Линейная_регрессия_и_Градиентный_спуск.ipynb

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   "metadata": {
    "id": "m9ird45arXbc"
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   "source": [
    "# Линейная регрессия"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Bdha_z3vqBWk"
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   "source": [
    "## Определение\n",
    "Линейная регрессия (англ. Linear regression) — используемая в статистике регрессионная модель зависимости одной (объясняемой, зависимой) переменной\n",
    "**$y$** от другой или нескольких других переменных (факторов, регрессоров, независимых переменных) $x$ с **линейной функцией** зависимости.\n",
    "\n",
    "Модель линейной регрессии является часто используемой и наиболее изученной в эконометрике. А именно изучены свойства оценок параметров, получаемых различными методами при предположениях о вероятностных характеристиках факторов, и случайных ошибок модели.\n",
    "\n",
    "Источник: [wikipedia.org](https://ru.wikipedia.org/wiki/%D0%9B%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%B0%D1%8F_%D1%80%D0%B5%D0%B3%D1%80%D0%B5%D1%81%D1%81%D0%B8%D1%8F)"
   ]
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   "metadata": {
    "id": "1rQ3IZhPsd0z"
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   "source": [
    "Линейная регрессия задается в виде:\n",
    "\n",
    "$$y_i = \\sum_{j=0}^{m}w_j X_{ij} + ε_i$$\n",
    "\n",
    "где\n",
    "* $\\vec{y}$ - целевая\n",
    "* $w$ - вектор весов\n",
    "* $X$ - матрица объектов-признаков\n",
    "* $ε$ - случайная непрогнозируемая ошибка\n",
    "\n",
    "**Метод наименьших квадратов (МНК, OLS, Ordinary Least Squares)** — один из базовых методов регрессионного анализа для оценки неизвестных параметров регрессионных моделей по выборочным данным. Метод основан на минимизации суммы квадратов остатков регрессии.\n",
    "\n",
    "Оценки, полученные по МНК, обладают следующими свойствами:\n",
    "\n",
    "\n",
    "1.   Оценки параметров являются **несмещенными** т. е. $M(b_1) = β_1$, $M(b_0) = β_0$ (математические ожидания оценок параметров равны их теоретическим значениям). Это вытекает из того, что $M(ε_i) = 0$, и говорит об отсутствии систематической ошибки в определении положения линии регрессии. Оценка, для которой смещение – разность между значением параметра и его оценкой – стремится к нулю при возрастании выборки – является *асимптотически несмещенной*.\n",
    "2.   Оценки параметров **состоятельны**, если при увеличении объема выборки надежность оценок увеличивается ($b_1$ наверняка близко к $β_1$, $b_0$ — близко к $β_0$), т.е. $D(b_0) → 0$, $D(b_1) → 0$ при $n → ∞$.\n",
    "3.   Оценки параметров **эффективны**, т. е. они имеют наименьшую дисперсию по сравнению с другими оценками данных параметров, линейными относительно величин $y_i$.\n",
    "\n",
    "Таким образом МНК-оценки являются несмещенными линейными оценками с минимальной дисперсией, имеющими нормальное распределение."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0N_l1fxuw1Ya"
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   "source": [
    "Для получения по МНК наилучших результатов требуется, чтобы выполнялся ряд предпосылок относительно случайного отклонения. Их также называют предпосылками Гаусса-Маркова. [Теорема Гаусса-Маркова](https://ru.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0_%D0%93%D0%B0%D1%83%D1%81%D1%81%D0%B0_%E2%80%94_%D0%9C%D0%B0%D1%80%D0%BA%D0%BE%D0%B2%D0%B0) гласит, что наилучшие оценки параметров уравнения регрессии могут быть получены при обязательном соблюдении следующих предпосылок:\n",
    "\n",
    "1. Математическое ожидание случайного отклонения $ε_i$ равно нулю: $M(ε_i) = 0$ для всех наблюдений.\n",
    ">Данное условие означает, что случайное отклонение в среднем не оказывает влияния на зависимую переменную, случайный член может быть положительным или отрицательным, но он не должен иметь систематического смещения.\n",
    "\n",
    "2. Дисперсия случайных отклонений постоянна: $D(ε_{ij}) = σ^2 = const$ для любых наблюдений $i$ и $j$.\n",
    "> Условие независимости дисперсии ошибки от номера наблюдения называется гомоскедастичностью (homoscedasticity). Невыполнимость этой предпосылки называется гетероскедастичностью (heteroscedasticity).\n",
    "\n",
    "3. Случайные отклонения $ε_i$ и $ε_j$ являются независимыми друг от друга для $i ≠ j$. Выполнимость этой предпосылки предполагает, что отсутствует систематическая связь между любыми случайными отклонениями. Величина и определенный знак любого случайного отклонения не должны быть причинами величины и знака любого другого отклонения.\n",
    "\n",
    "Записывая математически:\n",
    "\n",
    "$$\\forall i: \\mathbb{E}[\\epsilon_i] = 0$$\n",
    "\n",
    "$$\\forall i: Var(e_i) = \\sigma^2 < \\inf$$\n",
    "\n",
    "$$\\forall i \\neq j: Cov(\\epsilon_i, \\epsilon_j) = 0$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "8xDiR0Ij082S"
   },
   "source": [
    "Вернемся к формуле линейной регрессии: $y_i = \\sum_{j=0}^{m}w_j X_{ij} + ε_i$\n",
    "\n",
    "Из школьной программы всем известно уравнение линии на плоскости $y = ax +b$. Это уравнение определяется двумя параметрами $-$ *смещением* и *наклоном*. В этой формуле мы определяем их как $a$ и $b$, но чаще их можно увидеть как $w_1$ и $w_0$.\n",
    "\n",
    "Т.е. вместо $y = ax +b$ будет запись $y = w_0 + w_1 x$\n",
    "\n",
    "Почему обозначение через $w$? Так проще задавать **веса** (параметры) нашей модели вне зависимости от количества входов.\n",
    "\n",
    "Так в случае одного признака $[w_0, w_1]$ задаем $y = w_0 + w_1\\cdot x$\n",
    "\n",
    "В случае двух признаков $[w_0, w_1, w_2]$ - все аналогично, свободный член смещения и цифра, на которую мы домножаем каждую точку этого признака: $y = w_0 + w_1\\cdot x_1 + w_2\\cdot x_2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "sjdSSeGs2lCW"
   },
   "outputs": [],
   "source": [
    "# импорт необходимых библиотек\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn import datasets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OwdTQ3YIGE8j"
   },
   "source": [
    "Ниже представлен график линии с разными коэффициентами наклона и смещения"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 581
    },
    "id": "MbSM_MqS7ApH",
    "outputId": "de914d7c-d44f-425a-bc98-21d801f4d86e"
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f60efbb82e0>"
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     },
     "execution_count": 2,
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     "output_type": "execute_result"
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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 6))\n",
    "plt.title('График линии')\n",
    "plt.ylim((-35, 35))\n",
    "plt.ylabel('Y')\n",
    "plt.xlabel('X')\n",
    "\n",
    "w1 = 0.2 # наклон\n",
    "w0 = 10 # смещение\n",
    "x = np.arange(1, 40) # данные на вход\n",
    "y = w0 + x*w1 # поэлементно умножаем на наклон и поэлементно добавляем смещение\n",
    "plt.plot(x, y, label = f'Наклон {w1} смещение {w0}')\n",
    "\n",
    "w1 = 1 # наклон\n",
    "w0 = -15 # смещение\n",
    "x = np.arange(1, 40) # данные на вход\n",
    "y = w0 + x*w1 # поэлементно умножаем на наклон и поэлементно добавляем смещение\n",
    "plt.plot(x, y, label = f'Наклон {w1} смещение {w0}')\n",
    "\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "J7rxlWEipJCP"
   },
   "source": [
    "Точное решение задачи линейной регрессии возможно только в том случае, когда количество наблюдений (точек данных) равно количеству признаков в наборе данных. Тогда матрица  X  - квадратная, и может иметь обратную матрицу (см. рисунок 1)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ldd1ucjPpMka"
   },
   "source": [
    "![img_1.png](data:image/png;base64,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)\n",
    "\n",
    "Рисунок 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "paXV1VbrpVGi"
   },
   "source": [
    "В данном случае необходимо решить простейшую систему линейных уравнений: $X ⋅ W = Y$\n",
    "\n",
    "Решение: $W = X^{-1} ⋅ Y$\n",
    "\n",
    "Стоит отметить что обратная матрица существует не всегда, например когда матрица $X$ - [вырожденная](https://ru.wikipedia.org/wiki/%D0%92%D1%8B%D1%80%D0%BE%D0%B6%D0%B4%D0%B5%D0%BD%D0%BD%D0%B0%D1%8F_%D0%BC%D0%B0%D1%82%D1%80%D0%B8%D1%86%D0%B0). В любом случае, если количество наблюдений равно количеству признаков - хорошую модель на таких данных обучить не получится, поэтому во всех обучающих наборах данных количество наблюдений многократно больше количества признаков. (см. рисунок 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "xm2BlLWKpYXX"
   },
   "source": [
    "![img_2.png](data:image/png;base64,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)\n",
    "\n",
    "Рисунок 2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "D0pDmG_0pmIT"
   },
   "source": [
    "Если количество наблюдений больше количества признаков, то матрица $X$ перестает быть квадратной и обратную матрицу от нее взять не получится. Теперь у нас появляется переопределенная система линейных уравнений. У такой системы уравнений решение отсутствует, но существует приближенное решение. Существует псевдообратная матрица, которая даст решение такой системы с наименьшей квадратичной ошибкой.\n",
    "\n",
    "$$W = (X^T ⋅ X)^{-1} ⋅ X^T ⋅ Y$$\n",
    "\n",
    "Где:\n",
    "\n",
    "$(X^T ⋅ X)^{-1} ⋅ X^T$ - псевдообратная матрица\n",
    "\n",
    "> Примечание: если есть линейная зависимость между колонками, то псевдообратная матрица не существует."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "WBjM0lfaHv56"
   },
   "source": [
    "## Градиентный спуск\n",
    "На практике оптимальный вектор весов для обобщения информации в наборе данных вычисляют с помощью градиентного спуска.\n",
    "\n",
    "[Градиентный спуск, метод градиентного спуска](https://ru.wikipedia.org/wiki/%D0%93%D1%80%D0%B0%D0%B4%D0%B8%D0%B5%D0%BD%D1%82%D0%BD%D1%8B%D0%B9_%D1%81%D0%BF%D1%83%D1%81%D0%BA) — численный метод нахождения локального минимума или максимума функции с помощью движения вдоль градиента, один из основных численных методов современной оптимизации.\n",
    "\n",
    "Предполагается что между признаками (в простейшем случае он один - переменная $x$) и целевой переменной (переменная $y$) есть **линейная** зависимость. На практике признаков может быть больше, с каждым из них ищется линейная связь ($w_n \\cdot x_n$)\n",
    "\n",
    "Необходимо найти такие параметры линии $[w_0, \\cdots , w_n]$ (в простейшем случае их 2 $[w_0, w_1]$), чтобы ошибка была минимальной.\n",
    "\n",
    "Параметры мы изначально инициализируем случайными числами и затем итеративно, небольшими шагами (например, 0.001), будем уменьшать их в сторону минимизации ошибки.\n",
    "\n",
    "В зависимости от уравнения прямой ошибка (обозначим ее $J$) будет менятся - $J(W)$\n",
    "\n",
    "Тогда шагом в минимизации ошибки будет следующее выражение:\n",
    "\n",
    "$$W := W - \\alpha \\frac{d}{dW} J(W)$$\n",
    "\n",
    "Где\n",
    "* $W$ - вектор искомых параметров $[w_0, \\cdots , w_n]$\n",
    "* $J(W)$ - ошибка\n",
    "* Cимвол $:=$ означает, что значение на следующем шаге (слева) заменит выражение справа\n",
    "* Параметр $\\alpha$ - некоторая константа, например 0.001, чтобы спуск происходил без резких скачков\n",
    "* Производная (градиент, если параметров больше одного) $\\frac{d}{dW}J(W)$ показывает в какую сторону ошибка $J(W)$  будет возрастать при небольшом изменении $dW$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gtQ5OkRFKWt-"
   },
   "source": [
    "Ниже для понимания как метод градиентного спуска ищет локальный минимум функции - визуализируем график градиентного спуска по функции $y = x^2$. В данном случае очень удобная функция с точки зрения простоты дифференцирования."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 504
    },
    "id": "ZqYRy1tHIEsX",
    "outputId": "3b75c720-728d-49fd-b0e7-011c4cdb3afa"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f60ef9848b0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5, 5))\n",
    "plt.title('Градиентный спуск по функции W^2')\n",
    "plt.ylabel('J(W)')\n",
    "plt.xlabel('W')\n",
    "\n",
    "# точки по оси Ox\n",
    "data = np.linspace(-4, 4, 150)\n",
    "\n",
    "# построим сам график функции W^2\n",
    "def w_sqared(data):\n",
    "    return data**2\n",
    "\n",
    "# находим значение производной в точке\n",
    "def compute_deriv_w_sqared(point):\n",
    "    return 2*point\n",
    "\n",
    "# инициализируем случайным значеним\n",
    "w = 3.5\n",
    "\n",
    "# будем записывать значение W и соответсвую ему в точке ошибку\n",
    "w_pos = []\n",
    "error = []\n",
    "error_dict = {}\n",
    "indx = []\n",
    "\n",
    "\n",
    "# Возьмем 10 шагов\n",
    "for i in range(10):\n",
    "    # из старого значения w двигаемся в сторону убывания функции с шагом 0.05\n",
    "    w = w - 0.05 * compute_deriv_w_sqared(w)\n",
    "    #print(w, w_sqared(w))\n",
    "    indx.append(f'Итерация № {i}')\n",
    "    error_dict[w] = w_sqared(w)\n",
    "    w_pos.append(w)\n",
    "    error.append(w_sqared(w))\n",
    "\n",
    "plt.plot(data, w_sqared(data)) # парабола\n",
    "plt.scatter(w_pos, error) # точки на пораболе - итеративный спуск к точке минимума функции"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "N8Ix4TXlVBp6"
   },
   "source": [
    "С каждой новой итерацией видно что ошибка уменьшается и мы направляемся в сторону минимума, но так и не достигаем его."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 363
    },
    "id": "7HQXqF8uJDdC",
    "outputId": "457b47a5-b414-4994-d928-6b0a87a35565"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>position</th>\n",
       "      <th>error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Итерация № 0</th>\n",
       "      <td>3.150000</td>\n",
       "      <td>9.922500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Итерация № 1</th>\n",
       "      <td>2.835000</td>\n",
       "      <td>8.037225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Итерация № 2</th>\n",
       "      <td>2.551500</td>\n",
       "      <td>6.510152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Итерация № 3</th>\n",
       "      <td>2.296350</td>\n",
       "      <td>5.273223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Итерация № 4</th>\n",
       "      <td>2.066715</td>\n",
       "      <td>4.271311</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Итерация № 5</th>\n",
       "      <td>1.860043</td>\n",
       "      <td>3.459762</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Итерация № 6</th>\n",
       "      <td>1.674039</td>\n",
       "      <td>2.802407</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Итерация № 7</th>\n",
       "      <td>1.506635</td>\n",
       "      <td>2.269950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Итерация № 8</th>\n",
       "      <td>1.355972</td>\n",
       "      <td>1.838659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Итерация № 9</th>\n",
       "      <td>1.220375</td>\n",
       "      <td>1.489314</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              position     error\n",
       "Итерация № 0  3.150000  9.922500\n",
       "Итерация № 1  2.835000  8.037225\n",
       "Итерация № 2  2.551500  6.510152\n",
       "Итерация № 3  2.296350  5.273223\n",
       "Итерация № 4  2.066715  4.271311\n",
       "Итерация № 5  1.860043  3.459762\n",
       "Итерация № 6  1.674039  2.802407\n",
       "Итерация № 7  1.506635  2.269950\n",
       "Итерация № 8  1.355972  1.838659\n",
       "Итерация № 9  1.220375  1.489314"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ход обучения с результатом ошибки на каждой итерации\n",
    "# ошибкой в данном случае считается абсолютное отклонение от\n",
    "# начала координат по оси Oy\n",
    "pd_data = {'position': w_pos, 'error': error}\n",
    "pd.DataFrame(data=pd_data, index= indx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "SsLQ-BGuVMxB"
   },
   "source": [
    "На практике это зависит от:\n",
    "\n",
    "\n",
    "1.   Количества итераций (шагов градиентного спуска), в нашем случае было всего 10 шагов.\n",
    "2.   Скорости градиентного спуска (в нашем случае коэффициент скорости был равен 0.05).\n",
    "> Случайная инициализация весов тоже вносит небольшой вклад на первых итерациях, таким образом в некоторых инициализациях найти локальный минимум удастся немного быстрее.\n",
    "\n",
    "Регулировать скорость градиентного спуска нужно с осторожностью, так как при некоторых значениях можно просто проскочить локальный минимум, что будет показано ниже."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 504
    },
    "id": "YydpxL1IWGJz",
    "outputId": "3425ecab-748f-4642-b251-22fc14bd025d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f61205768c0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5, 5))\n",
    "plt.title('Градиентный спуск по функции W^2')\n",
    "plt.ylabel('J(W)')\n",
    "plt.xlabel('W')\n",
    "\n",
    "# значение оставим прежним\n",
    "w = 3.5\n",
    "\n",
    "w_pos = []\n",
    "error = []\n",
    "\n",
    "for i in range(10):\n",
    "    # изменим только скорость спуска\n",
    "    w = w - 0.95 * compute_deriv_w_sqared(w)\n",
    "    w_pos.append(w)\n",
    "    error.append(w_sqared(w))\n",
    "\n",
    "plt.plot(data, w_sqared(data))\n",
    "plt.scatter(w_pos, error)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zraM7nbAXjTR"
   },
   "source": [
    "При новом значении коэффициента скорости градиентного спуска (слишком высоком) мы сразу проскакиваем минимум, конечно его можно достигнуть и при таком значении скорости спуска, но придется сильно увеличить количество шагов, чего не хотелось бы делать, поэтому необходимо находить оптимальное соотношение скорости спуска и количества шагов для того чтобы достичь минимума функции за минимальное количество шагов.\n",
    "\n",
    "В дальнейшем, вы сможете автоматизировать процесс подбора скорости обучения для решения задач машинного обучения с помощью алгоритмов гиперпараметрической оптимизации, таких как Bayesian optimization, grid search или random search."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 504
    },
    "id": "cKpV5oPyYCqA",
    "outputId": "0ef2c63a-5e66-46b7-c7fb-8addc79e247f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f6120407f40>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5, 5))\n",
    "plt.title('Градиентный спуск по функции W^2')\n",
    "plt.ylabel('J(W)')\n",
    "plt.xlabel('W')\n",
    "\n",
    "# значение оставим прежним\n",
    "w = 3.5\n",
    "\n",
    "w_pos = []\n",
    "error = []\n",
    "\n",
    "for i in range(10):\n",
    "    # изменим только скорость спуска\n",
    "    w = w - 0.5 * compute_deriv_w_sqared(w)\n",
    "    w_pos.append(w)\n",
    "    error.append(w_sqared(w))\n",
    "\n",
    "plt.plot(data, w_sqared(data))\n",
    "plt.scatter(w_pos, error)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OjvShP3BZ2yo"
   },
   "source": [
    "Идеальное значение скорости спуска в данной задаче равна 0.5, при этом значении мы за один шаг попадаем в минимум функции."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "PniuNHEmb_Mh"
   },
   "source": [
    "## Как оценивать результат работы модели на реальных данных (метрики в задаче регрессии)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "F9DB-sFuq0Bd"
   },
   "source": [
    "### MAE (Mean absolute error) или средняя абсолютная ошибка\n",
    "\n",
    "В примере до этого мы рассматривали ситуацию, когда напрямую известно как выглядит зависимость входов от выходов ($J(w) = w^2$). В практических задачах эта зависимоть неизвестна и модели нужно будет найти зависимость между целевой переменной и признаками набора данных.\n",
    "\n",
    "Чтобы понять насколько точно модель делает свой прогноз относительно значений целевой переменной, необходим функционал позволяющий оценить ошибку. Есть несколько метрик по которым можно оценить качество прогнозов модели. Одной из них является **MAE (Mean absolute error) или средняя абсолютная ошибка**.\n",
    "\n",
    "$$J(W) = \\frac{1}{n}\\sum_{i=0}^{n} |y_i - \\hat{y}_i|$$\n",
    "Где:\n",
    "* J(W) - ошибка зависящая от параметров алгоритма $W = [w_0, w_1]$ в нашем простейшем случае\n",
    "* $n$ - количество точек (у нас было сгенерировано 250 точек)\n",
    "* $\\hat{y}_i$ - прогноз алгоритма $y = w_0 + w_1\\cdot x$ (y - целевое значение, х - единственный признак) для $i$-ой точки данных\n",
    "* $y_i$ - истинные значения (целевая метка)\n",
    "\n",
    "Суть заключается в том чтобы оценить разницу между истинным значением и предсказанным моделью. Модуль тут служит для компенсации отрицательноего значения ошибки).\n",
    "\n",
    "Но стоит обратить внимание, что модуль - **НЕ** дифференцируемая функция. Таким образом не представляется возможным оценить как изменение параметров алгоритма оказывает влияние на ошибку. Поэтому чаще всего используют **MSE (Mean squared error) или среднеквадратичную ошибку**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bmfONIeJrK3l"
   },
   "source": [
    "### MSE (Mean squared error) или среднеквадратичная ошибка."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bvzwYz2kqx8X"
   },
   "source": [
    "\n",
    "\n",
    " MSE легко дифференцируется и сильнее \"штрафует\" (квадратично) каждую точку, которая сильно отклоняется от реальных значений:\n",
    "$$J(W) = \\frac{1}{n}\\sum_{i=0}^{n} (y_i - \\hat{y}_i)^2$$\n",
    "\n",
    "Если параметров больше чем 1, то находят градиент функции ∇. Градиент функции - это вектор частных производных по параметрам.\n",
    "\n",
    "На момент нахождения частной производной относительно $w_1$, все другие $w_n$ считаются $const$.\n",
    "\n",
    "Производная по $w_1$:\n",
    "\n",
    "$$\\frac{dJ(W)}{dw_1} = \\frac{1}{n}\\sum_{i=0}^{n} (y_i - (w_0 + w_1 ⋅ x_i)^2)' = $$\n",
    "$$= \\frac{1}{n}\\sum_{i=0}^{n} 2(y_i - (w_0 + w_1 ⋅ x_i)) ⋅ (-x_i) = $$\n",
    "$$= -\\frac{2}{n}\\sum_{i=0}^{n} x_i(y_i - \\hat{y}_i)$$\n",
    "\n",
    "Аналогично находится производная по смещению ($w_0$):\n",
    "\n",
    "$$\\frac{dJ(W)}{dw_0} = -\\frac{2}{n}\\sum_{i=0}^{n} (y_i - \\hat{y}_i)$$\n",
    "\n",
    "Теперь если инициализировать $w_0$ и $w_1$ случайными значениями, их нужно обновлять по направлению минус градиент:\n",
    "\n",
    "$$w_0 = w_0 - \\alpha \\frac{dJ(W)}{dw_0}$$\n",
    "$$w_1 = w_1 - \\alpha \\frac{dJ(W)}{dw_1}$$\n",
    "\n",
    "Где $\\alpha$ - скорость спуска"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ynM-z068rS2e"
   },
   "source": [
    "## Обоснование выбора MSE\n",
    "\n",
    "Чтобы понять почему при решении задачи линейной регрессии принято прибегать к использованию среднеквадратической ошибки (Mean squared error) для начала нужно рассмотреть такие статистические методы как **метод максимального правдоподобия** и **минимизацию эмпирического риска**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5PSvDi1Srh2g"
   },
   "source": [
    "### Метод максимального правдоподобия\n",
    "\n",
    "Метод максимального правдоподобия (MLE — maximum likelihood estimation) — это метод оценивания неизвестного параметра путём максимизации функции правдоподобия. Основан на предположении о том, что вся информация о статистической выборке содержится в функции правдоподобия.\n",
    "\n",
    "Если предположить что нам известна условная вероятность получить на выходе модели машинного обучения наш ответ $y$ при входных данных $x$, и наша обучаящая выборка независимо одинаково распределена (в теории вероятностей и статистике, о наборе случайных величин говорят, что они являются независимыми (и) одинаково распределёнными, если каждая из них имеет такое же распределение, что и другие, и все величины являются независимыми в совокупности).\n",
    "\n",
    "Учитывая вышеизложенное, вероятность получить набор ответов $(y_1, y_2, ..., y_n)$ при заданных $(x_1, x_2, ..., x_n)$ будет равна:\n",
    "\n",
    "$$P(y_1, y_2, ..., y_n|x_1, x_2, ..., x_n) = \\prod P(y_i|x_i)$$\n",
    "\n",
    "Для облегчения задачи дифференцирования прологарифмируем формулу выше. Логарифм произведения является суммой, поэтому для практических вычислений предпочитают использовать логарифм функции правдоподобия.\n",
    "\n",
    "Тогда нашу задачу максимизации функции правдоподобия можно записать следующим образом:\n",
    "\n",
    "$$ln\\prod P(y_i|x_i) \\to max$$\n",
    "что будет эквивалентно\n",
    "$$\\sum_i log P(y_i|x_i) \\to max$$\n",
    "\n",
    "И если у нас есть множество моделей (А), нужно выбрать ту модель, что наилучшим образом обобщает информацию по всей нашей выборке, она и будет максимизировать функцию правдоподобия, а сама функция правдоподобия в данном случае будет иметь вид:\n",
    "\n",
    "$$W(A) = \\sum log p(y_i|x_i, A)$$\n",
    "\n",
    "Из всего множества моделей ($A$) выбирается  $A^* = argmax_{A}W(A)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "uV1Se8sFrnPS"
   },
   "source": [
    "### Минимизация эмпирического риска\n",
    "\n",
    "Эмпирический риск - это функционал качества, характеризующий среднюю ошибку алгоритма $A^*$ на выборке $X^n$.\n",
    "\n",
    "$$Q(A^*, X^n) = \\frac{1}{n}\\sum_{i=1}^n L(A^*(x_i), y^*(x_i))$$\n",
    "\n",
    "Где:\n",
    "\n",
    "$L(A^*(x_i), y^*(x_i))$ - функция потерь, характеризующая величину отклонения предсказанного моделью ответа от истинного значения ответа на произвольном объекте нашей выборки.\n",
    "\n",
    "**Метод минимизация эмпирического риска** заключается в том, чтобы в заданной модели алгоритмов $A = {A^*: X \\to Y}$ найти алгоритм, доставляющий минимальное значение функционалу эмпирического риска:\n",
    "\n",
    "$$A^* = argmin_{A^*\\in A} Q(A^*, X^n)$$\n",
    "\n",
    "> Метод максимизации правдоподобия эквивалентен минимизации эмпирического риска."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pNrIPcJQrypp"
   },
   "source": [
    "Мы предположили, что ошибка нормально распределена, $x$ – признаковое описание объекта. Тогда мы знаем как распределены ответы нашей функции и можем записать функцию правдоподобия выборки (т.е. произведение плотностей, в которые подставлены значения из обучающей выборки) и воспользоваться методом максимального правдоподобия (в котором для определения значений параметров берётся максимум правдоподобия, а чаще – его логарифма):\n",
    "\n",
    "$$P(y|x, w) = \\frac{1}{\\sqrt{2\\pi \\sigma^2}}exp(-\\frac{(y-w^T x)^2}{2\\sigma^2})$$\n",
    "\n",
    "Прологарифмировав функцию правдоподобия получим:\n",
    "\n",
    "$L(w) = log \\prod_i^n P(y_i|x_i, w) = \\sum_{i=1}^n(-\\frac{1}{2}log(2\\pi \\sigma^2) - \\frac{y_i - w^Tx_i)^2}{2\\sigma^2}) \\to max$\n",
    "\n",
    "Преобразовав, получим, что это эквивалентно минимизации:\n",
    "\n",
    "$$\\frac{1}{2\\sigma^2}\\sum_{i=1}^{n}(y_i - w^T x_i)^2 \\to min$$\n",
    "\n",
    "Что это эквивалентно минимизации MSE."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "w4B0kWn5FELW"
   },
   "source": [
    "## Стандартизация признаков\n",
    "<a id='standardization_of_features'></a>\n",
    "\n",
    "**Стоит учитывать что производная очень чувствительна к масштабу, и если признаки не прошли предварительную нормализацию (предпочтительно - стандартизацию), то шаги начнут резко менять параметры алгоритма, в следствии чего параметры уйдут в бесконечность или в 0.**\n",
    "\n",
    "Выполняя стандартизацию признаков мы устраняем влияние масштаба признаков и стабилизируем спуск по минус градиенту.\n",
    "\n",
    "$$x_{i, j} = \\frac{x_{i,j} - \\mu_j}{\\sigma_j}$$\n",
    "\n",
    "Где:\n",
    "* $j$ - номер столбца (признака)\n",
    "* $i$ - номер строки (точки данных)\n",
    "* $x_{i, j}$ - значение данных в строке $i$ столбца $j$\n",
    "* $\\mu_j$ - среднее (матожидание) значение в признаке $j$\n",
    "* $\\sigma_j$ - стандартное отклонение в признаке $j$\n",
    "\n",
    "Иными словами мы переносим середину распределения в 0 и сжимаем его так, чтоб стандартное отклонение было = 1 (как и дисперсия), что позитивно скажется на амплитуду разброса."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Nbc2iM7yE4GW"
   },
   "source": [
    "## Загрузка набора данных"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "MVtMWr8iFQ49"
   },
   "source": [
    "Загрузим датасет “penguins” из библиотеки [seaborn](https://seaborn.pydata.org/). Он содержит информацию о 344 пингвинах, обитающих в Антарктиде. Данные собраны в ходе экспедиции исследовательского корабля “Nathaniel B. Palmer” в 2012 году и включают информацию о следующих параметрах каждого пингвина:\n",
    "\n",
    "\n",
    "\n",
    "*   ID - уникальный идентификатор пингвина\n",
    "*   species - вид пингвина (Adelie, Chinstrap или Gentoo)\n",
    "*   bill_length_mm - длина клюва пингвина в миллиметрах\n",
    "*   bill_depth_mm - глубина клюва в миллиметрах\n",
    "*   flipper_length_mm - длина плавника в миллиметрах\n",
    "*   body_mass_g - масса тела пингвина в граммах\n",
    "\n",
    "\n",
    "> Чтобы посмотреть список всех наборов данных доступных в библиотеки seaborn выполните `seaborn.get_dataset_names()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 206
    },
    "id": "Rw2KGrl1IWdL",
    "outputId": "db96c380-526c-4a68-8c21-7c9effe98790"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>species</th>\n",
       "      <th>island</th>\n",
       "      <th>bill_length_mm</th>\n",
       "      <th>bill_depth_mm</th>\n",
       "      <th>flipper_length_mm</th>\n",
       "      <th>body_mass_g</th>\n",
       "      <th>sex</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>39.1</td>\n",
       "      <td>18.7</td>\n",
       "      <td>181.0</td>\n",
       "      <td>3750.0</td>\n",
       "      <td>Male</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>39.5</td>\n",
       "      <td>17.4</td>\n",
       "      <td>186.0</td>\n",
       "      <td>3800.0</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>40.3</td>\n",
       "      <td>18.0</td>\n",
       "      <td>195.0</td>\n",
       "      <td>3250.0</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>36.7</td>\n",
       "      <td>19.3</td>\n",
       "      <td>193.0</td>\n",
       "      <td>3450.0</td>\n",
       "      <td>Female</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Adelie</td>\n",
       "      <td>Torgersen</td>\n",
       "      <td>39.3</td>\n",
       "      <td>20.6</td>\n",
       "      <td>190.0</td>\n",
       "      <td>3650.0</td>\n",
       "      <td>Male</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  species     island  bill_length_mm  bill_depth_mm  flipper_length_mm  \\\n",
       "0  Adelie  Torgersen            39.1           18.7              181.0   \n",
       "1  Adelie  Torgersen            39.5           17.4              186.0   \n",
       "2  Adelie  Torgersen            40.3           18.0              195.0   \n",
       "4  Adelie  Torgersen            36.7           19.3              193.0   \n",
       "5  Adelie  Torgersen            39.3           20.6              190.0   \n",
       "\n",
       "   body_mass_g     sex  \n",
       "0       3750.0    Male  \n",
       "1       3800.0  Female  \n",
       "2       3250.0  Female  \n",
       "4       3450.0  Female  \n",
       "5       3650.0    Male  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = sns.load_dataset(\"penguins\")\n",
    "df.dropna(inplace=True)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "y-2SKauFGJml"
   },
   "source": [
    "Для простоты реализации алгоритма в этой рабочей тетради мы будем рассматривать только 2 колонки в данном наборе данных. Возьмем признак `flipper_length_mm`, а за целевую переменную `body_mass_g`. Будем исследовать взаимосвязь массы тела пингвина и длины плавника пингвина."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 206
    },
    "id": "bCn_MbVtGl0O",
    "outputId": "43b54a11-3b56-4ccd-b8df-0ecf1e3eca27"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>flipper_length_mm</th>\n",
       "      <th>body_mass_g</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>181.0</td>\n",
       "      <td>3750.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>186.0</td>\n",
       "      <td>3800.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>195.0</td>\n",
       "      <td>3250.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>193.0</td>\n",
       "      <td>3450.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>190.0</td>\n",
       "      <td>3650.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   flipper_length_mm  body_mass_g\n",
       "0              181.0       3750.0\n",
       "1              186.0       3800.0\n",
       "2              195.0       3250.0\n",
       "4              193.0       3450.0\n",
       "5              190.0       3650.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = df[['flipper_length_mm', 'body_mass_g']]\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-aleUvVuh-o2"
   },
   "source": [
    "## Создание, обучение и оценка работы модели"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "_uTtLK6LcEwX",
    "outputId": "9be527da-1cd3-41a9-d5e2-99a6477970fb"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12952.540720720719 64.66402402402403\n",
      "nan nan\n",
      "nan nan\n",
      "nan nan\n"
     ]
    }
   ],
   "source": [
    "# инициализация весов\n",
    "w1 = 1\n",
    "w0 = 1\n",
    "\n",
    "alpha = 0.01  # скорость спуска\n",
    "epochs = 700  # количество эпох (в данном случае шагов/итераций)\n",
    "\n",
    "error_train = [] # история изменения MSE в течении итераций во время обучения\n",
    "error_test = [] # история изменения MSE в течении итераций на тесте\n",
    "\n",
    "X = data['flipper_length_mm'] # длина плавника пингвина\n",
    "Y = data['body_mass_g'] # масса тела пингвина\n",
    "\n",
    "# разобьем точки на обучающую и тестовую выборки\n",
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.2)\n",
    "\n",
    "n = float(len(X)) # Число элементов в выборке\n",
    "\n",
    "for i in range(epochs):\n",
    "\n",
    "    Y_pred = w1*X_train + w0  # Текущее предсказание вектора Y\n",
    "    D_w1 = (-2/n) * sum(X_train * (y_train - Y_pred))  # Производная функции потерь по w1\n",
    "    D_w0 = (-2/n) * sum(y_train - Y_pred)  # Производная функции потерь по w0\n",
    "    w1 = w1 - alpha * D_w1  # Обновляем w1 по направлению минус градиента\n",
    "    w0 = w0 - alpha * D_w0  # Обновляем w0 по направлению минус градиента\n",
    "\n",
    "    Y_pred_test = w1*X_test + w0\n",
    "\n",
    "    error_train.append(((y_train - Y_pred)**2).mean())\n",
    "    error_test.append(((y_test - Y_pred_test)**2).mean())\n",
    "\n",
    "    if i%200==0: # будем отображать прогресс обучения каждые 10 итераций\n",
    "        print(w1, w0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qBnH7TR9kPTS"
   },
   "source": [
    "Визуализируем изменение MSE в ходе обучения и теста"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 462
    },
    "id": "yDaA7wtClpXw",
    "outputId": "06a09c61-2135-4871-afdd-22fab8655759"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(error_train, label='train MSE')\n",
    "sns.lineplot(error_test, label='test MSE')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "aV0dgF8NMTTd"
   },
   "source": [
    "Мы наблюдаем \"взрыв\" градиента, это именно то, о чем упоминалось в блоке **Стандартизация признаков**. Произошло это из-за того что абсолютные значения длин плавников неотмасштабированы.\n",
    "\n",
    "**Произведем процедуру стандартизации**\n",
    "\n",
    "При стандартизации признаков в машинном обучении рекомендуется применять её отдельно к обучающей выборке и к тестовой выборке. Это важно для избегания утечки информации из тестового набора данных в процессе обучения модели.\n",
    "\n",
    "Вот почему:\n",
    "\n",
    "1. *Имитация реальности*: В реальной жизни, когда модель применяется к новым данным, она не имеет доступа к будущим значениям. Поэтому, когда вы стандартизируете данные, используя параметры (например, среднее и стандартное отклонение), вы рассчитываете их только на основе обучающих данных.\n",
    "\n",
    "2. *Избегание утечки данных*: Если бы вы использовали параметры стандартизации, рассчитанные на всем наборе данных (включая тестовую выборку), это могло бы привести к информационной утечке, что может привести к завышенным ожиданиям от модели при тестировании на новых данных.\n",
    "\n",
    "3. *Реальная оценка обобщающей способности*: Использование отдельных параметров стандартизации для обучающей и тестовой выборок позволяет модели реально оценить её обобщающую способность на новых данных.\n",
    "\n",
    "Итак, когда вы работаете с данными, сначала разбивайте их на обучающую и тестовую выборки, а затем применяйте стандартизацию отдельно к каждому из них, используя параметры (например, среднее и стандартное отклонение), рассчитанные только на обучающей выборке."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "0VBPl4KhUBON"
   },
   "outputs": [],
   "source": [
    "# создаем копию датафрейма\n",
    "data_std = data.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# разбиваем на обучающую и тестовую выборки\n",
    "X = data_std['flipper_length_mm'] # длина плавника пингвина\n",
    "Y = data_std['body_mass_g'] # масса тела пингвина\n",
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Рассчитываем среднее и стандартное отклонение на обучающей выборке\n",
    "mean = np.mean(X_train, axis=0)\n",
    "std = np.std(X_train, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Применяем стандартизацию к обучающей и тестовой выборкам\n",
    "X_train_scaled = (X_train - mean) / std\n",
    "X_test_scaled = (X_test - mean) / std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# объединим стандартизованные выборки для визуализации на графике\n",
    "concatenated_series = pd.concat([X_train_scaled, X_test_scaled])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 427
    },
    "id": "nNWJH74YPKok",
    "outputId": "fc8bba6a-24b0-4308-93c8-97501a4d397c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Гистограмма после стандартизации')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(nrows=1, ncols=2, figsize=(12, 4))\n",
    "\n",
    "# График 1 гистограмма до стандартизации\n",
    "sns.histplot(data=data, x=\"flipper_length_mm\", ax=axs[0])\n",
    "axs[0].set_title('Гистограмма до стандартизации')\n",
    "\n",
    "\n",
    "# График 2 гистограмма после стандартизации\n",
    "sns.histplot(x=concatenated_series, ax=axs[1])\n",
    "axs[1].set_title('Гистограмма после стандартизации')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "UG_-EL1aitJ0"
   },
   "source": [
    "Теперь повторим обучение модели, но уже со стандартизованными признаками"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "nuStfCXuiyYm",
    "outputId": "60142a42-4a03-4d61-b44a-ae19224faada"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.298469696626482 68.26930930930929\n",
      "680.4384185073939 4046.2693469495853\n",
      "707.1074798395624 4205.05273832145\n",
      "708.1719856120505 4211.390638054229\n"
     ]
    }
   ],
   "source": [
    "# инициализация весов\n",
    "w1 = 1\n",
    "w0 = 1\n",
    "\n",
    "alpha = 0.01  # скорость спуска\n",
    "epochs = 700  # количество эпох (в данном случае шагов/итераций)\n",
    "\n",
    "error_train = [] # история изменения MSE в течении итераций во время обучения\n",
    "error_test = [] # история изменения MSE в течении итераций на тесте\n",
    "\n",
    "n = float(len(X)) # Число элементов в выборке\n",
    "\n",
    "for i in range(epochs):\n",
    "\n",
    "    Y_pred = w1*X_train_scaled + w0  # Текущее предсказание вектора Y\n",
    "    D_w1 = (-2/n) * sum(X_train_scaled * (y_train - Y_pred))  # Производная функции потерь по w1\n",
    "    D_w0 = (-2/n) * sum(y_train - Y_pred)  # Производная функции потерь по w0\n",
    "    w1 = w1 - alpha * D_w1  # Обновляем w1 по направлению минус градиента\n",
    "    w0 = w0 - alpha * D_w0  # Обновляем w0 по направлению минус градиента\n",
    "\n",
    "    Y_pred_test = w1*X_test_scaled + w0\n",
    "\n",
    "    error_train.append(((y_train - Y_pred)**2).mean())\n",
    "    error_test.append(((y_test - Y_pred_test)**2).mean())\n",
    "\n",
    "    if i%200==0: # будем отображать прогресс обучения каждые 200 итераций\n",
    "        print(w1, w0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "CGiz7OoYkd5P"
   },
   "source": [
    "Вновь визуализируем изменение MSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 462
    },
    "id": "OGj58InCjgGz",
    "outputId": "5eb8d50b-42f8-4980-c9ad-dae18205cd2a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(error_train, label='train MSE')\n",
    "sns.lineplot(error_test, label='test MSE')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "MbdweqOkqUuI"
   },
   "source": [
    "Построим нашу обобщающую линию по лучшим результатам после обучения"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 564
    },
    "id": "xSt6QfpWqvsq",
    "outputId": "b3deb644-3233-4fd3-eb4a-262905541ebe"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 6))\n",
    "plt.title(\"Зависимость Y от X\")\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "sns.scatterplot(x=concatenated_series, y=Y)\n",
    "\n",
    "plot_x = concatenated_series\n",
    "plot_y = w0 + w1*plot_x\n",
    "plt.plot(plot_x, plot_y, label = f'Наклон: {w1:.2f} \\nCмещение: {w0:.2f}')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для правильной интерпретации результатов модели машинного обучения при визуализации на графиках может быть полезно провести обратную процедуру стандартизации.\n",
    "\n",
    "Если вы стандартизировали ваши признаки перед подачей их в модель, результаты модели будут в терминах стандартных отклонений. Если вы хотите интерпретировать эти результаты в исходной шкале данных, вам потребуется провести обратную процедуру стандартизации."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_original_scale = concatenated_series * std + mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 6))\n",
    "plt.title(\"Зависимость Y от X\")\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "sns.scatterplot(x=X_original_scale, y=Y)\n",
    "\n",
    "plot_x = X_original_scale\n",
    "plot_y = w0 + w1*concatenated_series\n",
    "plt.plot(plot_x, plot_y, label = f'Наклон: {w1:.2f} \\nCмещение: {w0:.2f}')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "l9s7iA86lmnC"
   },
   "source": [
    "## Заключение\n",
    "\n",
    "В данной рабочей тетради мы познакомились с простой реализацией модели линейной регрессии на примере одного признака и целевой переменной, узнали как работает метод градиентного спуска и для чего он необходим, оценили влияние масштаба признаков на результат работы модели и важность предварительной обработки данных перед обучением модели, ознакомились с часто используемыми метриками качества для оценки работы модели.\n",
    "\n",
    "В следующей рабочей тетради будет рассказано о создании полиномиальных признаков для нахождения нелинейных зависимостей в данных, а также о способах борьбы с переобучением модели таких как регуляризация и отбор признаков."
   ]
  }
 ],
 "metadata": {
  "colab": {
   "provenance": [],
   "toc_visible": true
  },
  "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": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}