10.6_Mean_encoding.ipynb

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    "## Mean encoding\n",
    "\n",
    "In the previous lectures in this section on how to engineer the labels of categorical variables, we 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 the Risk Factor\n",
    "\n",
    "Replacing labels by the risk factor means essentially replacing the label by the mean of the target for that label. \n",
    "\n",
    "I have only seen this procedure applied in classifications scenarios, where the target can take just the values of 1 or 0. However, in principle, I don't see why this shouldn't be possible as well when the target is continuous. Just be mindful of over-fitting."
   ]
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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": {},
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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",
       "</div>"
      ],
      "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": [
    {
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       "<div>\n",
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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>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",
       "</div>"
      ],
      "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"
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     "execution_count": 4,
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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()) # check number of different labels in Cabin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>Cabin</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>M</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>C</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>M</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>C</td>\n",
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       "    <tr>\n",
       "      <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"
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   ],
   "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 risk factor should be calculated per label 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))"
      ]
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     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "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']], 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 target frequency for each label\n",
    "\n",
    "X_train.groupby(['Cabin'])['Survived'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': 0.42857142857142855,\n",
       " 'B': 0.77419354838709675,\n",
       " 'C': 0.5714285714285714,\n",
       " 'D': 0.69230769230769229,\n",
       " 'E': 0.7407407407407407,\n",
       " 'F': 0.66666666666666663,\n",
       " 'G': 0.5,\n",
       " 'M': 0.30360934182590232,\n",
       " 'T': 0.0}"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# and now let's do the same but capturing the result in a dictionary\n",
    "\n",
    "ordered_labels = X_train.groupby(['Cabin'])['Survived'].mean().to_dict()\n",
    "ordered_labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# replace the labels with the 'risk' (target frequency)\n",
    "# note that we calculated the frequencies based on the training set only\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": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
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       "\n",
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       "<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>0.740741</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>D</td>\n",
       "      <td>1</td>\n",
       "      <td>0.692308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>386</th>\n",
       "      <td>M</td>\n",
       "      <td>0</td>\n",
       "      <td>0.303609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>124</th>\n",
       "      <td>D</td>\n",
       "      <td>0</td>\n",
       "      <td>0.692308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>578</th>\n",
       "      <td>M</td>\n",
       "      <td>0</td>\n",
       "      <td>0.303609</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Cabin  Survived  Cabin_ordered\n",
       "857     E         1       0.740741\n",
       "52      D         1       0.692308\n",
       "386     M         0       0.303609\n",
       "124     D         0       0.692308\n",
       "578     M         0       0.303609"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# check the results\n",
    "\n",
    "X_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xcaecfce400>"
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     "execution_count": 12,
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O5uQyYtJCUg4c8zok42de7wkjgO7ApcBFwF9FpE3+Qqo6SVUTVTUxJibGb5WP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\nDQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xcaebf302e8>"
      ]
     },
     "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": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xcaed3e6a20>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xcaed398dd8>"
      ]
     },
     "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": {},
   "source": [
    "Here the relationship lies perfectly on a diagonal line, because this is how we replaced the categories. "
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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  "language_info": {
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    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  },
  "toc": {
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   "toc_section_display": "block",
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}