03.4_Rare_values.ipynb

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   "cell_type": "markdown",
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   "source": [
    "# Rare values\n",
    "\n",
    "## Labels that occur rarely\n",
    "\n",
    "Categorical variables are those which values are selected from a group of categories, also called labels. It is not unusual that different labels appear in  the dataset with different frequencies. Some categories may appear a lot in the dataset, whereas some other categories appear only in a few number of observations.\n",
    "\n",
    "Consider for example a dataset with information about loan applicants for the Lending Club data exercise where one of the variables is \"city where the applicant lives\". We can imagine that cities like 'New York' may appear a lot in the data set just because New York has a huge population. On the other hand, smaller towns like 'Leavenworth' will appear only on a few occasions (if at all, population < 2000 people), just because the population there is very small.\n",
    "\n",
    "Categorical variables in business datasets very often contain a few dominant labels that account for the majority of the observations and a large number of labels that appear only seldomly. \n",
    "\n",
    "### Are Rare Labels in a categorical variable a problem?\n",
    "\n",
    "Rare values can add a lot of information at the time of making an assessment or none at all. For example, consider a stockholder meeting where each person can vote in proportion to their number of shares. One of the shareholders owns 50% of the stock, and the other 999 shareholders own the remaining 50%. The outcome of the vote is largely influenced by the shareholder who holds the majority of the stock. The remaining shareholders may have an impact collectively, but they have virtually no impact individually. \n",
    "\n",
    "The same occurs in real life datasets. The label that is over-represented in the dataset tends to dominate the outcome, and those that are under-represented may have no impact individually, but could have an impact if considered collectively.\n",
    "\n",
    "More specifically,\n",
    "\n",
    "- Rare values in categorical variables tend to cause over-fitting, particularly in tree based methods.\n",
    "\n",
    "- A big number of infrequent labels adds noise, with little information, therefore causing over-fitting.\n",
    "\n",
    "- Rare labels may be present in training set, but not in test set, therefore causing over-fitting to the train set.\n",
    "\n",
    "- Rare labels may appear in the test set, and not in the train set. Thus, the machine learning model will not know how to evaluate it. \n",
    "\n",
    "\n",
    "**Note** Sometimes rare values, like outliers, are worth having a look at, in particular, when we are looking for rare instances (e.g., when the target is highly unbalanced). For example, if we are building a model to predict fraudulent applications, which are in essence rare, then a rare value in a certain variable, may be indeed important. This rare value could be telling us that the observation is most likely a fraudulent application, and therefore we would choose not to ignore it.\n",
    "\n",
    "I will show you how to tackle rare labels later in the course. Here I would like to give you an idea of how rare labels may affect the performance of machine learning algorithms. So, let's go ahead and see the effect of Rare Values in Categorical variables on Machine Learning models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Real Life example: \n",
    "\n",
    "### The Mercedes-Benz Greener Manufacturing challenge in Kaggle\n",
    "\n",
    "Daimler’s Mercedes-Benz cars are leaders in the premium car industry. With a huge selection of car features and options, customers can choose the customized Mercedes-Benz of their dreams.\n",
    "\n",
    "To ensure the safety and reliability of each and every unique car configuration before they hit the road, Daimler’s engineers have developed a robust testing system. Testing time varies depending on the different car features and options. The task is to predict the time it takes for a car with certain features to pass the testing. Therefore it is a regression problem: we need to estimate a continuous variable.\n",
    "\n",
    "The dataset contains a set of car features, the variable names are masked, so it is impossible to find out what each one of them means. The variable to predict is _y_: time to pass the testing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "====================================================================================================\n",
    "\n",
    "To download the Mercedes-Benz Greener Manufacturing dataset from Kaggle go ahead to this [website](https://www.kaggle.com/c/mercedes-benz-greener-manufacturing/data)\n",
    "\n",
    "Scroll down to the bottom of the page, and click on the link 'train.csv.zip', and then click the 'download' blue button towards the right of the screen, to download the dataset.\n",
    "Unzip it, and save it to a directory of your choice.\n",
    "\n",
    "**Note that you need to be logged in to Kaggle in order to download the datasets**.\n",
    "\n",
    "If you save it in the same directory from which you are running this notebook and name the file 'mercedesbenz.csv' then you can load it the same way I will load it below.\n",
    "\n",
    "===================================================================================================="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "% matplotlib inline\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.ensemble import AdaBoostRegressor\n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "from sklearn.ensemble import GradientBoostingRegressor\n",
    "\n",
    "from sklearn.metrics import mean_squared_error, r2_score\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\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>y</th>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>X3</th>\n",
       "      <th>X6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>130.81</td>\n",
       "      <td>v</td>\n",
       "      <td>at</td>\n",
       "      <td>a</td>\n",
       "      <td>j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>88.53</td>\n",
       "      <td>t</td>\n",
       "      <td>av</td>\n",
       "      <td>e</td>\n",
       "      <td>l</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>76.26</td>\n",
       "      <td>w</td>\n",
       "      <td>n</td>\n",
       "      <td>c</td>\n",
       "      <td>j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>80.62</td>\n",
       "      <td>t</td>\n",
       "      <td>n</td>\n",
       "      <td>f</td>\n",
       "      <td>l</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>78.02</td>\n",
       "      <td>v</td>\n",
       "      <td>n</td>\n",
       "      <td>f</td>\n",
       "      <td>d</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "        y X1  X2 X3 X6\n",
       "0  130.81  v  at  a  j\n",
       "1   88.53  t  av  e  l\n",
       "2   76.26  w   n  c  j\n",
       "3   80.62  t   n  f  l\n",
       "4   78.02  v   n  f  d"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's load the dataset with just the columns that we need for this exercise\n",
    "\n",
    "data = pd.read_csv('mercedesbenz.csv', usecols=['X1', 'X2', 'X3', 'X6'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Variable names and variable values are masked intentionally by Mercedes Benz. This is common practice in the industry, and it is done to protect intellectual property and personal information, if any."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "variable:  X1  number of labels:  27\n",
      "variable:  X2  number of labels:  44\n",
      "variable:  X3  number of labels:  7\n",
      "variable:  X6  number of labels:  12\n",
      "total cars:  4209\n"
     ]
    }
   ],
   "source": [
    "# let's check at the different number of labels within each variable\n",
    "cols_to_use = ['X1', 'X2', 'X3', 'X6']\n",
    "\n",
    "for col in cols_to_use:\n",
    "    print('variable: ', col, ' number of labels: ', len(data[col].unique()))\n",
    "    \n",
    "print('total cars: ', len(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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REX2iyR7JE5KmUZ5EKGkG8FSrUUVERN9okkjOBS4DdpH058A1wEdbjSoiIvpGk7O2LpJ0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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x272e8859e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NlsqPBh/NxmxfLGklTbIT8BLb328NshvNgtXb8n88ra1tSf+P5jDC1cB7bP9b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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x272fd36d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x272fef2eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x273004a860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's plot how frequently appears each label \n",
    "# within a variable in the dataset\n",
    "\n",
    "total_cars = len(data)\n",
    "\n",
    "for col in cols_to_use:\n",
    "    # count the number of observations per label and divide by total \n",
    "    # number of cars\n",
    "    temp_df = pd.Series(data[col].value_counts() / total_cars)\n",
    "    \n",
    "    # make plot with the above percentages\n",
    "    fig = temp_df.sort_values(ascending=False).plot.bar()\n",
    "    fig.set_xlabel(col)\n",
    "    fig.set_ylabel('percentage of cars')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that for each of the above variables, some labels appear in more than 10% of the cars in the dataset, and very many appear in less than 10% or even 5% of the cars. These are infrequent labels or **Rare Values** and could cause over-fitting.\n",
    "\n",
    "### How is the target, \"time to pass testing\", related to these categories?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>X3</th>\n",
       "      <th>X3_perc_cars</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>c</td>\n",
       "      <td>0.461392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>f</td>\n",
       "      <td>0.255643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>a</td>\n",
       "      <td>0.104538</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>d</td>\n",
       "      <td>0.068900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>g</td>\n",
       "      <td>0.057258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>e</td>\n",
       "      <td>0.038727</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>b</td>\n",
       "      <td>0.013542</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  X3  X3_perc_cars\n",
       "0  c      0.461392\n",
       "1  f      0.255643\n",
       "2  a      0.104538\n",
       "3  d      0.068900\n",
       "4  g      0.057258\n",
       "5  e      0.038727\n",
       "6  b      0.013542"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# I will work first the the variable X3\n",
    "\n",
    "# Let's calculate again the frequency of the different categories/labels\n",
    "# in X3\n",
    "\n",
    "temp_df = pd.Series(data['X3'].value_counts() / total_cars).reset_index()\n",
    "temp_df.columns = ['X3', 'X3_perc_cars']\n",
    "temp_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "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>X3</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>a</td>\n",
       "      <td>102.507477</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>b</td>\n",
       "      <td>100.239649</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>c</td>\n",
       "      <td>101.959269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>d</td>\n",
       "      <td>105.114414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>e</td>\n",
       "      <td>100.033190</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>f</td>\n",
       "      <td>96.564507</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>g</td>\n",
       "      <td>100.428672</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  X3           y\n",
       "0  a  102.507477\n",
       "1  b  100.239649\n",
       "2  c  101.959269\n",
       "3  d  105.114414\n",
       "4  e  100.033190\n",
       "5  f   96.564507\n",
       "6  g  100.428672"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# now let's calculate the mean \"time to pass testing\"\n",
    "# for each label in X3\n",
    "\n",
    "data.groupby(['X3'])['y'].mean().reset_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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>X3</th>\n",
       "      <th>X3_perc_cars</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>c</td>\n",
       "      <td>0.461392</td>\n",
       "      <td>101.959269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>f</td>\n",
       "      <td>0.255643</td>\n",
       "      <td>96.564507</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>a</td>\n",
       "      <td>0.104538</td>\n",
       "      <td>102.507477</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>d</td>\n",
       "      <td>0.068900</td>\n",
       "      <td>105.114414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>g</td>\n",
       "      <td>0.057258</td>\n",
       "      <td>100.428672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>e</td>\n",
       "      <td>0.038727</td>\n",
       "      <td>100.033190</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>b</td>\n",
       "      <td>0.013542</td>\n",
       "      <td>100.239649</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  X3  X3_perc_cars           y\n",
       "0  c      0.461392  101.959269\n",
       "1  f      0.255643   96.564507\n",
       "2  a      0.104538  102.507477\n",
       "3  d      0.068900  105.114414\n",
       "4  g      0.057258  100.428672\n",
       "5  e      0.038727  100.033190\n",
       "6  b      0.013542  100.239649"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Let's combine the 2 previous dataframes\n",
    "# I will merge the second dataframe with the mean\n",
    "# time to pass testing onto the first one with the\n",
    "# frequency of labels (which I called temp_df)\n",
    "\n",
    "temp_df = temp_df.merge(\n",
    "    data.groupby(['X3'])['y'].mean().reset_index(), on='X3', how='left')\n",
    "\n",
    "temp_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x272fe17dd8>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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OqYQGh3odKSAkT9C158Qe/rPkP17HMcZchosWGao6TFUrAv1VNUpVK/q3OqpqRYYxl/Dh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\nGFf8P6xz8e3sHdm0AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x273004acc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's make a combined plot of the label frequency and\n",
    "# the time to pass testing.\n",
    "# This will help us  visualise the relationship between the\n",
    "# target and the labels of X3\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "plt.xticks(temp_df.index, temp_df['X3'], rotation=0)\n",
    "\n",
    "ax2 = ax.twinx()\n",
    "ax.bar(temp_df.index, temp_df[\"X3_perc_cars\"], color='lightgrey')\n",
    "ax2.plot(temp_df.index, temp_df[\"y\"], color='green', label='Seconds')\n",
    "ax.set_ylabel('percentage of cars per category')\n",
    "ax2.set_ylabel('Seconds')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cars where X3 is f pass the test relatively quickly, whereas cars with the category d seem to take a longer time to pass the test.\n",
    "\n",
    "Cars where X3 is b, take around 100 seconds to pass the test. However, b is present in less than 10% of the cars. Why is this important? Well, because if we do not have a lot of cars to learn from, we could be under or over-estimating the effect if b on the time to pass a test.\n",
    "\n",
    "In the next cell, I will combine all the above lines of code in a loop, and repeat the exercise for the remaining variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TObfuuUy7fBp7R+9l/nXzuafzPZxV9SzH12xYpSGfDfqMb6/5lvCwcC6dfikX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\nw4GJmZmZtQwHJmZmZtYy/h/9Dr9OZYFcmQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x27300d9748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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TwJdsXHcE8AwJM1zHOhGRAuBPwBWqWuPLta7xLFPVeao6LypqYFXPGyisH6Rp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\neyg6kjwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2730092588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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J4CFV/R0oJyK3+TyZMbncKz++wss/vky3ut0Y02ZMniswUl1Z6kq61O7CiOUj2H54u9tx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\nMowxxhjjE/8PKZXFnqd9848AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x272fa34eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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FBhUbeJKhckJlBp0/iDX3ruGbW7+he8PujF04ljPHnckl71zCv1b9i2Xblh2b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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2730490e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's automate the above process for all the categorical variables\n",
    "\n",
    "for col in cols_to_use:\n",
    "    # calculate the frequency of the different labels in the variable\n",
    "    temp_df = pd.Series(data[col].value_counts() / total_cars).reset_index()\n",
    "\n",
    "    # rename the columns\n",
    "    temp_df.columns = [col, col + '_perc_cars']\n",
    "\n",
    "    # merge onto the mean time to pass the test\n",
    "    temp_df = temp_df.merge(\n",
    "        data.groupby([col])['y'].mean().reset_index(), on=col, how='left')\n",
    "\n",
    "    # plot the figure as shown above\n",
    "    fig, ax = plt.subplots(figsize=(8, 4))\n",
    "    plt.xticks(temp_df.index, temp_df[col], rotation=0)\n",
    "    ax2 = ax.twinx()\n",
    "\n",
    "    ax.bar(\n",
    "        temp_df.index,\n",
    "        temp_df[col + '_perc_cars'],\n",
    "        color='lightgrey',\n",
    "        label=col)\n",
    "\n",
    "    ax2.plot(\n",
    "        temp_df.index,\n",
    "        temp_df[\"y\"],\n",
    "        color='green',\n",
    "    )\n",
    "\n",
    "    ax.set_ylabel('percentage of cars per category')\n",
    "    ax2.set_ylabel('Seconds')\n",
    "    ax.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Different labels within each variable seem to have a different influence in the time to pass the test. Take your time to explore the graphs and draw some conclusions.\n",
    "\n",
    "Look then in particular at the variable X2: in the plot, the target \"y\" varies a lot among the rare categories. It goes up and down over the infrequent categories. In fact, it looks quite noisy. This rare labels could indeed be very predictive, or they could be introducing noise rather than information. And because the labels are under-represented among the cars, we are unsure whether they have a true impact on the time to pass. We could be under or over-estimating their impact due to the fact that we have information for few cars.\n",
    "\n",
    "This plot would bring more value, if we plotted the errors of the mean time to pass the test. This would give us an idea of how much the mean value of the target varies within each label. Why don't you go ahead and do so? Plot first the distribution of the target y. If it is somewhat normal, then the error will be the standard deviation. Otherwise you can plot the interquantile range."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Remove rare labels: grouping under a new label\n",
    "\n",
    "One way of tackling rare or infrequent values, is to group them under an umbrella category called 'Rare' or 'Other'. I will say more on this in a dedicated section of the course. Now I will group infrequent labels in each of the variables into one category called 'Rare' because I want to show you how this affects the performance of machine learning algorithms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "aa    0.197909\n",
       "s     0.142077\n",
       "b     0.140651\n",
       "l     0.140176\n",
       "v     0.096935\n",
       "r     0.059634\n",
       "i     0.048230\n",
       "a     0.033975\n",
       "c     0.028748\n",
       "o     0.019482\n",
       "w     0.012354\n",
       "z     0.010929\n",
       "u     0.008791\n",
       "e     0.007840\n",
       "m     0.007603\n",
       "t     0.007365\n",
       "h     0.006890\n",
       "y     0.005464\n",
       "f     0.005464\n",
       "j     0.005227\n",
       "n     0.004514\n",
       "k     0.004039\n",
       "p     0.002138\n",
       "g     0.001426\n",
       "d     0.000713\n",
       "ab    0.000713\n",
       "q     0.000713\n",
       "Name: X1, dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# grouping rare labels into one category\n",
    "\n",
    "# I will replace all the labels that appear in less than 10%\n",
    "# of the observations by the new label 'rare'\n",
    "\n",
    "# first I calculate the frequency of the categories\n",
    "# or in other words, the % of cars in each category for  \n",
    "# the variable X1\n",
    "\n",
    "temp_df = pd.Series(data['X1'].value_counts() / total_cars)\n",
    "temp_df.sort_values(ascending=False)\n",
    "temp_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['aa', 's', 'b', 'l'], dtype='object')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# visualise those labels that appear in\n",
    "# more than 10 % of the cars\n",
    "temp_df[temp_df >= 0.1].index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Only 4 categories are relatively common across the different cars. The remaining appear only in a few cars. Therefore, how they affect the time to pass the test is difficult to know with certainty."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'a': 'rare',\n",
       " 'aa': 'aa',\n",
       " 'ab': 'rare',\n",
       " 'b': 'b',\n",
       " 'c': 'rare',\n",
       " 'd': 'rare',\n",
       " 'e': 'rare',\n",
       " 'f': 'rare',\n",
       " 'g': 'rare',\n",
       " 'h': 'rare',\n",
       " 'i': 'rare',\n",
       " 'j': 'rare',\n",
       " 'k': 'rare',\n",
       " 'l': 'l',\n",
       " 'm': 'rare',\n",
       " 'n': 'rare',\n",
       " 'o': 'rare',\n",
       " 'p': 'rare',\n",
       " 'q': 'rare',\n",
       " 'r': 'rare',\n",
       " 's': 's',\n",
       " 't': 'rare',\n",
       " 'u': 'rare',\n",
       " 'v': 'rare',\n",
       " 'w': 'rare',\n",
       " 'y': 'rare',\n",
       " 'z': 'rare'}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's create a dictionary to replace the rare labels with the\n",
    "# string 'rare'\n",
    "\n",
    "grouping_dict = {\n",
    "    k: ('rare' if k not in temp_df[temp_df >= 0.1].index else k)\n",
    "    for k in temp_df.index\n",
    "}\n",
    "\n",
    "grouping_dict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the category appears in > 10% of the cars, then we keep its name, otherwise, we will replace their name by 'rare', using the dictionary created above.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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>X1</th>\n",
       "      <th>X1_grouped</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>v</td>\n",
       "      <td>rare</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>t</td>\n",
       "      <td>rare</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>w</td>\n",
       "      <td>rare</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>t</td>\n",
       "      <td>rare</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>v</td>\n",
       "      <td>rare</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>b</td>\n",
       "      <td>b</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>r</td>\n",
       "      <td>rare</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>l</td>\n",
       "      <td>l</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>s</td>\n",
       "      <td>s</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>b</td>\n",
       "      <td>b</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  X1 X1_grouped\n",
       "0  v       rare\n",
       "1  t       rare\n",
       "2  w       rare\n",
       "3  t       rare\n",
       "4  v       rare\n",
       "5  b          b\n",
       "6  r       rare\n",
       "7  l          l\n",
       "8  s          s\n",
       "9  b          b"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# now we replace the categories\n",
    "\n",
    "data['X1_grouped'] = data['X1'].map(grouping_dict)\n",
    "data[['X1', 'X1_grouped']].head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['X1', 'X2', 'X3', 'X6']"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cols_to_use"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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>y</th>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>X3</th>\n",
       "      <th>X6</th>\n",
       "      <th>X1_grouped</th>\n",
       "      <th>X2_grouped</th>\n",
       "      <th>X3_grouped</th>\n",
       "      <th>X6_grouped</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>130.81</td>\n",
       "      <td>v</td>\n",
       "      <td>at</td>\n",
       "      <td>a</td>\n",
       "      <td>j</td>\n",
       "      <td>rare</td>\n",
       "      <td>rare</td>\n",
       "      <td>a</td>\n",
       "      <td>j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>88.53</td>\n",
       "      <td>t</td>\n",
       "      <td>av</td>\n",
       "      <td>e</td>\n",
       "      <td>l</td>\n",
       "      <td>rare</td>\n",
       "      <td>rare</td>\n",
       "      <td>rare</td>\n",
       "      <td>l</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>76.26</td>\n",
       "      <td>w</td>\n",
       "      <td>n</td>\n",
       "      <td>c</td>\n",
       "      <td>j</td>\n",
       "      <td>rare</td>\n",
       "      <td>rare</td>\n",
       "      <td>c</td>\n",
       "      <td>j</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>80.62</td>\n",
       "      <td>t</td>\n",
       "      <td>n</td>\n",
       "      <td>f</td>\n",
       "      <td>l</td>\n",
       "      <td>rare</td>\n",
       "      <td>rare</td>\n",
       "      <td>f</td>\n",
       "      <td>l</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>78.02</td>\n",
       "      <td>v</td>\n",
       "      <td>n</td>\n",
       "      <td>f</td>\n",
       "      <td>d</td>\n",
       "      <td>rare</td>\n",
       "      <td>rare</td>\n",
       "      <td>f</td>\n",
       "      <td>d</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        y X1  X2 X3 X6 X1_grouped X2_grouped X3_grouped X6_grouped\n",
       "0  130.81  v  at  a  j       rare       rare          a          j\n",
       "1   88.53  t  av  e  l       rare       rare       rare          l\n",
       "2   76.26  w   n  c  j       rare       rare          c          j\n",
       "3   80.62  t   n  f  l       rare       rare          f          l\n",
       "4   78.02  v   n  f  d       rare       rare          f          d"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's automate the replacement of infrequent categories\n",
    "# by the label 'rare' in the remaining categorical variables\n",
    "\n",
    "# I start from 1 because I already replaced the first variable in\n",
    "# the list\n",
    "for col in cols_to_use[1:]:\n",
    "    \n",
    "    # calculate the % of cars in each category\n",
    "    temp_df = pd.Series(data[col].value_counts() / total_cars)\n",
    "\n",
    "    # create a dictionary to replace the rare labels with the\n",
    "    # string 'rare'\n",
    "    grouping_dict = {\n",
    "        k: ('rare' if k not in temp_df[temp_df >= 0.1].index else k)\n",
    "        for k in temp_df.index\n",
    "    }\n",
    "    \n",
    "    # replace the rare labels\n",
    "    data[col + '_grouped'] = data[col].map(grouping_dict)\n",
    "\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Vfog82fPYXRhjshg3VUjBQBi+ieZewVcRFOzvYMZkdZdjLvPyjy9zc/Gbubfq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\nytKtE8AfJT0raVxtF5E0TtISSUsqKirS+DpmZrk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      "text/plain": [
       "<matplotlib.figure.Figure at 0x273052b9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kGB0rd+TbXd9y69RbaVK+CWeccEbUkUQiZ2aFgJ3unmRmVYFqwPvuvje1Y8Nc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\niBy1/W3hV6stvPw/FRkiIpIuelbrSd2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      "text/plain": [
       "<matplotlib.figure.Figure at 0x272fcf1f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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jFxGRy4B78C0BAuBqmJibBdJ+Pdvm5k1M8VWmRBn6JfZj6b6lzP51dt4NTEgY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\nMQFhRYYxxhhjAsKKDGOMMcYExP8DpVJLQEpC9VwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x27306c0978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2JJOKZXuWUeeDOgxdOZS/Nvwrax5YQ9NyTR2373hjRyLDI5mwdoIPUxqTdaxIMTmCqjJk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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2730637e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's go ahead and plot the bar plots indicating the % of cars per\n",
    "# label and the time to pass the test, for each of the new variables\n",
    "\n",
    "for col in ['X1_grouped', 'X2_grouped', 'X3_grouped', 'X6_grouped']:\n",
    "    \n",
    "    # calculate the frequency of the different labels in the variable\n",
    "    temp_df = pd.Series(data[col].value_counts() / total_cars).reset_index()\n",
    "\n",
    "    # rename the columns\n",
    "    temp_df.columns = [col, col + '_perc_cars']\n",
    "\n",
    "    # merge onto the mean time to pass the test\n",
    "    temp_df = temp_df.merge(\n",
    "        data.groupby([col])['y'].mean().reset_index(), on=col, how='left')\n",
    "\n",
    "    # plot\n",
    "    fig, ax = plt.subplots(figsize=(8, 4))\n",
    "    plt.xticks(temp_df.index, temp_df[col], rotation=0)\n",
    "    ax2 = ax.twinx()\n",
    "\n",
    "    ax.bar(\n",
    "        temp_df.index,\n",
    "        temp_df[col + '_perc_cars'],\n",
    "        color='lightgrey',\n",
    "        label=col)\n",
    "\n",
    "    ax2.plot(\n",
    "        temp_df.index,\n",
    "        temp_df[\"y\"],\n",
    "        color='green',\n",
    "    )\n",
    "\n",
    "    ax.set_ylabel('percentage of cars per category')\n",
    "    ax2.set_ylabel('Seconds')\n",
    "    ax.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we can see for example, that cars with the the label f for variable X3, tend to spend less time in testing, and all the infrequent labels together tend to behave overall like the features c and a as well, in terms of time to pass the test.\n",
    "\n",
    "In the ideal scenario, we would also like to have the standard deviation / interquantile range for the time to pass the test, to get an idea of how variable the time to pass is for each category."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Rare labels lead to uneven distribution of categories in train and test sets\n",
    "\n",
    "Similarly to highly cardinal variables, rare or infrequent labels often land only on the training set, or only on the testing set. If present only in the training set, they may lead to overfitting. If present only on the testing set, the machine learning algorithm will not know how to handle them, as it has not seen it during training. Let's explore this further."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((2946, 4), (1263, 4))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's separate into training and testing set\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    data[cols_to_use], data.y, test_size=0.3, random_state=0)\n",
    "\n",
    "X_train.shape, X_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['l', 'aa', 'au', 'o', 'af', 'c', 'am']\n"
     ]
    }
   ],
   "source": [
    "# Let's find out labels present only in the training set\n",
    "# I will use X2 as example\n",
    "\n",
    "unique_to_train_set = [\n",
    "    x for x in X_train['X2'].unique() if x not in X_test['X2'].unique()\n",
    "]\n",
    "\n",
    "print(unique_to_train_set)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 7 categories present in the train set and are not present in the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['ar', 'j']\n"
     ]
    }
   ],
   "source": [
    "# Let's find out labels present only in the test set\n",
    "\n",
    "unique_to_test_set = [\n",
    "    x for x in X_test['X2'].unique() if x not in X_train['X2'].unique()\n",
    "]\n",
    "\n",
    "print(unique_to_test_set)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, there are 2 rare values present in the test set only."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Effect of rare labels on machine learning algorithms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe thead th {\n",
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       "        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>y</th>\n",
       "      <th>X1</th>\n",
       "      <th>X2</th>\n",
       "      <th>X3</th>\n",
       "      <th>X6</th>\n",
       "      <th>X1_grouped</th>\n",
       "      <th>X2_grouped</th>\n",
       "      <th>X3_grouped</th>\n",
       "      <th>X6_grouped</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>130.81</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>88.53</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>76.26</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>80.62</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>78.02</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>92.93</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>128.76</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>91.91</td>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>108.67</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>126.99</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        y  X1  X2  X3  X6  X1_grouped  X2_grouped  X3_grouped  X6_grouped\n",
       "0  130.81   0   0   0   0           0           0           0           0\n",
       "1   88.53   1   1   1   1           0           0           1           1\n",
       "2   76.26   2   2   2   0           0           0           2           0\n",
       "3   80.62   1   2   3   1           0           0           3           1\n",
       "4   78.02   0   2   3   2           0           0           3           2\n",
       "5   92.93   3   3   2   3           1           0           2           3\n",
       "6  128.76   4   3   3   3           0           0           3           3\n",
       "7   91.91   5   4   3   0           2           1           3           0\n",
       "8  108.67   6   4   1   4           3           1           1           4\n",
       "9  126.99   3   5   2   5           1           0           2           3"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# In order to use this variables to build machine learning using sklearn\n",
    "# first we need to replace the labels by numbers.\n",
    "\n",
    "# The correct way to do this, is to first separate into training and test\n",
    "# sets. And then create a replacing dictionary using the train set\n",
    "# and replace the strings both in train and test using the dictionary\n",
    "# created.\n",
    "\n",
    "# This will lead to the introduction of missing values / NaN in the\n",
    "# test set, for those labels that are not present in the train set\n",
    "# we saw this effect in the previous lecture\n",
    "\n",
    "# in the section dedicated to rare values later in the course, I will\n",
    "# show you how to avoid this problem\n",
    "\n",
    "# now, in order to speed up the demonstration, I will replace the\n",
    "# labels by strings in the entire dataset, and then divide into\n",
    "# train and test. \n",
    "# but remember: THIS IS NOT GOOD PRACTICE!\n",
    "\n",
    "# original variables\n",
    "for col in cols_to_use:\n",
    "    # create the dic and replace the strings in one line\n",
    "    data.loc[:, col] = data.loc[:, col].map(\n",
    "        {k: i\n",
    "         for i, k in enumerate(data[col].unique(), 0)})\n",
    "\n",
    "# variables with grouped categories\n",
    "for col in ['X1_grouped', 'X6_grouped', 'X3_grouped', 'X2_grouped']:\n",
    "    # create the dic and replace the strings in one line\n",
    "    data.loc[:, col] = data.loc[:, col].map(\n",
    "        {k: i\n",
    "         for i, k in enumerate(data[col].unique(), 0)})\n",
    "\n",
    "data.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['X1', 'X2', 'X3', 'X6']"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's remind ourselves the original columns\n",
    "cols_to_use"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['X1_grouped', 'X6_grouped', 'X3_grouped', 'X2_grouped']"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's add the grouped variables to a list\n",
    "cols_grouped = ['X1_grouped', 'X6_grouped', 'X3_grouped', 'X2_grouped']\n",
    "cols_grouped"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# let's combine the list of variables\n",
    "cols = cols_to_use+cols_grouped"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((2946, 8), (1263, 8))"
      ]
     },
     "execution_count": 26,
     "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[cols],\n",
    "    data.y,\n",
    "    test_size=0.3,\n",
    "    random_state=0)\n",
    "\n",
    "X_train.shape, X_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next I will build a series of machine learning algorithms, using comparatively the original categorical variables, and those where the infrequent labels were grouped, and then examine their performance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random Forests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train set\n",
      "Random Forests mse: 73.91420367780387\n",
      "Random Forests r2: 0.524089147901724\n",
      "Test set\n",
      "Random Forests mse: 151.10099965156573\n",
      "Random Forests r2: 0.1261592100558474\n"
     ]
    }
   ],
   "source": [
    "# model built on data with infrequent categories (original)\n",
    "\n",
    "# call the model\n",
    "rf = RandomForestRegressor(n_estimators=300,\n",
    "                           max_depth=34,\n",
    "                           random_state=39)\n",
    "\n",
    "# train the model\n",
    "rf.fit(X_train[cols_to_use], y_train)\n",
    "\n",
    "# make and print predictions in train and test sets\n",
    "print('Train set')\n",
    "pred = rf.predict(X_train[cols_to_use])\n",
    "print('Random Forests mse: {}'.format(mean_squared_error(y_train, pred)))\n",
    "print('Random Forests r2: {}'.format(r2_score(y_train, pred)))\n",
    "print('Test set')\n",
    "pred = rf.predict(X_test[cols_to_use])\n",
    "print('Random Forests mse: {}'.format(mean_squared_error(y_test, pred)))\n",
    "print('Random Forests r2: {}'.format(r2_score(y_test, pred)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see from the mean squared error and the r2 that the Random Forests are over-fitting to the train set. The mse for the train set is less than half the value of the mse of the test set. The r2 in the test set is significantly lower than the one in the train set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train set\n",
      "Random Forests mse: 136.10890251001152\n",
      "Random Forests r2: 0.12363658744046446\n",
      "Test set\n",
      "Random Forests mse: 154.78054883151322\n",
      "Random Forests r2: 0.10487979979742335\n"
     ]
    }
   ],
   "source": [
    "# model built on data with rare values grouped into one category: rare\n",
    "\n",
    "# call the model\n",
    "rf = RandomForestRegressor(n_estimators=300,\n",
    "                           max_depth=4,\n",
    "                           random_state=39)\n",
    "\n",
    "# train the model\n",
    "rf.fit(X_train[cols_grouped], y_train)\n",
    "\n",
    "# make and print preditions\n",
    "print('Train set')\n",
    "pred = rf.predict(X_train[cols_grouped])\n",
    "print('Random Forests mse: {}'.format(mean_squared_error(y_train, pred)))\n",
    "print('Random Forests r2: {}'.format(r2_score(y_train, pred)))\n",
    "print('Test set')\n",
    "pred = rf.predict(X_test[cols_grouped])\n",
    "print('Random Forests mse: {}'.format(mean_squared_error(y_test, pred)))\n",
    "print('Random Forests r2: {}'.format(r2_score(y_test, pred)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see an improvement in Random Forests: when we train the model using all the labels, the model has a strong over-fit to the training set. However, when we train the model using fewer categories, the Random Forests over-fit much less (mse 73 vs mse 136; r2 0.12 vs 0.52). In addition, the second model still keeps a similar generalisation power to unseen data.\n",
    "\n",
    "Disclaimer: I am using a max_depth of 4, in order to make the forest overfit, so that I can show you the effect of rare labels on this algorithm. We can indeed improve the fit and generalisation by building less and more shallow trees."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### AdaBoost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train set\n",
      "AdaBoost mse: 152.55660134599108\n",
      "AdaBoost r2: 0.017734907132739508\n",
      "Test set\n",
      "AdaBoost mse: 172.10171312106795\n",
      "AdaBoost r2: 0.004708788881281345\n"
     ]
    }
   ],
   "source": [
    "# model build on data with all the categories\n",
    "\n",
    "ada = AdaBoostRegressor(n_estimators=400, random_state=44)\n",
    "ada.fit(X_train[cols_to_use], y_train)\n",
    "print('Train set')\n",
    "pred = ada.predict(X_train[cols_to_use])\n",
    "print('AdaBoost mse: {}'.format(mean_squared_error(y_train, pred)))\n",
    "print('AdaBoost r2: {}'.format(r2_score(y_train, pred)))\n",
    "print('Test set')\n",
    "pred = ada.predict(X_test[cols_to_use])\n",
    "print('AdaBoost mse: {}'.format(mean_squared_error(y_test, pred)))\n",
    "print('AdaBoost r2: {}'.format(r2_score(y_test, pred)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train set\n",
      "AdaBoost mse: 149.4235105602519\n",
      "AdaBoost r2: 0.03790791626156742\n",
      "Test set\n",
      "AdaBoost mse: 166.59119412837987\n",
      "AdaBoost r2: 0.036576984860637984\n"
     ]
    }
   ],
   "source": [
    "# model build on data with fewer categories in Cabin Variable\n",
    "\n",
    "ada = AdaBoostRegressor(n_estimators=400, random_state=44)\n",
    "ada.fit(X_train[cols_grouped], y_train)\n",
    "print('Train set')\n",
    "pred = ada.predict(X_train[cols_grouped])\n",
    "print('AdaBoost mse: {}'.format(mean_squared_error(y_train, pred)))\n",
    "print('AdaBoost r2: {}'.format(r2_score(y_train, pred)))\n",
    "print('Test set')\n",
    "pred = ada.predict(X_test[cols_grouped])\n",
    "print('AdaBoost mse: {}'.format(mean_squared_error(y_test, pred)))\n",
    "print('AdaBoost r2: {}'.format(r2_score(y_test, pred)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "We see an improvement in Adaboost when trained using the variables with less categories. The mse is smaller in the latter and the r2 is higher, both for the training and testing sets."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train set\n",
      "Linear Regression mse: 154.61105621770932\n",
      "Linear Regression r2: 0.004506903312812227\n",
      "Test set\n",
      "Linear Regression mse: 172.95013673475464\n",
      "Linear Regression r2e: -0.00019777800114084698\n"
     ]
    }
   ],
   "source": [
    "# model build on data with plenty of categories\n",
    "\n",
    "linreg = LinearRegression()\n",
    "linreg.fit(X_train[cols_to_use], y_train)\n",
    "print('Train set')\n",
    "pred = linreg.predict(X_train[cols_to_use])\n",
    "print('Linear Regression mse: {}'.format(mean_squared_error(y_train, pred)))\n",
    "print('Linear Regression r2: {}'.format(r2_score(y_train, pred)))\n",
    "print('Test set')\n",
    "pred = linreg.predict(X_test[cols_to_use])\n",
    "print('Linear Regression mse: {}'.format(mean_squared_error(y_test, pred)))\n",
    "print('Linear Regression r2e: {}'.format(r2_score(y_test, pred)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train set\n",
      "Linear Regression mse: 151.4575537952273\n",
      "Linear Regression r2: 0.024811336700465203\n",
      "Test set\n",
      "Linear Regression mse: 169.30336571670514\n",
      "Linear Regression r2e: 0.020892071003870694\n"
     ]
    }
   ],
   "source": [
    "# model build on data with infrequent categories grouped under one label\n",
    "\n",
    "linreg = LinearRegression()\n",
    "linreg.fit(X_train[cols_grouped], y_train)\n",
    "print('Train set')\n",
    "pred = linreg.predict(X_train[cols_grouped])\n",
    "print('Linear Regression mse: {}'.format(mean_squared_error(y_train, pred)))\n",
    "print('Linear Regression r2: {}'.format(r2_score(y_train, pred)))\n",
    "print('Test set')\n",
    "pred = linreg.predict(X_test[cols_grouped])\n",
    "print('Linear Regression mse: {}'.format(mean_squared_error(y_test, pred)))\n",
    "print('Linear Regression r2e: {}'.format(r2_score(y_test, pred)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here again, the Linear Regression also benefited from removing rare labels: the mse has decreased in both train and test sets, and the r2 has increased. So now you know how having less categories and grouping the infrequent ones into one single group can increase the performance of the machine learning models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**That is all for this demonstration. I hope you enjoyed the notebook, and see you in the next one.**"
   ]
  }
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