Линейная модель и градиентный спуск.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "985989a6-a2fd-4902-90d1-488f0d66eef0",
   "metadata": {},
   "source": [
    "## Линейная модель\n",
    "\n",
    "Линейная модель - это математическая модель, используемая в машинном обучении для предсказания значений на основе линейной комбинации входных признаков. Она предполагает, что выходное значение (прогноз) можно выразить как взвешенную сумму входных признаков с добавлением смещения (bias). Математически это можно записать следующим образом:\n",
    "\n",
    "\n",
    "$\\hat{y} = w_1x_1 + w_2x_2 + \\ldots + w_nx_n + b$\n",
    "\n",
    "где:\n",
    "- $\\hat{y}$ - прогнозируемое значение,\n",
    "- $w_1, w_2, \\ldots, w_n$ - веса (параметры) модели для каждого признака,\n",
    "- $x_1, x_2, \\ldots, x_n$ - входные признаки,\n",
    "- $b$ - смещение (bias).\n",
    "\n",
    "### Вычисление выхода линейной модели\n",
    "\n",
    "Для вычисления выхода линейной модели, просто подставьте значения признаков в уравнение, используя соответствующие веса и смещение. Матричная формула для вычисления выхода линейной модели для набора данных \\(X\\) выглядит следующим образом:\n",
    "\n",
    "$\\hat{Y} = X \\cdot \\mathbf{w} + b$\n",
    "\n",
    "где:\n",
    "- $\\hat{Y}$ - вектор прогнозов для всего набора данных,\n",
    "- $X$ - матрица признаков, где каждая строка представляет один образец, а столбцы - признаки,\n",
    "- $\\mathbf{w}$ - вектор весов модели,\n",
    "- $b$ - смещение (bias).\n",
    "\n",
    "### Обучение линейной модели\n",
    "\n",
    "Обучение линейной модели заключается в настройке параметров (весов и смещения) так, чтобы они наилучшим образом соответствовали обучающим данным. Одним из наиболее распространенных методов обучения линейной модели является градиентный спуск.\n",
    "\n",
    "### Градиентный спуск\n",
    "\n",
    "Градиентный спуск - это метод оптимизации, используемый для обновления параметров модели с целью минимизации функции потерь. Функция потерь оценивает, насколько хорошо модель предсказывает реальные значения на обучающих данных.\n",
    "\n",
    "Для линейной регрессии, часто используется среднеквадратичная ошибка (Mean Squared Error - MSE) в качестве функции потерь:\n",
    "\n",
    "$MSE = \\frac{1}{N} \\sum_{i=1}^{N} (y_i - \\hat{y}_i)^2$\n",
    "\n",
    "где:\n",
    "- $N$ - количество обучающих примеров,\n",
    "- $y_i$ - реальное значение для i-го примера,\n",
    "- $\\hat{y}_i$ - прогнозированное значение для i-го примера.\n",
    "\n",
    "### Корректировка весов модели\n",
    "\n",
    "Для обновления весов модели в методе градиентного спуска, используется градиент функции потерь по отношению к параметрам модели. Градиент показывает направление наибольшего увеличения функции потерь, поэтому мы двигаемся в противоположном направлении градиента, чтобы уменьшить потери. Формула для обновления весов выглядит следующим образом:\n",
    "\n",
    "$\\mathbf{w}_{\\text{новые}} = \\mathbf{w}_{\\text{старые}} - \\text{learning_rate} \\cdot \\nabla L$\n",
    "\n",
    "где:\n",
    "- $\\mathbf{w}_{\\text{новые}}$ - новые веса после обновления,\n",
    "- $\\mathbf{w}_{\\text{старые}}$ - текущие веса,\n",
    "- $\\text{learning_rate}$ - скорость обучения (коэффициент, контролирующий размер шага градиентного спуска),\n",
    "- $\\nabla L$ - градиент функции потерь по параметрам модели.\n",
    "\n",
    "Этот процесс повторяется до достижения сходимости или определенного числа итераций.\n",
    "\n",
    "## Классификатор на линейной модели\n",
    "\n",
    "На линейной модели можно построить и классификатор. Для этого нужно выход линейной модели отбразить в интервал от 0 до 1. В этом нам поможет логистическая функция:\n",
    "\n",
    "$\\sigma(z) = \\frac{1}{1 + e^{-z}}$\n",
    "\n",
    "Для обучения скорректируем функцию потерь. Нетрудно показать, что функция, называемая кросс-энтропией на самом деле соответствует максимизации правдоподобия (кстати, почитайте про правдоподобие), ниже представлено выражение для нее\n",
    "\n",
    "$BCE = -\\frac{1}{N} \\sum_{i=1}^{N} \\left(y_i \\log(\\hat{y}_i) + (1 - y_i) \\log(1 - \\hat{y}_i)\\right)$\n",
    "\n",
    "где:\n",
    "- $N$ - количество обучающих примеров,\n",
    "- $y_i$ - истинная метка класса (0 или 1) для i-го примера,\n",
    "- $\\hat{y}_i$ - вероятность принадлежности к классу 1 для i-го примера (выход сигмоидной функции).\n",
    "\n",
    "Будем считать, что модель относит объект к 1 классу, если ее выход $>=0.5$, иначе - 0 класс.\n",
    "\n",
    "## Как считать градиенты\n",
    "\n",
    "Приведу градиент для кросс-энтропии:\n",
    "\n",
    "$\\nabla_{\\mathbf{w}} \\text{BCE} = -\\frac{1}{N} \\mathbf{X}^T (\\mathbf{y} - \\hat{\\mathbf{y}})$\n",
    "\n",
    "Для MSE вычислить градиент самостоятельно"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9a04ef46-22ed-49ba-a1d0-da06c40829b1",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "class LinearModel:\n",
    "    def __init__(self, num_features, bias = 0):\n",
    "        self.num_features = num_features\n",
    "        self.weights = np.zeros(num_features)\n",
    "        self.bias = bias\n",
    "\n",
    "    def __call__(self, X):\n",
    "        return np.dot(X, self.weights) + self.bias\n",
    "\n",
    "\n",
    "class LinearRegressor(LinearModel):\n",
    "    def fit(self, X, y, learning_rate=0.01, epochs=100):\n",
    "        error_history = []\n",
    "        for _ in range(epochs):\n",
    "            predictions = self(X)\n",
    "            error = y - predictions\n",
    "            gradient = -2 / len(X) * np.dot(X.T, error)\n",
    "            self.weights -= learning_rate * gradient\n",
    "            self.bias -= learning_rate * np.mean(error)\n",
    "            current_error = ((y - predictions) ** 2).sum()\n",
    "            error_history.append(current_error)\n",
    "        return error_history\n",
    "\n",
    "    def predict(self, X):\n",
    "        return self(X)\n",
    "\n",
    "\n",
    "class LinearClassifier(LinearModel):\n",
    "    def fit(self, X, y, learning_rate=0.01, epochs=100):\n",
    "        error_history = []\n",
    "        for _ in range(epochs):\n",
    "            predictions = self(X)\n",
    "            sigmoid = self.calc_sigmoid(predictions)\n",
    "            error = y - sigmoid\n",
    "            gradient = -np.dot(X.T, error) / len(X)\n",
    "            self.weights -= learning_rate * gradient\n",
    "            self.bias -= learning_rate * np.mean(error)\n",
    "            current_error = -np.mean(y * np.log(sigmoid) + (1 - y) * np.log(1 - sigmoid))\n",
    "            error_history.append(current_error)\n",
    "        return error_history\n",
    "\n",
    "    def predict(self, X):\n",
    "        predictions = self(X)\n",
    "        sigmoid = self.calc_sigmoid(predictions)\n",
    "        return np.round(sigmoid)\n",
    "\n",
    "    def predict_proba(self, X):\n",
    "        predictions = self(X)\n",
    "        sigmoid = self.calc_sigmoid(predictions)\n",
    "        return sigmoid\n",
    "    \n",
    "    def calc_sigmoid(self, predictions):\n",
    "        return 1 / (1 + np.exp(-predictions))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e0bb8fc-ec29-4cd7-a693-ac77b0a46cff",
   "metadata": {},
   "source": [
    "## Проверьте модели на данных\n",
    "\n",
    "### Линейная модель\n",
    "\n",
    "#### Description:\n",
    "The Student Performance Dataset is a dataset designed to examine the factors influencing academic student performance. The dataset consists of 10,000 student records, with each record containing information about various predictors and a performance index.\n",
    "\n",
    "#### Variables:\n",
    "- Hours Studied: The total number of hours spent studying by each student.\n",
    "- Previous Scores: The scores obtained by students in previous tests.\n",
    "- Extracurricular Activities: Whether the student participates in extracurricular activities (Yes or No).\n",
    "- Sleep Hours: The average number of hours of sleep the student had per day.\n",
    "- Sample Question Papers Practiced: The number of sample question papers the student practiced.\n",
    "\n",
    "#### Target Variable:\n",
    "\n",
    "- Performance Index: A measure of the overall performance of each student. The performance index represents the student's academic performance and has been rounded to the nearest integer. The index ranges from 10 to 100, with higher values indicating better performance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "47687e94-a2d2-4c25-8d48-54d13d621fb8",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "031d71d4-ceeb-4611-8a43-7012308a19e6",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Hours Studied  Previous Scores Extracurricular Activities  Sleep Hours  \\\n",
      "0              7               99                        Yes            9   \n",
      "1              4               82                         No            4   \n",
      "2              8               51                        Yes            7   \n",
      "3              5               52                        Yes            5   \n",
      "4              7               75                         No            8   \n",
      "\n",
      "   Sample Question Papers Practiced  Performance Index  \n",
      "0                                 1               91.0  \n",
      "1                                 2               65.0  \n",
      "2                                 2               45.0  \n",
      "3                                 2               36.0  \n",
      "4                                 5               66.0  \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_16735/3840284791.py:6: FutureWarning: Downcasting behavior in `replace` is deprecated and will be removed in a future version. To retain the old behavior, explicitly call `result.infer_objects(copy=False)`. To opt-in to the future behavior, set `pd.set_option('future.no_silent_downcasting', True)`\n",
      "  X['Extracurricular Activities'] = X['Extracurricular Activities'].replace({'Yes': 1, 'No': 0})\n"
     ]
    }
   ],
   "source": [
    "data = pd.read_csv('Student_Performance.csv')\n",
    "print(data.head())\n",
    "\n",
    "Y = data[\"Performance Index\"]\n",
    "X = data.drop(\"Performance Index\", axis=1)\n",
    "X['Extracurricular Activities'] = X['Extracurricular Activities'].replace({'Yes': 1, 'No': 0})\n",
    "X = X.to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c5a2ec08-17d8-4e11-9f20-b2ccd9a9f760",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Вычислите среднее по столбцам.\n",
    "mean = np.mean(X, axis=0)\n",
    "\n",
    "# Вычислите стандартное отклонение по столбцам.\n",
    "std = np.std(X, axis=0)\n",
    "\n",
    "# Нормализуйте данные по столбцам (стандартное масштабирование).\n",
    "normalized_X = (X - mean) / std\n",
    "\n",
    "# Нормализуйте и выходные данные\n",
    "normalized_Y = (Y - np.mean(Y, axis=0)) / np.std(Y, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e5c8fdd2-2f45-4765-900a-a0d949c8d96f",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "lr = LinearRegressor(num_features=X.shape[1])\n",
    "history = lr.fit(normalized_X, normalized_Y, epochs=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c5f2b9d0-6210-4107-8c47-1893ded1cdb1",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "epochs = range(1, len(history) + 1)\n",
    "\n",
    "# Постройте график обучения.\n",
    "plt.plot(epochs, history, 'b', label='MSE')\n",
    "plt.title('График обучения')\n",
    "plt.xlabel('Эпохи')\n",
    "plt.ylabel('MSE')\n",
    "plt.legend()\n",
    "\n",
    "# Отобразите график.\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e91f08e-3089-4464-9763-27fef0a1a74a",
   "metadata": {},
   "source": [
    "### Классификатор\n",
    "#### Context\n",
    "When a bank receives a loan application, based on the applicant’s profile the bank has to make a decision regarding whether to go ahead with the loan approval or not. Two types of risks are associated with the bank’s decision.\"\n",
    "\n",
    "\"If the applicant is a good credit risk, i.e. is likely to repay the loan, then not approving the loan to the person results in a loss of business to the bank\n",
    "If the applicant is a bad credit risk, i.e. is not likely to repay the loan, then approving the loan to the person results in a financial loss to the bank.\"\n",
    "\n",
    "The predictors that may potentially have any influence on Creditability:\n",
    "\n",
    "Account Balance: No account (1), None (No balance) (2), Some Balance (3)\n",
    "\n",
    "Payment Status: Some Problems (1), Paid Up (2), No Problems (in this bank) (3)\n",
    "\n",
    "Savings/Stock Value: None, Below 100 DM, [100, 1000] DM, Above 1000 DM\n",
    "\n",
    "Employment Length: Below 1 year (including unemployed), [1, 4), [4, 7), Above 7\n",
    "\n",
    "Sex/Marital Status: Male Divorced/Single, Male Married/Widowed, Female\n",
    "\n",
    "No of Credits at this bank: 1, More than 1\n",
    "\n",
    "Guarantor: None, Yes\n",
    "\n",
    "Concurrent Credits: Other Banks or Dept Stores, None\n",
    "\n",
    "ForeignWorker variable may be dropped from the study\n",
    "\n",
    "Purpose of Credit: New car, Used car, Home Related, Other"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ffcd3871-36fb-4cf4-8178-7f8e267909a1",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Creditability  Account_Balance  Duration_of_Credit_monthly  \\\n",
      "0              1                1                          18   \n",
      "1              1                1                           9   \n",
      "2              1                2                          12   \n",
      "3              1                1                          12   \n",
      "4              1                1                          12   \n",
      "\n",
      "   Payment_Status_of_Previous_Credit  Purpose  Credit_Amount  \\\n",
      "0                                  4        2           1049   \n",
      "1                                  4        0           2799   \n",
      "2                                  2        9            841   \n",
      "3                                  4        0           2122   \n",
      "4                                  4        0           2171   \n",
      "\n",
      "   Value_Savings_Stocks  Length_of_current_employment  Instalment_per_cent  \\\n",
      "0                     1                             2                    4   \n",
      "1                     1                             3                    2   \n",
      "2                     2                             4                    2   \n",
      "3                     1                             3                    3   \n",
      "4                     1                             3                    4   \n",
      "\n",
      "   Sex_Marital_Status  ...  Duration_in_Current_address  \\\n",
      "0                   2  ...                            4   \n",
      "1                   3  ...                            2   \n",
      "2                   2  ...                            4   \n",
      "3                   3  ...                            2   \n",
      "4                   3  ...                            4   \n",
      "\n",
      "   Most_valuable_available_asset  Age_years  Concurrent_Credits  \\\n",
      "0                              2         21                   3   \n",
      "1                              1         36                   3   \n",
      "2                              1         23                   3   \n",
      "3                              1         39                   3   \n",
      "4                              2         38                   1   \n",
      "\n",
      "   Type_of_apartment  No_of_Credits_at_this_Bank  Occupation  \\\n",
      "0                  1                           1           3   \n",
      "1                  1                           2           3   \n",
      "2                  1                           1           2   \n",
      "3                  1                           2           2   \n",
      "4                  2                           2           2   \n",
      "\n",
      "   No_of_dependents  Telephone  Foreign_Worker  \n",
      "0                 1          1               1  \n",
      "1                 2          1               1  \n",
      "2                 1          1               1  \n",
      "3                 2          1               2  \n",
      "4                 1          1               2  \n",
      "\n",
      "[5 rows x 21 columns]\n"
     ]
    }
   ],
   "source": [
    "data = pd.read_csv('german.csv', sep=';')\n",
    "print(data.head())\n",
    "Y = data[\"Creditability\"]\n",
    "X = data[[\n",
    "    'Account_Balance', \n",
    "    'Payment_Status_of_Previous_Credit', \n",
    "    'Value_Savings_Stocks', \n",
    "    'Length_of_current_employment', \n",
    "    'Sex_Marital_Status', \n",
    "    'No_of_Credits_at_this_Bank', \n",
    "    'Guarantors',\n",
    "    'Concurrent_Credits',\n",
    "    'Foreign_Worker', \n",
    "    'Purpose'\n",
    "]]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3f5185da-6c3a-4a4e-aece-10f028d70695",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       Creditability  Account_Balance  Duration_of_Credit_monthly  \\\n",
      "count    1000.000000      1000.000000                 1000.000000   \n",
      "mean        0.700000         2.577000                   20.903000   \n",
      "std         0.458487         1.257638                   12.058814   \n",
      "min         0.000000         1.000000                    4.000000   \n",
      "25%         0.000000         1.000000                   12.000000   \n",
      "50%         1.000000         2.000000                   18.000000   \n",
      "75%         1.000000         4.000000                   24.000000   \n",
      "max         1.000000         4.000000                   72.000000   \n",
      "\n",
      "       Payment_Status_of_Previous_Credit      Purpose  Credit_Amount  \\\n",
      "count                         1000.00000  1000.000000     1000.00000   \n",
      "mean                             2.54500     2.828000     3271.24800   \n",
      "std                              1.08312     2.744439     2822.75176   \n",
      "min                              0.00000     0.000000      250.00000   \n",
      "25%                              2.00000     1.000000     1365.50000   \n",
      "50%                              2.00000     2.000000     2319.50000   \n",
      "75%                              4.00000     3.000000     3972.25000   \n",
      "max                              4.00000    10.000000    18424.00000   \n",
      "\n",
      "       Value_Savings_Stocks  Length_of_current_employment  \\\n",
      "count           1000.000000                   1000.000000   \n",
      "mean               2.105000                      3.384000   \n",
      "std                1.580023                      1.208306   \n",
      "min                1.000000                      1.000000   \n",
      "25%                1.000000                      3.000000   \n",
      "50%                1.000000                      3.000000   \n",
      "75%                3.000000                      5.000000   \n",
      "max                5.000000                      5.000000   \n",
      "\n",
      "       Instalment_per_cent  Sex_Marital_Status  ...  \\\n",
      "count          1000.000000          1000.00000  ...   \n",
      "mean              2.973000             2.68200  ...   \n",
      "std               1.118715             0.70808  ...   \n",
      "min               1.000000             1.00000  ...   \n",
      "25%               2.000000             2.00000  ...   \n",
      "50%               3.000000             3.00000  ...   \n",
      "75%               4.000000             3.00000  ...   \n",
      "max               4.000000             4.00000  ...   \n",
      "\n",
      "       Duration_in_Current_address  Most_valuable_available_asset   Age_years  \\\n",
      "count                  1000.000000                    1000.000000  1000.00000   \n",
      "mean                      2.845000                       2.358000    35.54200   \n",
      "std                       1.103718                       1.050209    11.35267   \n",
      "min                       1.000000                       1.000000    19.00000   \n",
      "25%                       2.000000                       1.000000    27.00000   \n",
      "50%                       3.000000                       2.000000    33.00000   \n",
      "75%                       4.000000                       3.000000    42.00000   \n",
      "max                       4.000000                       4.000000    75.00000   \n",
      "\n",
      "       Concurrent_Credits  Type_of_apartment  No_of_Credits_at_this_Bank  \\\n",
      "count         1000.000000        1000.000000                 1000.000000   \n",
      "mean             2.675000           1.928000                    1.407000   \n",
      "std              0.705601           0.530186                    0.577654   \n",
      "min              1.000000           1.000000                    1.000000   \n",
      "25%              3.000000           2.000000                    1.000000   \n",
      "50%              3.000000           2.000000                    1.000000   \n",
      "75%              3.000000           2.000000                    2.000000   \n",
      "max              3.000000           3.000000                    4.000000   \n",
      "\n",
      "        Occupation  No_of_dependents    Telephone  Foreign_Worker  \n",
      "count  1000.000000       1000.000000  1000.000000     1000.000000  \n",
      "mean      2.904000          1.155000     1.404000        1.037000  \n",
      "std       0.653614          0.362086     0.490943        0.188856  \n",
      "min       1.000000          1.000000     1.000000        1.000000  \n",
      "25%       3.000000          1.000000     1.000000        1.000000  \n",
      "50%       3.000000          1.000000     1.000000        1.000000  \n",
      "75%       3.000000          1.000000     2.000000        1.000000  \n",
      "max       4.000000          2.000000     2.000000        2.000000  \n",
      "\n",
      "[8 rows x 21 columns]\n"
     ]
    }
   ],
   "source": [
    "print(data.describe())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f5cc712a-7d9b-4121-af7a-f5107b5d95b4",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Вычислите среднее по столбцам.\n",
    "mean = np.mean(X, axis=0)\n",
    "\n",
    "# Вычислите стандартное отклонение по столбцам.\n",
    "std = np.std(X, axis=0)\n",
    "\n",
    "# Нормализуйте данные по столбцам (стандартное масштабирование).\n",
    "normalized_X = (X - mean) / std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "37c38a96-4e7d-46f1-8d11-031e3c6e7924",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "lc = LinearClassifier(num_features=normalized_X.shape[1])\n",
    "history = lc.fit(normalized_X, (Y - np.mean(Y, axis=0)) / np.std(Y, axis=0), epochs=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "764abb9b-2fc3-4859-be34-06099840a914",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "epochs = range(1, len(history) + 1)\n",
    "\n",
    "# Постройте график обучения.\n",
    "plt.plot(epochs, history, 'b', label='BCE')\n",
    "plt.title('График обучения')\n",
    "plt.xlabel('Эпохи')\n",
    "plt.ylabel('BCE')\n",
    "plt.legend()\n",
    "\n",
    "# Отобразите график.\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "0fb2e181-a6c8-429d-bd55-2d8645c193a4",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy:  0.737\n"
     ]
    }
   ],
   "source": [
    "pred = lc.predict(normalized_X)\n",
    "print('accuracy: ', (pred == Y).sum() / len(Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee311e77-efda-4f2f-bd13-308822206894",
   "metadata": {},
   "source": [
    "Вычислите для этой модели ROC-AUC, precision, recall и f1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a1e4aaad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ROC-AUC: 0.7667690476190476\n",
      "precision: 0.7598097502972652\n",
      "recall: 0.9128571428571428\n",
      "f1: 0.8293316028552887\n"
     ]
    }
   ],
   "source": [
    "import sklearn.metrics as skm\n",
    "\n",
    "print(f\"ROC-AUC: {skm.roc_auc_score(Y, lc.predict_proba(normalized_X))}\")\n",
    "print(f\"precision: {skm.precision_score(Y, pred)}\")\n",
    "print(f\"recall: {skm.recall_score(Y, pred)}\")\n",
    "print(f\"f1: {skm.f1_score(Y, pred)}\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}