HW/HW4/Week_4-Evaluation.ipynb

{
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   "cell_type": "code",
   "execution_count": 1,
   "id": "38d8c0d9",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Intel(R) Extension for Scikit-learn* enabled (https://github.com/intel/scikit-learn-intelex)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import wget\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline  \n",
    "from sklearnex import patch_sklearn, config_context\n",
    "patch_sklearn()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1233a02b",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.feature_extraction import DictVectorizer\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import accuracy_score\n",
    "from sklearn.metrics import roc_curve\n",
    "from sklearn.metrics import roc_auc_score\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5674cf2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"last\" #change to 'all' if needed"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4eabbe4",
   "metadata": {},
   "source": [
    "## Dataset\n",
    "\n",
    "In this homework, we will use Credit Card Data from book \"Econometric Analysis\".\n",
    "\n",
    "Here's a wget-able [link](https://raw.githubusercontent.com/alexeygrigorev/datasets/master/AER_credit_card_data.csv):\n",
    "\n",
    "```bash\n",
    "wget https://raw.githubusercontent.com/alexeygrigorev/datasets/master/AER_credit_card_data.csv\n",
    "```\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "12c4cc0b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r",
      "  0% [                                                                              ]     0 / 73250\r",
      " 11% [........                                                                      ]  8192 / 73250\r",
      " 22% [.................                                                             ] 16384 / 73250\r",
      " 33% [..........................                                                    ] 24576 / 73250\r",
      " 44% [..................................                                            ] 32768 / 73250\r",
      " 55% [...........................................                                   ] 40960 / 73250\r",
      " 67% [....................................................                          ] 49152 / 73250\r",
      " 78% [.............................................................                 ] 57344 / 73250\r",
      " 89% [.....................................................................         ] 65536 / 73250\r",
      "100% [..............................................................................] 73250 / 73250"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'AER_credit_card_data (2).csv'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "wget.download(\"https://raw.githubusercontent.com/alexeygrigorev/datasets/master/AER_credit_card_data.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f8bf450",
   "metadata": {},
   "source": [
    "## Preparation\n",
    "\n",
    "* The goal of this homework is to inspect the output of different evaluation metrics by creating a classification model (target column `card`). \n",
    "* Create the target variable by mapping `yes` to 1 and `no` to 0. \n",
    "* Split the dataset into 3 parts: train/validation/test with 60%/20%/20% distribution. Use `train_test_split` funciton for that with `random_state=1`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "7fb3981c",
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>card</th>\n",
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       "      <th>income</th>\n",
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       "      <th>months</th>\n",
       "      <th>majorcards</th>\n",
       "      <th>active</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>yes</td>\n",
       "      <td>0</td>\n",
       "      <td>37.66667</td>\n",
       "      <td>4.5200</td>\n",
       "      <td>0.033270</td>\n",
       "      <td>124.983300</td>\n",
       "      <td>yes</td>\n",
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       "      <td>no</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>yes</td>\n",
       "      <td>0</td>\n",
       "      <td>33.66667</td>\n",
       "      <td>4.5000</td>\n",
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       "      <td>15.000000</td>\n",
       "      <td>yes</td>\n",
       "      <td>no</td>\n",
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       "      <th>3</th>\n",
       "      <td>yes</td>\n",
       "      <td>0</td>\n",
       "      <td>30.50000</td>\n",
       "      <td>2.5400</td>\n",
       "      <td>0.065214</td>\n",
       "      <td>137.869200</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
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       "      <th>4</th>\n",
       "      <td>yes</td>\n",
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       "      <td>yes</td>\n",
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       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "  card  reports       age  income     share  expenditure owner selfemp  \\\n",
       "0  yes        0  37.66667  4.5200  0.033270   124.983300   yes      no   \n",
       "1  yes        0  33.25000  2.4200  0.005217     9.854167    no      no   \n",
       "2  yes        0  33.66667  4.5000  0.004156    15.000000   yes      no   \n",
       "3  yes        0  30.50000  2.5400  0.065214   137.869200    no      no   \n",
       "4  yes        0  32.16667  9.7867  0.067051   546.503300   yes      no   \n",
       "\n",
       "   dependents  months  majorcards  active  \n",
       "0           3      54           1      12  \n",
       "1           3      34           1      13  \n",
       "2           4      58           1       5  \n",
       "3           0      25           1       7  \n",
       "4           2      64           1       5  "
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df =pd.read_csv(\"AER_credit_card_data.csv\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "8b457fdf",
   "metadata": {},
   "outputs": [
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       "      <th>share</th>\n",
       "      <th>expenditure</th>\n",
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       "      <th>selfemp</th>\n",
       "      <th>dependents</th>\n",
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       "      <td>yes</td>\n",
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       "      <td>no</td>\n",
       "      <td>no</td>\n",
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       "      <td>yes</td>\n",
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       "      <th>3</th>\n",
       "      <td>yes</td>\n",
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       "      <td>30.50000</td>\n",
       "      <td>2.5400</td>\n",
       "      <td>0.065214</td>\n",
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       "      <td>no</td>\n",
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       "      <td>32.16667</td>\n",
       "      <td>9.7867</td>\n",
       "      <td>0.067051</td>\n",
       "      <td>546.503300</td>\n",
       "      <td>yes</td>\n",
       "      <td>no</td>\n",
       "      <td>2</td>\n",
       "      <td>64</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>yes</td>\n",
       "      <td>0</td>\n",
       "      <td>23.25000</td>\n",
       "      <td>2.5000</td>\n",
       "      <td>0.044438</td>\n",
       "      <td>91.996670</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>0</td>\n",
       "      <td>54</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>yes</td>\n",
       "      <td>0</td>\n",
       "      <td>27.91667</td>\n",
       "      <td>3.9600</td>\n",
       "      <td>0.012576</td>\n",
       "      <td>40.833330</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>yes</td>\n",
       "      <td>0</td>\n",
       "      <td>29.16667</td>\n",
       "      <td>2.3700</td>\n",
       "      <td>0.076434</td>\n",
       "      <td>150.790000</td>\n",
       "      <td>yes</td>\n",
       "      <td>no</td>\n",
       "      <td>0</td>\n",
       "      <td>77</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>yes</td>\n",
       "      <td>0</td>\n",
       "      <td>37.00000</td>\n",
       "      <td>3.8000</td>\n",
       "      <td>0.245628</td>\n",
       "      <td>777.821700</td>\n",
       "      <td>yes</td>\n",
       "      <td>no</td>\n",
       "      <td>0</td>\n",
       "      <td>97</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>yes</td>\n",
       "      <td>0</td>\n",
       "      <td>28.41667</td>\n",
       "      <td>3.2000</td>\n",
       "      <td>0.019780</td>\n",
       "      <td>52.580000</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>0</td>\n",
       "      <td>65</td>\n",
       "      <td>1</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
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      "text/plain": [
       "  card  reports       age  income     share  expenditure owner selfemp  \\\n",
       "0  yes        0  37.66667  4.5200  0.033270   124.983300   yes      no   \n",
       "1  yes        0  33.25000  2.4200  0.005217     9.854167    no      no   \n",
       "2  yes        0  33.66667  4.5000  0.004156    15.000000   yes      no   \n",
       "3  yes        0  30.50000  2.5400  0.065214   137.869200    no      no   \n",
       "4  yes        0  32.16667  9.7867  0.067051   546.503300   yes      no   \n",
       "5  yes        0  23.25000  2.5000  0.044438    91.996670    no      no   \n",
       "6  yes        0  27.91667  3.9600  0.012576    40.833330    no      no   \n",
       "7  yes        0  29.16667  2.3700  0.076434   150.790000   yes      no   \n",
       "8  yes        0  37.00000  3.8000  0.245628   777.821700   yes      no   \n",
       "9  yes        0  28.41667  3.2000  0.019780    52.580000    no      no   \n",
       "\n",
       "   dependents  months  majorcards  active  \n",
       "0           3      54           1      12  \n",
       "1           3      34           1      13  \n",
       "2           4      58           1       5  \n",
       "3           0      25           1       7  \n",
       "4           2      64           1       5  \n",
       "5           0      54           1       1  \n",
       "6           2       7           1       5  \n",
       "7           0      77           1       3  \n",
       "8           0      97           1       6  \n",
       "9           0      65           1      18  "
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# for column names:\n",
    "df.columns = df.columns.str.lower().str.replace(' ', '_')\n",
    "\n",
    "# for data in the dataframe:\n",
    "strings = list(df.dtypes[df.dtypes == 'object'].index)\n",
    "for col in strings:\n",
    "    df[col] = df[col].str.lower().str.replace(' ', '_')\n",
    "\n",
    "df.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "cffd2434",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "card           0\n",
       "reports        0\n",
       "age            0\n",
       "income         0\n",
       "share          0\n",
       "expenditure    0\n",
       "owner          0\n",
       "selfemp        0\n",
       "dependents     0\n",
       "months         0\n",
       "majorcards     0\n",
       "active         0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# checking if any missing values exist in any of the columns:\n",
    "df.isna().sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "f4a2d37e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Mona\\AppData\\Local\\Temp\\ipykernel_3568\\4121548936.py:5: UserWarning: To output multiple subplots, the figure containing the passed axes is being cleared.\n",
      "  df.hist(bins=100, ax=ax, layout=(3, 3), column=df.columns.values)\n"
     ]
    },
    {
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      "text/plain": [
       "<Figure size 1500x1000 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# INSPECTING HISTOGRAM:\n",
    "\n",
    "fig = plt.figure(figsize=(15,10))\n",
    "ax = plt.gca()\n",
    "df.hist(bins=100, ax=ax, layout=(3, 3), column=df.columns.values)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "aac0bd4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0       yes\n",
       "1       yes\n",
       "2       yes\n",
       "3       yes\n",
       "4       yes\n",
       "       ... \n",
       "1314    yes\n",
       "1315     no\n",
       "1316    yes\n",
       "1317    yes\n",
       "1318    yes\n",
       "Name: card, Length: 1319, dtype: object"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "target = df[\"card\"].copy()\n",
    "target\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "e255efb6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0       1\n",
       "1       1\n",
       "2       1\n",
       "3       1\n",
       "4       1\n",
       "       ..\n",
       "1314    1\n",
       "1315    0\n",
       "1316    1\n",
       "1317    1\n",
       "1318    1\n",
       "Name: card, Length: 1319, dtype: int64"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binary01 = lambda x: 1 if x==\"yes\" else (0 if x==\"no\" else float('NaN'))\n",
    "target = target.apply(binary01)\n",
    "target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "ca44b80f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+/Hm7l+EyIedlu0vT0NAQ1q9fj+Li4jkvw2VOIRoMBmzYsMHiMt1169YhOTkZ+fn5C7hmZCuFQoFz584hOTnZrte5xJ7cfNmu0Wi0GJ/usl0Si0uE3N7LdkksLhFyM1sv2yWxuETI7b1sl8TiEiHnZbuubVFfhehIvGx3aRocHMSdO3fkxy0tLbhx4wb8/f0RHBxs20IkF/LZZ59Jer1e8vT0lDZs2CDV1dUt9CrRLH7++WcJgNVPenq6zctwmfPk5Lpc4picXBtDTsJjyEl4DDkJjyEn4THkJDyGnITHkJPwGHISHkNOwmPISXgMOQnvf8bkGgT0sKnXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(2,2))\n",
    "ax = plt.gca()\n",
    "target.hist(bins=4, ax=ax)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5dea6b7c",
   "metadata": {},
   "source": [
    "We have a class imbalance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "871c803b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# checking if any NaN were added to the target after conversion:\n",
    "target.isna().sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "2f0d900b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>reports</th>\n",
       "      <th>age</th>\n",
       "      <th>income</th>\n",
       "      <th>share</th>\n",
       "      <th>expenditure</th>\n",
       "      <th>owner</th>\n",
       "      <th>selfemp</th>\n",
       "      <th>dependents</th>\n",
       "      <th>months</th>\n",
       "      <th>majorcards</th>\n",
       "      <th>active</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>37.66667</td>\n",
       "      <td>4.5200</td>\n",
       "      <td>0.033270</td>\n",
       "      <td>124.983300</td>\n",
       "      <td>yes</td>\n",
       "      <td>no</td>\n",
       "      <td>3</td>\n",
       "      <td>54</td>\n",
       "      <td>1</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>33.25000</td>\n",
       "      <td>2.4200</td>\n",
       "      <td>0.005217</td>\n",
       "      <td>9.854167</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>3</td>\n",
       "      <td>34</td>\n",
       "      <td>1</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>33.66667</td>\n",
       "      <td>4.5000</td>\n",
       "      <td>0.004156</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>yes</td>\n",
       "      <td>no</td>\n",
       "      <td>4</td>\n",
       "      <td>58</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>30.50000</td>\n",
       "      <td>2.5400</td>\n",
       "      <td>0.065214</td>\n",
       "      <td>137.869200</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>0</td>\n",
       "      <td>25</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>32.16667</td>\n",
       "      <td>9.7867</td>\n",
       "      <td>0.067051</td>\n",
       "      <td>546.503300</td>\n",
       "      <td>yes</td>\n",
       "      <td>no</td>\n",
       "      <td>2</td>\n",
       "      <td>64</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1314</th>\n",
       "      <td>0</td>\n",
       "      <td>33.58333</td>\n",
       "      <td>4.5660</td>\n",
       "      <td>0.002146</td>\n",
       "      <td>7.333333</td>\n",
       "      <td>yes</td>\n",
       "      <td>no</td>\n",
       "      <td>0</td>\n",
       "      <td>94</td>\n",
       "      <td>1</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1315</th>\n",
       "      <td>5</td>\n",
       "      <td>23.91667</td>\n",
       "      <td>3.1920</td>\n",
       "      <td>0.000376</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>3</td>\n",
       "      <td>12</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1316</th>\n",
       "      <td>0</td>\n",
       "      <td>40.58333</td>\n",
       "      <td>4.6000</td>\n",
       "      <td>0.026513</td>\n",
       "      <td>101.298300</td>\n",
       "      <td>yes</td>\n",
       "      <td>no</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1317</th>\n",
       "      <td>0</td>\n",
       "      <td>32.83333</td>\n",
       "      <td>3.7000</td>\n",
       "      <td>0.008999</td>\n",
       "      <td>26.996670</td>\n",
       "      <td>no</td>\n",
       "      <td>yes</td>\n",
       "      <td>0</td>\n",
       "      <td>60</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1318</th>\n",
       "      <td>0</td>\n",
       "      <td>48.25000</td>\n",
       "      <td>3.7000</td>\n",
       "      <td>0.111619</td>\n",
       "      <td>344.157500</td>\n",
       "      <td>yes</td>\n",
       "      <td>no</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1319 rows × 11 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      reports       age  income     share  expenditure owner selfemp  \\\n",
       "0           0  37.66667  4.5200  0.033270   124.983300   yes      no   \n",
       "1           0  33.25000  2.4200  0.005217     9.854167    no      no   \n",
       "2           0  33.66667  4.5000  0.004156    15.000000   yes      no   \n",
       "3           0  30.50000  2.5400  0.065214   137.869200    no      no   \n",
       "4           0  32.16667  9.7867  0.067051   546.503300   yes      no   \n",
       "...       ...       ...     ...       ...          ...   ...     ...   \n",
       "1314        0  33.58333  4.5660  0.002146     7.333333   yes      no   \n",
       "1315        5  23.91667  3.1920  0.000376     0.000000    no      no   \n",
       "1316        0  40.58333  4.6000  0.026513   101.298300   yes      no   \n",
       "1317        0  32.83333  3.7000  0.008999    26.996670    no     yes   \n",
       "1318        0  48.25000  3.7000  0.111619   344.157500   yes      no   \n",
       "\n",
       "      dependents  months  majorcards  active  \n",
       "0              3      54           1      12  \n",
       "1              3      34           1      13  \n",
       "2              4      58           1       5  \n",
       "3              0      25           1       7  \n",
       "4              2      64           1       5  \n",
       "...          ...     ...         ...     ...  \n",
       "1314           0      94           1      19  \n",
       "1315           3      12           1       5  \n",
       "1316           2       1           1       2  \n",
       "1317           0      60           1       7  \n",
       "1318           2       2           1       0  \n",
       "\n",
       "[1319 rows x 11 columns]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features = df.drop(columns = \"card\").copy()\n",
    "features"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "129ee956",
   "metadata": {},
   "source": [
    "## Question 1\n",
    "\n",
    "ROC AUC could also be used to evaluate feature importance of numerical variables. \n",
    "\n",
    "Let's do that\n",
    "\n",
    "* For each numerical variable, use it as score and compute AUC with the `card` variable.\n",
    "* Use the training dataset for that.\n",
    "\n",
    "If your AUC is < 0.5, invert this variable by putting \"-\" in front\n",
    "\n",
    "(e.g. `-df_train['expenditure']`)\n",
    "\n",
    "AUC can go below 0.5 if the variable is negatively correlated with the target varialble. You can change the direction of the correlation by negating this variable - then negative correlation becomes positive.\n",
    "\n",
    "Which numerical variable (among the following 4) has the highest AUC?\n",
    "\n",
    "- `reports`\n",
    "- `dependents`\n",
    "- `active`\n",
    "- `share`\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "b5b06204",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "x_train_full, x_test, y_train_full, y_test = train_test_split(features, target, test_size=0.2, random_state=42)\n",
    "x_train, x_val, y_train, y_val = train_test_split(x_train_full, y_train_full, test_size=0.25, random_state=42)\n",
    "\n",
    "splits = [x_train_full, x_train, x_val, x_test]\n",
    "for split in splits:\n",
    "        split.reset_index(inplace = True)\n",
    "        \n",
    "splits = [y_train_full,y_train, y_val, y_test]\n",
    "for split in splits:\n",
    "         split.reset_index(drop = True, inplace = True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "345336b1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AUC is 0.726507 for column \"reports\" with target variable \"card\n",
      "AUC is 0.554801 for column \"dependents\" with target variable \"card\n",
      "AUC is 0.561475 for column \"active\" with target variable \"card\n",
      "AUC is 0.992087 for column \"share\" with target variable \"card\n"
     ]
    }
   ],
   "source": [
    "columns_AUC = ['reports', 'dependents', 'active','share']\n",
    "\n",
    "for column in columns_AUC:\n",
    "        AUC = roc_auc_score(y_train, x_train[column])\n",
    "        if AUC < 0.5:\n",
    "            AUC = roc_auc_score(y_train, -x_train[column])\n",
    "        \n",
    "        print (\"AUC is %f for column \\\"%s\\\" with target variable \\\"card\" %(AUC, column))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "842f1447",
   "metadata": {},
   "source": [
    "## Training the model\n",
    "\n",
    "From now on, use these columns only:\n",
    "\n",
    "```\n",
    "[\"reports\", \"age\", \"income\", \"share\", \"expenditure\", \"dependents\", \"months\", \"majorcards\", \"active\", \"owner\", \"selfemp\"]\n",
    "```\n",
    "\n",
    "Apply one-hot-encoding using `DictVectorizer` and train the logistic regression with these parameters:\n",
    "\n",
    "```\n",
    "LogisticRegression(solver='liblinear', C=1.0, max_iter=1000)\n",
    "```\n",
    "## Question 2\n",
    "\n",
    "What's the AUC of this model on the validation dataset? (round to 3 digits)\n",
    "\n",
    "- 0.615\n",
    "- 0.515\n",
    "- 0.715\n",
    "- 0.995"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "b36514b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_columns = [\"reports\", \"age\", \"income\", \"share\", \"expenditure\", \"dependents\", \"months\", \"majorcards\", \"active\", \"owner\", \"selfemp\"]\n",
    "x_train = x_train[feature_columns]\n",
    "x_val = x_val[feature_columns]\n",
    "x_test = x_test[feature_columns]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "f3125c04",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.feature_extraction import DictVectorizer\n",
    "\n",
    "def dvectorizer(df_train, df_val):\n",
    "    \n",
    "\n",
    "    dv = DictVectorizer(sparse=False)\n",
    "    \n",
    "    df_train_dict = df_train.to_dict(orient='records')\n",
    "    df_train_OH = dv.fit_transform(df_train_dict)\n",
    "    \n",
    "    df_val_dict = df_val.to_dict(orient='records')\n",
    "    df_val_OH = dv.fit_transform(df_val_dict)\n",
    "    \n",
    "    \n",
    "    return df_train_OH , df_val_OH \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "a8299e14",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.977"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "\n",
    "x_train_OH, x_val_OH = dvectorizer(x_train, x_val)\n",
    "\n",
    "model = LogisticRegression(solver=\"liblinear\", C=1.0, max_iter=1000, random_state=42)\n",
    "model.fit(x_train_OH, y_train)\n",
    "y_pred = model.predict(x_val_OH)\n",
    "\n",
    "accuracy = round(accuracy_score(y_val, y_pred),3)\n",
    "accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b3a32e9",
   "metadata": {},
   "source": [
    "## Question 3\n",
    "\n",
    "Now let's compute precision and recall for our model.\n",
    "\n",
    "* Evaluate the model on all thresholds from 0.0 to 1.0 with step 0.01\n",
    "* For each threshold, compute precision and recall\n",
    "* Plot them\n",
    "\n",
    "\n",
    "At which threshold precision and recall curves intersect?\n",
    "\n",
    "* 0.1\n",
    "* 0.3\n",
    "* 0.6\n",
    "* 0.8\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "872d322a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>threshold</th>\n",
       "      <th>precision</th>\n",
       "      <th>recall</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.776515</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.1</td>\n",
       "      <td>0.901786</td>\n",
       "      <td>0.985366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.961538</td>\n",
       "      <td>0.975610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>0.3</td>\n",
       "      <td>0.980392</td>\n",
       "      <td>0.975610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>0.4</td>\n",
       "      <td>0.990099</td>\n",
       "      <td>0.975610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>0.5</td>\n",
       "      <td>0.995025</td>\n",
       "      <td>0.975610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>0.6</td>\n",
       "      <td>0.995025</td>\n",
       "      <td>0.975610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>0.7</td>\n",
       "      <td>0.995025</td>\n",
       "      <td>0.975610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>0.8</td>\n",
       "      <td>0.995025</td>\n",
       "      <td>0.975610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>0.9</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.975610</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    threshold  precision    recall\n",
       "0         0.0   0.776515  1.000000\n",
       "10        0.1   0.901786  0.985366\n",
       "20        0.2   0.961538  0.975610\n",
       "30        0.3   0.980392  0.975610\n",
       "40        0.4   0.990099  0.975610\n",
       "50        0.5   0.995025  0.975610\n",
       "60        0.6   0.995025  0.975610\n",
       "70        0.7   0.995025  0.975610\n",
       "80        0.8   0.995025  0.975610\n",
       "90        0.9   1.000000  0.975610"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import precision_score\n",
    "from sklearn.metrics import recall_score\n",
    "\n",
    "y_pred_prob = model.predict_proba(x_val_OH)[:, 1]\n",
    "\n",
    "scores = []\n",
    "thresholds = np.arange(0,1, 0.01)\n",
    "\n",
    "\n",
    "for t in thresholds:\n",
    "    \n",
    "    precision = precision_score(y_val, y_pred_prob >= t, average = 'binary')\n",
    "    recall = recall_score(y_val,y_pred_prob >= t, average = 'binary')\n",
    "    scores.append((t, precision, recall))\n",
    "    \n",
    "columns = ['threshold', 'precision','recall']\n",
    "df_scores = pd.DataFrame(scores, columns=columns)\n",
    "df_scores[::10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "8d02ff08",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x285d1cbcb50>"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(df_scores.threshold, df_scores['precision'], label='Precision')\n",
    "plt.plot(df_scores.threshold, df_scores['recall'], label='Recall')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "4c9eaa39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25    0.25\n",
       "26    0.26\n",
       "27    0.27\n",
       "28    0.28\n",
       "29    0.29\n",
       "Name: threshold, dtype: float64"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "intersect_idx = df_scores.index[df_scores.precision == df_scores.recall].tolist()\n",
    "df_scores.threshold[intersect_idx].round(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0edb6351",
   "metadata": {},
   "source": [
    "After the intersection points, if one increases, the other decreases"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ffc744c",
   "metadata": {},
   "source": [
    "\n",
    "## Question 4\n",
    "\n",
    "Precision and recall are conflicting - when one grows, the other goes down. That's why they are often combined into the F1 score - a metrics that takes into account both\n",
    "\n",
    "This is the formula for computing F1:\n",
    "\n",
    "F1 = 2 * P * R / (P + R)\n",
    "\n",
    "Where P is precision and R is recall.\n",
    "\n",
    "Let's compute F1 for all thresholds from 0.0 to 1.0 with increment 0.01\n",
    "\n",
    "At which threshold F1 is maximal?\n",
    "\n",
    "- 0.1\n",
    "- 0.4\n",
    "- 0.6\n",
    "- 0.7\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "774f2dba",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "maximum F1 score is 0.988 at threshold 0.88\n"
     ]
    }
   ],
   "source": [
    "df_scores[\"f1\"] = (2 * df_scores.precision * df_scores.recall) / (df_scores.precision + df_scores.recall)\n",
    "\n",
    "max_F1 = df_scores[\"f1\"].max()\n",
    "max_F1_idx = df_scores[\"f1\"].idxmax()\n",
    "max_F1_t = df_scores.threshold[max_F1_idx].round(2)\n",
    "\n",
    "\n",
    "print (\"maximum F1 score is %.3f at threshold %.2f\" %(max_F1, max_F1_t))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25a58ffa",
   "metadata": {},
   "source": [
    "Just to check with inbuilt F1 score in sklearn:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "5c5af1ae",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Points in the PR curve where P and R intersect:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>threshold</th>\n",
       "      <th>precision</th>\n",
       "      <th>recall</th>\n",
       "      <th>f1</th>\n",
       "      <th>f1_sklearn</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.976</td>\n",
       "      <td>0.976</td>\n",
       "      <td>0.976</td>\n",
       "      <td>0.976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.26</td>\n",
       "      <td>0.976</td>\n",
       "      <td>0.976</td>\n",
       "      <td>0.976</td>\n",
       "      <td>0.976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.27</td>\n",
       "      <td>0.976</td>\n",
       "      <td>0.976</td>\n",
       "      <td>0.976</td>\n",
       "      <td>0.976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.28</td>\n",
       "      <td>0.976</td>\n",
       "      <td>0.976</td>\n",
       "      <td>0.976</td>\n",
       "      <td>0.976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.29</td>\n",
       "      <td>0.976</td>\n",
       "      <td>0.976</td>\n",
       "      <td>0.976</td>\n",
       "      <td>0.976</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    threshold  precision  recall     f1  f1_sklearn\n",
       "25       0.25      0.976   0.976  0.976       0.976\n",
       "26       0.26      0.976   0.976  0.976       0.976\n",
       "27       0.27      0.976   0.976  0.976       0.976\n",
       "28       0.28      0.976   0.976  0.976       0.976\n",
       "29       0.29      0.976   0.976  0.976       0.976"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import precision_score\n",
    "from sklearn.metrics import recall_score\n",
    "from sklearn.metrics import f1_score\n",
    "\n",
    "\n",
    "y_pred_prob = model.predict_proba(x_val_OH)[:, 1]\n",
    "\n",
    "scores_f1 = []\n",
    "thresholds = np.arange(0,1, 0.01)\n",
    "\n",
    "for t in thresholds:\n",
    "    f1 = f1_score(y_val, y_pred_prob >= t)\n",
    "    scores_f1.append((f1))\n",
    "    \n",
    "df_scores[\"f1_sklearn\"] = scores_f1\n",
    "\n",
    "print(\"Points in the PR curve where P and R intersect:\")\n",
    "df_scores.loc[df_scores.precision == df_scores.recall].round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "bfbdadfe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Point in the PR curve where F1 is maximum:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>threshold</th>\n",
       "      <th>precision</th>\n",
       "      <th>recall</th>\n",
       "      <th>f1</th>\n",
       "      <th>f1_sklearn</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>0.88</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.976</td>\n",
       "      <td>0.988</td>\n",
       "      <td>0.988</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    threshold  precision  recall     f1  f1_sklearn\n",
       "88       0.88        1.0   0.976  0.988       0.988"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"Point in the PR curve where F1 is maximum:\")\n",
    "df_scores.iloc[df_scores.f1.idxmax(), :].round(3).to_frame().T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bd09da0",
   "metadata": {},
   "source": [
    "The point of intersection in a plot with both precision and recall is not necessarily the threshold \n",
    "of best performing model performance. However, this point can give us a good balance point where neither \n",
    "precision nor recall is increasing or decreasing. For overall best performance, choose threshold where F1 is maximized.\n",
    "\n",
    "PR curves are used for using a threshold for our predicted values when we have a class imbalance. ROC curves are better for choosing threshold for balanced class binary problem."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f98c0c7",
   "metadata": {},
   "source": [
    "## Question 5\n",
    "\n",
    "Use the `KFold` class from Scikit-Learn to evaluate our model on 5 different folds:\n",
    "\n",
    "```\n",
    "KFold(n_splits=5, shuffle=True, random_state=1)\n",
    "```\n",
    "\n",
    "* Iterate over different folds of `df_full_train`\n",
    "* Split the data into train and validation\n",
    "* Train the model on train with these parameters: `LogisticRegression(solver='liblinear', C=1.0, max_iter=1000)`\n",
    "* Use AUC to evaluate the model on validation\n",
    "\n",
    "\n",
    "How large is standard devidation of the AUC scores across different folds?\n",
    "\n",
    "- 0.003\n",
    "- 0.014\n",
    "- 0.09\n",
    "- 0.24\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "3cd0c85a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import KFold\n",
    "from tqdm.auto import tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "9fa55534",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With solver= 'liblinear', mean of AUC-ROC over 5-fold validation is 0.988 and std is +- 0.003\n"
     ]
    }
   ],
   "source": [
    "n_splits = 5\n",
    "\n",
    "    \n",
    "kfold = KFold(n_splits=n_splits, shuffle=True, random_state=1)\n",
    "scores = []\n",
    "\n",
    "for train_idx, val_idx in kfold.split(x_train_full):\n",
    "\n",
    "    df_train = x_train_full.iloc[train_idx]\n",
    "    df_val = x_train_full.iloc[val_idx]\n",
    "\n",
    "    df_train_OH, df_val_OH = dvectorizer(df_train, df_val)\n",
    "\n",
    "    y_train = y_train_full.iloc[train_idx]\n",
    "    y_val = y_train_full.iloc[val_idx]\n",
    "\n",
    "    y_train.reset_index(drop = True, inplace = True)\n",
    "    y_val.reset_index(drop = True, inplace = True)\n",
    "\n",
    "\n",
    "    model = LogisticRegression(solver=\"liblinear\", C=1.0, max_iter=1000, random_state=42)\n",
    "    model.fit(df_train_OH, y_train)\n",
    "\n",
    "    y_pred =  model.predict(df_val_OH)\n",
    "    # y_pred =  model.predict_proba(X)[:, 1]\n",
    "\n",
    "    auc = roc_auc_score(y_val, y_pred)\n",
    "    scores.append(auc)\n",
    "\n",
    "print('With solver= \\'liblinear\\', mean of AUC-ROC over 5-fold validation is %.3f and std is +- %.3f' % (np.mean(scores), np.std(scores)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f81ec33c",
   "metadata": {},
   "source": [
    "check liblinear, and SAG in previous to see diff. Also, note the parameters and what they do"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "289f51eb",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Mona\\anaconda3\\envs\\mlzoomcamp\\lib\\site-packages\\sklearn\\linear_model\\_sag.py:352: ConvergenceWarning: The max_iter was reached which means the coef_ did not converge\n",
      "  warnings.warn(\n",
      "C:\\Users\\Mona\\anaconda3\\envs\\mlzoomcamp\\lib\\site-packages\\sklearn\\linear_model\\_sag.py:352: ConvergenceWarning: The max_iter was reached which means the coef_ did not converge\n",
      "  warnings.warn(\n",
      "C:\\Users\\Mona\\anaconda3\\envs\\mlzoomcamp\\lib\\site-packages\\sklearn\\linear_model\\_sag.py:352: ConvergenceWarning: The max_iter was reached which means the coef_ did not converge\n",
      "  warnings.warn(\n",
      "C:\\Users\\Mona\\anaconda3\\envs\\mlzoomcamp\\lib\\site-packages\\sklearn\\linear_model\\_sag.py:352: ConvergenceWarning: The max_iter was reached which means the coef_ did not converge\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With solver= 'sag', mean of AUC-ROC over 5-fold validation is 0.978 and std is +- 0.006\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Mona\\anaconda3\\envs\\mlzoomcamp\\lib\\site-packages\\sklearn\\linear_model\\_sag.py:352: ConvergenceWarning: The max_iter was reached which means the coef_ did not converge\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "n_splits = 5\n",
    "\n",
    "    \n",
    "kfold = KFold(n_splits=n_splits, shuffle=True, random_state=1)\n",
    "scores = []\n",
    "\n",
    "for train_idx, val_idx in kfold.split(x_train_full):\n",
    "\n",
    "    df_train = x_train_full.iloc[train_idx]\n",
    "    df_val = x_train_full.iloc[val_idx]\n",
    "\n",
    "    df_train_OH, df_val_OH = dvectorizer(df_train, df_val)\n",
    "\n",
    "    y_train = y_train_full.iloc[train_idx]\n",
    "    y_val = y_train_full.iloc[val_idx]\n",
    "\n",
    "    y_train.reset_index(drop = True, inplace = True)\n",
    "    y_val.reset_index(drop = True, inplace = True)\n",
    "\n",
    "\n",
    "    model = LogisticRegression(solver=\"sag\", C=1.0, max_iter=1000, random_state=42)\n",
    "    model.fit(df_train_OH, y_train)\n",
    "\n",
    "    y_pred =  model.predict(df_val_OH)\n",
    "\n",
    "    auc = roc_auc_score(y_val, y_pred)\n",
    "    scores.append(auc)\n",
    "\n",
    "print('With solver= \\'sag\\', mean of AUC-ROC over 5-fold validation is %.3f and std is +- %.3f' % (np.mean(scores), np.std(scores)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b966932",
   "metadata": {},
   "source": [
    "SAG would probably perform better if we ran model for more iterations, but for now, liblinear performs better with lower std over 5 folds."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70a97f14",
   "metadata": {},
   "source": [
    "## Question 6\n",
    "\n",
    "Now let's use 5-Fold cross-validation to find the best parameter C\n",
    "\n",
    "* Iterate over the following C values: `[0.01, 0.1, 1, 10]`\n",
    "* Initialize `KFold` with the same parameters as previously\n",
    "* Use these parametes for the model: `LogisticRegression(solver='liblinear', C=C, max_iter=1000)`\n",
    "* Compute the mean score as well as the std (round the mean and std to 3 decimal digits)\n",
    "\n",
    "\n",
    "Which C leads to the best mean score?\n",
    "\n",
    "- 0.01\n",
    "- 0.1\n",
    "- 1\n",
    "- 10\n",
    "\n",
    "If you have ties, select the score with the lowest std. If you still have ties, select the smallest C\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "8018bd17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c29ec63836104cd6b142a1ecc4ee06b5",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/4 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With C=0.01, mean of AUC-ROC over 5-fold validation is 0.9873 and std is +- 0.0019\n",
      "With C=0.10, mean of AUC-ROC over 5-fold validation is 0.9876 and std is +- 0.0027\n",
      "With C=1.00, mean of AUC-ROC over 5-fold validation is 0.9878 and std is +- 0.0030\n",
      "With C=10.00, mean of AUC-ROC over 5-fold validation is 0.9874 and std is +- 0.0039\n"
     ]
    }
   ],
   "source": [
    "n_splits = 5\n",
    "\n",
    "    \n",
    "kfold = KFold(n_splits=n_splits, shuffle=True, random_state=1)\n",
    "scores = []\n",
    "\n",
    "for C in tqdm([0.01, 0.1, 1, 10]):\n",
    "\n",
    "    for train_idx, val_idx in kfold.split(x_train_full):\n",
    "\n",
    "        df_train = x_train_full.iloc[train_idx]\n",
    "        df_val = x_train_full.iloc[val_idx]\n",
    "\n",
    "        df_train_OH, df_val_OH = dvectorizer(df_train, df_val)\n",
    "\n",
    "        y_train = y_train_full.iloc[train_idx]\n",
    "        y_val = y_train_full.iloc[val_idx]\n",
    "\n",
    "        y_train.reset_index(drop = True, inplace = True)\n",
    "        y_val.reset_index(drop = True, inplace = True)\n",
    "\n",
    "\n",
    "        model = LogisticRegression(solver=\"liblinear\", C=C, max_iter=1000, random_state=42)\n",
    "        model = model.fit(df_train_OH, y_train)\n",
    "\n",
    "        y_pred =  model.predict(df_val_OH)\n",
    "\n",
    "        auc = roc_auc_score(y_val, y_pred)\n",
    "        scores.append(auc)\n",
    "\n",
    "    print('With C=%.2f, mean of AUC-ROC over 5-fold validation is %.4f and std is +- %.4f' % (C, np.mean(scores), np.std(scores)))\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60381896",
   "metadata": {},
   "source": [
    "Best results are at C= 1.00 with highest mean AUC-ROC of 0.9878\n",
    "\n",
    "From the docs: \n",
    "\n",
    "C denotes inverse of regularization strength; must be a positive float. Like in support vector machines, smaller values specify stronger regularization."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bfbb8d37",
   "metadata": {},
   "source": [
    "## Submit the results\n",
    "\n",
    "* Submit your results here: https://forms.gle/8TfKNRd5Jq7sGK5M9\n",
    "* You can submit your solution multiple times. In this case, only the last submission will be used \n",
    "* If your answer doesn't match options exactly, select the closest one"
   ]
  }
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