Стохастический градиентный и координатный спуски.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {},
      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NyHIGVhfa_Wf"
      },
      "source": [
        "# Стохастический градиентный и координатный спуски"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gn6lluIADUKa"
      },
      "source": [
        "Для каждого задания указано количество баллов (если они оцениваются отдельно) + 1 балл за аккуратное и полное выполнение всего задания"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "txCccYvha_Wv"
      },
      "source": [
        "## Загрузка и подготовка данных"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NbyOzeZ6a_Wx"
      },
      "source": [
        "**Загрузите уже знакомый вам файл *Advertising.csv* как объект DataFrame.** "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {
        "id": "E1L4_xeDa_Wz"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "(200, 5)\n"
          ]
        },
        {
          "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>Unnamed: 0</th>\n",
              "      <th>TV</th>\n",
              "      <th>radio</th>\n",
              "      <th>newspaper</th>\n",
              "      <th>sales</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1</td>\n",
              "      <td>230.1</td>\n",
              "      <td>37.8</td>\n",
              "      <td>69.2</td>\n",
              "      <td>22.1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>2</td>\n",
              "      <td>44.5</td>\n",
              "      <td>39.3</td>\n",
              "      <td>45.1</td>\n",
              "      <td>10.4</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Unnamed: 0     TV  radio  newspaper  sales\n",
              "0           1  230.1   37.8       69.2   22.1\n",
              "1           2   44.5   39.3       45.1   10.4"
            ]
          },
          "execution_count": 42,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "data = pd.read_csv('Advertising.zip')\n",
        "print(data.shape)\n",
        "data.head(2)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bf4aVFndDUKf"
      },
      "source": [
        "**Проверьте, есть ли в данных пропуски и, если они есть - удалите их**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 43,
      "metadata": {
        "id": "tiVeFnR5DUKg"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Unnamed: 0    0\n",
              "TV            0\n",
              "radio         0\n",
              "newspaper     0\n",
              "sales         0\n",
              "dtype: int64"
            ]
          },
          "execution_count": 43,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "data.isna().sum()\n",
        "# Пропусков нет"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rTkiqPr_DUKh"
      },
      "source": [
        "**Преобразуйте ваши признаки в массивы NumPy и разделите их на переменные X (предикторы) и y(целевая переменная)** "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {
        "id": "R9OHIRB3a_Xa"
      },
      "outputs": [],
      "source": [
        "X = np.array(data.drop(['Unnamed: 0', 'sales'], axis=1))\n",
        "y = np.array(data['sales'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KCvjSoHEDUKo"
      },
      "source": [
        "## Координатный спуск (3 балла)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yjNm8dATDUKq"
      },
      "source": [
        "**Добавим единичный столбец для того, чтобы у нас был свободный коэффициент в уравнении регрессии:**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {
        "id": "LMgq0fmKDUKr"
      },
      "outputs": [],
      "source": [
        "X = np.hstack([np.ones((X.shape[0], 1)), X])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R008OQwcDUKt"
      },
      "source": [
        "**Нормализуем данные: обычно это необходимо для корректной работы алгоритма**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {
        "id": "2Sk7Wx-SDUKt"
      },
      "outputs": [],
      "source": [
        "X = X / np.sqrt(np.sum(np.square(X), axis=0))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F_pHHbAdDUKu"
      },
      "source": [
        "**Реализуйте алгоритм координатного спуска:** (3 балла)\n",
        "\n",
        "Ниже приведен алгоритм:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jBQ8vT5UDUKu"
      },
      "source": [
        "<a href=\"https://ibb.co/Th3BQFn\"><img src=\"https://i.ibb.co/DK2DBS6/zascas.jpg\" alt=\"zascas\" border=\"0\"></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5ce_yM20DUKv"
      },
      "source": [
        "Примечание: 1000 итераций здесь указаны для этого задания, на самом деле их может быть намного больше, нет детерменированного значения."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "y3IdiHm9DUKv"
      },
      "source": [
        "Вам необходимо реализовать координатный спуск, и вывести веса в модели линейной регрессии."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {
        "id": "Vsi3d9OfDUKw"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "  Веса в модели линейной регрессии:\n",
            " [ 41.56217205 110.13144155  73.52860638  -0.55006384]\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1296x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# создаем нулевой вектор весов размерность равной количеству признаков\n",
        "w = np.zeros(X.shape[1])\n",
        "w_for_viz = np.zeros((1000,len(w))) # массив весов для визуализации\n",
        "\n",
        "r = y  # начальное условие \n",
        "for i in range(1000):  # 1000 итераций по заданию\n",
        "    for j in range(len(w)): # перебор координат\n",
        "        r = r + X[:,j]*w[j]\n",
        "        w[j] = X[:,j]@r\n",
        "        r = r - X[:,j]*w[j]\n",
        "    w_for_viz[i] = w\n",
        "print(f'  Веса в модели линейной регрессии:\\n {w}')\n",
        "\n",
        "# ВИЗУАЛИЗАЦИЯ\n",
        "fig, axx = plt.subplots(figsize=(18, 4))\n",
        "plt.suptitle('Сходимость алгоритма координатного спуска', fontsize=20)\n",
        "plt.plot(w_for_viz)\n",
        "axx.set_xlim(0,50)\n",
        "axx.hlines( w_for_viz[999], 0, 999, linestyles='dotted')\n",
        "plt.xlabel('Итерации')\n",
        "plt.ylabel('Веса')\n",
        "plt.tight_layout()\n",
        "plt.show();"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a3jG-7UADUKx"
      },
      "source": [
        "Сравните результаты с реализацией линейной регрессии из библиотеки sklearn:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {
        "id": "SBl-1Yb5DUKy"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "  Веса в модели линейной регрессии:\n",
            " [ 41.56217205 110.13144155  73.52860638  -0.55006384]\n"
          ]
        }
      ],
      "source": [
        "from sklearn.linear_model import LinearRegression\n",
        " \n",
        "model = LinearRegression(fit_intercept=False)\n",
        "model.fit(X, y)\n",
        " \n",
        "print(f'  Веса в модели линейной регрессии:\\n {model.coef_}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hIl0AGLyDUKy"
      },
      "source": [
        "### Результаты совпали."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VCGwFnPdDUKz"
      },
      "source": [
        "## Стохастический градиентный спуск (6 баллов)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5u7Q2YJla_Xk"
      },
      "source": [
        "**Отмасштабируйте столбцы исходной матрицы *X* (которую мы не нормализовали еще!). Для того, чтобы это сделать, надо вычесть из каждого значения среднее и разделить на стандартное отклонение** (0.5 баллов)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {
        "id": "9cEpV_5La_Xo"
      },
      "outputs": [],
      "source": [
        "X = np.array(data.drop(['Unnamed: 0', 'sales'], axis=1))\n",
        "X = (X - np.mean(X, axis=0))/np.std(X, axis=0)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8WkNYILHDUK1"
      },
      "source": [
        "**Добавим единичный столбец**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {
        "id": "EVl5tEGtDUK1"
      },
      "outputs": [],
      "source": [
        "X = np.hstack([np.ones((X.shape[0], 1)), X])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m53tZA5fDUK1"
      },
      "source": [
        "**Создайте функцию mse_error для вычисления среднеквадратичной ошибки, принимающую два аргумента: реальные значения и предсказывающие, и возвращающую значение mse** (0.5 балла)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "metadata": {
        "id": "0cvtC08Aa_YK"
      },
      "outputs": [],
      "source": [
        "def mse_error(y_true, y_pred):\n",
        "    \"\"\"Функция для вычисления среднеквадратичной ошибки. \n",
        "    Аргументы:\n",
        "                y_true -  реальные значения,\n",
        "                y_pred -  предсказываемые значения.\n",
        "    Возвращает:\n",
        "                значение среднеквадратичной ошибки.\n",
        "    \"\"\"\n",
        "    return np.sum((y_true - y_pred)**2) / len(y_true)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lpOLhdvBDUK2"
      },
      "source": [
        "**Сделайте наивный прогноз: предскажите продажи средним значением. После этого рассчитайте среднеквадратичную ошибку для этого прогноза** (0.5 балла)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {
        "id": "kLV_XljVa_YZ"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Наивный прогноз: mse_error = 27.085743750000002\n"
          ]
        }
      ],
      "source": [
        "y_pred = np.full(len(y), np.mean(y))\n",
        "mse_error(y, y_pred)\n",
        "print(f'Наивный прогноз: mse_error = {mse_error(y, y_pred)}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BbybL2ola_ZM"
      },
      "source": [
        "**Создайте функцию *lin_pred*, которая может по матрице предикторов *X* и вектору весов линейной модели *w* получить вектор прогнозов** (0.5 балла)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 53,
      "metadata": {
        "id": "1Cyz-Luaa_ZO"
      },
      "outputs": [],
      "source": [
        "def lin_pred(X, w):\n",
        "    \"\"\"Функция вычисления вектора прогноза. \n",
        "    Аргументы:\n",
        "                X -  массив предикторов размерностью (M, N),\n",
        "                w -  вектор весов размерностью N.\n",
        "    Возвращает:\n",
        "                вектор прогнозов размерностью M.\n",
        "    \"\"\"\n",
        "    return X@w"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BU4adBrya_Zm"
      },
      "source": [
        "**Создайте функцию *stoch_grad_step* для реализации шага стохастического градиентного спуска. (1.5 балла) \n",
        "Функция должна принимать на вход следующие аргументы:**\n",
        "* матрицу *X*\n",
        "* вектора *y* и *w*\n",
        "* число *train_ind* - индекс объекта обучающей выборки (строки матрицы *X*), по которому считается изменение весов\n",
        "* число *$\\eta$* (eta) - шаг градиентного спуска\n",
        "\n",
        "Результатом будет вектор обновленных весов"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dyLY-P02DUK5"
      },
      "source": [
        "Шаг для стохастического градиентного спуска выглядит следующим образом:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ORsAyIKNDUK5"
      },
      "source": [
        "$$\\Large w_j \\leftarrow w_j - \\frac{2\\eta}{\\ell} \\sum_{i=1}^\\ell{{x_{ij}((w_0 + w_1x_{i1} + w_2x_{i2} +  w_3x_{i3}) - y_i)}}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CQl2FrpuDUK6"
      },
      "source": [
        "Для того, чтобы написать функцию, нужно сделать следующее:\n",
        "    \n",
        "*  посчитать направление изменения: умножить объект обучающей выборки на 2 и на разницу между предсказанным значением и реальным, а потом поделить на количество элементов в выборке.\n",
        "* вернуть разницу между вектором весов и направлением изменения, умноженным на шаг градиентного спуска"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "metadata": {},
      "outputs": [],
      "source": [
        "def stoch_grad_step(X, y, w, train_ind, eta):\n",
        "    \"\"\"Функция реализации шага стохастического градиентного спуска. \n",
        "    Аргументы:\n",
        "                X -  массив предикторов размерностью (M, N),\n",
        "                y - массив целевой переменной размерностью M,\n",
        "                w -  вектор весов размерностью N,\n",
        "                train_ind - индекс объекта обучающей выборки, по которому считается изменение весов,\n",
        "                eta - шаг градиентного спуска.\n",
        "    Возвращает:\n",
        "                вектор обновленных весов размерностью N.\n",
        "    \"\"\"\n",
        "    direction = 2*X[train_ind]*(lin_pred(X[train_ind], w) - y[train_ind])\n",
        "    return w - direction*eta\n",
        "    "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pXwIFd0Ma_Zx"
      },
      "source": [
        "**Создайте функцию *stochastic_gradient_descent*, для реализации стохастического градиентного спуска (2.5 балла)**\n",
        "\n",
        "**Функция принимает на вход следующие аргументы:**\n",
        "- Матрицу признаков X\n",
        "- Целевую переменнную\n",
        "- Изначальную точку (веса модели)\n",
        "- Параметр, определяющий темп обучения\n",
        "- Максимальное число итераций\n",
        "- Евклидово расстояние между векторами весов на соседних итерациях градиентного спуска,при котором алгоритм прекращает работу \n",
        "\n",
        "**На каждой итерации в вектор (список) должно записываться текущее значение среднеквадратичной ошибки. Функция должна возвращать вектор весов $w$, а также вектор (список) ошибок.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZVeoNF1JDUK7"
      },
      "source": [
        "Алгоритм следующий:\n",
        "    \n",
        "* Инициализируйте расстояние между векторами весов на соседних итерациях большим числом (можно бесконечностью)\n",
        "* Создайте пустой список для фиксации ошибок\n",
        "* Создайте счетчик итераций\n",
        "* Реализуйте оновной цикл обучения пока расстояние между векторами весов больше того, при котором надо прекратить работу (когда расстояния станут слишком маленькими - значит, мы застряли в одном месте) и количество итераций меньше максимально разрешенного: сгенерируйте случайный индекс, запишите текущую ошибку в вектор ошибок, запишите в переменную текущий шаг стохастического спуска с использованием функции, написанной ранее. Далее рассчитайте текущее расстояние между векторами весов и прибавьте к счетчику итераций 1.\n",
        "* Верните вектор весов и вектор ошибок"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 55,
      "metadata": {
        "id": "CD_xcFNfa_Zy"
      },
      "outputs": [],
      "source": [
        "def stochastic_gradient_descent(X, y, w, eta, max_iter, tol):\n",
        "    \"\"\"Функция реализации стохастического градиентного спуска. \n",
        "    Аргументы:\n",
        "                X -  массив предикторов размерностью (M, N),\n",
        "                y - массив целевой переменной размерностью M,\n",
        "                w -  вектор весов размерностью N,\n",
        "                eta - шаг градиентного спуска,\n",
        "                max_iter - максимальное число итераций,\n",
        "                tol - евклидово расстояние между векторами весов на соседних \n",
        "                итерациях градиентного спуска,при котором алгоритм прекращает работу.\n",
        "    Возвращает:\n",
        "                вектор весов размерностью N\n",
        "                и список ошибок.\n",
        "    \"\"\"\n",
        "    \n",
        "    dist = np.inf  # расстояние между векторами\n",
        "    mse_list = []  # список ошибок\n",
        "    count = 0      # счетчик итераций\n",
        "        \n",
        "    while dist>tol and count<max_iter:\n",
        "        train_ind = np.random.randint(len(y))\n",
        "        mse_list.append(mse_error(y, lin_pred(X, w)))\n",
        "        w_i = stoch_grad_step(X, y, w, train_ind, eta)\n",
        "        dist = np.linalg.norm(w_i - w)\n",
        "        w = w_i\n",
        "        count += 1\n",
        "    return w, mse_list"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0OqHO1Rta_Z7"
      },
      "source": [
        " **Запустите $10^5$ итераций стохастического градиентного спуска. Укажите вектор начальных весов, состоящий из нулей. Можете поэкспериментировать с параметром, отвечающим за темп обучения.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N6fHHT6vDUK8"
      },
      "source": [
        "**Постройте график зависимости ошибки от номера итерации**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 56,
      "metadata": {
        "id": "zsSfHDzLDUK9"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 1296x288 with 4 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "w = np.zeros(X.shape[1]) # начальные веса\n",
        "eta = 0.01               # темп обучения\n",
        "max_iter = 1E5           # максимальное кол-во итераций\n",
        "tol = 1E-3               # критерий остановки (расстояние между векторами)\n",
        "np.random.seed(42)\n",
        "w_, mse_list = stochastic_gradient_descent(X, y, w, eta, max_iter, tol)\n",
        "\n",
        "\n",
        "\n",
        "# ВИЗУАЛИЗАЦИЯ\n",
        "fig, axx = plt.subplots(1, 4,  figsize=(18, 4))\n",
        "\n",
        "fig.suptitle('График зависимости ошибки от номера итерации \\\n",
        "стохастического градиентного спуска при разном темпе обучения', fontsize=15)\n",
        "axx[0].plot(list(range(len(mse_list))), mse_list)\n",
        "axx[0].annotate(f'eta = {eta}', (50, 150), fontsize=20)\n",
        "\n",
        "\n",
        "w = np.zeros(X.shape[1])\n",
        "eta = 0.005               # темп обучения\n",
        "w_1, mse_list_1 = stochastic_gradient_descent(X, y, w, eta, max_iter, tol)\n",
        "axx[1].plot(list(range(len(mse_list_1))), mse_list_1)\n",
        "axx[1].annotate(f'eta = {eta}', (100, 150), fontsize=20)\n",
        "\n",
        "\n",
        "w = np.zeros(X.shape[1])\n",
        "eta = 0.05               # темп обучения\n",
        "w_1, mse_list_1 = stochastic_gradient_descent(X, y, w, eta, max_iter, tol)\n",
        "axx[2].plot(list(range(len(mse_list_1))), mse_list_1)\n",
        "axx[2].annotate(f'eta = {eta}', (100, 150), fontsize=20)\n",
        "\n",
        "\n",
        "w = np.zeros(X.shape[1])\n",
        "eta = 0.001               # темп обучения\n",
        "w_1, mse_list_1 = stochastic_gradient_descent(X, y, w, eta, max_iter, tol)\n",
        "axx[3].plot(list(range(len(mse_list_1))), mse_list_1)\n",
        "axx[3].annotate(f'eta = {eta}', (100, 150), fontsize=20)\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show();\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O-MVOcJ6a_aY"
      },
      "source": [
        "**Выведите вектор весов, к которому сошелся метод.**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 57,
      "metadata": {
        "id": "MPjVkXe4DUK9"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[13.14942188  3.73937733  2.57176943  0.93417699]\n"
          ]
        }
      ],
      "source": [
        "print(w_)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qabzMc3Qa_a5"
      },
      "source": [
        "**Выведите среднеквадратичную ошибку на последней итерации.**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 58,
      "metadata": {
        "id": "7tPWleMIa_a7"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "4.37799509672313\n",
            "Прогноз: mse_error = 4.37799509672313\n"
          ]
        }
      ],
      "source": [
        "print(mse_list[-1])\n",
        "print(f'Прогноз: mse_error = {mse_list[-1]}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Выводы\n",
        "\n",
        "Без применения библиотек машинного обучения реализованы алгоритмы координатного и стохастического спусков для решения задачи линейной регрессии. Полученные значения параметров линейной регрессии совпадают с вычисленными с помощью специализированных библиотек. Продемонстрирован процесс минимизации функции потерь (MSE) в алгоритме стохастического спуска. Полученное оптимальное значение MSE ~ 4 существенно лучше наивного прогноза MSE ~ 27. Проиллюстрирована зависимость сходимости алгоритма стохастического градиентного спуска от темпа обучения."
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "Практика_Оптимизация.ipynb",
      "provenance": [],
      "toc_visible": true
    },
    "kernelspec": {
      "display_name": "Python 3.9.12 64-bit",
      "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": "3.9.12"
    },
    "vscode": {
      "interpreter": {
        "hash": "93e5499867a482d1f69126f65754e04e21327fbe16c28c259dff18a59fe0a8c0"
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}