lab3_1.ipynb

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  "metadata": {
    "colab": {
      "name": "Linear Regression lab 3.1-3.4",
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    },
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
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    "language_info": {
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        "name": "ipython",
        "version": 3
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      "file_extension": ".py",
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      "version": "3.7.4"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LkTpaRRWZNc3"
      },
      "source": [
        "# Линейная регрессия\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ro-ttLpiZNdC"
      },
      "source": [
        "Линейные методы предполагают, что между признаками объекта и целевой переменной существует линейная зависимость, то есть:\n",
        "$$ \\hat{y} = w_1 x_1 + w_2 x_2 + ... + w_k x_k + b,$$\n",
        "где $\\hat{y}$ - целевая переменная (что мы хотим предсказать), $x_i$ - i-ый признак объекта $x$, $w_i$ - вес $i$-го признака, $b$ - bias (смещение, свободный член).\n",
        "\n",
        "В задаче линейной регрессии $\\hat{y}$ - это действительное число.\n",
        "\n",
        "Часто для упрощения записи вводят дополнительный фиктивный признак $x_0$, который всегда равен 1, тогда bias - вес этого признака. В этом случае формула может быть записана как скалярное произведение:\n",
        "$$ \\hat{y} = <w, x> $$\n",
        "\n",
        "В матричной форме формулу можно переписать следующим образом:\n",
        "$$ \\hat{y} = Xw,$$\n",
        "$\\hat{y}$ - вектор значений целевой переменной размера $n$, $X$ - матрица значений признаков объектов размера $n \\times k$, w - вектор весов размера $k$. То есть в наших данных имеется $n$ объектов, каждый их которых описан $k$ признаками.\n",
        "\n",
        "Таким образом, в матричной форме модель задаётся следующим образом:\n",
        "$$ y = Xw + \\epsilon$$ \n",
        "\n",
        "Важно отметить, что параметрами этой модели являются веса $w$. Когда говорят об обучении какого-либо алгоритма машинного обучения, как правило, имеют в виду настройку весов, т.е. параметров модели.  "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ixnX1G4yDVcG"
      },
      "source": [
        "На практике $\\hat{y} $ может отличается от реальных значений, которые принимает целевая переменная $y$. Разницу между реальным значением и предсказанным, обозначим как $\\epsilon$ - вектор значений случайной переменной, соответствующая случайной, непрогнозируемой ошибке модели. Ограничения, которые накладываются на эту модель:\n",
        "* математическое ожидание случайных ошибок $\\epsilon$ равно нулю,\n",
        "* дисперсия случайных ошибок одинакова и конечна,\n",
        "* случайные ошибки не скоррелированы."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HJyN9MkMDTod"
      },
      "source": [
        "Один из способов вычислить значения параметров модели, давно знаком - это наименьших квадратов, который минимизирует среднеквадратичную ошибку между реальным значением зависимой переменной и прогнозом, выданным моделью. Решение по методу наименьших квадратов дает:\n",
        "$$ w = (X^TX)^{-1}X^TY $$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y5HVNycSZNc5"
      },
      "source": [
        "Загрузим необходимые библиотеки"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Lrhz2sFvZNc7"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "from matplotlib import pyplot as plt\n",
        "plt.style.use('ggplot')\n",
        "%matplotlib inline"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dFQqRj1lZNdg"
      },
      "source": [
        "## Оценка результатов\n",
        "\n",
        "Чтобы оценить качество работы алгоритма нам необходимо применяют разные метрики. Наиболее частые метрики средневадратичная и средняя абсолютная ошибки. Вычислим эти метрики на обучающей и на тестовой выборках. \n",
        "\n",
        " * *mean_absolute_error* - средняя абсолютная ошибка $|y_i - \\hat{y}_i|$\n",
        " * *mean_squared_error* - средняя квадратичная ошибка $(y_i - \\hat{y}_i)^2$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2sEDF-oXRsVw"
      },
      "source": [
        "## Задание 3.1"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aStEfJYSZNdE"
      },
      "source": [
        "Пример 1. Сгенерируем искусственные данные. Сначала поработаем с простейшим одномерным случаем, когда у нас значение $y$ будет зависеть только от одного значения $x$.\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d3tzSTkrZNdF"
      },
      "source": [
        "def generate_data(n_points=20):\n",
        "  \"\"\"\n",
        "    Принимает на вход n_points точек \n",
        "    Возвращает данные для обучения и теста\n",
        "  \"\"\"\n",
        "  X = np.linspace(-5, 5, n_points)\n",
        "  y = 10 * X - 7\n",
        "\n",
        "  X_train = X[0::2].reshape(-1, 1)\n",
        "  y_train = y[0::2] + np.random.randn(int(n_points/2)) * 10\n",
        "\n",
        "  X_test = X[1::2].reshape(-1, 1)\n",
        "  y_test = y[1::2] + np.random.randn(int(n_points/2)) * 10\n",
        "\n",
        "  print(f'Generated {len(X_train)} train samples and {len(X_test)} test samples')\n",
        "  return X, X_train, y_train, X_test, y_test"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bnYHO2TjZNdJ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5d99857e-03f1-41ba-9b35-d7404d372ed8"
      },
      "source": [
        "X, X_train, y_train, X_test, y_test = generate_data(100)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Generated 50 train samples and 50 test samples\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q0l76cbaKzYg"
      },
      "source": [
        "### Реализуйте настройку w и b с помощью рассмотренного выше метода наименьших квадратов.\n",
        "### Найдите значения метрик MSE и MAE. Сравните с результатами из sklearn\n",
        "\n",
        "from sklearn.base import BaseEstimator, RegressorMixin\n",
        "from numpy.linalg import inv\n",
        "\n",
        "\n",
        "class CustomLinearRegression(BaseEstimator, RegressorMixin):\n",
        "  def fit(self, X, y, alpha: float = 0.01):\n",
        "    X = np.column_stack((X, np.ones(X.shape[0]).astype(float)))\n",
        "    self.w = inv((X.transpose() @ X + alpha * np.eye(X.shape[1]))) @ X.transpose() @ y\n",
        "    return self\n",
        "\n",
        "  def predict(self, X, is_added_bias: bool = False):\n",
        "    X = np.column_stack((X, np.ones(X.shape[0]).astype(float)))\n",
        "    return X @ self.w"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Xd2X8xDDfO1d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        },
        "outputId": "236b3fc7-e280-4ee3-d0eb-e189f08b51ad"
      },
      "source": [
        "from sklearn.metrics import mean_absolute_error, mean_squared_error\n",
        "y_pred = CustomLinearRegression().fit(X_train, y_train).predict(X_test)\n",
        "print(mean_absolute_error(y_pred, y_test), mean_squared_error(y_pred, y_test))\n",
        "plt.scatter(X_test, y_test)\n",
        "plt.plot(X_test, y_pred)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "8.275662172793435 98.02806814941923\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f8f372673d0>]"
            ]
          },
          "metadata": {},
          "execution_count": 46
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8i7PGGsHfhib",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        },
        "outputId": "ee3787bd-e41f-42e0-981f-2a0c0050e037"
      },
      "source": [
        "from sklearn.linear_model import LinearRegression\n",
        "y_pred = LinearRegression().fit(X_train, y_train).predict(X_test)\n",
        "print(mean_absolute_error(y_pred, y_test), mean_squared_error(y_pred, y_test))\n",
        "plt.scatter(X_test, y_test)\n",
        "plt.plot(X_test, y_pred)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "8.275820571984966 98.02959693428522\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f8f371d4090>]"
            ]
          },
          "metadata": {},
          "execution_count": 47
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "luGJoQXHRzu7"
      },
      "source": [
        "## Задание 3.2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KKKQZDzWMv-j"
      },
      "source": [
        "Пример 2. Не всегда в задаче регрессии в качестве решения выступает прямая, как в предыдущем случае. Рассмотрим ещё один пример, в котором у объектов всё ещё один признак. Но теперь мы будм брать случайную точку на синусоиде и добавлять к ней шум — таким образом получим целевую переменную, признаком в этом случае будет координата $x$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aULennJThZxH"
      },
      "source": [
        "def generate_wave_set(n_support=1000, n_train=25, std=0.3):\n",
        "    data = {}\n",
        "    # выберем некоторое количество точек из промежутка от 0 до 2*pi\n",
        "    data['support'] = np.linspace(0, 2*np.pi, num=n_support)\n",
        "    # для каждой посчитаем значение sin(x) + 1\n",
        "    # это будет ground truth\n",
        "    data['values'] = np.sin(data['support']) + 1\n",
        "    # из support посемплируем некоторое количество точек с возвратом, это будут признаки\n",
        "    data['x_train'] = np.sort(np.random.choice(data['support'], size=n_train, replace=True))\n",
        "    # опять посчитаем sin(x) + 1 и добавим шум, получим целевую переменную\n",
        "    data['y_train'] = np.sin(data['x_train']) + 1 + np.random.normal(0, std, size=data['x_train'].shape[0])\n",
        "    return data\n",
        "\n",
        "data = generate_wave_set(1000, 250)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3CBnODv1QYn_",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "48a4f7b3-4f2d-4234-eb47-165810233e97"
      },
      "source": [
        "### попробуйте реализовать настройку w и b с помощью рассмотренного выше метода наименьших квадратов.\n",
        "### Найдите значения метрик MSE и MAE\n",
        "# print(data['x_train'].reshape(-1, 1).shape, data['y_train'].reshape(1, -1).shape)\n",
        "reshaped_x_train = data['x_train'].reshape(-1, 1)\n",
        "\n",
        "y_pred = LinearRegression().fit(reshaped_x_train, data['y_train']).predict(reshaped_x_train)\n",
        "plt.scatter(data['x_train'], data['y_train'])\n",
        "plt.plot(data['x_train'], y_pred)\n",
        "print(mean_absolute_error(y_pred, data['y_train']), mean_squared_error(y_pred, data['y_train']))\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.4242301906637897 0.2532101896492624\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o9iBgsGVQyOD"
      },
      "source": [
        "Конечно, такое решение нас вряд ли может устроить. Нужно применить полинимиальную регрессию. Идея здесь такая. Каждый признак в исходную формулу может входить не только в первой степени, но и во второй, в третьей и так далее. То есть для случая, когда у нас только один признак:\n",
        "$$ \\hat{y} = w_1 x_1 + w_2 x_1^2 + ... + w_k x_1^k + b,$$ "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "95m0fULWR4m5"
      },
      "source": [
        "## Задание 3.3"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eyzS3rlzSuDU"
      },
      "source": [
        "class PolinomialRegression(BaseEstimator, RegressorMixin):\n",
        "\n",
        "  def fit(self, X, y, X_degrees, alpha=0.01):\n",
        "    self.X_degrees = X_degrees\n",
        "    self.X_train = np.empty([X.shape[0], X_degrees.sum() + 1])\n",
        "    count = 0\n",
        "    for degree_idx in range(X_degrees.shape[0]):\n",
        "      if X_degrees[degree_idx] == 0:\n",
        "        continue\n",
        "      for i in range(X_degrees[degree_idx] + 1):\n",
        "        self.X_train[:, count] = X[:, degree_idx] ** i\n",
        "        count += 1\n",
        "    self.w = inv((self.X_train.transpose() @ self.X_train + alpha * np.eye(self.X_train.shape[1]))) @ self.X_train.transpose() @ y\n",
        "    return self\n",
        "\n",
        "  def predict(self, X):\n",
        "    self.X_test = np.empty([X.shape[0], self.X_degrees.sum() + 1])\n",
        "    count = 0\n",
        "    for degree_idx in range(self.X_degrees.shape[0]):\n",
        "      if self.X_degrees[degree_idx] == 0:\n",
        "        continue\n",
        "      for i in range(self.X_degrees[degree_idx] + 1):\n",
        "        self.X_test[:, count] = X[:, degree_idx] ** i\n",
        "        count += 1        \n",
        "    return self.X_test @ self.w\n",
        "\n",
        "### Реализуйте полиномиальную регрессию. Сделайте визуализацию для полиномов разных степеней. \n",
        "### Полином какой степени подходит больше других? Почему?"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6JLf2mk7oYWp",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "1e4edda9-bf12-4bdd-b9f7-30e1771b71bb"
      },
      "source": [
        "# 3 dimensions test\n",
        "y_pred = PolinomialRegression().fit(reshaped_x_train, reshaped_y_train, np.array([3])).predict(reshaped_x_train)\n",
        "plt.scatter(data['x_train'], data['y_train'])\n",
        "plt.plot(data['x_train'], y_pred)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f8f370bcad0>]"
            ]
          },
          "metadata": {},
          "execution_count": 51
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "toTz6ACup8i4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "29408947-f227-4359-ef36-067a592bf19d"
      },
      "source": [
        "# Because the linear regression is \n",
        "# a special case of polinomial regression,\n",
        "# we can easyly use PolinomialFeatures to scale LR up to PR\n",
        "\n",
        "from sklearn.preprocessing import PolynomialFeatures\n",
        "\n",
        "PF_3_reshaped_x_train = PolynomialFeatures(3).fit_transform(reshaped_x_train)\n",
        "\n",
        "y_pred = LinearRegression().fit(PF_3_reshaped_x_train, data['y_train']).predict(PF_3_reshaped_x_train)\n",
        "plt.scatter(data['x_train'], data['y_train'])\n",
        "plt.plot(data['x_train'], y_pred)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f8f3703a6d0>]"
            ]
          },
          "metadata": {},
          "execution_count": 52
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SyuvYQygtaL7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 778
        },
        "outputId": "99de4a33-8cdb-49f8-f929-d0da8229d2ec"
      },
      "source": [
        "# Lets check other number of features:\n",
        "# 2\n",
        "fig2 = plt.figure()\n",
        "poly2 = fig2.add_subplot()\n",
        "pred2 = PolinomialRegression().fit(reshaped_x_train, data['y_train'], np.array([2])).predict(reshaped_x_train)\n",
        "poly2.scatter(data['x_train'], data['y_train'])\n",
        "poly2.plot(data['x_train'], pred2)\n",
        "\n",
        "# 5\n",
        "fig5 = plt.figure()\n",
        "poly5 = fig5.add_subplot()\n",
        "pred5 = PolinomialRegression().fit(reshaped_x_train, data['y_train'], np.array([5])).predict(reshaped_x_train)\n",
        "poly5.scatter(data['x_train'], data['y_train'])\n",
        "poly5.plot(data['x_train'], pred5)\n",
        "\n",
        "# 13\n",
        "fig10 = plt.figure()\n",
        "poly10 = fig10.add_subplot()\n",
        "pred10 = PolinomialRegression().fit(reshaped_x_train, data['y_train'], np.array([10])).predict(reshaped_x_train)\n",
        "poly10.scatter(data['x_train'], data['y_train'])\n",
        "poly10.plot(data['x_train'], pred10)\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f8f36f40790>]"
            ]
          },
          "metadata": {},
          "execution_count": 53
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aImXhyCAvcm4"
      },
      "source": [
        "Для решения задачи нам нужно найти полином наименьшей степени, который наиболее верно будет отображать закономерность представленных данных. С повышением степени полинома наши предсказания будут сильнее зависеть от шума в полученных данных.\n",
        "  \n",
        "Мой выбор –– это полином 3ей степени. С его помощью мы можем отобразить присутствущее 2 экстремума и, как следствие, показать синусоидальную зависимость на заданном отрезке."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "feMIFS82ZNdn"
      },
      "source": [
        "# Реальный датасет"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_NVLc80wZNdn"
      },
      "source": [
        "Возьмём реальный набор данных Boston из sklearn.datasets. Этот датасет описывает средние цены на недвижимость в районах Бостона в тысячах долларов.\n",
        "\n",
        "Примеры признаков объектов недвижимости: количество преступлений на душу населения, процент старых домов в районе, количество учеников на одного учителя и т.д. Обратите внимание на то, что данные уже оцифрованы там, где изначально признаки были качественными."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yMC-plFGZNdo"
      },
      "source": [
        "Загрузим датасет, выведем информацию"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZN6sApHcZNdo"
      },
      "source": [
        "from sklearn.datasets import load_boston\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YBgnP7HcZNdq",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e0dd768c-2113-4b8e-b994-5c37042fce7b"
      },
      "source": [
        "house_data = load_boston()\n",
        "info_house_data = pd.DataFrame(data=house_data.data,\n",
        "                     columns=house_data.feature_names)\n",
        "info_house_data.info()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 506 entries, 0 to 505\n",
            "Data columns (total 13 columns):\n",
            " #   Column   Non-Null Count  Dtype  \n",
            "---  ------   --------------  -----  \n",
            " 0   CRIM     506 non-null    float64\n",
            " 1   ZN       506 non-null    float64\n",
            " 2   INDUS    506 non-null    float64\n",
            " 3   CHAS     506 non-null    float64\n",
            " 4   NOX      506 non-null    float64\n",
            " 5   RM       506 non-null    float64\n",
            " 6   AGE      506 non-null    float64\n",
            " 7   DIS      506 non-null    float64\n",
            " 8   RAD      506 non-null    float64\n",
            " 9   TAX      506 non-null    float64\n",
            " 10  PTRATIO  506 non-null    float64\n",
            " 11  B        506 non-null    float64\n",
            " 12  LSTAT    506 non-null    float64\n",
            "dtypes: float64(13)\n",
            "memory usage: 51.5 KB\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kjL3jxlqgHWs"
      },
      "source": [
        "## Задание 3.4"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "whSyulRIyfPj"
      },
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.preprocessing import StandardScaler"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jYGHHEspyoof"
      },
      "source": [
        "X, y = load_boston(return_X_y=True)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X9C2C_Yj_aDw",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e2151dd9-5933-43c9-965e-0483b3f37279"
      },
      "source": [
        "X_train, X_test, y_train, y_test = train_test_split(X, y)\n",
        "X_train = StandardScaler().fit_transform(X_train)\n",
        "X_test = StandardScaler().fit_transform(X_test)\n",
        "\n",
        "lr_full = CustomLinearRegression().fit(X_train, y_train)\n",
        "y_pred = lr_full.predict(X_test)\n",
        "print('Error MAE:', mean_absolute_error(y_pred, y_test), 'Error MSE:', mean_squared_error(y_pred, y_test))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Error MAE: 3.3843078564678795 Error MSE: 23.897773515880726\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LK-r8XYtChJt"
      },
      "source": [
        "# 0 CRIM - per capita crime rate by town\n",
        "# 1 ZN - proportion of residential land zoned for lots over 25,000 sq.ft.\n",
        "# 2 INDUS - proportion of non-retail business acres per town.\n",
        "# 3 CHAS - Charles River dummy variable (1 if tract bounds river; 0 otherwise)\n",
        "# 4 NOX - nitric oxides concentration (parts per 10 million)\n",
        "# 5 RM - average number of rooms per dwelling\n",
        "# 6 AGE - proportion of owner-occupied units built prior to 1940\n",
        "# 7 DIS - weighted distances to five Boston employment centres\n",
        "# 8 RAD - index of accessibility to radial highways\n",
        "# 9 TAX - full-value property-tax rate per $10,000\n",
        "# 10 PTRATIO - pupil-teacher ratio by town\n",
        "# 11 B - 1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town\n",
        "# 12 LSTAT - % lower status of the population"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c5Nil6mnCPLG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4570d586-dad5-4709-cfab-4370493273f6"
      },
      "source": [
        "feature_mask = [4, 5, 7, 9, 10, 11, 12]\n",
        "X_train_main = X_train[:, feature_mask]\n",
        "X_test_main = X_test[:, feature_mask]\n",
        "y_pred = CustomLinearRegression().fit(X_train_main, y_train).predict(X_test_main)\n",
        "print('Error MAE:', mean_absolute_error(y_pred, y_test), 'Error MSE:', mean_squared_error(y_pred, y_test))"
      ],
      "execution_count": 74,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Error MAE: 3.371075016157593 Error MSE: 24.642128060040065\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PbTQGLKagJN5"
      },
      "source": [
        "### оставьте в наборе данных только 7 наиболее значимых признаков\n",
        "### настройте параметры линейной регрессии и сравните метрики качества (MSE и MAE) для полного датасета и усечённого"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3FRcGH34D4MX"
      },
      "source": [
        "Для усеченного датасета мы немного ухудшаем точность наших предсказаний, но делаем процесс обучения и предсказания более быстрым и менее затратным по памяти."
      ]
    }
  ]
}