{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "E6Ld9nmrdu11" }, "source": [ "# Phystech@DataScience\n", "## Занятие 2. Введение в машинное обучение. Линейная регрессия.\n", "\n", "*Примечание.* Подробнее про работу с различными библиотеками Питона можно посмотреть в наших туториалах.\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:31.359489Z", "start_time": "2021-02-17T16:30:30.626327Z" }, "id": "x-ocQGTeV0C1" }, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "import scipy.stats as sps\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "sns.set(style='darkgrid', font_scale=1.5)\n", "\n", "from sklearn.metrics import mean_squared_error, mean_absolute_error\n", "from sklearn.linear_model import LinearRegression\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": { "id": "u6JWzXD0E0JQ" }, "source": [ "### Пример построения линейной регрессии\n", "\n", "Скачаем данные, полученные из книги \"Модели и концепции физики: механика.\n", "Лабораторный практикум.\n", "Обработка результатов измерений.\"" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:31.366612Z", "start_time": "2021-02-17T16:30:31.361139Z" }, "id": "9QnN-lBFEV15" }, "outputs": [], "source": [ "data = pd.read_csv(\"lab_data.csv\", index_col='Unnamed: 0') " ] }, { "cell_type": "markdown", "metadata": { "id": "QXbptLGOrPfY" }, "source": [ "Посмотрим на данные" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:31.395716Z", "start_time": "2021-02-17T16:30:31.368333Z" }, "colab": { "base_uri": "https://localhost:8080/", "height": 514 }, "id": "XUu3AQFeYHm8", "outputId": "ef78b98e-6bd0-4d9c-efe6-a9d5c9760182" }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " n h T I\n", "0 1.0 0.0 2.48 1.78\n", "1 2.0 0.5 2.47 1.74\n", "2 3.0 1.0 2.50 1.86\n", "3 4.0 1.5 2.54 2.00\n", "4 5.0 2.0 2.62 2.30\n", "5 6.0 2.5 2.71 2.63\n", "6 7.0 3.0 2.79 2.97\n", "7 8.0 3.5 2.91 3.46\n", "8 9.0 4.0 3.05 4.07\n", "9 10.0 4.5 3.16 4.56\n", "10 11.0 5.0 3.31 5.26\n", "11 12.0 5.5 3.47 6.05\n", "12 13.0 6.0 3.62 6.82\n", "13 14.0 6.5 3.80 7.79\n", "14 15.0 7.0 3.95 8.63" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data" ] }, { "cell_type": "markdown", "metadata": { "id": "R91qIbbLGywr" }, "source": [ "Нас интересуют столбцы `data.I` — измерения момента инерции, `data.h` — измерения расстояния до оси вращения.\n", "\n", "По данным хотим оценить параметры $m, I_0$ в модели $I = I_0 + m h^2 +\\varepsilon$.\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "iOYMjVzKHdFH" }, "source": [ "Заведем модель линейной регрессии из библиотеки `sklearn`:\n", "\n", "`sklearn.linear_model.LinearRegression(*, fit_intercept=True, normalize=False, copy_X=True, n_jobs=None, positive=False)`\n", "* Параметр `fit_intercept` отвечает за то, нужно ли включать в модель свободный член. В случае `fit_intercept=True` модели не нужно передавать признак из всех единиц для того, чтобы она оценивала свободный член.\n", "По умолчанию `fit_intercept=True`.\n", "* Параметр `normalize=False` отвечает за то, нужно ли сделать нормализацию данных.\n", "\n", "\n", "В нашем случае свободный член — это $I_0$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:31.401579Z", "start_time": "2021-02-17T16:30:31.398428Z" }, "id": "mNvTZ-lHg6XQ" }, "outputs": [], "source": [ "lin = LinearRegression(fit_intercept=True)" ] }, { "cell_type": "markdown", "metadata": { "id": "OpuWvkRSH3Dd" }, "source": [ "Обучим модель. Для этого используем функцию `lin.fit(X, y)`\n", "\n", "* `X` — матрица размера `n_samples` $\\times$ `n_features`;\n", "* `y` — стоблец размера `n_samples` (матрица `n_samples` $\\times$ 1).\n", "\n", "Сформируем матрицу признаков $X$ из значений квадрата расстояния $h^2$ для каждого измерения.\n", "Массив `data.h**2` одномерный поскольку у нас всего один признак, поэтому нужно изменить его `shape` для того, чтобы можно было подать на вход функции `fit`." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:31.415277Z", "start_time": "2021-02-17T16:30:31.403045Z" }, "id": "OYF4dskSJ08F" }, "outputs": [], "source": [ "X = np.array(data.h**2).reshape(-1, 1) " ] }, { "cell_type": "markdown", "metadata": { "id": "LDRiYLfHst7Z" }, "source": [ "Отдельно выделим целевую переменную $I$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:31.419021Z", "start_time": "2021-02-17T16:30:31.416654Z" }, "id": "FA41x6AEMUyX" }, "outputs": [], "source": [ "y = data.I" ] }, { "cell_type": "markdown", "metadata": { "id": "PEhmiy9xs2AG" }, "source": [ "Обучаем линейную регрессию" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:31.436758Z", "start_time": "2021-02-17T16:30:31.421283Z" }, "id": "EwjpHI0-hE9Q" }, "outputs": [], "source": [ "lin = lin.fit(X, y)" ] }, { "cell_type": "markdown", "metadata": { "id": "NMYbzt3qMsal" }, "source": [ "напечатаем массив коэффициентов. В данном случаем только один коэффициент\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:31.444260Z", "start_time": "2021-02-17T16:30:31.439626Z" }, "colab": { "base_uri": "https://localhost:8080/" }, "id": "xXzcu2tFMqZL", "outputId": "e2a5d228-9e2a-47b2-e819-1b3faf2f0ff8" }, "outputs": [ { "data": { "text/plain": [ "array([0.14196886])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lin.coef_" ] }, { "cell_type": "markdown", "metadata": { "id": "2UVSHpbBNP4x" }, "source": [ "Свободный член:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:31.452400Z", "start_time": "2021-02-17T16:30:31.445903Z" }, "colab": { "base_uri": "https://localhost:8080/" }, "id": "w5lN-xUdNSPI", "outputId": "45a983ec-0e55-4098-ebf4-d6c069250859" }, "outputs": [ { "data": { "text/plain": [ "1.7263600917431186" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lin.intercept_" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:31.461627Z", "start_time": "2021-02-17T16:30:31.454383Z" }, "colab": { "base_uri": "https://localhost:8080/" }, "id": "wLZU4NKtNlgA", "outputId": "c8a6f94a-16b9-4624-d82b-e500fe2c436e" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Оценка I_0: 1.726\n", "Оценка m: 0.142\n" ] } ], "source": [ "print(f\"Оценка I_0: {lin.intercept_ :.4}\")\n", "print(f\"Оценка m: {lin.coef_[0] :.4}\")" ] }, { "cell_type": "markdown", "metadata": { "id": "8v2io0rdatN8" }, "source": [ "Предсказание:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:31.470726Z", "start_time": "2021-02-17T16:30:31.463477Z" }, "id": "RZuU5D8AbDA3" }, "outputs": [], "source": [ "y_pred = lin.predict(X)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:31.480354Z", "start_time": "2021-02-17T16:30:31.472273Z" }, "colab": { "base_uri": "https://localhost:8080/" }, "id": "lgKwRHLnbICd", "outputId": "277ad1e4-ccf6-4c10-e96d-41f044baac00" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1.72636009 1.76185231 1.86832895 2.04579003 2.29423554 2.61366548\n", " 3.00407985 3.46547865 3.99786188 4.60122954 5.27558163 6.02091815\n", " 6.83723911 7.72454449 8.68283431]\n" ] } ], "source": [ "print(y_pred)" ] }, { "cell_type": "markdown", "metadata": { "id": "I8mkpUdeRHgh" }, "source": [ "Построим предсказание на новых объектах. В данном случае в качестве новых объектов возьмем сетку чисел, используемую для построения графика." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:31.488739Z", "start_time": "2021-02-17T16:30:31.481911Z" }, "id": "iyF3qoWlRB5O" }, "outputs": [], "source": [ "grid = np.arange(-1, 53).reshape(-1, 1) # Нужный размер вектора-столбца\n", "\n", "y_pred_grid = lin.predict(grid)" ] }, { "cell_type": "markdown", "metadata": { "id": "lOHn1-z2N3OI" }, "source": [ "Посмотрим на график зависимости" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:31.878472Z", "start_time": "2021-02-17T16:30:31.490949Z" }, "colab": { "base_uri": "https://localhost:8080/", "height": 487 }, "id": "zzVXCHKCefSZ", "outputId": "52a47119-745f-43ec-ccc2-7e7bf51f746e" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10, 7))\n", "\n", "plt.scatter(data.h**2, data.I, color='red', linewidths=6, label=\"Измерения\")\n", "\n", "plt.plot(grid, y_pred_grid, linewidth=4, label=\"Предсказаниe\")\n", "\n", "# вспомогательные функции построения графика\n", "plt.xlabel(\"$h^2$, см$^2$\")\n", "plt.ylabel(\"$I$, г м$^2$ \")\n", "plt.title(\"Зависимость $I$ от $h^2$\")\n", "plt.legend()\n", "plt.grid(linestyle='--')\n", "plt.xlim((-1, 52))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "i-yLwqaAaGz-" }, "source": [ "Посчитаем различные метрики качества:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:31.884161Z", "start_time": "2021-02-17T16:30:31.880059Z" }, "colab": { "base_uri": "https://localhost:8080/" }, "id": "ytKiGwoOaEsx", "outputId": "06d06b8f-b827-41c8-a04f-71a7cdf1e385" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MSE: 0.00149\n", "MAE: 0.0323\n" ] } ], "source": [ "print(f\"MSE: {mean_squared_error(y, y_pred) :.3}\")\n", "print(f\"MAE: {mean_absolute_error(y, y_pred) :.3}\")" ] }, { "cell_type": "markdown", "metadata": { "id": "Wd6C1uNhN7X2" }, "source": [ "### Переобучение и недообучение" ] }, { "cell_type": "markdown", "metadata": { "id": "6SLOdNqxN-z8" }, "source": [ "Создадим сетку из 10 равноудаленных точек на отрезке от 0 до 1." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:31.894816Z", "start_time": "2021-02-17T16:30:31.885749Z" }, "id": "Zt4bsCncm20l" }, "outputs": [], "source": [ "x = np.linspace(0, 1, 10) " ] }, { "cell_type": "markdown", "metadata": { "id": "C0sVXXueOL6p" }, "source": [ "Предположим, что истинная зависимость имеет вид $$y(x) = 5 x - 6 x^2.$$\n", "\n", "Данные получаются по следующему принципу\n", "$$y_i = 5 x_i - 6 x^2_i + \\varepsilon_i,$$\n", "$$\\varepsilon_i \\sim \\mathcal{N}(0, 0.25).$$\n", "\n", "Получим искусственно эти данные. Обратите внимание, что в параметрах нормального распределения в коде указывается не дисперсия, а стандартное отклонение, которое равно корню из дисперсии." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:31.905586Z", "start_time": "2021-02-17T16:30:31.896394Z" }, "id": "qWXJfZnpsuE5" }, "outputs": [], "source": [ "y = 5 * x - 6 * x**2 + sps.norm(loc=0, scale=0.5).rvs(size=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Построим график полученных данных" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:32.128882Z", "start_time": "2021-02-17T16:30:31.907070Z" }, "colab": { "base_uri": "https://localhost:8080/", "height": 461 }, "id": "EZvLVvx1sy1H", "outputId": "6f38b7cf-6936-448c-d8a3-6e65e26f8fdc" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10, 7))\n", "plt.scatter(x, y, linewidths=6, color='red', label=\"Выборка\")\n", "\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$ \")\n", "plt.legend()\n", "plt.grid(linestyle='--')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "x3tCrLj-PWHu" }, "source": [ "**1.** Обозначим $\\bar x = (x_1, \\ldots x_n)^T$, $\\bar 1 = (1, \\ldots 1)^T$.\n", "\n", "Обучим первую модель линейной регрессии, которая в матричном виде записывается как\n", "$$Y = X\\theta + \\varepsilon,$$\n", "где \n", "* $X = (\\bar 1, \\bar x)$ — константный признак и $x$;\n", "* $\\theta = (\\theta_0, \\theta_1)$ — вектор из двух коэффициентов.\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:32.137020Z", "start_time": "2021-02-17T16:30:32.130541Z" }, "id": "K-tmxwtos3sd" }, "outputs": [ { "data": { "text/plain": [ "LinearRegression()" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X1 = np.array(x).reshape(-1, 1)\n", "\n", "lin1 = LinearRegression()\n", "lin1.fit(X1, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Построим предсказания по сетке" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:32.147127Z", "start_time": "2021-02-17T16:30:32.138549Z" }, "id": "ZTXL9JWQResL" }, "outputs": [], "source": [ "grid = np.linspace(0, 1, 100) # сетка для построения графика предсказания\n", "grid1 = grid.reshape(-1, 1) # переведем ее в нужный размер\n", "y_pred1 = lin1.predict(grid1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Визуализируем их на графике" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:32.366370Z", "start_time": "2021-02-17T16:30:32.148684Z" }, "colab": { "base_uri": "https://localhost:8080/", "height": 481 }, "id": "nsmynn5Vtu-P", "outputId": "dd33bf76-ae83-4705-ce23-1f8d4b432a15" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10, 7))\n", "plt.scatter(x, y, linewidths=6, color = 'red')\n", "\n", "plt.plot(grid, y_pred1, linewidth = 4, label=\"Приближение\")\n", "\n", "plt.title(\"Приближение многочленом степени 1\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$ \")\n", "plt.legend()\n", "plt.grid(linestyle='--')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "c41H1fx_SEOP" }, "source": [ "**Недообучение!** В данном случае мы обучили слишком простую модель, которая не смогла уловить все закономерности в данных." ] }, { "cell_type": "markdown", "metadata": { "id": "PwpWmjQQQYOq" }, "source": [ "**2.** Обучим вторую модель линейной регрессии, которая в матричном виде записывается как\n", "$$Y = X\\theta + \\varepsilon,$$\n", "где \n", "* $X = (\\bar 1, \\bar x, \\bar x^2, \\ldots \\bar x^{10})$ — константный признак и первые 10 степеней признака $x$;\n", "* $\\theta = (\\theta_0, \\theta_1, \\theta_2, \\ldots \\theta_10)$ — вектор коэффициентов." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:32.376463Z", "start_time": "2021-02-17T16:30:32.367991Z" }, "id": "BWfi5mxmt0Hx" }, "outputs": [ { "data": { "text/plain": [ "LinearRegression()" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X2 = np.array([x**k for k in range(1, 11)]).T # создаем все степени признака\n", "\n", "lin2 = LinearRegression()\n", "lin2.fit(X2, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Построим предсказания по сетке" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:32.385480Z", "start_time": "2021-02-17T16:30:32.378849Z" }, "id": "oAAHPp1NuGWO" }, "outputs": [], "source": [ "grid2 = np.array([grid**k for k in range(1, 11)]).T # признаки для объектов сетки\n", "y_pred2 = lin2.predict(grid2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Визуализируем их на графике" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:32.610996Z", "start_time": "2021-02-17T16:30:32.387241Z" }, "colab": { "base_uri": "https://localhost:8080/", "height": 481 }, "id": "raLMLlepuO6Z", "outputId": "46d21626-461d-4e56-f371-d9611e9d7b2c" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10, 7))\n", "plt.scatter(x, y, linewidths=6, color = 'red')\n", "\n", "plt.plot(grid, y_pred2, linewidth = 4, label=\"Приближение\")\n", "\n", "plt.title(\"Приближение многочленом степени 10\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$ \")\n", "plt.legend()\n", "plt.grid(linestyle='--')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "wBcI1EDNSKlx" }, "source": [ "**Переобучение!** В данном случае модель слишком сложная, она обучилась закономерностям, которых нет в обучающих данных." ] }, { "cell_type": "markdown", "metadata": { "id": "TPBYqFBcRqrl" }, "source": [ "**3.** Обучим третью модель линейной регрессии, которая в матричном виде записывается как\n", "$$Y = X\\theta + \\varepsilon,$$\n", "где \n", "* $X = (\\bar 1, \\bar x, \\bar x^2)$ — константный признак и первые две степени признака $x$;\n", "* $\\theta = (\\theta_0, \\theta_1, \\theta_2)$ — вектор коэффициентов.\n" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:32.617978Z", "start_time": "2021-02-17T16:30:32.612621Z" } }, "outputs": [ { "data": { "text/plain": [ "LinearRegression()" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X3 = np.array([x**k for k in range(1, 3)]).T # создаем все степени признака\n", "\n", "lin3 = LinearRegression()\n", "lin3.fit(X3, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Построим предсказания по сетке" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:32.625891Z", "start_time": "2021-02-17T16:30:32.619349Z" }, "id": "OqYpFuekR-qg" }, "outputs": [], "source": [ "grid3 = np.array([grid**k for k in range(1, 3)]).T # признаки для объектов сетки\n", "y_pred3 = lin3.predict(grid3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Визуализируем их на графике" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "ExecuteTime": { "end_time": "2021-02-17T16:30:32.893127Z", "start_time": "2021-02-17T16:30:32.628972Z" }, "colab": { "base_uri": "https://localhost:8080/", "height": 481 }, "id": "OjI_pvv_yB8g", "outputId": "e810b0d0-f541-406f-d92c-8ac12c382afc" }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10, 7))\n", "plt.scatter(x, y, linewidths=6, color = 'red')\n", "grid = np.linspace(0, 1, 100)\n", "plt.plot(grid, y_pred3, linewidth = 4, label=\"Приближение\")\n", "plt.plot(grid, 5* grid - 6* grid**2, linewidth = 4, label=\"Истинная зависимость\")\n", "plt.title(\"Приближение многочленом степени 2\")\n", "plt.xlabel(\"$x$\")\n", "plt.ylabel(\"$y$ \")\n", "plt.legend()\n", "plt.grid(linestyle='--')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": { "id": "qV9d9qF7SNkw" }, "source": [ "Зависимость не так уж плохо приближена.\n", "\n", "**Вывод.**\n", "\n", "Стоит выбирать некоторый оптимум между простыми и сложными моделями. Слишком простые могут недообучиться, не уловив тем самым основные закономерности в данных. Слишком сложные модели могут переобучиться и показывать закономерности, которых нет в обучающих данных." ] } ], "metadata": { "colab": { "collapsed_sections": [], "name": "Линейная регрессия.ipynb", "provenance": [] }, "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 1 }