jupyter_notebooks/III_machine_learning_supervised.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Обучение с учителем\n",
    "\n",
    "Алгоритмы, которые требуют размеченной выборки для обучения, называются алгоритмами обучения с учителем. \"Разметить выборку\" означает поставить в соответствие объекту обучающей выборки значение целевой переменной (таргета) которое алгоритм машинного обучения  должен \"выучить\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Обычно большие объёмы дорого размечать - можно пользоваться сервисами типа \"Яндекс.Толока\", либо своими силами размечать."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Классификация\n",
    "\n",
    "## Постановка задачи классификации\n",
    "\n",
    "Классификация - задача для алгоритмов машинного обучения восстановить на объектах обучающей выборки **метки классов**. Классы - конечный (дискретный) набор целевых переменных. Например, в задаче фильтрации спама два класса: спам (метка $1$) и не спам (метка $0$)\n",
    "\n",
    "Существует бинарная классификация (когда классов всего два: $0$ и $1$) и мультиклассовая классификация, когда классов несколько. Если научились классифицировать на два класса, то и на несколько получиться: метод One vs All "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Продемострируем работу алгоритма классификации на данных по оттоку, которые содержатся в файле `data/client_segmentation.csv`. В файле содержится информация по клиентам оператора связи о том, как изменилось потребление услуг оператора за два месяца:\n",
    "* call_diff доля звонков\n",
    "* sms_diff доля смс\n",
    "* доля интернет-трафика traffic_diff\n",
    "\n",
    "Все показатели вычисляются по формуле\n",
    "\n",
    "$$\n",
    "\\frac{\\text{new_value}-\\text{old_value}}{\\text{old_value}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В последней колонке `customes_class` содержится метка по оттоку:\n",
    "* $0$ - активный пользователя\n",
    "* $1$ - \"спящий\" пользователь (редко пользуется услугами)\n",
    "* $2$ - пользователь, который ушел в отток"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "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>call_diff</th>\n",
       "      <th>sms_diff</th>\n",
       "      <th>traffic_diff</th>\n",
       "      <th>customes_class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.666421</td>\n",
       "      <td>0.444911</td>\n",
       "      <td>-0.273538</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.889273</td>\n",
       "      <td>-0.537896</td>\n",
       "      <td>-1.959469</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.841503</td>\n",
       "      <td>0.846665</td>\n",
       "      <td>0.727606</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.389749</td>\n",
       "      <td>0.390911</td>\n",
       "      <td>1.789246</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1.228211</td>\n",
       "      <td>-1.375899</td>\n",
       "      <td>-1.434209</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   call_diff  sms_diff  traffic_diff  customes_class\n",
       "0  -0.666421  0.444911     -0.273538               0\n",
       "1  -0.889273 -0.537896     -1.959469               2\n",
       "2  -0.841503  0.846665      0.727606               0\n",
       "3   1.389749  0.390911      1.789246               1\n",
       "4  -1.228211 -1.375899     -1.434209               2"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline\n",
    "np.set_printoptions(precision=4)\n",
    "\n",
    "df_source = pd.read_csv(\n",
    "    'data/client_segmentation.csv', \n",
    "    dtype={'call_diff': np.float32, 'call_diff': np.float32, 'traffic_diff': np.float32, 'customes_class': np.uint16}\n",
    ")\n",
    "X = df_source[['call_diff','sms_diff','traffic_diff']].values\n",
    "y = df_source.customes_class.values\n",
    "\n",
    "df_source.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f71a0891b00>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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C7SclfVfSzbbP2r6v6kwl3SrpbkkfLV7fp4q9wgy2SzpR9Mr3tHIMvNTpeFlxKT0AJMWVmACQFAUOAElR4ACQFAUOAElR4ACQFAUOAElR4ACQ1P8DJdmogfRCIJ8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_source.sms_diff.hist(bins=8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    34\n",
       "2    33\n",
       "1    33\n",
       "Name: customes_class, dtype: int64"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_source.customes_class.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Построим наивный байесовский классификатор - мы уже использовали этот алгоритм в начале курса, когда говорили про теорию вероятностей.\n",
    "\n",
    "Оценим качество классификатора: сколько пользователей предсказали правильно"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Точность предсказаний: 0.95\n"
     ]
    }
   ],
   "source": [
    "from sklearn.naive_bayes import GaussianNB\n",
    "\n",
    "naive_bayes = GaussianNB() # создаём экземпляр класса\n",
    "naive_bayes.fit(X, y) # обучение модели\n",
    "predicted_classes = naive_bayes.predict(X) # предсказание (эксплуатация модели)\n",
    "\n",
    "accuracy = (predicted_classes == y).sum() / len(y)\n",
    "\n",
    "print(f'Точность предсказаний: {accuracy}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Можно вытащить, например, априорные вероятности классов"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.34 0.33 0.33]\n"
     ]
    }
   ],
   "source": [
    "print(naive_bayes.class_prior_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Алгоритмы классификации\n",
    "\n",
    "Алгоритмы приводятся в виде ссылок на документацию sklearn\n",
    "\n",
    "### [Наивный Байесовский классификатор](https://scikit-learn.org/stable/modules/naive_bayes.html)\n",
    "\n",
    "Классификатор основан на вероятностном подходе: подсчёт частот встречаемости фичей.\n",
    "\n",
    "Очень просто реализовать, поэтому работает достаточно быстро. Применим  на больших объёмах данных в случае, когда количество фичей не очень большое.\n",
    "\n",
    "### [Метод $K$ ближайших соседей](https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.KNeighborsClassifier.html)\n",
    "\n",
    "Т.н. \"ленивый\" (lazy algorithm) алгоритм классификации, который работает за два шага:\n",
    "\n",
    "* запоминает объекты обучающей выборки и их классы\n",
    "* в момент предсказания для объекта находит $k$ самых близких объектов из обучающей выборки и присваивает новому объекту класс большинства его \"соседей\"\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Логистическая регрессия](https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression)\n",
    "\n",
    "Алгоритм, основанный на идеях линейной регрессии. Применим для бинарной классификации, на выходе выдаёт вероятность того, что объект принадлежит классу $1$, которая вычисляется по формуле\n",
    "\n",
    "$$\n",
    "P(y==1 | x) = \\frac{1}{1+e^{z}}\n",
    "$$\n",
    "\n",
    "Где $z$ - линейная комбинация фичей объекта\n",
    "$$\n",
    "z = \\theta^T x = \\theta_1 x_1 + \\theta_2 x_2 + \\ldots + \\theta_n x_n\n",
    "$$\n",
    "\n",
    "Обучение сводится к вычислению оптимального набора $\\theta = [\\theta_1, \\theta_2, \\ldots, \\theta_n]$\n",
    "\n",
    "Статья [пережёвываем логистическую регрессию](https://m.habr.com/ru/post/485872/)_\n",
    "\n",
    "\n",
    "**Примечание**: другой пример линейного классификатора - [машина опорных векторов](https://scikit-learn.org/stable/modules/svm.html#classification)\n",
    "\n",
    "В этом алгоритме мы обучаем вектор весов $W$ таким образом, чтобы прямая $y=W^TX$, задаваемая этими весами, проходила на максимальном удалении от точек обоих классов\n",
    "\n",
    "![svm_hyperplane.png](img/svm_hyperplane.png)\n",
    "\n",
    "Отличная [статья на Хабре про SVM](https://habr.com/ru/company/ods/blog/484148/) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Дерево принятия решений]()\n",
    "\n",
    "Дерево принятия решений в задачах классификации можно представить как последовательность вопросов о фичах объекта, которая приводит к однозначному определению класса объекта. Каждый следующий вопрос зависит от того, какой ответ был получен на предыдущем шаге\n",
    "\n",
    "Как каждый такой вопрос - это проверка признака по некоторому \"порогу разбиения\" и разбиение выборки на две части по этому порогу. Порог разбиения выбирается таким образом, чтобы минимизировать энтропию (т.е. уменьшить неопределенность) в двух получившихся частях выборки.\n",
    "\n",
    "Более подробно ( в т.ч. про энтропию) можно почитать в [Статье от ODS](https://habr.com/ru/company/ods/blog/322534)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import tree\n",
    "\n",
    "clf = tree.DecisionTreeClassifier().fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Предсказания одного дерева получаем по формуле"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Точность предсказаний: 1.0\n"
     ]
    }
   ],
   "source": [
    "predicted_classes = clf.predict(X)\n",
    "\n",
    "accuracy = (predicted_classes == y).sum() / len(y)\n",
    "\n",
    "print(f'Точность предсказаний: {accuracy}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Визуализация дерева принятия решений"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(197.83636363636364, 195.696, 'X[0] <= 0.259\\ngini = 0.667\\nsamples = 100\\nvalue = [34, 33, 33]'),\n",
       " Text(121.74545454545455, 152.208, 'X[1] <= 0.629\\ngini = 0.528\\nsamples = 68\\nvalue = [33, 2, 33]'),\n",
       " Text(60.872727272727275, 108.72, 'X[2] <= -0.411\\ngini = 0.26\\nsamples = 39\\nvalue = [6, 0, 33]'),\n",
       " Text(30.436363636363637, 65.232, 'gini = 0.0\\nsamples = 26\\nvalue = [0, 0, 26]'),\n",
       " Text(91.30909090909091, 65.232, 'X[1] <= -0.702\\ngini = 0.497\\nsamples = 13\\nvalue = [6, 0, 7]'),\n",
       " Text(60.872727272727275, 21.744, 'gini = 0.0\\nsamples = 7\\nvalue = [0, 0, 7]'),\n",
       " Text(121.74545454545455, 21.744, 'gini = 0.0\\nsamples = 6\\nvalue = [6, 0, 0]'),\n",
       " Text(182.61818181818182, 108.72, 'X[0] <= -0.32\\ngini = 0.128\\nsamples = 29\\nvalue = [27, 2, 0]'),\n",
       " Text(152.1818181818182, 65.232, 'gini = 0.0\\nsamples = 27\\nvalue = [27, 0, 0]'),\n",
       " Text(213.05454545454546, 65.232, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 2, 0]'),\n",
       " Text(273.92727272727274, 152.208, 'X[1] <= -0.899\\ngini = 0.061\\nsamples = 32\\nvalue = [1, 31, 0]'),\n",
       " Text(243.4909090909091, 108.72, 'gini = 0.0\\nsamples = 1\\nvalue = [1, 0, 0]'),\n",
       " Text(304.3636363636364, 108.72, 'gini = 0.0\\nsamples = 31\\nvalue = [0, 31, 0]')]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "tree.plot_tree(clf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Классификатор на случайных деревьях](https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html#sklearn.ensemble.RandomForestClassifier)\n",
    "\n",
    "Строим большое количество случайных деревьев, а итоговое предсказание - результат \"голосования\" деревьев\n",
    "\n",
    "![random_forest_introduction.jpg](img/random_forest_introduction.jpg)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Почему это работает?\n",
    "\n",
    "Если у каждого дерева вероятность правильного предсказания выше, чем 0.5 то у чем больше таких деревьев тем выше вероятнсть правильного ответа"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Метрики классификации\n",
    "\n",
    "Все метрики классификации основаны на следующей таблице, которая содержит возможные исходы работы классификатора: ошибочные и корректные.\n",
    "\n",
    "![confusion_matrix.png](img/confusion_matrix.png)\n",
    "\n",
    "В таблице 4 исхода применения классификатора:\n",
    "\n",
    "* `true positive`: класс $1$ предсказали правильно\n",
    "* `false positive`: класс $1$ предсказали неправильно\n",
    "* `true negative`: класс $0$ предсказали правильно\n",
    "* `false negative`: класс $0$ предсказали неправильно\n",
    "\n",
    "На числах, которые находятся в ячейках таблицы можно построить огромное количество метрик\n",
    "\n",
    "Для начала посчитаем собственно confusion matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Кoличество объектов в тестовой выборке: 33\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "from sklearn.model_selection import train_test_split\n",
    "import itertools\n",
    "\n",
    "# сводим задачу к бинарной классификации\n",
    "df_source = pd.read_csv(\n",
    "    'data/client_segmentation.csv', \n",
    "    dtype={'call_diff': np.float32, 'call_diff': np.float32, 'traffic_diff': np.float32, 'customes_class': np.uint16}\n",
    ")\n",
    "df_source[(df_source.customes_class==2) & (df_source.call_diff>1.1)] = 0\n",
    "df_source[(df_source.customes_class==2) & (df_source.call_diff<=1.1)] = 1\n",
    "X = df_source[['call_diff','sms_diff','traffic_diff']].values\n",
    "y = df_source.customes_class.values\n",
    "\n",
    "def plot_confusion_matrix(cm, classes,\n",
    "                          title='Confusion matrix',\n",
    "                          cmap=plt.cm.Blues):\n",
    "    \"\"\"\n",
    "    This function prints and plots the confusion matrix.\n",
    "    Normalization can be applied by setting `normalize=True`.\n",
    "    \"\"\"\n",
    "    plt.imshow(cm, interpolation='nearest', cmap=cmap)\n",
    "    plt.title(title)\n",
    "    plt.colorbar()\n",
    "    tick_marks = np.arange(len(classes))\n",
    "    plt.xticks(tick_marks, classes, rotation=45)\n",
    "    plt.yticks(tick_marks, classes)\n",
    "\n",
    "    thresh = cm.max() / 2.\n",
    "    for i, j in itertools.product(range(cm.shape[0]), range(cm.shape[1])):\n",
    "        plt.text(j, i, cm[i, j],\n",
    "                 horizontalalignment=\"center\",\n",
    "                 color=\"white\" if cm[i, j] > thresh else \"black\")\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)\n",
    "naive_bayes.fit(X_train, y_train)\n",
    "y_pred = naive_bayes.predict(X_test)\n",
    "\n",
    "conf_matrix = confusion_matrix(y_test, y_pred)\n",
    "plot_confusion_matrix(\n",
    "    conf_matrix,\n",
    "    classes=['active', 'churn'],\n",
    "    title='Confusion matrix, without normalization'\n",
    ")\n",
    "print(f'Кoличество объектов в тестовой выборке: {len(y_pred)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Активно используются следующие метрики\n",
    "\n",
    "**Accuracy**\n",
    "\n",
    "$$\n",
    "\\frac{TP + TN}{TP + TN + FP + FN}\n",
    "$$\n",
    "\n",
    "**Precision**\n",
    "$$\n",
    "\\frac{TP}{TP + FP}\n",
    "$$\n",
    "\n",
    "**Recall**\n",
    "$$\n",
    "\\frac{TP}{TP + FN}\n",
    "$$\n",
    "\n",
    "**F1-score**\n",
    "$$\n",
    "2\\frac{precision\\cdot recall}{precision + recall}\n",
    "$$\n",
    "\n",
    "**Logistic Loss**\n",
    "$$\n",
    "-\\frac{1}{l}\\sum_{i=1}^{l}\\left(y_i \\log\\hat{y}_i + (1-y_i) \\log(1-\\hat{y}_i)\\right)\n",
    "$$\n",
    "\n",
    "\n",
    "Про метрики есть хороший разбор на хабре [в статье про метрики](https://habr.com/ru/company/ods/blog/328372/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy_score:\t0.8787878787878788\n",
      "log_loss:\t4.186566811348581\n",
      "f1_score:\t0.9166666666666666\n",
      "precision_score:\t0.9166666666666666\n",
      "recall_score:\t0.9166666666666666\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score, log_loss, f1_score, precision_score, recall_score\n",
    "\n",
    "for f in [accuracy_score, log_loss, f1_score, precision_score, recall_score]:\n",
    "    print(f'{f.__name__}:\\t{f(y_test, y_pred)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Домашнее задание\n",
    "\n",
    "Найдите лучший классификатор по метрике `f1_score`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# --------- ВАШ КОД ТУТ --------\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# ------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Регрессия\n",
    "\n",
    "Регрессия - это семейство алгоритмов машинного обучения с учителем, цель которых состоит в востановлении **непрерывной** зависимости целевой переменной от фичей.\n",
    "\n",
    "Допустим, у нас есть нормализованные данные по количеству просмотров контента в онлайн-кинотеатре ivi\n",
    "\n",
    "* в датасете всего одна фича: время, когда было сделано наблюдение\n",
    "* целевая переменная - количество просмотров в этот момент времени\n",
    "\n",
    "Мы хотим научиться предсказывать количество просмотров (напрерывную переменную) по времения суток"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "df = pd.read_csv('data/content_views_toy_set.csv', encoding='utf8')\n",
    "df.plot.scatter(x='time', y='content_views')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Линейная регрессия"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Впервые термин *регрессия* в статистике был использован английским исследователем Френсисом Гальтоном (1886) в  исследовании вопроса наследования физических характеристик человека (конкретно - роста человека). Было обнаружено, что в целом сыновья высоких отцов, оказались более высокими, чем сыновья отцов с низким ростом. Более интересным было то, что разброс в росте сыновей был меньшим, чем разброс в росте отцов. Так проявлялась тенденция возвращения роста сыновей к среднему (regression to mediocrity), то есть «регресс».\n",
    "\n",
    "Реализация этого алгоритма есть в библиотеке sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "X = df['time'].values\n",
    "y = df['content_views'].values\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)\n",
    "reg = LinearRegression().fit(X_train.reshape(-1, 1), y_train)\n",
    "\n",
    "# строим график\n",
    "margin = 0.3\n",
    "support = np.arange(X.min(), X.max(), step=0.1)\n",
    "\n",
    "# строим предсказание\n",
    "y_hat = reg.predict(support.reshape(-1, 1))\n",
    "\n",
    "plt.plot(support, y_hat, 'b--', alpha=0.5, label='prediction')\n",
    "plt.scatter(X_train, y_train, 40, 'g', 'o', alpha=0.8, label='data')\n",
    "plt.xlim(X.min() - margin, X.max() + margin)\n",
    "plt.ylim(y.min() - margin, y.max() + margin)\n",
    "plt.legend(loc='upper right', prop={'size': 20})\n",
    "plt.title('Fitted linear regression')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Если вспомнить модель линейной регрессии, то обучение модели сводится к нахождению коэффициентов $w_1,\\ldots,w_n$:\n",
    "$$\n",
    "\\forall x_i: h(x) = w_0 + w_1x_i^1 + \\ldots + w_nx_i^n = \\sum_{j=1}^{n}w_jx_i^j = \\overline{x}_i^T\\overline{w}\n",
    "$$\n",
    "\n",
    "\"Достать\" коэффициенты из модели можно через аттрибут `coef_`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "коэффициенты линейной регрессии w=[-0.29424462], качество модели 0.5831098740865217\n"
     ]
    }
   ],
   "source": [
    "print(\n",
    "    f'коэффициенты линейной регрессии w={reg.coef_},',\n",
    "    f'качество модели {reg.score(X_test.reshape(-1,1), y_test)}'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Линейная регрессия очень хорошо интерпретируется: чем больше по модулю значение коэффициента $w_i$, тем сильнее фича $x_i$ влияет на предсказания модели.\n",
    "\n",
    "Кажется, что линейная комбинация фичей сильно ограничивает модель и не позволяет улавливать сложные зависимости.\n",
    "\n",
    "Чтобы модель улавливала нелинейные зависимости, мы можем добавить в датасет степени исходной переменной. Допустим, построим предсказания на полиноме пятой степени:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.6102, 5.9498, 2.2894, 1.4277, 2.6416, 3.5284, 4.541 , 4.1259,\n",
       "       0.1384, 5.4467, 3.7737, 4.3334, 1.1824, 4.107 , 1.5346, 4.6228,\n",
       "       0.1572, 2.9246, 0.1887, 5.4152, 4.5724, 3.3146, 5.1574, 1.4717,\n",
       "       3.2705, 2.7988, 5.9687, 2.912 , 1.2705, 5.3083, 2.0189, 3.9183,\n",
       "       4.9372])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def generate_degrees(source_data: list, degree: int):\n",
    "    \"\"\"Функция, которая принимает на вход одномерный массив, а возвращает n-мерный\n",
    "    Для каждой степени от 1 до  degree возводим x в эту степень\n",
    "    \"\"\"\n",
    "    return np.array([\n",
    "          source_data**n for n in range(1, degree + 1)  \n",
    "    ]).T\n",
    "\n",
    "X_train_5 = generate_degrees(X_train, 5)\n",
    "X_test_5 = generate_degrees(X_test, 5)\n",
    "reg_5 = LinearRegression().fit(X_train_5, y_train)\n",
    "\n",
    "# строим график\n",
    "margin = 0.3\n",
    "support = np.arange(X.min(), X.max(), step=0.1)\n",
    "\n",
    "X_test_support = generate_degrees(support, 5)\n",
    "y_hat = reg_5.predict(X_test_support)\n",
    "\n",
    "plt.plot(support, y_hat, 'b--', alpha=0.5, label='prediction')\n",
    "plt.scatter(X_train, y_train, 40, 'g', 'o', alpha=0.8, label='data')\n",
    "plt.xlim(X.min() - margin, X.max() + margin)\n",
    "plt.ylim(y.min() - margin, y.max() + margin)\n",
    "plt.legend(loc='upper right', prop={'size': 20})\n",
    "plt.title('Fitted linear regression')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Посмотрим на модель, которая у нас обучилась - вместо одной фичи в матрице **объекты $\\times$ признаки** стало пять фичей"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "коэффициенты линейной регрессии w=[ 2.48283062e+00 -1.19385669e+00  8.71731563e-02  2.15650198e-02\n",
      " -2.38912640e-03],\n",
      " качество модели 0.9123\n"
     ]
    }
   ],
   "source": [
    "print(\n",
    "    f'коэффициенты линейной регрессии w={reg_5.coef_},\\n',\n",
    "    f'качество модели {reg_5.score(X_test_5, y_test):.4f}'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Домашнее задание.\n",
    "\n",
    "Пользуясь методом `.score` подберите наилучшее значение степени полинома"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# --------- ВАШ КОД ТУТ --------\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# ------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Случайный лес\n",
    "\n",
    "Алгорим случайного можно применять для регрессии аналогично тому, как он применяется для классификации\n",
    "\n",
    "* рандомизировано построить несколько деревьев\n",
    "* каждое дерево независимо предсказывает значение в точке\n",
    "* итоговое предсказание - усреднённое значение предсказаний деревьев ансамбля"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "коэффициенты важности фичей w=[1.], качество модели 0.9610\n"
     ]
    }
   ],
   "source": [
    "from sklearn.ensemble import RandomForestRegressor\n",
    "\n",
    "rf = RandomForestRegressor(n_estimators=10).fit(X_train.reshape(-1, 1), y_train)\n",
    "print(\n",
    "    f'коэффициенты важности фичей w={rf.feature_importances_},',\n",
    "    f'качество модели {rf.score(X_train.reshape(-1, 1), y_train):.4f}'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Выводы\n",
    "\n",
    "* в задаче обучения с учителем обязательно нужно тратить время на разметку\n",
    "* проблема дисбаланса классов\n",
    "* можно слишком сильно подогнать модель под обучающую выборку - это явление переобучения, о нём поговорим в следующих занятиях"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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