4. Poisson Regression/3. Poisson Regression with Scikit-Learn.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# **Poisson Regression**: Smoking and Lung Cancer Dataset 🫁"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This dataset has information from a Canadian study of mortality by age and smoking status."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# **Poisson Regression with Scikit-Learn**\n",
    "\n",
    "$\\qquad$ <span style=\"color:gray\"><b>0.</b> Settings </span><br>\n",
    "$\\qquad$ <span style=\"color:gray\"><b>1.</b> Dataset </span><br>\n",
    "$\\qquad$ <span style=\"color:gray\"><b>2.</b> Data Preprocessing </span><br>\n",
    "$\\qquad$ <span style=\"color:gray\"><b>3.</b> Data Preparation </span><br>\n",
    "$\\qquad$ <span style=\"color:gray\"><b>4.</b> Poisson Regression with Scikit-Learn </span><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **0.** Settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Libraries\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import PoissonRegressor\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "from io import StringIO\n",
    "import pandas as pd  \n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **1.** Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "    DATASET INFORMATIONS\n",
    "\n",
    "    |-------|------------|---------------------------------------------------------------------|\n",
    "    | Name  | Data Type  | Description                                                         |\n",
    "    |-------|------------|---------------------------------------------------------------------|\n",
    "    | age   | continuous | Age at the start of follow-up: in five-year age groups coded 1 to 9 |\n",
    "    | smoke | nominal    | Smoking: no, cigar_pipe_only, cigarette_plus, cigarette_only        |\n",
    "    | pop   | nominal    | Population: number of male pensioners followed                      |\n",
    "    | dead  | nominal    | Number of deaths in a six-year period                               |\n",
    "    |-------|------------|---------------------------------------------------------------------|\n",
    "    \n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>smoke</th>\n",
       "      <th>pop</th>\n",
       "      <th>dead</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>40-44</td>\n",
       "      <td>no</td>\n",
       "      <td>656</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>45-59</td>\n",
       "      <td>no</td>\n",
       "      <td>359</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>50-54</td>\n",
       "      <td>no</td>\n",
       "      <td>249</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>55-59</td>\n",
       "      <td>no</td>\n",
       "      <td>632</td>\n",
       "      <td>55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>60-64</td>\n",
       "      <td>no</td>\n",
       "      <td>1067</td>\n",
       "      <td>117</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     age smoke   pop  dead\n",
       "0  40-44    no   656    18\n",
       "1  45-59    no   359    22\n",
       "2  50-54    no   249    19\n",
       "3  55-59    no   632    55\n",
       "4  60-64    no  1067   117"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Since the data is in a .dat format (available at: https://data.princeton.edu/wws509/datasets/smoking.dat)\n",
    "\n",
    "temp = u\"\"\"\n",
    "     age         smoke   pop dead\n",
    "1  40-44            no   656   18\n",
    "2  45-59            no   359   22\n",
    "3  50-54            no   249   19\n",
    "4  55-59            no   632   55\n",
    "5  60-64            no  1067  117\n",
    "6  65-69            no   897  170\n",
    "7  70-74            no   668  179\n",
    "8  75-79            no   361  120\n",
    "9    80+            no   274  120\n",
    "10 40-44 cigarPipeOnly   145    2\n",
    "11 45-59 cigarPipeOnly   104    4\n",
    "12 50-54 cigarPipeOnly    98    3\n",
    "13 55-59 cigarPipeOnly   372   38\n",
    "14 60-64 cigarPipeOnly   846  113\n",
    "15 65-69 cigarPipeOnly   949  173\n",
    "16 70-74 cigarPipeOnly   824  212\n",
    "17 75-79 cigarPipeOnly   667  243\n",
    "18   80+ cigarPipeOnly   537  253\n",
    "19 40-44 cigarrettePlus 4531  149\n",
    "20 45-59 cigarrettePlus 3030  169\n",
    "21 50-54 cigarrettePlus 2267  193\n",
    "22 55-59 cigarrettePlus 4682  576\n",
    "23 60-64 cigarrettePlus 6052 1001\n",
    "24 65-69 cigarrettePlus 3880  901\n",
    "25 70-74 cigarrettePlus 2033  613\n",
    "26 75-79 cigarrettePlus  871  337\n",
    "27   80+ cigarrettePlus  345  189\n",
    "28 40-44 cigarretteOnly 3410  124\n",
    "29 45-59 cigarretteOnly 2239  140\n",
    "30 50-54 cigarretteOnly 1851  187\n",
    "31 55-59 cigarretteOnly 3270  514\n",
    "32 60-64 cigarretteOnly 3791  778\n",
    "33 65-69 cigarretteOnly 2421  689\n",
    "34 70-74 cigarretteOnly 1195  432\n",
    "35 75-79 cigarretteOnly  436  214\n",
    "36   80+ cigarretteOnly  113   63\n",
    "\"\"\"\n",
    "\n",
    "data = pd.read_fwf(StringIO(temp), usecols = ['age', 'smoke', 'pop', 'dead'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['age', 'smoke', 'pop', 'dead'], dtype='object')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 36 entries, 0 to 35\n",
      "Data columns (total 4 columns):\n",
      " #   Column  Non-Null Count  Dtype \n",
      "---  ------  --------------  ----- \n",
      " 0   age     36 non-null     object\n",
      " 1   smoke   36 non-null     object\n",
      " 2   pop     36 non-null     int64 \n",
      " 3   dead    36 non-null     int64 \n",
      "dtypes: int64(2), object(2)\n",
      "memory usage: 1.2+ KB\n"
     ]
    }
   ],
   "source": [
    "data.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **2.** Data Preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "age      0\n",
       "smoke    0\n",
       "pop      0\n",
       "dead     0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Null elements\n",
    "data.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "age      False\n",
       "smoke    False\n",
       "pop      False\n",
       "dead     False\n",
       "dtype: bool"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.isnull().any()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(36, 4)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['age', 'smoke', 'pop', 'dead'], dtype='object')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 36 entries, 0 to 35\n",
      "Data columns (total 4 columns):\n",
      " #   Column  Non-Null Count  Dtype \n",
      "---  ------  --------------  ----- \n",
      " 0   age     36 non-null     object\n",
      " 1   smoke   36 non-null     object\n",
      " 2   pop     36 non-null     int64 \n",
      " 3   dead    36 non-null     int64 \n",
      "dtypes: int64(2), object(2)\n",
      "memory usage: 1.2+ KB\n"
     ]
    }
   ],
   "source": [
    "data.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th></th>\n",
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       "      <th>smoke</th>\n",
       "      <th>pop</th>\n",
       "      <th>dead</th>\n",
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       "      <td>40-44</td>\n",
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       "      <td>656</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>45-59</td>\n",
       "      <td>no</td>\n",
       "      <td>359</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>50-54</td>\n",
       "      <td>no</td>\n",
       "      <td>249</td>\n",
       "      <td>19</td>\n",
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       "      <th>3</th>\n",
       "      <td>55-59</td>\n",
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       "      <th>4</th>\n",
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       "      <td>no</td>\n",
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       "      <td>117</td>\n",
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      "text/plain": [
       "     age smoke   pop  dead\n",
       "0  40-44    no   656    18\n",
       "1  45-59    no   359    22\n",
       "2  50-54    no   249    19\n",
       "3  55-59    no   632    55\n",
       "4  60-64    no  1067   117"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['40-44' '45-59' '50-54' '55-59' '60-64' '65-69' '70-74' '75-79' '80+']\n",
      "['no' 'cigarPipeOnly' 'cigarrettePlus' 'cigarretteOnly']\n"
     ]
    }
   ],
   "source": [
    "# Convert all the categorical data into numerical data\n",
    "print(data['age'].unique())\n",
    "print(data['smoke'].unique())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Encode categorical features\n",
    "labelEncoder_X = LabelEncoder()\n",
    "data['age']    = labelEncoder_X.fit_transform(data['age'])\n",
    "data['smoke']  = labelEncoder_X.fit_transform(data['smoke'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 36 entries, 0 to 35\n",
      "Data columns (total 4 columns):\n",
      " #   Column  Non-Null Count  Dtype\n",
      "---  ------  --------------  -----\n",
      " 0   age     36 non-null     int32\n",
      " 1   smoke   36 non-null     int32\n",
      " 2   pop     36 non-null     int64\n",
      " 3   dead    36 non-null     int64\n",
      "dtypes: int32(2), int64(2)\n",
      "memory usage: 992.0 bytes\n"
     ]
    }
   ],
   "source": [
    "data.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>smoke</th>\n",
       "      <th>pop</th>\n",
       "      <th>dead</th>\n",
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       "      <th>0</th>\n",
       "      <td>0</td>\n",
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       "      <td>656</td>\n",
       "      <td>18</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>359</td>\n",
       "      <td>22</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>249</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>632</td>\n",
       "      <td>55</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>1067</td>\n",
       "      <td>117</td>\n",
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       "  </tbody>\n",
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      "text/plain": [
       "   age  smoke   pop  dead\n",
       "0    0      3   656    18\n",
       "1    1      3   359    22\n",
       "2    2      3   249    19\n",
       "3    3      3   632    55\n",
       "4    4      3  1067   117"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "New encoding:\n",
    "\n",
    "* `age`\n",
    "\n",
    "$\\qquad\\quad$ 0 = 40-44<br>\t\n",
    "$\\qquad\\quad$ 1 = 45-59<br>\t\n",
    "$\\qquad\\quad$ 2 = 50-54<br>\t\n",
    "$\\qquad\\quad$ 3 = 55-59<br>\n",
    "$\\qquad\\quad$ 4 = 60-64<br>\n",
    "$\\qquad\\quad$ 5 = 65-69<br>\t\n",
    "$\\qquad\\quad$ 6 = 70-74<br>\t\n",
    "$\\qquad\\quad$ 7 = 75-79<br>\t\n",
    "$\\qquad\\quad$ 8 = 80+<br>\n",
    "\n",
    "* `smoke`\n",
    "\n",
    "$\\qquad\\quad$ 3 = no<br>\n",
    "$\\qquad\\quad$ 0 = cigarPipeOnly<br>\n",
    "$\\qquad\\quad$ 2 = cigarettePlus<br>\n",
    "$\\qquad\\quad$ 1 = cigaretteOnly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **3.** Data Preparation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data[['age', 'pop', 'smoke']]\n",
    "Y = data['dead']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(28, 3)\n",
      "(8, 3)\n",
      "(28,)\n",
      "(8,)\n"
     ]
    }
   ],
   "source": [
    "# Split into train and validation\n",
    "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size = 0.2, random_state=5)\n",
    "print(X_train.shape)\n",
    "print(X_test.shape)\n",
    "print(Y_train.shape)\n",
    "print(Y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **4.** Poisson Regression with **Scikit-Learn**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Normalization of the features\n",
    "Scaler_X = StandardScaler()\n",
    "X_train  = Scaler_X.fit_transform(X_train)\n",
    "X_test   = Scaler_X.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2885.467064</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>56.818936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>323.205870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>136.146962</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>123.159962</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>23.393923</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>165.172620</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             0\n",
       "0   748.925100\n",
       "1  2885.467064\n",
       "2    56.818936\n",
       "3   323.205870\n",
       "4   136.146962\n",
       "5   123.159962\n",
       "6    23.393923\n",
       "7   165.172620"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create linear regression object\n",
    "model = PoissonRegressor();\n",
    "\n",
    "# Train the model using the training sets\n",
    "model.fit(X_train, Y_train);\n",
    "\n",
    "# Predictions\n",
    "Y_pred = model.predict(X_test);\n",
    "pd.DataFrame(Y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    dead\n",
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       "19   169"
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   "source": [
    "# True values\n",
    "pd.DataFrame(Y_test)"
   ]
  }
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