notebooks/02-ml.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Probabilidad de Default\n",
    "- La probabilidad de que una persona no termine pagando su prestamo es la probabilidad de Default\n",
    "- Los valores que toma ```loan_status```\n",
    "    - 0 si el cliente pago su prestamo\n",
    "    - 1 si el cliente no pagó su prestamo\n",
    "    \n",
    "Los algoritmos de clasificación que se probaran para este dataset serán \n",
    "- Regresion Logisticas\n",
    "- Arbol de Decicion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Regresion Logistica\n",
    "Para la regresion logistica tomamos todos los valores como un vector $X$, los multiplicamos por una serie de pesos $W$ y les aplicamos una funcion sigmoide\n",
    "$$ f(X) = Y = X * W$$\n",
    "$$ g(X) = \\frac{1}{1+ e^{-Y}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import roc_curve, \\\n",
    "                            classification_report, \\\n",
    "                            precision_recall_fscore_support, \\\n",
    "                            roc_auc_score, \\\n",
    "                            confusion_matrix\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "cr_loan_clean = pd.read_csv(\"data/cr_loan_nout_nmiss.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>person_age</th>\n",
       "      <th>person_income</th>\n",
       "      <th>person_home_ownership</th>\n",
       "      <th>person_emp_length</th>\n",
       "      <th>loan_intent</th>\n",
       "      <th>loan_grade</th>\n",
       "      <th>loan_amnt</th>\n",
       "      <th>loan_int_rate</th>\n",
       "      <th>loan_status</th>\n",
       "      <th>loan_percent_income</th>\n",
       "      <th>cb_person_default_on_file</th>\n",
       "      <th>cb_person_cred_hist_length</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>21</td>\n",
       "      <td>9600</td>\n",
       "      <td>OWN</td>\n",
       "      <td>5</td>\n",
       "      <td>EDUCATION</td>\n",
       "      <td>B</td>\n",
       "      <td>1000</td>\n",
       "      <td>11.14</td>\n",
       "      <td>0</td>\n",
       "      <td>0.10</td>\n",
       "      <td>N</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>25</td>\n",
       "      <td>9600</td>\n",
       "      <td>MORTGAGE</td>\n",
       "      <td>1</td>\n",
       "      <td>MEDICAL</td>\n",
       "      <td>C</td>\n",
       "      <td>5500</td>\n",
       "      <td>12.87</td>\n",
       "      <td>1</td>\n",
       "      <td>0.57</td>\n",
       "      <td>N</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>23</td>\n",
       "      <td>65500</td>\n",
       "      <td>RENT</td>\n",
       "      <td>4</td>\n",
       "      <td>MEDICAL</td>\n",
       "      <td>C</td>\n",
       "      <td>35000</td>\n",
       "      <td>15.23</td>\n",
       "      <td>1</td>\n",
       "      <td>0.53</td>\n",
       "      <td>N</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>24</td>\n",
       "      <td>54400</td>\n",
       "      <td>RENT</td>\n",
       "      <td>8</td>\n",
       "      <td>MEDICAL</td>\n",
       "      <td>C</td>\n",
       "      <td>35000</td>\n",
       "      <td>14.27</td>\n",
       "      <td>1</td>\n",
       "      <td>0.55</td>\n",
       "      <td>Y</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>21</td>\n",
       "      <td>9900</td>\n",
       "      <td>OWN</td>\n",
       "      <td>2</td>\n",
       "      <td>VENTURE</td>\n",
       "      <td>A</td>\n",
       "      <td>2500</td>\n",
       "      <td>7.14</td>\n",
       "      <td>1</td>\n",
       "      <td>0.25</td>\n",
       "      <td>N</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   person_age  person_income person_home_ownership  person_emp_length  \\\n",
       "0          21           9600                   OWN                  5   \n",
       "1          25           9600              MORTGAGE                  1   \n",
       "2          23          65500                  RENT                  4   \n",
       "3          24          54400                  RENT                  8   \n",
       "4          21           9900                   OWN                  2   \n",
       "\n",
       "  loan_intent loan_grade  loan_amnt  loan_int_rate  loan_status  \\\n",
       "0   EDUCATION          B       1000          11.14            0   \n",
       "1     MEDICAL          C       5500          12.87            1   \n",
       "2     MEDICAL          C      35000          15.23            1   \n",
       "3     MEDICAL          C      35000          14.27            1   \n",
       "4     VENTURE          A       2500           7.14            1   \n",
       "\n",
       "   loan_percent_income cb_person_default_on_file  cb_person_cred_hist_length  \n",
       "0                 0.10                         N                           2  \n",
       "1                 0.57                         N                           3  \n",
       "2                 0.53                         N                           2  \n",
       "3                 0.55                         Y                           4  \n",
       "4                 0.25                         N                           2  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Utilizando solamente el interes del prestamo como parametro\n",
    "cr_loan_clean.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# LogisticRegression??"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# clf_logistic_single.intercept_??"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'C': 1.0, 'class_weight': None, 'dual': False, 'fit_intercept': True, 'intercept_scaling': 1, 'l1_ratio': None, 'max_iter': 100, 'multi_class': 'warn', 'n_jobs': None, 'penalty': 'l2', 'random_state': None, 'solver': 'lbfgs', 'tol': 0.0001, 'verbose': 0, 'warm_start': False}\n",
      "[-4.45785901]\n"
     ]
    }
   ],
   "source": [
    "# Separar los features de la variable a predecir\n",
    "X = cr_loan_clean[['loan_int_rate']]\n",
    "y = cr_loan_clean[['loan_status']]\n",
    "\n",
    "# Entrenar el modelo\n",
    "clf_logistic_single = LogisticRegression(solver='lbfgs')\n",
    "clf_logistic_single.fit(X, np.ravel(y))\n",
    "\n",
    "# Parametros del modelo\n",
    "print(clf_logistic_single.get_params())\n",
    "\n",
    "print(clf_logistic_single.intercept_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-4.21645549]\n"
     ]
    }
   ],
   "source": [
    "# Regresion logisitica con multiples features\n",
    "X_multi = cr_loan_clean[['loan_int_rate','person_emp_length']]\n",
    "\n",
    "# Variable a predecir\n",
    "y = cr_loan_clean[['loan_status']]\n",
    "\n",
    "# Creacion y entrenamiento de la regresion logistica\n",
    "clf_logistic_multi = LogisticRegression(solver='lbfgs').fit(X_multi, np.ravel(y))\n",
    "\n",
    "# Intercept\n",
    "print(clf_logistic_multi.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El valor de intercept_ se hacerca a cero. Esto significa que las probabilidades de un registro con un valor no predeterminado se acercan a cero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.28517496e-09 -2.27622202e-09 -2.17211991e-05]]\n"
     ]
    }
   ],
   "source": [
    "# Se crean los datasets\n",
    "X = cr_loan_clean[['loan_int_rate','person_emp_length','person_income']]\n",
    "y = cr_loan_clean[['loan_status']]\n",
    "\n",
    "# Se divide el dataset en conjuntos de entrenamiento y testing\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.4, random_state=123)\n",
    "\n",
    "# Creacion y entrenamiento del modelo de regresion\n",
    "clf_logistic = LogisticRegression(solver='lbfgs').fit(X_train, np.ravel(y_train))\n",
    "\n",
    "# Impresion de los coeficientes de los modelos\n",
    "print(clf_logistic.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Los coeficientes indican si la correlacion es positiva o negativa con respecto a la variable que buscamos predecir"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Manejo de Variables Categóricas\n",
    "Para manejar las variables categoricas utilizamos lo que se llama ```one hot encoding```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creacion de dos datasets, uno con features numericos \n",
    "# y otro con features categoricos\n",
    "cred_num = cr_loan_clean.select_dtypes(exclude=['object'])\n",
    "cred_str = cr_loan_clean.select_dtypes(include=['object'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>person_home_ownership</th>\n",
       "      <th>loan_intent</th>\n",
       "      <th>loan_grade</th>\n",
       "      <th>cb_person_default_on_file</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>OWN</td>\n",
       "      <td>EDUCATION</td>\n",
       "      <td>B</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>MORTGAGE</td>\n",
       "      <td>MEDICAL</td>\n",
       "      <td>C</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>RENT</td>\n",
       "      <td>MEDICAL</td>\n",
       "      <td>C</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>RENT</td>\n",
       "      <td>MEDICAL</td>\n",
       "      <td>C</td>\n",
       "      <td>Y</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>OWN</td>\n",
       "      <td>VENTURE</td>\n",
       "      <td>A</td>\n",
       "      <td>N</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  person_home_ownership loan_intent loan_grade cb_person_default_on_file\n",
       "0                   OWN   EDUCATION          B                         N\n",
       "1              MORTGAGE     MEDICAL          C                         N\n",
       "2                  RENT     MEDICAL          C                         N\n",
       "3                  RENT     MEDICAL          C                         Y\n",
       "4                   OWN     VENTURE          A                         N"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cred_str.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# One-hot encode de las columnas no numericas\n",
    "cred_str_onehot = pd.get_dummies(cred_str)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>person_home_ownership_MORTGAGE</th>\n",
       "      <th>person_home_ownership_OTHER</th>\n",
       "      <th>person_home_ownership_OWN</th>\n",
       "      <th>person_home_ownership_RENT</th>\n",
       "      <th>loan_intent_DEBTCONSOLIDATION</th>\n",
       "      <th>loan_intent_EDUCATION</th>\n",
       "      <th>loan_intent_HOMEIMPROVEMENT</th>\n",
       "      <th>loan_intent_MEDICAL</th>\n",
       "      <th>loan_intent_PERSONAL</th>\n",
       "      <th>loan_intent_VENTURE</th>\n",
       "      <th>loan_grade_A</th>\n",
       "      <th>loan_grade_B</th>\n",
       "      <th>loan_grade_C</th>\n",
       "      <th>loan_grade_D</th>\n",
       "      <th>loan_grade_E</th>\n",
       "      <th>loan_grade_F</th>\n",
       "      <th>loan_grade_G</th>\n",
       "      <th>cb_person_default_on_file_N</th>\n",
       "      <th>cb_person_default_on_file_Y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1</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>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</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>1</td>\n",
       "      <td>1</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>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   person_home_ownership_MORTGAGE  person_home_ownership_OTHER  \\\n",
       "0                               0                            0   \n",
       "1                               1                            0   \n",
       "2                               0                            0   \n",
       "3                               0                            0   \n",
       "4                               0                            0   \n",
       "\n",
       "   person_home_ownership_OWN  person_home_ownership_RENT  \\\n",
       "0                          1                           0   \n",
       "1                          0                           0   \n",
       "2                          0                           1   \n",
       "3                          0                           1   \n",
       "4                          1                           0   \n",
       "\n",
       "   loan_intent_DEBTCONSOLIDATION  loan_intent_EDUCATION  \\\n",
       "0                              0                      1   \n",
       "1                              0                      0   \n",
       "2                              0                      0   \n",
       "3                              0                      0   \n",
       "4                              0                      0   \n",
       "\n",
       "   loan_intent_HOMEIMPROVEMENT  loan_intent_MEDICAL  loan_intent_PERSONAL  \\\n",
       "0                            0                    0                     0   \n",
       "1                            0                    1                     0   \n",
       "2                            0                    1                     0   \n",
       "3                            0                    1                     0   \n",
       "4                            0                    0                     0   \n",
       "\n",
       "   loan_intent_VENTURE  loan_grade_A  loan_grade_B  loan_grade_C  \\\n",
       "0                    0             0             1             0   \n",
       "1                    0             0             0             1   \n",
       "2                    0             0             0             1   \n",
       "3                    0             0             0             1   \n",
       "4                    1             1             0             0   \n",
       "\n",
       "   loan_grade_D  loan_grade_E  loan_grade_F  loan_grade_G  \\\n",
       "0             0             0             0             0   \n",
       "1             0             0             0             0   \n",
       "2             0             0             0             0   \n",
       "3             0             0             0             0   \n",
       "4             0             0             0             0   \n",
       "\n",
       "   cb_person_default_on_file_N  cb_person_default_on_file_Y  \n",
       "0                            1                            0  \n",
       "1                            1                            0  \n",
       "2                            1                            0  \n",
       "3                            0                            1  \n",
       "4                            1                            0  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cred_str_onehot.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['person_age', 'person_income', 'person_emp_length', 'loan_amnt',\n",
      "       'loan_int_rate', 'loan_status', 'loan_percent_income',\n",
      "       'cb_person_cred_hist_length', 'person_home_ownership_MORTGAGE',\n",
      "       'person_home_ownership_OTHER', 'person_home_ownership_OWN',\n",
      "       'person_home_ownership_RENT', 'loan_intent_DEBTCONSOLIDATION',\n",
      "       'loan_intent_EDUCATION', 'loan_intent_HOMEIMPROVEMENT',\n",
      "       'loan_intent_MEDICAL', 'loan_intent_PERSONAL', 'loan_intent_VENTURE',\n",
      "       'loan_grade_A', 'loan_grade_B', 'loan_grade_C', 'loan_grade_D',\n",
      "       'loan_grade_E', 'loan_grade_F', 'loan_grade_G',\n",
      "       'cb_person_default_on_file_N', 'cb_person_default_on_file_Y'],\n",
      "      dtype='object') 27\n"
     ]
    }
   ],
   "source": [
    "# Union entre el dataset con el one-hot-encoding y el dataset con features numericos\n",
    "cr_loan_prep = pd.concat([cred_num, cred_str_onehot], axis=1)\n",
    "print(cr_loan_prep.columns, len(cr_loan_prep.columns))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Separacion de los features y la variable a predecir\n",
    "columns = list(cr_loan_prep.columns)\n",
    "X_columns = [column for column in columns if column != 'loan_status']\n",
    "X = cr_loan_prep[X_columns]\n",
    "y = cr_loan_prep[['loan_status']]\n",
    "\n",
    "# Creacion del dataset de entrenamiento y de testing\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=.4, random_state=123)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>loan_status</th>\n",
       "      <th>prob_default</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.445779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.223447</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0.288558</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0.169358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>0.114182</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   loan_status  prob_default\n",
       "0            1      0.445779\n",
       "1            1      0.223447\n",
       "2            0      0.288558\n",
       "3            0      0.169358\n",
       "4            1      0.114182"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Train the logistic regression model on the training data\n",
    "clf_logistic = LogisticRegression(solver='lbfgs').fit(X_train, np.ravel(y_train))\n",
    "\n",
    "# Create predictions of probability for loan status using test data\n",
    "pred = clf_logistic.predict_proba(X_test)\n",
    "\n",
    "# Create dataframes of first five predictions, and first five true labels\n",
    "preds_df = pd.DataFrame(pred[:,1][0:5], columns = ['prob_default'])\n",
    "true_df = y_test.head()\n",
    "\n",
    "# Concatenate and print the two data frames for comparison\n",
    "# print(pd.concat([true_df.reset_index(drop = True), preds_df], axis = 1))\n",
    "comparison = pd.concat([true_df.reset_index(drop = True), preds_df], axis = 1)\n",
    "comparison.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Medir el performance de la Regresion Logistica\n",
    "Una buena manera de medir el ```performance``` del modelo es usando ```accuracy``` que concieste en:\n",
    "\n",
    "$$accuracy = \\frac{Numero\\,de\\,predicciones\\,correctas}{Numero\\,de\\,predicciones}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8025288526816021"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf_logistic.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "prob_default = pd.DataFrame(pred[:,1], columns=['prod_default'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Otra manera de evaluar el performance de un modelo es utilizando una ```Curva ROV```\n",
    "\n",
    "```specificity``` o ```fallout``` es el ```false positive rate```, mientras que ```sensitivity``` es el ```true positive rate```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1045a7320>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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38OYPu2gb2YK3ruvHkPQ4s8sSDZBAF82jcENtmMd2gStXSK9xLzX17ZUszT3M/w1sxz1jMwkPltjwVPKbEa7lsMG2ufDpZcb6xI8hbYK5NYkmKy6rJjjQaKZ156gM7hwFfdtLDxZPJ4EuXGP/Stj4Nvz8XO22gX+WMPdCX6zfx4Mfb+Di3on8cVxnCXIvIoEuzk7et/C/kSdvS7sIzvknRKebU5M4IwePVfDnjzfw+fr9ZLVpyYXd5XsObyOBLs5M2SFYOBVyP6rdNmUtxHc3ryZxxr7dcpA7Z6+hvNrOPed1Yuo5HaWZlheSQBdNozXs+wlm1enTcelCaDfKvJrEWUuKakGXti15ZGJX0lqFm12OOEMS6KJxtkrY8CYc3gA//7t2e7sxcPF88JO+Hd7G4dC8vWw3m/aV8Pgl3UlPiODdGweYXZY4SxLo4tTsVbD6WVh878nbw1rDlBwIlYl9vdH2Q8e5b04OK3cXcU5GvDTTshAJdNGww5vgzaza9ZBYuGEHBLc0ryZxVqrtDmYs3sGzX2+jRaA/T/ymB5f0TpRmWhYigS5Oph2w/B/w/f3GeqfJMG4m+MvM7N6uuLyaGYt3MKpzKx6e0IVWEdJMy2ok0IVxa2XHp7D3e9j4DpQfMrYPeAgG/8Xc2sRZqai287+Ve7iyfzviwoP54s6htImUJ3atSgLdl2kHfHUz5Myo3RYSA52vglEvQZCMdvBmK3Yd4b45OewoLKVDXDhD0uMkzC1OAt1XlR+GNzKhvNBY73QZDPkbRHU0ty5x1o5X2vjnF5uZ+eNukqJb8Pb10kzLV0ig+6LDG+HNmrk5UycY98hl0mXLmDpzJT/uOMy1g9tz95hOhEkzLZ8hv2lfUrzTaJq1f4Wx3mkyXDDL3JqESxwtqyI4wJ8WQf78YUwGoOjTLtrssoSbSaD7guJdsP1j+PZOYz08CXpMgwEPmFqWcI356/bx0MfruaR3En8c35k+7aSZlq+SQLe61c/Bt3fUrp/3OnS91rx6hMscLKngwY/Xs2DDAbolRjKxZ6LZJQmTSaBblb0K5l0MOz4z1gc/Ct1vkqc7LeKbzQe4c/YaKm0Opo/L5IYhHQiQZlo+TwLdirZ9aIQ5GFO9XbsZgiLMrUm4VEpMKD2So/jLhC50jJfhpcIggW4FWsPWObD7S9g8G6qPG9t73QYjnpFJmC3A7tC89cMuNu8v4Z+X9iCtVQRvX9/f7LKEh5FA93Y75sOH59euR2dARDIMegQSB5lXl3CZbQeOcd8HOazOO8qITtJMS5yaBLq3KtwAb3WtXY/OgEmfQXSaeTUJl6qyOfjPou38+5tcwoL9eeaynkzs2VaaaYlTcirQlVJjgWcBf+BVrfXjDRwzHHgGCAQKtdbDXFinqKvsUG2Yx/eESxdAaCtzaxIuV1JRzWtLdzKmSwIPT+hCXHiw2SUJD9dooCul/IEXgNFAPrBCKTVPa72xzjFRwIvAWK11nlJK0qU52Kvg8ymw5T1jPftuGPYvc2sSLlVRbee9FXu4eoDRTGvBneeQ0FK6IgrnOHOF3g/I1VrvAFBKzQYmAhvrHHMFMFdrnQegtT7o6kJ92v4VsPg+2PNt7bZ+02Ho382rSbjcTzsOM33uOnYWlpLWKpzBaXES5qJJnAn0RGBPnfV8oP7X6xlAoFLqOyACeFZrPbP+GymlpgJTAVJSUs6kXt9iq4DXUuF4gbEeEm08rn/uCyD3US3jWEU1//hiM+8syyM5pgX/vaE/g9OkmZZoOmcCvaHk0A28Tx/gXKAF8KNSapnWeutJP6T1DGAGQHZ2dv33EHWtfwMWXFe7fsVP0KafefWIZjN15iqW7TzM9UM68IcxGYQGyVgFcWac+ZuTDyTXWU8CCho4plBrXQqUKqUWAz2ArYimObwR5l8NB1cb6wMehEEPy1hyizlSWkWLQKOZ1t3ndUIp6J0izbTE2XEmJVYA6UqpDkqpIGAyMK/eMR8DQ5VSAUqpUIxbMptcW6rFOezw/gijre2JMD/vdRj8iIS5hWitmbe2gFFPLeLpr4zrnT7toiXMhUs0eoWutbYppW4FFmAMW3xda71BKTWtZv/LWutNSqkvgBzAgTG0cX1zFm4p+UvgvXNq1y9bBEnnnPp44ZX2F1fwp4/W89WmA/RIiuTi3tJMS7iW0tqcW9nZ2dl65cqVpny2x9DaaGn783PGeq/bYfiT4Cf3UK3m601GM61qh4M/jO7EdUM64O8nX2yLplNKrdJaZze0T5LDTLMGw74fjdcT5kL6JHPrEc2mXWwYvdtF85cJXWgfF2Z2OcKiJNDNoDVsnlUb5rcfh0D5l9xK7A7NG0t3smnfMZ78bQ/SWoXz1nUySkk0Lwl0M3x1M+T8x3h91SoJc4vZeuAY987JYc2eo4zMbCXNtITbSKC7k3bAG52haCsk9IHLFkNgqNlVCRepsjl46bvtPP/tNiJCAnl2ck8m9JBmWsJ9JNDdpeBHmFXTzjY8CX7zjYS5xZRUVPPmDzsZ360ND12QRaw00xJuJoHe3KrLYP5VkPuhsd7nLhjyNwiQf9mtoLzKzqzlefzfoPa/NNNqJf1XhEkk0JtTSR680s54HZ0B579r3GoRlvDD9kKmf7COvCNldGodweC0OAlzYSoJ9OagNSx/HL6/31hv1cvoxeIfaG5dwiVKKqr5+/zNzFqeR7vYUGbdOICBqbFmlyWEBLrLVRTBzB5wbI8xMfPoV6DTb6U7ooVMnbmS5TuPcNM5HblzVAYtgmQEi/AMEuiuojX8+Aj8+HDttluLJcgt4vDxSkKDAmgR5M+9YzPxV4oeyVFmlyXESaTrkytsmwuvp9eG+fCn4PfVEuYWoLXm4zV7T2qm1TslWsJceCS5Qj9bT9YJ7dAEuHEXBMgXY1awr7icP324nq83H6RnchSX9kkyuyQhTksC/WzMGlL7+tZiCG5pXi3CpRZuPMDv31uD3aF58IIsrhnUXpppCY8ngX6mNr8HBUuN19P2S5hbTIe4MLLbR/PIhK6kxMoDYMI7yD30prJXwaJ74LPJxvr5syAswdyaxFmz2R3MWLydu95bA0Baq3DevLafhLnwKnKF3lSf/Ba2f2y8lpa3lrBpXwn3fZBDTn4xo7MSpJmW8FoS6M7QDph9DuxfDo5qaH8eTPoM/ORfem9WabPzwrfbefHbXKJCA3nhit6M79ZammkJryWB3hjtgDeyoGiLsZ59D2TfJWFuAccrbLyzbDcTerTlwQuyiA4LMrskIc6KBPrpvDsADq0FW4WxfkeFNNXycmVVNt79KY9rB3cgtqaZVnyE/E6FNUigN2Tfclh0N+z7yVgf/JjRJVHC3KstzS1k+twc9hwpJ6tNSwalxUmYC0uRQK9vzUvw9e+M18nD4YL3ITTe1JLE2Skur+Zvn23ivZV76BAXxntTB9C/ozTTEtYjgV5XSV5tmF+zEWI7m1uPcImb3l7Jil1FTBuWyp2j0mUEi7AsCfS65l1sLIc/JWHu5Q4dqyQs2J/QoADuG5tJgJ8f3ZIizS5LiGYlDxadsPIpOLDKeN37DnNrEWdMa83c1fmMfnoRTy80mmn1SomWMBc+Qa7QT1jxD2N52zFQ8t85b7T3aDkPfLiO77YcondKFJf1TTa7JCHcSgId4IOxUHYQkoZBULjZ1Ygz8OWG/fz+vTVo4OELs7h6oDTTEr5HAv2FGGOWIYBRL5lbi2gyrTVKKVJbhTOgYywPT+hCcoz0XxG+ybcDPWeGEeYh0XDzIXn604vY7A5eWbKTLftLeGZyL1Ljw3ntmr5mlyWEqXw30CtLYOFNxuur10qYe5GNBSXc+8Fa1u8t4bwu0kxLiBN8M9Dt1fBGJ+N195ugpXx55g0qqu08/00uLy/aTlRoEC9d2Ztx3dqYXZYQHsM3A33R3VC6H/yDYejfza5GOKm00sa7y/OY2DORBy/oTFSoNNMSoi6nxucppcYqpbYopXKVUtNPc1xfpZRdKXWp60p0MVsF/Pyc8fq2Y8b9c+GxSittzFi8HbtDExsezMLfn8OTv+0hYS5EAxq9QldK+QMvAKOBfGCFUmqe1npjA8f9A1jQHIW6zNe3GsvMy8E/0NxaxGkt3nqIP85dR0FxOV0TIxmUGkdsuDTTEuJUnLlC7wfkaq13aK2rgNnAxAaOuw34ADjowvpcb/1rxnL8O+bWIU7paFkVd/9vLVNeX05woB//u2kgg1LjzC5LCI/nzD30RGBPnfV8oH/dA5RSicAkYCRwyrFjSqmpwFSAlJSUptZ69opyjWV8d3ka1INNfXsVq3YXccuIVG4bKc20hHCWM4He0ON2ut76M8B9Wmv76abv0lrPAGYAZGdn13+P5rfsUWM5eobbP1qc3sFjFYQHBxAaFMD94zsT6K/o0lb6rwjRFM4Eej5Qd1xfElBQ75hsYHZNmMcB45VSNq31Ry6p0lV2fg4RydCmf+PHCrfQWjNnVT6PfbaJ3/RJ4k8XZNEzOcrssoTwSs4E+gogXSnVAdgLTAauqHuA1rrDiddKqTeBTz0uzMsKofwQDHjI7EpEjT1Hyrj/w3Us2VZI3/bRXN7fhNtwQlhIo4GutbYppW7FGL3iD7yutd6glJpWs//lZq7RNT6/yljGdTG3DgHAF+v3c9f7a1DAIxO7cFX/dvhJMy0hzopTDxZprecD8+ttazDItdbXnH1ZLqY17FoAYW2g02/NrsannWimlZEQzuC0OP58YRZJ0dJMSwhX8I2hHiufNJbtzzO3Dh9WbXfwwre53DF7DQAd48N5ZUq2hLkQLuQbgb75XWN57vPm1uGj1u8tZuLzS/nXgi3YtabSZje7JCEsyfq9XBx2OPgzdJoMgWFmV+NTKqrtPPv1NmYs3kFMWBD/uboP53VpbXZZQliW9QM97ytjGS5d+dytrMrO+yv2cEnvRB4Yn0VkqLRaEKI5WT/QVz1jLHvdZm4dPuJ4pY13lu3mxqEdiQkLYuFdw4gJk0ZaQriD9QP9aC6EtYbIDo0fK87Kd1sO8sCH6ykoLqdHUhQDU2MlzIVwI2sHusNmBHrqBLMrsbSi0ioe/Wwjc1fvJa1VOHOmDaJPO2lLLIS7WTvQD/5sLMMTza3D4m56ZxWrdxdx+8g0bhmZRnCANNMSwgzWDvR1rxrL3neaW4cFHSypICw4gLDgAB4Y35lAfz+y2rY0uywhfJq1x6FvmwvKH2IyzK7EMrTWvL9iD+c+tYinFm4FoEdylIS5EB7A2lfo5YVyu8WF8g4bzbS+zy2kX4cYrpRmWkJ4FOsGet43xrLdKHPrsIgv1u/j9++txd9P8dhFXbmiX4o00xLCw1g30Hd+bix73W5uHV7uRDOtTq1bMiwjnocuzKJtVAuzyxJCNMC699DXvw4BodCql9mVeKUqm4N/f72N22evQWtNh7gwXr66j4S5EB7MuoFecQTCEuA0U+KJhuXkH2XC89/zZM2XnlV2h8kVCSGcYc1bLtXlxrLdaHPr8DIV1XaeXriVV5bsID4imFemZDM6K8HssoQQTrJmoBdtMZYxnc2tw8uUVdmZsyqfy/omM31cZyJbSDMtIbyJNQO9cJ2xjJXp5hpzrKKat5ft5qZzUokJC+Kru4YRLf1XhPBK1gz0soPGUh4oOq1vNh/ggQ/Xc6Ckgl7J0QxMjZUwF8KLWTPQj+81li3izK3DQx0+Xskjn27k4zUFZCSE8+KVg+iVIs20hPB2Fg30AmMpMxQ16OZ3VvPzniLuHJXO74anERRg3cFOQvgSiwb6XohON7sKj7K/uIKIEKOZ1oMXZBEU4Een1hFmlyWEcCFrXpoV74T4HmZX4RG01sxansfoOs20uiVFSpgLYUHWvEIv3Q8R0jhq9+FSpn+wjh93HGZgx1imDGxndklCiGZkvUCvLgdth+Aosysx1fx1+7jr/TUE+vnx94u7MblvMkqemhXC0qwX6KU1X4iiTS3DLCeaaXVu05KRma148IIs2kRK/xUhfIH17qHnfWsso3zrS9Eqm4NnvtrKrbN+/qWZ1otX9pEwF8KHWC/Qd3xiLFNGmFuHG63Zc5QL//09z3y1jQA/Jc20hPBR1rvlcmyPsQy1flOp8io7Ty3cwmvf76RVRAiv/V8253a2/kRsjnIAAAusSURBVHkLIRpmvUA/shmi0nyibW5FtZ0Pfy7g8n4pTB+XSUSINNMSwpc5dctFKTVWKbVFKZWrlJrewP4rlVI5NX9+UEqZNwjcVm7pLoslFdU8/802bHYH0WFBfH3XMP46qZuEuRCi8St0pZQ/8AIwGsgHViil5mmtN9Y5bCcwTGtdpJQaB8wA+jdHwadVut9YxmS6/aPd4auNB3jgo3UcOlZJn3YxDEyNJTJUglwIYXDmlks/IFdrvQNAKTUbmAj8Euha6x/qHL8MSHJlkU4ryTOW0dbqsnj4eCUPf7KRT9YWkNk6glemZNM9ybfH2Qshfs2ZQE8E9tRZz+f0V9/XA583tEMpNRWYCpCS0gxPcu74zFha7Ar9RDOtu0ZnMG1YqjTTEkI0yJlAb+jbxQaf2lFKjcAI9CEN7ddaz8C4HUN2drbrn/w5tttYtu7r8rd2t33F5bQMCSQsOICHLjSaaWUkSP8VIcSpOXOplw8k11lPAgrqH6SU6g68CkzUWh92TXlNtHUOJPSBgGBTPt4VHA7Nf3/azeinFvPkl0Yzra6JkRLmQohGOXOFvgJIV0p1APYCk4Er6h6glEoB5gJXa623urxKZ1QUQXWpV08MvbOwlOkf5PDTziMMTovlmkHtzS5JCOFFGg10rbVNKXUrsADwB17XWm9QSk2r2f8y8BAQC7xY0wDKprXObr6yG7DrS2MZ1satH+sqn+UYzbSCAvz45yXd+U12kjTTEkI0iVMPFmmt5wPz6217uc7rG4AbXFtaEx1cbSzTLza1jKY60UyrS9uWjM5K4MELskhoGWJ2WUIIL2Sd4RJHc41lhDkjJpuq0mbnqS+3cMu7q9Fa0z4ujOev6C1hLoQ4Y9YJdFsFKO84ndV5RVzw3Pc8900uIQH+0kxLCOES1unlcnS7x38hWlZl44kFW3njh520aRnCG9f2ZUSnVmaXJYSwCOsEetkBSGxw+LvHqKx28ElOAVcPaMe9YzMJD7bOP34hhPmskSj2aqg8Cv6eN/68uLyat37Yxe+GpxIdFsRXdw0jsoX0XxFCuJ41Av3AKmMZ3tbcOupZsGE/D360nsOlVfTvEEP/jrES5kKIZmONQN+/wlhmXm5uHTUOHavk4Xkb+GzdPjq3aclr/9eXbkmRZpclhLA4awR63tfGCJfIDmZXAsDv/ruKtXuKuXtMBjcNSyXQ3ztG3wghvJs1Ar1kJ/gFmDpL0d6j5US2CCQ8OIA/X9iF4AA/0qX/ihDCjaxx6VhRBC3NuTp3ODQzf9zFmKcW8VSdZloS5kIId/P+K3StjYmh241x+0dvP3Sc6R/ksGJXEUPT47h2cHu31yCEECd4f6CfmHYu3r3TmH6aU8Bd768lJMCPf13anUv7SDMtIYS5vD/Qcz8ylsnD3fJxJ5ppdUuMZGyX1vzpgs60ipD+K0II83n/PfTSfcayTfPOSV1RbedfCzZz8ztGM612sWE8d3kvCXMhhMfw/kA/ssVYhsQ020es2n2E859bwgvfbicsOECaaQkhPJL333LJ+9pYNsP969JKG/9asIW3ftxF28gWvHVdP4ZlxLv8c4QQwhW8P9ArDkNUarO8dbXdwfx1+5gyoB33SDMtIYSH8+6EKskzlimjXPaWR8uqeGPpLm4bmUZUaBBf/WEYLUOk/4oQwvN5d6DvXmgsXTTC5fN1+3jw4w0UlVUxKDWW/h1jJcyFEF7DuwP9RFOuswz0gyUVPPTxBr7YsJ8ubVvy1nV96dJWmmkJIbyLdwf60W3GMjThrN7mlndXsza/mPvGZnLj0A4ESDMtIYQX8u5AL9oGEclnNMIlv6iMqNAgwoMDeHhCF0IC/UmND2+GIoUQwj2891JUO4weLrFZTfoxh0Pz5tKdjHl6MU9+aYxh79I2UsJcCOH1vPcKvfSAsWxCoOceNJpprdxdxLCMeK4f4hn904UQwhW8N9DzFxvLuO5OHT5vbQF3v7+W0GB/nvptDyb1SpRmWkIIS/HeQN/+sbFsZISLw6Hx81P0SIpkfLfWPHB+FvERnjeZtBBCnC3vvIeuNez6EhL6QGT7Bg+pqLbz+OebmfbOql+aaT0zuZeEuRDCsrwz0Iu2Go/8dzi/wd3Ldx5h/LNLeHnRdqJDg6i2azcXKIQQ7uedt1xKdhnLVr1O2ny80sY/Pt/M28t2kxzTgneu78+Q9Dj31yeEECbwzkA/lGMsYzqdtNlmd/Dlxv1cN7gDd5+XQWiQd56eEEKcCe9MvBMtc6PSKCqt4o2lO7n93HSiQoP4+g/DpSuiEMInOXUPXSk1Vim1RSmVq5Sa3sB+pZR6rmZ/jlKqt+tLrWPXArR/EJ9tKGT004t48bvtrM47CiBhLoTwWY0GulLKH3gBGAdkAZcrpeo/zTMOSK/5MxV4ycV11tLGF5xr/Adxy7uraRPZgnm3DqFfh+absUgIIbyBM5ez/YBcrfUOAKXUbGAisLHOMROBmVprDSxTSkUppdporfe5vOJN/wVgSXEifxyXyfVDpJmWEEKAc4GeCOyps54P1J+RuaFjEoGTAl0pNRXjCp6UlJSm1mqISqWo41Vc2O8fdEhse2bvIYQQFuRMoDf0fHz9gd3OHIPWegYwAyA7O/vMBoe3HUj0pIFEn9EPCyGEdTlzryIfSK6zngQUnMExQgghmpEzgb4CSFdKdVBKBQGTgXn1jpkHTKkZ7TIAKG6W++dCCCFOqdFbLlprm1LqVmAB4A+8rrXeoJSaVrP/ZWA+MB7IBcqAa5uvZCGEEA1xatC21no+RmjX3fZyndcauMW1pQkhhGgKGe8nhBAWIYEuhBAWIYEuhBAWIYEuhBAWobQ2Z/IHpdQhYPcZ/ngcUOjCcryBnLNvkHP2DWdzzu201vEN7TAt0M+GUmql1jrb7DrcSc7ZN8g5+4bmOme55SKEEBYhgS6EEBbhrYE+w+wCTCDn7BvknH1Ds5yzV95DF0II8WveeoUuhBCiHgl0IYSwCI8OdI+bnNoNnDjnK2vONUcp9YNSqocZdbpSY+dc57i+Sim7UupSd9bXHJw5Z6XUcKXUGqXUBqXUInfX6GpO/N2OVEp9opRaW3POXt21VSn1ulLqoFJq/Sn2uz6/tNYe+QejVe92oCMQBKwFsuodMx74HGPGpAHAT2bX7YZzHgRE17we5wvnXOe4bzC6fl5qdt1u+D1HYczbm1Kz3srsut1wzvcD/6h5HQ8cAYLMrv0szvkcoDew/hT7XZ5fnnyF/svk1FrrKuDE5NR1/TI5tdZ6GRCllGrj7kJdqNFz1lr/oLUuqlldhjE7lDdz5vcMcBvwAXDQncU1E2fO+QpgrtY6D0Br7e3n7cw5ayBCKaWAcIxAt7m3TNfRWi/GOIdTcXl+eXKgn2ri6aYe402aej7XY/wX3ps1es5KqURgEvAy1uDM7zkDiFZKfaeUWqWUmuK26pqHM+f8PNAZY/rKdcAdWmuHe8ozhcvzy6kJLkzissmpvYjT56OUGoER6EOataLm58w5PwPcp7W2GxdvXs+Zcw4A+gDnAi2AH5VSy7TWW5u7uGbizDmfB6wBRgKpwEKl1BKtdUlzF2cSl+eXJwe6L05O7dT5KKW6A68C47TWh91UW3Nx5pyzgdk1YR4HjFdK2bTWH7mnRJdz9u92oda6FChVSi0GegDeGujOnPO1wOPauMGcq5TaCWQCy91Totu5PL88+ZaLL05O3eg5K6VSgLnA1V58tVZXo+este6gtW6vtW4PzAF+58VhDs793f4YGKqUClBKhQL9gU1urtOVnDnnPIz/I0EplQB0Ana4tUr3cnl+eewVuvbByamdPOeHgFjgxZorVpv24k51Tp6zpThzzlrrTUqpL4AcwAG8qrVucPibN3Dy9/wo8KZSah3G7Yj7tNZe21ZXKTULGA7EKaXygT8DgdB8+SWP/gshhEV48i0XIYQQTSCBLoQQFiGBLoQQFiGBLoQQFiGBLoQQFiGBLoQQFiGBLoQQFvH/jXpaHpAhG3EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "specificity, sensitivity, threshold = roc_curve(y_test, prob_default)\n",
    "plt.plot([0, 1], [0, 1], linestyle='--')\n",
    "plt.plot(specificity, sensitivity, color='darkorange')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.7643248801355148\n"
     ]
    }
   ],
   "source": [
    "auc = roc_auc_score(y_test, prob_default)\n",
    "print(auc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como el modelo en lugar de retornar 1s y 0s retorna una probabilidad al clasificar los registros, podemos definir un umbral o ```threshold``` de acuerdo a lo que creamos que debemos considerar como un ```Default``` o no. Para esto definamos ahora la siguiente condicion en base a las probabilidades que obtenemos\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "Probabilidad\\>de\\>Default =\n",
    "\\begin{cases}\n",
    "probabilidad\\>predicha <= 0.5, & 0\\>\\>(No\\>Default) \\\\\n",
    "probabilidad\\>predicha > 0.5, & 1\\>\\>(Default)\n",
    "\\end{cases}\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>prob_default</th>\n",
       "      <th>loan_status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.445779</td>\n",
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       "      <td>2</td>\n",
       "      <td>0.288558</td>\n",
       "      <td>0</td>\n",
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       "      <td>3</td>\n",
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       "      <td>0</td>\n",
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       "      <td>4</td>\n",
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      ],
      "text/plain": [
       "   prob_default  loan_status\n",
       "0      0.445779            0\n",
       "1      0.223447            0\n",
       "2      0.288558            0\n",
       "3      0.169358            0\n",
       "4      0.114182            0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = clf_logistic.predict_proba(X_test)\n",
    "preds_df = pd.DataFrame(preds[:,1], columns=['prob_default'])\n",
    "# preds_df.head()\n",
    "preds_df['loan_status'] = preds_df['prob_default'].apply(lambda x: 1 if x > 0.5 else 0)\n",
    "preds_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pred_status = pd.DataFrame(preds_df['loan_status'])\n",
    "# specificity, sensitivity, threshold = roc_curve(y_test, pred_status)\n",
    "# plt.plot(specificity, sensitivity, color='darkorange')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      " Non-Default       0.81      0.98      0.89      9198\n",
      "     Default       0.71      0.17      0.27      2586\n",
      "\n",
      "    accuracy                           0.80     11784\n",
      "   macro avg       0.76      0.57      0.58     11784\n",
      "weighted avg       0.79      0.80      0.75     11784\n",
      "\n"
     ]
    }
   ],
   "source": [
    "target_names = ['Non-Default', 'Default']\n",
    "print(classification_report(y_test, preds_df['loan_status'], target_names=target_names))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(array([0.80742729, 0.71264368]), array([0.98097412, 0.16782676]), array([0.8857802 , 0.27167449]), array([9198, 2586]))\n"
     ]
    }
   ],
   "source": [
    "print(precision_recall_fscore_support(y_test,preds_df['loan_status']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matriz de Confusion\n",
    "En el caso de predecir ```Non Defaults``` y ```Defaults de prestamos```, la matriz de confusión se distribuye de la siguiente manera\n",
    "<img src=\"images/confusion-matrix.png\" class=\"center\" alt=\"Matriz de Confusion\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[9023  175]\n",
      " [2152  434]]\n"
     ]
    }
   ],
   "source": [
    "# confusion_matrix??\n",
    "preds_df['loan_status'] = preds_df['prob_default'].apply(lambda x: 1 if x > 0.5 else 0)\n",
    "\n",
    "# confusion matrix\n",
    "print(confusion_matrix(y_test,preds_df['loan_status']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>prob_default</th>\n",
       "      <th>loan_status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.445779</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>0.223447</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0.288558</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0.169358</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
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      ],
      "text/plain": [
       "   prob_default  loan_status\n",
       "0      0.445779            0\n",
       "1      0.223447            0\n",
       "2      0.288558            0\n",
       "3      0.169358            0\n",
       "4      0.114182            0"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0    9862\n",
      "1    1922\n",
      "Name: loan_status, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "preds_df['loan_status'] = preds_df['prob_default'].apply(lambda x: 1 if x > 0.4 else 0)\n",
    "print(preds_df['loan_status'].value_counts())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1922"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_defaults = preds_df['loan_status'].value_counts()[1]\n",
    "num_defaults"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.46403712296983757"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# recall obtenido de la matriz de reporte de clasificacion\n",
    "default_recall = precision_recall_fscore_support(y_test,preds_df['loan_status'])[1][1]\n",
    "default_recall"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9583.600936895346"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Obtenemos el monto promedio de los prestamos\n",
    "avg_loan_amnt = cr_loan_clean['loan_amnt'].mean()\n",
    "avg_loan_amnt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9872265.223119883\n"
     ]
    }
   ],
   "source": [
    "# Estimacion de la pérdida inesperada\n",
    "print(avg_loan_amnt * num_defaults * (1 - default_recall))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Segun este estimado, la perdida puede llegar a 9.87 millones de dolares\n",
    "\n",
    "Pero esto fue porque el recall para un threshold de 0.4 era más elevado. Pero cual es una buena manera de determinar este threshold?\n",
    "Definamos un arrays con diferentes ```thresholds```, los diferentes ```recalls``` y el ```accuracy``` con los diferentes thresholds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8025288526816021"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Pruebas para calcular accuracy\n",
    "preds_df_for_acc = pd.DataFrame(pred[:,1], columns = ['prob_default'])\n",
    "preds_df_for_acc = pd.concat([preds_df_for_acc, y_test.reset_index()], axis=1)\n",
    "preds_df_for_acc['predicted'] = preds_df['prob_default'].apply(lambda x: 1 if x > 0.5 else 0)\n",
    "preds_df_for_acc['correct_ones'] = np.where(preds_df_for_acc['predicted'] == preds_df_for_acc['loan_status'],\n",
    "                                           1, 0)\n",
    "preds_df_for_acc['correct_ones'].sum()/len(preds_df_for_acc['correct_ones'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lista de posibles Thresholds\n",
    "thresh = list()\n",
    "for i in range(66):\n",
    "    x = i/100\n",
    "    if (x >= 0.2):\n",
    "        thresh.append(x)\n",
    "\n",
    "ticks = list()\n",
    "for i in range(66):\n",
    "    x = i/100\n",
    "    if (i%5==0 and x >= 0.2):\n",
    "        ticks.append(x)        \n",
    "\n",
    "# Lista de los recalls para dichos thresholds\n",
    "default_recalls = list()\n",
    "for t in thresh:\n",
    "    r = precision_recall_fscore_support(y_test, \n",
    "                                        preds_df['prob_default'].apply(lambda x: 1 if x > t else 0))[1][1]\n",
    "    default_recalls.append(r)\n",
    "\n",
    "non_default_recalls = list()\n",
    "for t in thresh:\n",
    "    r = precision_recall_fscore_support(y_test, \n",
    "                                        preds_df['prob_default'].apply(lambda x: 1 if x > t else 0))[1][0]\n",
    "    non_default_recalls.append(r)\n",
    "    \n",
    "accuracy_scores = list()\n",
    "preds_df_for_acc = pd.DataFrame(pred[:,1], columns = ['prob_default'])\n",
    "preds_df_for_acc = pd.concat([preds_df_for_acc, y_test.reset_index()], axis=1)\n",
    "for t in thresh:\n",
    "    preds_df_for_acc['predicted'] = preds_df['prob_default'].apply(lambda x: 1 if x > t else 0)\n",
    "    preds_df_for_acc['correct_ones'] = np.where(preds_df_for_acc['predicted'] == preds_df_for_acc['loan_status'],\n",
    "                                                1, 0)\n",
    "    acc = preds_df_for_acc['correct_ones'].sum()/len(preds_df_for_acc['correct_ones'])\n",
    "    accuracy_scores.append(acc)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plt.plot(thresh,accuracy_scores)\n",
    "# plt.plot(default_recalls,accuracy_scores)\n",
    "# plt.plot(non_default_recalls,accuracy_scores)\n",
    "plt.plot(thresh, default_recalls)\n",
    "plt.plot(thresh, non_default_recalls)\n",
    "plt.plot(thresh, accuracy_scores)\n",
    "plt.xlabel(\"Probability Threshold\")\n",
    "plt.xticks(ticks)\n",
    "plt.legend([\"Default Recall\",\"Non-default Recall\",\"Model Accuracy\"])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En el grafico se puede ver que la interseccion o convergencia de ambas metricas se da cuando el threshold es igual a 0.275. Si miramos las metricas aplicamos ese threshold tendriamos algo parecido a lo siguiente\n",
    "\n",
    "Debemos recordar que lo que buscamos es predecir los ```defaults```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7012050237610319"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds_df_for_acc = pd.DataFrame(pred[:,1], columns = ['prob_default'])\n",
    "preds_df_for_acc = pd.concat([preds_df_for_acc, y_test.reset_index()], axis=1)\n",
    "preds_df_for_acc['predicted'] = preds_df['prob_default'].apply(lambda x: 1 if x > 0.275 else 0)\n",
    "preds_df_for_acc['correct_ones'] = np.where(preds_df_for_acc['predicted'] == preds_df_for_acc['loan_status'],\n",
    "                                           1, 0)\n",
    "preds_df_for_acc['correct_ones'].sum()/len(preds_df_for_acc['correct_ones'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      " Non-Default       0.89      0.71      0.79      9198\n",
      "     Default       0.39      0.68      0.50      2586\n",
      "\n",
      "    accuracy                           0.70     11784\n",
      "   macro avg       0.64      0.69      0.64     11784\n",
      "weighted avg       0.78      0.70      0.72     11784\n",
      "\n"
     ]
    }
   ],
   "source": [
    "preds_df['loan_status'] = preds_df['prob_default'].apply(lambda x: 1 if x > 0.275 else 0)\n",
    "print(classification_report(y_test, preds_df['loan_status'], target_names=target_names))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}