06.07-Probability-Ratio-Encoding.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Target guided encodings\n",
    "\n",
    "In the previous lectures in this section, we learned how to convert a label into a number, by using one hot encoding, replacing by a digit or replacing by frequency or counts of observations. These methods are simple, make (almost) 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 target mean (mean encoding / target encoding)\n",
    "- Replacing the labels by the probability ratio of the target being 1 or 0\n",
    "- Weight of evidence.\n",
    "\n",
    "All of the above methods have something in common:\n",
    "\n",
    "- the encoding is **guided by the target**, and\n",
    "- they create a **monotonic relationship** between the variable and the target.\n",
    "\n",
    "\n",
    "### Monotonicity\n",
    "\n",
    "A monotonic relationship is a relationship that does one of the following:\n",
    "\n",
    "- (1) as the value of one variable increases, so does the value of the other variable; or\n",
    "- (2) as the value of one variable increases, the value of the other variable decreases.\n",
    "\n",
    "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 value decreases.\n",
    "\n",
    "\n",
    "\n",
    "### Advantages of target guided encodings\n",
    "\n",
    "- Capture information within the category, therefore creating more predictive features\n",
    "- Create a monotonic relationship between the variable and the target, therefore suitable for linear models\n",
    "- Do not expand the feature space\n",
    "\n",
    "\n",
    "### Limitations\n",
    "\n",
    "- Prone to cause over-fitting\n",
    "- Difficult to cross-validate with current libraries\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",
    "\n",
    "## Probability Ratio Encoding\n",
    "\n",
    "These encoding is suitable for classification problems only, where the target is binary.\n",
    "\n",
    "For each category, we calculate the mean of target=1, that is the probability of the target being 1 ( P(1) ), and the probability of the target=0 ( P(0) ). And then, we calculate the ratio P(1)/P(0), and replace the categories by that ratio.\n",
    "\n",
    "\n",
    "## In this demo:\n",
    "\n",
    "We will see how to perform one hot encoding with:\n",
    "- pandas\n",
    "- Feature-Engine\n",
    "\n",
    "And the advantages and limitations of each implementation using the Titanic dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# to split the datasets\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "# for encoding with feature-engine\n",
    "from feature_engine.categorical_encoders import WoERatioCategoricalEncoder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\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>sex</th>\n",
       "      <th>cabin</th>\n",
       "      <th>embarked</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>female</td>\n",
       "      <td>B5</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>male</td>\n",
       "      <td>C22</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>female</td>\n",
       "      <td>C22</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>male</td>\n",
       "      <td>C22</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>female</td>\n",
       "      <td>C22</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   survived     sex cabin embarked\n",
       "0         1  female    B5        S\n",
       "1         1    male   C22        S\n",
       "2         0  female   C22        S\n",
       "3         0    male   C22        S\n",
       "4         0  female   C22        S"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# load dataset\n",
    "\n",
    "data = pd.read_csv(\n",
    "    '../titanic.csv',\n",
    "    usecols=['cabin', 'sex', 'embarked', 'survived'])\n",
    "\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1307, 4)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's remove obserrvations with na in embarked\n",
    "\n",
    "data.dropna(subset=['embarked'], inplace=True)\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Now we extract the first letter of the cabin\n",
    "# to create a simpler variable for the demo\n",
    "\n",
    "data['cabin'] = data['cabin'].astype(str).str[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1306, 4)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# and we remove the observations where cabin = T\n",
    "# because they are too few\n",
    "\n",
    "data = data[data['cabin']!= 'T']\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "survived :  2  labels\n",
      "sex :  2  labels\n",
      "cabin :  8  labels\n",
      "embarked :  3  labels\n"
     ]
    }
   ],
   "source": [
    "# let's have a look at how many labels each variable has\n",
    "\n",
    "for col in data.columns:\n",
    "    print(col, ': ', len(data[col].unique()), ' labels')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['B', 'C', 'E', 'D', 'A', 'n', 'F', 'G'], dtype=object)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's explore the unique categories\n",
    "data['cabin'].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['female', 'male'], dtype=object)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['sex'].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['S', 'C', 'Q'], dtype=object)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['embarked'].unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Encoding important\n",
    "\n",
    "We calculate the ratio  P(1)/P(0) using the train set, and then use those mappings in the test set.\n",
    "\n",
    "Note that to implement this in pandas, we need to keep the target in the training set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((914, 4), (392, 4))"
      ]
     },
     "execution_count": 10,
     "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(\n",
    "    data[['cabin', 'sex', 'embarked', 'survived']],  # this time we keep the target!!\n",
    "    data['survived'],  # target\n",
    "    test_size=0.3,  # percentage of obs in test set\n",
    "    random_state=0)  # seed to ensure reproducibility\n",
    "\n",
    "X_train.shape, X_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Explore original relationship between categorical variables and target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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 relationship of the categories with the target\n",
    "\n",
    "for var in ['cabin', 'sex', 'embarked']:\n",
    "    \n",
    "    fig = plt.figure()\n",
    "    fig = X_train.groupby([var])['survived'].mean().plot()\n",
    "    fig.set_title('Relationship between {} and Survival'.format(var))\n",
    "    fig.set_ylabel('Mean Survival')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see that the relationship between the target and cabin and embarked goes up and down, depending on the category.\n",
    "\n",
    "\n",
    "## Probability ratio encoding with pandas\n",
    "\n",
    "\n",
    "### Advantages\n",
    "\n",
    "- quick\n",
    "- returns pandas dataframe\n",
    "\n",
    "### Limitations of pandas:\n",
    "\n",
    "- it does not preserve information from train data to propagate to test data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <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",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>0.411765</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.738095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>0.600000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>0.696970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>E</th>\n",
       "      <td>0.700000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>F</th>\n",
       "      <td>0.769231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>G</th>\n",
       "      <td>0.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n</th>\n",
       "      <td>0.292199</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       survived\n",
       "cabin          \n",
       "A      0.411765\n",
       "B      0.738095\n",
       "C      0.600000\n",
       "D      0.696970\n",
       "E      0.700000\n",
       "F      0.769231\n",
       "G      0.750000\n",
       "n      0.292199"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's calculate the probability of survived = 1 per category\n",
    "\n",
    "prob_df = X_train.groupby(['cabin'])['survived'].mean()\n",
    "\n",
    "# and capture it into a dataframe\n",
    "prob_df = pd.DataFrame(prob_df)\n",
    "prob_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\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>died</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cabin</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>0.411765</td>\n",
       "      <td>0.588235</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.738095</td>\n",
       "      <td>0.261905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>0.600000</td>\n",
       "      <td>0.400000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>0.696970</td>\n",
       "      <td>0.303030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>E</th>\n",
       "      <td>0.700000</td>\n",
       "      <td>0.300000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>F</th>\n",
       "      <td>0.769231</td>\n",
       "      <td>0.230769</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>G</th>\n",
       "      <td>0.750000</td>\n",
       "      <td>0.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n</th>\n",
       "      <td>0.292199</td>\n",
       "      <td>0.707801</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       survived      died\n",
       "cabin                    \n",
       "A      0.411765  0.588235\n",
       "B      0.738095  0.261905\n",
       "C      0.600000  0.400000\n",
       "D      0.696970  0.303030\n",
       "E      0.700000  0.300000\n",
       "F      0.769231  0.230769\n",
       "G      0.750000  0.250000\n",
       "n      0.292199  0.707801"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# and now the probability of survived = 0\n",
    "\n",
    "prob_df['died'] = 1 - prob_df['survived']\n",
    "\n",
    "prob_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\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>died</th>\n",
       "      <th>ratio</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cabin</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>0.411765</td>\n",
       "      <td>0.588235</td>\n",
       "      <td>0.700000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.738095</td>\n",
       "      <td>0.261905</td>\n",
       "      <td>2.818182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>0.600000</td>\n",
       "      <td>0.400000</td>\n",
       "      <td>1.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>0.696970</td>\n",
       "      <td>0.303030</td>\n",
       "      <td>2.300000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>E</th>\n",
       "      <td>0.700000</td>\n",
       "      <td>0.300000</td>\n",
       "      <td>2.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>F</th>\n",
       "      <td>0.769231</td>\n",
       "      <td>0.230769</td>\n",
       "      <td>3.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>G</th>\n",
       "      <td>0.750000</td>\n",
       "      <td>0.250000</td>\n",
       "      <td>3.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n</th>\n",
       "      <td>0.292199</td>\n",
       "      <td>0.707801</td>\n",
       "      <td>0.412826</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       survived      died     ratio\n",
       "cabin                              \n",
       "A      0.411765  0.588235  0.700000\n",
       "B      0.738095  0.261905  2.818182\n",
       "C      0.600000  0.400000  1.500000\n",
       "D      0.696970  0.303030  2.300000\n",
       "E      0.700000  0.300000  2.333333\n",
       "F      0.769231  0.230769  3.333333\n",
       "G      0.750000  0.250000  3.000000\n",
       "n      0.292199  0.707801  0.412826"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#  and now the ratio\n",
    "\n",
    "prob_df['ratio'] = prob_df['survived'] / prob_df['died']\n",
    "\n",
    "prob_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': 0.7,\n",
       " 'B': 2.818181818181819,\n",
       " 'C': 1.4999999999999998,\n",
       " 'D': 2.3000000000000007,\n",
       " 'E': 2.333333333333333,\n",
       " 'F': 3.333333333333334,\n",
       " 'G': 3.0,\n",
       " 'n': 0.4128256513026052}"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# and now let's capture the ratio in a dictionary\n",
    "\n",
    "ordered_labels = prob_df['ratio'].to_dict()\n",
    "\n",
    "ordered_labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# now, we replace the labels with the ratios\n",
    "\n",
    "X_train['cabin'] = X_train['cabin'].map(ordered_labels)\n",
    "X_test['cabin'] = X_test['cabin'].map(ordered_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "843     0.412826\n",
       "869     0.412826\n",
       "430     0.412826\n",
       "481     0.412826\n",
       "1308    0.412826\n",
       "456     0.412826\n",
       "118     2.300000\n",
       "485     2.300000\n",
       "297     0.412826\n",
       "263     2.333333\n",
       "Name: cabin, dtype: float64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's explore the result\n",
    "\n",
    "X_train['cabin'].head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we can turn the previous commands into 2 functions\n",
    "\n",
    "\n",
    "def find_category_mappings(df, variable, target):\n",
    "\n",
    "    tmp = pd.DataFrame(df.groupby([variable])[target].mean())\n",
    "    \n",
    "    tmp['non-target'] = 1 - tmp[target]\n",
    "    \n",
    "    tmp['ratio'] = tmp[target] / tmp['non-target']\n",
    "\n",
    "    return tmp['ratio'].to_dict()\n",
    "\n",
    "\n",
    "def integer_encode(train, test, variable, ordinal_mapping):\n",
    "\n",
    "    X_train[variable] = X_train[variable].map(ordinal_mapping)\n",
    "    X_test[variable] = X_test[variable].map(ordinal_mapping)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# and now we run a loop over the remaining categorical variables\n",
    "\n",
    "for variable in ['sex', 'embarked']:\n",
    "    \n",
    "    mappings = find_category_mappings(X_train, variable, 'survived')\n",
    "    \n",
    "    integer_encode(X_train, X_test, variable, mappings)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\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>sex</th>\n",
       "      <th>embarked</th>\n",
       "      <th>survived</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>843</th>\n",
       "      <td>0.412826</td>\n",
       "      <td>0.218107</td>\n",
       "      <td>0.509434</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>869</th>\n",
       "      <td>0.412826</td>\n",
       "      <td>0.218107</td>\n",
       "      <td>0.509434</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>430</th>\n",
       "      <td>0.412826</td>\n",
       "      <td>2.788235</td>\n",
       "      <td>0.509434</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>481</th>\n",
       "      <td>0.412826</td>\n",
       "      <td>2.788235</td>\n",
       "      <td>1.160920</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1308</th>\n",
       "      <td>0.412826</td>\n",
       "      <td>0.218107</td>\n",
       "      <td>0.509434</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         cabin       sex  embarked  survived\n",
       "843   0.412826  0.218107  0.509434         0\n",
       "869   0.412826  0.218107  0.509434         0\n",
       "430   0.412826  2.788235  0.509434         1\n",
       "481   0.412826  2.788235  1.160920         1\n",
       "1308  0.412826  0.218107  0.509434         0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's see the result\n",
    "\n",
    "X_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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 inspect the newly created monotonic relationship\n",
    "# between the categorical variables and the target\n",
    "\n",
    "for var in ['cabin', 'sex', 'embarked']:\n",
    "    \n",
    "    fig = plt.figure()\n",
    "    fig = X_train.groupby([var])['survived'].mean().plot()\n",
    "    fig.set_title('Monotonic relationship between {} and Survival'.format(var))\n",
    "    fig.set_ylabel('Mean Survived')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note the monotonic relationships between the mean target and the categories.\n",
    "\n",
    "### Note\n",
    "\n",
    "Replacing categorical labels with this code and method will generate missing values for categories present in the test set that were not seen in the training set. Therefore it is extremely important to handle rare labels before-hand. I will explain how to do this, in a later notebook.\n",
    "\n",
    "**In addition, it will create NA or Inf if the probability of target = 0 is zero, as the division by zero is not defined.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probability Ratio Encoding with Feature-Engine\n",
    "\n",
    "If using Feature-Engine, instead of pandas, we do not need to keep the target variable in the training dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((914, 3), (392, 3))"
      ]
     },
     "execution_count": 22,
     "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(\n",
    "    data[['cabin', 'sex', 'embarked']], # predictors\n",
    "    data['survived'],  # target\n",
    "    test_size=0.3,  # percentage of obs in test set\n",
    "    random_state=0)  # seed to ensure reproducibility\n",
    "\n",
    "X_train.shape, X_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "ratio_enc = WoERatioCategoricalEncoder(\n",
    "    encoding_method = 'ratio',\n",
    "    variables=['cabin', 'sex', 'embarked'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "WoERatioCategoricalEncoder(encoding_method='ratio',\n",
       "                           variables=['cabin', 'sex', 'embarked'])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# when fitting the transformer, we need to pass the target as well\n",
    "# just like with any Scikit-learn predictor class\n",
    "\n",
    "ratio_enc.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'cabin': {'A': 0.7,\n",
       "  'B': 2.818181818181819,\n",
       "  'C': 1.4999999999999998,\n",
       "  'D': 2.3000000000000007,\n",
       "  'E': 2.333333333333333,\n",
       "  'F': 3.333333333333334,\n",
       "  'G': 3.0,\n",
       "  'n': 0.4128256513026052},\n",
       " 'sex': {'female': 2.788235294117647, 'male': 0.21810699588477367},\n",
       " 'embarked': {'C': 1.160919540229885,\n",
       "  'Q': 0.4333333333333333,\n",
       "  'S': 0.5094339622641509}}"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# in the encoder dict we see the P(1)/P(0) for each\n",
    "# category for each of the indicated variables\n",
    "\n",
    "ratio_enc.encoder_dict_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['cabin', 'sex', 'embarked']"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# this is the list of variables that the encoder will transform\n",
    "\n",
    "ratio_enc.variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\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>sex</th>\n",
       "      <th>embarked</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>843</th>\n",
       "      <td>0.412826</td>\n",
       "      <td>0.218107</td>\n",
       "      <td>0.509434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>869</th>\n",
       "      <td>0.412826</td>\n",
       "      <td>0.218107</td>\n",
       "      <td>0.509434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>430</th>\n",
       "      <td>0.412826</td>\n",
       "      <td>2.788235</td>\n",
       "      <td>0.509434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>481</th>\n",
       "      <td>0.412826</td>\n",
       "      <td>2.788235</td>\n",
       "      <td>1.160920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1308</th>\n",
       "      <td>0.412826</td>\n",
       "      <td>0.218107</td>\n",
       "      <td>0.509434</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         cabin       sex  embarked\n",
       "843   0.412826  0.218107  0.509434\n",
       "869   0.412826  0.218107  0.509434\n",
       "430   0.412826  2.788235  0.509434\n",
       "481   0.412826  2.788235  1.160920\n",
       "1308  0.412826  0.218107  0.509434"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train = ratio_enc.transform(X_train)\n",
    "X_test = ratio_enc.transform(X_test)\n",
    "\n",
    "# let's explore the result\n",
    "X_train.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**\n",
    "\n",
    "If the argument variables is left to None, then the encoder will automatically identify all categorical variables. Is that not sweet?\n",
    "\n",
    "The encoder will not encode numerical variables. So if some of your numerical variables are in fact categories, you will need to re-cast them as object before using the encoder.\n",
    "\n",
    "If there is a label in the test set that was not present in the train set, the encoder will through and error, to alert you of this behaviour.\n",
    "\n",
    "Finally, if the probability of target = 0 is zero for any category, the encoder will raise an error as the division by zero is not defined."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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