZqyWSVq+e6ZUTw6HApIi4Ip9bBTgDOMwtusTdR2bzkDdZOYO0srWPpNMi4npJL0bEc40DlJKGksYQrGSSvgPcIOnmiDgQICI+lPTbJpduSVqt3J1U3mKR59lHZs2QtAZwAamO/lmk/Q/+IWm1qoQwW9IPSCUtnigx3EVe3kJzeVL33vH53NVVl8yIiOn5/GGk9/XoXMbccFIwm5eZwMMR8VBETAFuJG2Ic5ekvjkhfJtUVnlARPyzzGAXdXlDo3dJs8OuJa0bWbIxMTTWLpK0BGlfi/0jYkxZ8bZGHlMwm4M8Q+V9YAlgJHApaeOVU0illJcDZkfEr3KZi0/a0+5bbZGknYD1IuLXTc4vS9rtbkpE/EDSRsBbwLve1OiL3FIwa0LSbsBQoF9ETAB2BPYi1TBah7SV5kjydo0R8S8nhHLlMYRzgVeanFd+Dwfm47HAdaSKp04Ic+CBZrMqkr5GqntzXEQ8L6lTRLwo6VuklbCdImJGbkksI2lx4FN/wJRHkkh7VxwfEX/P+1T0BMY3ziiKiAmSRpOmDm8XEQ3lRdy6OSmYfd5s4L6IeFDSV4CDJb0DvBcRNwEz8qDyKcAujYOWVioBywPdJC0N3A5MAWZJuhS4lzTDaGdg+4h4vqxA2wJ3H5ll+Rtnd2CjvFL5PFIN/WWA70sakK+ZCXw7Il4oL1prrCmVB4//CPQndSH9MSJ2AR4FDiO17sYBey8q5a8XhJOCLfIkdYbKzJXHgdHALcALETGYNCX1TlKp5QD+mj9krCSStgYeyV1FAP8mbYSzBml2GHnAuStpFTOedlqMk4It0iRtC5yQV7Y2Ogt4CfihpB4RMZXUWljTFU9bjdWAb5Aq1S4ZEaOB64E3ga0kbZ8nDKyQz1lBnpJqiyxJm5KKpN2ef98YEW/m+5Yh7dX7X8A9wPdJO6a9VFK4VkVSX1Ito36kWWJb5vNrkzbG2ZXU9XdmRDxbUphtkpOCLbLyDmn9SDWNdgUagBsi4t9V1+xMGkN43TumtR6S1gIGAwcDFwPfInUVbRQRk/OssE65lWfzwUnBFln5gyNyVdMdSOsR3gauq04MVj5Jm5CmmU6JiMfyuV8DPye1DP4BvBkR65UXZfvgKam2SJG0SmMXUURMz7OJiIh7ct397YHt8irlJSPiJyWGa4Ck7wL/A4wAFpM0BXiBtJnRDaQuvv2BH+RtUfeOiFllxdvWeaDZFhl54PFfkk5sPJf36G1MDHeRVisfAvyQtLWmlSiXqBgE/CAifgRMB5Yi7YH9R9JA8qkRcXdEHEAqbueEsADcUrBFQq6cuQ9ptfIASbMi4gL4LDHk6aarA+sDG0fE2PIitmxx0ufUhLzV6VbASqQS5S+SVid/LKlzRMyIiLfKC7V9cFKwRcVE4LKIeFjSLcDNkqhODPm613BCKF3j3skR0SDpAWA4aTbRVcCvSQvVTiCtSxhNmgxgC4GTgrVrklYGOkfEG8DDALmm0V5UJQZJ2wCvRsTTJYZrgKRdgL0kLQacHBEnS7qYtD/CDbme0RO5128J+FxStwXkMQVrtyTtTVqZfIOkMyXt0Xhfrn+zF6m20R2kaY3+YClZTghnkbY6nUkqV07uFnodOE/SKnl8qC8wvqRQ2y1PSbV2KZc/uBs4CngX2A1YFxgZEVdWXfcrUn2crV0orVySupMGj6+MiLslrUmadfQEcAcwi/xeATOAI13LaOFz95G1V51I3zQ/jIi3JF0PTCCVQHg3Iv4maXVSn/S3nRDKJWnxiPhI0mF5L+VlgLuAW4FlgZOBqyNiUC5W+FFETC4z5vbKLQVrV3Ktoin59i9JH/rHR8R7knoDB5LWH5wuqRPQ3YXSypXHc9YC/kDaQznyeMJGuUBhY4tu2Twt1WrIYwrWbuTdt66UdKOkPsDvSKUrTpK0fET8hzTGsJ2klSJiphNCuSTtSNrR7rmIqGxWFBGfkgaTGz+jXgam5ERuNeSkYO1C3hntHOA3pDnsZ+UtMv9KWvB0iaSvApvkh3xcSqBWIWk90vtzRp4q3EtSb0n9oFLKfLakQ4FjgCsad1Kz2nFSsPZia+C2iHiYNHtlcUknk3blupZUIuEC4MfAsW4htApdSGUqVpDUn/Q+nQfcI+lgAEnfAPYADo6IMWUFuijxmIK1C7nr6BjgAeBY0iKn7qTKmX/K22v2IPVZTysrTvs8SZsB3yNVO/05cDmpNXcd8G3SXggdG8eJrPbcP2dtlqQNSK3dT/NsoiVIFTPvyzumIekMUh2jB/3B0npI6hARsyPiUUmzgYcj4uZcbuQRSXcDsyPC3Xx15u4ja5PyAOU1pG+Z10vaICJuBH4LTM2brQD8E5ieZ7NYiSStKWnTvP2pGs/nGUZ35NshaV9gAzzuUwq3FKzNyf3P5wFHRMRD+ZtmZ0m9I+IdSbOA4/PvzYH982wWK4mkPUk72b2Vf0ZKuipviKO8p0Un4ADgRNJ75uJ2JfCYgrU5krYEpkXEk5JWJFXLHEraRe3/gAdJ/dFrAdd7x7Ry5ZbBNcDFubtoL9K4wXTg3IiYVHXtHsDzETGunGjNScHarPxhcyxpN67LJW1OWoewhfdSbj3y+zSUlKCvymsPvgXsArwWEZdJ2pj0Pr5YZqzmMQVrwyJiBjAkJ4QOEfEIcBsubNeq5PfpfGBPSd+KiNnAI6SS11vkCQKbAZ4m3Ao4KVirVz1AKaljPtcRICI+yL9nS9oH2JC0eM1al4dJeyIcKGmLiJgVEX8hbZizUkRcEBFvlxuigQearZWbxwBlh5wMugEDgCOBAzxA2fpExDRJ15JacYPz6vLppGJ3TuKtiMcUrNWazwHK/UllsT2o3IrlqcGbAYcD04CLIuKZcqOyak4K1moVHKD8BjDZA5RtS+7+izy+YK2IxxSs1So4QPlNPEDZ5uQxBSeEVsgtBWvVJHUBfgSsB1wTEQ/l8w8Ah0bEqyWGZ9bueKDZWjUPUJrVl1sK1iZ4gNKsPpwUrE3xAKVZbTkpmJlZhWcfmZlZhZOCmZlVOCmYmVmFk4KZmVU4KZiZWYWTgpmZVTgpmM0HSbdJGiVpjKSB+dyhkv4p6QFJf5D023x+WUk3SxqRfzYrN3qzefM6BbP5IGmZiHg/F+MbAewAPEra3GcKcB/wbEQcLekvwKUR8YikLwH3RMRapQVvVoBrH5nNn2Pz5vIAqwAHAg9GxPsAkm4E1sj3bwusLanxsUtK6hERU+oZsNn8cFIwK0jSVqQP+k0j4uNcqfVlYG7f/jvkaz+pT4RmC85jCmbF9QQ+yAnhq6Rd4LoCW0paWlInYK+q64cDRzceSFq/rtGatYCTgllxdwOdJD0HnAk8Qdo3+n+BJ4F7gbFA4zahxwL9JT0naSzw4/qHbDZ/PNBstoAkdY+Ij3JL4VZgSETcWnZcZi3hloLZgjtN0mjgBeB14LaS4zFrMbcUzMyswi0FMzOrcFIwM7MKJwUzM6twUjAzswonBTMzq3BSMDOziv8H8lQaSEKSoIAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's explore how many observations we have per bin\n",
    "\n",
    "t1 = train_t.groupby(['age'])['age'].count() / len(train_t)\n",
    "t2 = test_t.groupby(['age'])['age'].count() / len(test_t)\n",
    "\n",
    "tmp = pd.concat([t1, t2], axis=1)\n",
    "tmp.columns = ['train', 'test']\n",
    "tmp.plot.bar()\n",
    "plt.xticks(rotation=45)\n",
    "plt.ylabel('Number of observations per bin')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most of the observations are in the middle bucket, which indicates that this variable is not very predictive. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Number of observations per bin')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's explore how many observations we have per bin\n",
    "\n",
    "t1 = train_t.groupby(['fare'])['fare'].count() / len(train_t)\n",
    "t2 = test_t.groupby(['fare'])['fare'].count() / len(test_t)\n",
    "\n",
    "tmp = pd.concat([t1, t2], axis=1)\n",
    "tmp.columns = ['train', 'test']\n",
    "tmp.plot.bar()\n",
    "plt.xticks(rotation=45)\n",
    "plt.ylabel('Number of observations per bin')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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