Gaussian.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gaussian model\n",
    "Gaussian Model is a model based on the Bayes Theorem, so it's a pure probabilistic model, let see more about this model and the models based on Bayes Theorem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LinearRegression, BayesianRidge, SGDRegressor\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.naive_bayes import GaussianNB, BernoulliNB, MultinomialNB\n",
    "from sklearn.metrics import f1_score, classification_report, confusion_matrix, mean_absolute_error, mean_squared_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_hair = pd.read_csv('C:/Users/alberto.rubiales/PycharmProjects/Pycharm/Bayes-model/Factor-Hair-Revised.csv', sep=';')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "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>Quality</th>\n",
       "      <th>Comunication</th>\n",
       "      <th>Hability</th>\n",
       "      <th>polite</th>\n",
       "      <th>Advertising</th>\n",
       "      <th>products</th>\n",
       "      <th>staff_image</th>\n",
       "      <th>price</th>\n",
       "      <th>Customer_care</th>\n",
       "      <th>order_billing</th>\n",
       "      <th>speed</th>\n",
       "      <th>Satisfaction</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8.5</td>\n",
       "      <td>3.9</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.9</td>\n",
       "      <td>4.8</td>\n",
       "      <td>4.9</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.8</td>\n",
       "      <td>4.7</td>\n",
       "      <td>5.0</td>\n",
       "      <td>3.7</td>\n",
       "      <td>8.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>8.2</td>\n",
       "      <td>2.7</td>\n",
       "      <td>5.1</td>\n",
       "      <td>7.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>7.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>5.3</td>\n",
       "      <td>5.5</td>\n",
       "      <td>3.9</td>\n",
       "      <td>4.9</td>\n",
       "      <td>5.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>9.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.6</td>\n",
       "      <td>5.6</td>\n",
       "      <td>5.4</td>\n",
       "      <td>7.4</td>\n",
       "      <td>5.8</td>\n",
       "      <td>4.5</td>\n",
       "      <td>6.2</td>\n",
       "      <td>5.4</td>\n",
       "      <td>4.5</td>\n",
       "      <td>8.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>6.4</td>\n",
       "      <td>3.3</td>\n",
       "      <td>7.0</td>\n",
       "      <td>3.7</td>\n",
       "      <td>4.7</td>\n",
       "      <td>4.7</td>\n",
       "      <td>4.5</td>\n",
       "      <td>8.8</td>\n",
       "      <td>7.0</td>\n",
       "      <td>4.3</td>\n",
       "      <td>3.0</td>\n",
       "      <td>4.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9.0</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.2</td>\n",
       "      <td>4.6</td>\n",
       "      <td>2.2</td>\n",
       "      <td>6.0</td>\n",
       "      <td>4.5</td>\n",
       "      <td>6.8</td>\n",
       "      <td>6.1</td>\n",
       "      <td>4.5</td>\n",
       "      <td>3.5</td>\n",
       "      <td>7.1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Quality  Comunication  Hability  polite  Advertising  products  \\\n",
       "0      8.5           3.9       2.5     5.9          4.8       4.9   \n",
       "1      8.2           2.7       5.1     7.2          3.4       7.9   \n",
       "2      9.2           3.4       5.6     5.6          5.4       7.4   \n",
       "3      6.4           3.3       7.0     3.7          4.7       4.7   \n",
       "4      9.0           3.4       5.2     4.6          2.2       6.0   \n",
       "\n",
       "   staff_image  price  Customer_care  order_billing  speed  Satisfaction  \n",
       "0          6.0    6.8            4.7            5.0    3.7           8.2  \n",
       "1          3.1    5.3            5.5            3.9    4.9           5.7  \n",
       "2          5.8    4.5            6.2            5.4    4.5           8.9  \n",
       "3          4.5    8.8            7.0            4.3    3.0           4.8  \n",
       "4          4.5    6.8            6.1            4.5    3.5           7.1  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_hair[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "train = df_hair.drop(columns=['Satisfaction'])\n",
    "test = df_hair['Satisfaction']\n",
    "X_train, X_test, y_train, y_test = train_test_split(train, test, test_size=0.20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min satisfaction: 4.7\n",
      "Max satisfaction: 9.9\n"
     ]
    }
   ],
   "source": [
    "print('Min satisfaction:', test.min())\n",
    "print('Max satisfaction:', test.max())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classification\n",
    "\n",
    "### Hyperparameters\n",
    "* priors: weights that we can pass to the algorithm in order to balance our dataset\n",
    "* var_smoothing: is to solve the \"Zero Probability Problem\" (when we have 0 rows of one class) here the algorithm use Laplace Transformation, this rule assume that the dataset is large enough that adding one row of each class will not make a difference in the estimated probability.\n",
    "\n",
    "First of all we need to create the classes, so we are going to create two classes of cliente, satisfy client and non satisfy client"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 8., 14.,  7., 17., 14., 17., 10.,  7.,  5.,  1.]),\n",
       " array([4.7 , 5.22, 5.74, 6.26, 6.78, 7.3 , 7.82, 8.34, 8.86, 9.38, 9.9 ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(df_hair['Satisfaction'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def satisfaction_classification(satisfaction):\n",
    "    if satisfaction <=7:\n",
    "        return 0 #user unsatisfy\n",
    "    else:\n",
    "        return 1 #user satisfy\n",
    "    \n",
    "df_hair['satisfaction_class'] = df_hair.apply(lambda x: satisfaction_classification(x['Satisfaction']), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_hair['satisfaction_class'].mean() #perfect we have a completly balanced dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_2 = df_hair.drop(columns=['Satisfaction', 'satisfaction_class'])\n",
    "test_2 = df_hair['satisfaction_class']\n",
    "X_train_2, X_test_2, y_train_2, y_test_2 = train_test_split(train_2, test_2, test_size=0.20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CLASSIFICATION IN TRAIN\n",
      "\n",
      "CONFUSION MATRIX:\n",
      " [[27  2]\n",
      " [11 40]]\n",
      "\n",
      "F1 SCORE:\n",
      " 0.8602150537634408\n",
      "\n",
      "CLASSIFICATION REPORT\n",
      "               precision    recall  f1-score   support\n",
      "\n",
      "           0       0.71      0.93      0.81        29\n",
      "           1       0.95      0.78      0.86        51\n",
      "\n",
      "    accuracy                           0.84        80\n",
      "   macro avg       0.83      0.86      0.83        80\n",
      "weighted avg       0.86      0.84      0.84        80\n",
      "\n"
     ]
    }
   ],
   "source": [
    "#instance\n",
    "nb = GaussianNB()\n",
    "\n",
    "#train\n",
    "nb.fit(X_train_2, y_train_2)\n",
    "\n",
    "#train preds\n",
    "preds_train = nb.predict(X_train_2)\n",
    "\n",
    "#metrics classifications in train\n",
    "print('CLASSIFICATION IN TRAIN')\n",
    "print()\n",
    "print('CONFUSION MATRIX:\\n', confusion_matrix(preds_train, y_train_2))\n",
    "print()\n",
    "print('F1 SCORE:\\n', f1_score(preds_train, y_train_2))\n",
    "print()\n",
    "print('CLASSIFICATION REPORT\\n',classification_report(preds_train, y_train_2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CLASSIFICATION IN TEST\n",
      "\n",
      "CONFUSION MATRIX:\n",
      " [[10  1]\n",
      " [ 2  7]]\n",
      "\n",
      "F1 SCORE:\n",
      " 0.823529411764706\n",
      "\n",
      "CLASSIFICATION REPORT\n",
      "               precision    recall  f1-score   support\n",
      "\n",
      "           0       0.83      0.91      0.87        11\n",
      "           1       0.88      0.78      0.82         9\n",
      "\n",
      "    accuracy                           0.85        20\n",
      "   macro avg       0.85      0.84      0.85        20\n",
      "weighted avg       0.85      0.85      0.85        20\n",
      "\n"
     ]
    }
   ],
   "source": [
    "#Classification in test\n",
    "preds_trest = nb.predict(X_test_2)\n",
    "\n",
    "#metrics classifications in train\n",
    "print('CLASSIFICATION IN TEST')\n",
    "print()\n",
    "print('CONFUSION MATRIX:\\n', confusion_matrix(preds_trest, y_test_2))\n",
    "print()\n",
    "print('F1 SCORE:\\n', f1_score(preds_trest, y_test_2))\n",
    "print()\n",
    "print('CLASSIFICATION REPORT\\n',classification_report(preds_trest, y_test_2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conclusion\n",
    "Most of the time bayes based models do not give good results, that's because they're based on pure probabilities. Which means that this models assume that the features are independent of each other, this is an assumption that in real life normally is not true, because in real life, features are almost always dependent on each other, whether we know them or not."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**There is not a bayes model for regresion**, this is obvious because, bayes theorem only works with probabilitys, but there is implementations of bayes in some models. I was thinking in put the example of a Bayesian Ridge model, but i am not going to do because is not a bayesian model. It's actually a linear model that during the calculation of the results infers probabilities of the Betas based on a normal distribution, but as i said it's a Linear model, so for the avoidance of confusion, we're going to stay here."
   ]
  }
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