10.7_Probability_ratio_encoding.ipynb

{
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    "## Probability ratio encoding\n",
    "\n",
    "In the previous lectures in this section on how to engineer the labels of categorical variables, you learnt how to convert a label into a number, by using one hot encoding or replacing by frequency or counts. These methods are simple, make no assumptions and work generally well in different scenarios.\n",
    "\n",
    "There are however methods that allow us to capture information while pre-processing the labels of categorical variables. These methods include:\n",
    "\n",
    "- Ordering the labels according to the target\n",
    "- Replacing labels by the risk (of the target)\n",
    "- Replacing the labels by the joint probability of the target being 1 or 0\n",
    "- Weight of evidence.\n",
    "\n",
    "### Monotonicity\n",
    "\n",
    "All these methods create a monotonic relationship between the categorical variable and the target. A monotonic relationship is a relationship that does one of the following: (1) as the value of one variable increases, so does the value of the other variable; or (2) as the value of one variable increases, the other variable value decreases. In this case, as the value of the independent variable (predictor) increases, so does the target, or conversely, as the value of the variable increases, the target decreases.\n",
    "\n",
    "In general:\n",
    "\n",
    "### Advantages\n",
    "\n",
    "- Capture information within the label, therefore rendering more predictive features\n",
    "- Creates a monotonic relationship between the variable and the target\n",
    "- Does not expand the feature space\n",
    "\n",
    "### Disadvantage\n",
    "\n",
    "- Prone to cause over-fitting\n",
    "\n",
    "\n",
    "### Note\n",
    "\n",
    "The methods discussed in this and the coming 3 lectures can be also used on numerical variables, after discretisation. This creates a monotonic relationship between the numerical variable and the target, and therefore improves the performance of linear models. I will discuss this in more detail in the section \"Discretisation\".\n",
    "\n",
    "\n",
    "### Replace labels by joint probability of the target being 1 or 0\n",
    "\n",
    "For each label, we calculate the mean of target=1, that is the probability of being 1 ( P(1) ), and also the probability of the target=0 ( P(0) ). And then, we calculate the ratio P(1)/P(0), and replace the labels by that ratio."
   ]
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  {
   "cell_type": "code",
   "execution_count": 1,
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   "source": [
    "import pandas as pd\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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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>Cabin</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>C85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>C123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "   Survived Cabin\n",
       "0         0   NaN\n",
       "1         1   C85\n",
       "2         1   NaN\n",
       "3         1  C123\n",
       "4         0   NaN"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's load again the titanic dataset\n",
    "\n",
    "data = pd.read_csv('titanic.csv', usecols=['Cabin', 'Survived'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Survived</th>\n",
       "      <th>Cabin</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>Missing</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>C85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>Missing</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>C123</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>Missing</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "   Survived    Cabin\n",
       "0         0  Missing\n",
       "1         1      C85\n",
       "2         1  Missing\n",
       "3         1     C123\n",
       "4         0  Missing"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's first fill NA values with an additional label\n",
    "\n",
    "data.Cabin.fillna('Missing', inplace=True)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "148"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "# Cabin has indeed a lot of labels, here for simplicity, I will capture the first letter of the cabin, \n",
    "# but the procedure could be done as well without any prior variable manipulation\n",
    "\n",
    "len(data.Cabin.unique())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Survived</th>\n",
       "      <th>Cabin</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <th>0</th>\n",
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       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>M</td>\n",
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      "text/plain": [
       "   Survived Cabin\n",
       "0         0     M\n",
       "1         1     C\n",
       "2         1     M\n",
       "3         1     C\n",
       "4         0     M"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now we extract the first letter of the cabin\n",
    "\n",
    "data['Cabin'] = data['Cabin'].astype(str).str[0]\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['M', 'C', 'E', 'G', 'D', 'A', 'B', 'F', 'T'], dtype=object)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check the labels\n",
    "data.Cabin.unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Important\n",
    "\n",
    "The calculation of the probability ratios to replace the labels should be done considering ONLY on the training set, and then expanded it to the test set.\n",
    "See below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((623, 2), (268, 2))"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's separate into training and testing set\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(data[['Cabin', 'Survived']],\n",
    "                                                    data.Survived, test_size=0.3,\n",
    "                                                    random_state=0)\n",
    "X_train.shape, X_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Cabin\n",
       "A    0.428571\n",
       "B    0.774194\n",
       "C    0.571429\n",
       "D    0.692308\n",
       "E    0.740741\n",
       "F    0.666667\n",
       "G    0.500000\n",
       "M    0.303609\n",
       "T    0.000000\n",
       "Name: Survived, dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's calculate the probability of Survived (target=1)\n",
    "X_train.groupby(['Cabin'])['Survived'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Survived</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cabin</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
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       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>0.428571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.774194</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>0.571429</td>\n",
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       "      <th>D</th>\n",
       "      <td>0.692308</td>\n",
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       "    <tr>\n",
       "      <th>E</th>\n",
       "      <td>0.740741</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>F</th>\n",
       "      <td>0.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>G</th>\n",
       "      <td>0.500000</td>\n",
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       "    <tr>\n",
       "      <th>M</th>\n",
       "      <td>0.303609</td>\n",
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       "    <tr>\n",
       "      <th>T</th>\n",
       "      <td>0.000000</td>\n",
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      ],
      "text/plain": [
       "       Survived\n",
       "Cabin          \n",
       "A      0.428571\n",
       "B      0.774194\n",
       "C      0.571429\n",
       "D      0.692308\n",
       "E      0.740741\n",
       "F      0.666667\n",
       "G      0.500000\n",
       "M      0.303609\n",
       "T      0.000000"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's make a dataframe with the above\n",
    "\n",
    "prob_df = X_train.groupby(['Cabin'])['Survived'].mean()\n",
    "prob_df = pd.DataFrame(prob_df)\n",
    "prob_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Survived</th>\n",
       "      <th>Died</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cabin</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>0.428571</td>\n",
       "      <td>0.571429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.774194</td>\n",
       "      <td>0.225806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>0.571429</td>\n",
       "      <td>0.428571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>0.692308</td>\n",
       "      <td>0.307692</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>E</th>\n",
       "      <td>0.740741</td>\n",
       "      <td>0.259259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>F</th>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>G</th>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>M</th>\n",
       "      <td>0.303609</td>\n",
       "      <td>0.696391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>T</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Survived      Died\n",
       "Cabin                    \n",
       "A      0.428571  0.571429\n",
       "B      0.774194  0.225806\n",
       "C      0.571429  0.428571\n",
       "D      0.692308  0.307692\n",
       "E      0.740741  0.259259\n",
       "F      0.666667  0.333333\n",
       "G      0.500000  0.500000\n",
       "M      0.303609  0.696391\n",
       "T      0.000000  1.000000"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# now let's  calculate the probability of target = 0 (people who did not survive)\n",
    "prob_df = X_train.groupby(['Cabin'])['Survived'].mean()\n",
    "prob_df = pd.DataFrame(prob_df)\n",
    "prob_df['Died'] = 1-prob_df.Survived\n",
    "prob_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
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       "      <th>A</th>\n",
       "      <td>0.428571</td>\n",
       "      <td>0.571429</td>\n",
       "      <td>0.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.774194</td>\n",
       "      <td>0.225806</td>\n",
       "      <td>3.428571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>0.571429</td>\n",
       "      <td>0.428571</td>\n",
       "      <td>1.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>0.692308</td>\n",
       "      <td>0.307692</td>\n",
       "      <td>2.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>E</th>\n",
       "      <td>0.740741</td>\n",
       "      <td>0.259259</td>\n",
       "      <td>2.857143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>F</th>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>G</th>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>M</th>\n",
       "      <td>0.303609</td>\n",
       "      <td>0.696391</td>\n",
       "      <td>0.435976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>T</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Survived      Died     ratio\n",
       "Cabin                              \n",
       "A      0.428571  0.571429  0.750000\n",
       "B      0.774194  0.225806  3.428571\n",
       "C      0.571429  0.428571  1.333333\n",
       "D      0.692308  0.307692  2.250000\n",
       "E      0.740741  0.259259  2.857143\n",
       "F      0.666667  0.333333  2.000000\n",
       "G      0.500000  0.500000  1.000000\n",
       "M      0.303609  0.696391  0.435976\n",
       "T      0.000000  1.000000  0.000000"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  and now the ratio\n",
    "\n",
    "prob_df['ratio'] = prob_df.Survived/prob_df.Died\n",
    "prob_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': 0.75,\n",
       " 'B': 3.4285714285714279,\n",
       " 'C': 1.3333333333333333,\n",
       " 'D': 2.25,\n",
       " 'E': 2.8571428571428563,\n",
       " 'F': 1.9999999999999998,\n",
       " 'G': 1.0,\n",
       " 'M': 0.4359756097560975,\n",
       " 'T': 0.0}"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's make a dictionary with the above ratio\n",
    "\n",
    "prob_df['ratio'].to_dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ordered_labels = prob_df['ratio'].to_dict()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# replace the labels with the ratios\n",
    "\n",
    "X_train['Cabin_ordered'] = X_train.Cabin.map(ordered_labels)\n",
    "X_test['Cabin_ordered'] = X_test.Cabin.map(ordered_labels)"
   ]
  },
  {
   "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",
       "    }\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>Cabin</th>\n",
       "      <th>Survived</th>\n",
       "      <th>Cabin_ordered</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>857</th>\n",
       "      <td>E</td>\n",
       "      <td>1</td>\n",
       "      <td>2.857143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>D</td>\n",
       "      <td>1</td>\n",
       "      <td>2.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>386</th>\n",
       "      <td>M</td>\n",
       "      <td>0</td>\n",
       "      <td>0.435976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>124</th>\n",
       "      <td>D</td>\n",
       "      <td>0</td>\n",
       "      <td>2.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>578</th>\n",
       "      <td>M</td>\n",
       "      <td>0</td>\n",
       "      <td>0.435976</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Cabin  Survived  Cabin_ordered\n",
       "857     E         1       2.857143\n",
       "52      D         1       2.250000\n",
       "386     M         0       0.435976\n",
       "124     D         0       2.250000\n",
       "578     M         0       0.435976"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check the results\n",
    "\n",
    "X_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x8813c6f860>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NoxARMo5l897iHbz101ZuemMxbetHcXvfFlzRpRFVIsK9XhVjiiWhdv98YmKiBksfzdv3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\nDQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8812c10048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the original variable\n",
    "\n",
    "fig = plt.figure()\n",
    "fig = X_train.groupby(['Cabin'])['Survived'].mean().plot()\n",
    "fig.set_title('Normal relationship between variable and target')\n",
    "fig.set_ylabel('Survived')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x88140ebf60>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JU7g7T7y/gc899A57D5bzly+ewm3n6fqBiEQn2hvT/wB8BzgE4O5LCJrClgTi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\nRBqrRSWFvG17mTkvn6tP6c/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x8812c10198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the transformed result: the monotonic variable\n",
    "\n",
    "fig = plt.figure()\n",
    "fig = X_train.groupby(['Cabin_ordered'])['Survived'].mean().plot()\n",
    "fig.set_title('Monotonic relationship between variable and target')\n",
    "fig.set_ylabel('Survived')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "As you can see in the above plot, there is now a monotonic relationship between the variable Cabin and probability of survival. The higher the Cabin number, the more likely the person was to survive.\n",
    "\n",
    "### Note\n",
    "\n",
    "Monotonic does not mean strictly linear. Monotonic means that it increases constantly, or it decreases constantly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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