hw4_linreg.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Интеллектуальный анализ данных – весна 2021\n",
    "## Домашнее задание 4: kNN. Линейные модели. Работа с признаками"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Правила:\n",
    "\n",
    "* Домашнее задание оценивается в 10 баллов.\n",
    "\n",
    "* Можно использовать без доказательства любые результаты, встречавшиеся на лекциях или семинарах по курсу, если получение этих результатов не является вопросом задания.\n",
    "\n",
    "* Можно использовать любые свободные источники с *обязательным* указанием ссылки на них.\n",
    "\n",
    "* Плагиат не допускается. При обнаружении случаев списывания, 0 за работу выставляется всем участникам нарушения, даже если можно установить, кто у кого списал.\n",
    "\n",
    "* Старайтесь сделать код как можно более оптимальным. В частности, будет штрафоваться использование циклов в тех случаях, когда операцию можно совершить при помощи инструментов библиотек, о которых рассказывалось в курсе.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задание 1:  Визуализация решающих поверхностей в kNN."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В этом задании мы изобразим решающую поверхность для классификатора kNN, чтобы наглядно увидеть, как классификатор принимает решения для новых объектов. Для простоты будем работать со встроенным в `sklearn` набором данных `wine`, содержащим информацию о характеристиках трёх видов вина. Описание набора можно найти [здесь](https://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_wine.html#sklearn.datasets.load_wine) и [здесь](https://rdrr.io/cran/rattle.data/man/wine.html). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Загрузим набор данных и сохраним информацию о признаках в переменную `X`, а о зависимой переменной – в переменную `y`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>alcohol</th>\n",
       "      <th>malic_acid</th>\n",
       "      <th>ash</th>\n",
       "      <th>alcalinity_of_ash</th>\n",
       "      <th>magnesium</th>\n",
       "      <th>total_phenols</th>\n",
       "      <th>flavanoids</th>\n",
       "      <th>nonflavanoid_phenols</th>\n",
       "      <th>proanthocyanins</th>\n",
       "      <th>color_intensity</th>\n",
       "      <th>hue</th>\n",
       "      <th>od280/od315_of_diluted_wines</th>\n",
       "      <th>proline</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>14.23</td>\n",
       "      <td>1.71</td>\n",
       "      <td>2.43</td>\n",
       "      <td>15.6</td>\n",
       "      <td>127.0</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.06</td>\n",
       "      <td>0.28</td>\n",
       "      <td>2.29</td>\n",
       "      <td>5.64</td>\n",
       "      <td>1.04</td>\n",
       "      <td>3.92</td>\n",
       "      <td>1065.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>13.20</td>\n",
       "      <td>1.78</td>\n",
       "      <td>2.14</td>\n",
       "      <td>11.2</td>\n",
       "      <td>100.0</td>\n",
       "      <td>2.65</td>\n",
       "      <td>2.76</td>\n",
       "      <td>0.26</td>\n",
       "      <td>1.28</td>\n",
       "      <td>4.38</td>\n",
       "      <td>1.05</td>\n",
       "      <td>3.40</td>\n",
       "      <td>1050.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.16</td>\n",
       "      <td>2.36</td>\n",
       "      <td>2.67</td>\n",
       "      <td>18.6</td>\n",
       "      <td>101.0</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.24</td>\n",
       "      <td>0.30</td>\n",
       "      <td>2.81</td>\n",
       "      <td>5.68</td>\n",
       "      <td>1.03</td>\n",
       "      <td>3.17</td>\n",
       "      <td>1185.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>14.37</td>\n",
       "      <td>1.95</td>\n",
       "      <td>2.50</td>\n",
       "      <td>16.8</td>\n",
       "      <td>113.0</td>\n",
       "      <td>3.85</td>\n",
       "      <td>3.49</td>\n",
       "      <td>0.24</td>\n",
       "      <td>2.18</td>\n",
       "      <td>7.80</td>\n",
       "      <td>0.86</td>\n",
       "      <td>3.45</td>\n",
       "      <td>1480.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>13.24</td>\n",
       "      <td>2.59</td>\n",
       "      <td>2.87</td>\n",
       "      <td>21.0</td>\n",
       "      <td>118.0</td>\n",
       "      <td>2.80</td>\n",
       "      <td>2.69</td>\n",
       "      <td>0.39</td>\n",
       "      <td>1.82</td>\n",
       "      <td>4.32</td>\n",
       "      <td>1.04</td>\n",
       "      <td>2.93</td>\n",
       "      <td>735.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>14.20</td>\n",
       "      <td>1.76</td>\n",
       "      <td>2.45</td>\n",
       "      <td>15.2</td>\n",
       "      <td>112.0</td>\n",
       "      <td>3.27</td>\n",
       "      <td>3.39</td>\n",
       "      <td>0.34</td>\n",
       "      <td>1.97</td>\n",
       "      <td>6.75</td>\n",
       "      <td>1.05</td>\n",
       "      <td>2.85</td>\n",
       "      <td>1450.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>14.39</td>\n",
       "      <td>1.87</td>\n",
       "      <td>2.45</td>\n",
       "      <td>14.6</td>\n",
       "      <td>96.0</td>\n",
       "      <td>2.50</td>\n",
       "      <td>2.52</td>\n",
       "      <td>0.30</td>\n",
       "      <td>1.98</td>\n",
       "      <td>5.25</td>\n",
       "      <td>1.02</td>\n",
       "      <td>3.58</td>\n",
       "      <td>1290.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>14.06</td>\n",
       "      <td>2.15</td>\n",
       "      <td>2.61</td>\n",
       "      <td>17.6</td>\n",
       "      <td>121.0</td>\n",
       "      <td>2.60</td>\n",
       "      <td>2.51</td>\n",
       "      <td>0.31</td>\n",
       "      <td>1.25</td>\n",
       "      <td>5.05</td>\n",
       "      <td>1.06</td>\n",
       "      <td>3.58</td>\n",
       "      <td>1295.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   alcohol  malic_acid   ash  alcalinity_of_ash  magnesium  total_phenols  \\\n",
       "0    14.23        1.71  2.43               15.6      127.0           2.80   \n",
       "1    13.20        1.78  2.14               11.2      100.0           2.65   \n",
       "2    13.16        2.36  2.67               18.6      101.0           2.80   \n",
       "3    14.37        1.95  2.50               16.8      113.0           3.85   \n",
       "4    13.24        2.59  2.87               21.0      118.0           2.80   \n",
       "5    14.20        1.76  2.45               15.2      112.0           3.27   \n",
       "6    14.39        1.87  2.45               14.6       96.0           2.50   \n",
       "7    14.06        2.15  2.61               17.6      121.0           2.60   \n",
       "\n",
       "   flavanoids  nonflavanoid_phenols  proanthocyanins  color_intensity   hue  \\\n",
       "0        3.06                  0.28             2.29             5.64  1.04   \n",
       "1        2.76                  0.26             1.28             4.38  1.05   \n",
       "2        3.24                  0.30             2.81             5.68  1.03   \n",
       "3        3.49                  0.24             2.18             7.80  0.86   \n",
       "4        2.69                  0.39             1.82             4.32  1.04   \n",
       "5        3.39                  0.34             1.97             6.75  1.05   \n",
       "6        2.52                  0.30             1.98             5.25  1.02   \n",
       "7        2.51                  0.31             1.25             5.05  1.06   \n",
       "\n",
       "   od280/od315_of_diluted_wines  proline  \n",
       "0                          3.92   1065.0  \n",
       "1                          3.40   1050.0  \n",
       "2                          3.17   1185.0  \n",
       "3                          3.45   1480.0  \n",
       "4                          2.93    735.0  \n",
       "5                          2.85   1450.0  \n",
       "6                          3.58   1290.0  \n",
       "7                          3.58   1295.0  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_wine\n",
    "\n",
    "data = load_wine()\n",
    "X = pd.DataFrame(data['data'], columns = data['feature_names'])\n",
    "y = data['target']\n",
    "X.head(8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 1.1 (0.5 балла)** Есть ли в наборе данных пропущенные значения? Если да, то удалите их. Есть ли в наборе данных категориальные переменные? Если да, то закодируйте их при помощи OneHot-кодирования."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 178 entries, 0 to 177\n",
      "Data columns (total 13 columns):\n",
      " #   Column                        Non-Null Count  Dtype  \n",
      "---  ------                        --------------  -----  \n",
      " 0   alcohol                       178 non-null    float64\n",
      " 1   malic_acid                    178 non-null    float64\n",
      " 2   ash                           178 non-null    float64\n",
      " 3   alcalinity_of_ash             178 non-null    float64\n",
      " 4   magnesium                     178 non-null    float64\n",
      " 5   total_phenols                 178 non-null    float64\n",
      " 6   flavanoids                    178 non-null    float64\n",
      " 7   nonflavanoid_phenols          178 non-null    float64\n",
      " 8   proanthocyanins               178 non-null    float64\n",
      " 9   color_intensity               178 non-null    float64\n",
      " 10  hue                           178 non-null    float64\n",
      " 11  od280/od315_of_diluted_wines  178 non-null    float64\n",
      " 12  proline                       178 non-null    float64\n",
      "dtypes: float64(13)\n",
      "memory usage: 18.2 KB\n"
     ]
    }
   ],
   "source": [
    "X.info()\n",
    "# пропущенных значений нет, все признаки не категориальные (по смыслу и по факту)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 1.2 (0.5 балла)** Используя функцию `train_test_split()`, разделите выборку на тренировочную и тестовую, и долю тестовой выборки задайте равной 0.3. Так как разбиение осуществляется случайным образом, не забудьте зафиксировать `np.random.seed()` для воспроизводимости результатов."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "x_train, x_test, y_train, y_test = train_test_split(X, y, test_size = 0.3, random_state=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 1.3 (1 балл)** На тренировочной выборке обучите шесть классификаторов kNN, отличающихся только числом соседей. Для первого классификатора число соседей поставьте равным 1, для второго - 3, для третьего – 5, для четвертого – 10, для пятого – 15 и для шестого – 25 (обратите внимание на параметр `n_neighbours` класса `KNeighborsClassifier`). Для обучения используйте только два признака: `alcohol` и `magnesium` – и евклидово расстояние. Не забудьте масштабировать признаки, например, при помощи модуля `StandardScaler`.\n",
    "\n",
    "Выведите долю правильных ответов на тренировочной и тестовой выборках для каждого классификатора."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy for 1 neighbors for test is: 0.630 Accuracy for 1 neighbors for train is: 0.992\n",
      "Accuracy for 3 neighbors for test is: 0.648 Accuracy for 3 neighbors for train is: 0.855\n",
      "Accuracy for 5 neighbors for test is: 0.648 Accuracy for 5 neighbors for train is: 0.782\n",
      "Accuracy for 10 neighbors for test is: 0.648 Accuracy for 10 neighbors for train is: 0.766\n",
      "Accuracy for 15 neighbors for test is: 0.648 Accuracy for 15 neighbors for train is: 0.718\n",
      "Accuracy for 25 neighbors for test is: 0.741 Accuracy for 25 neighbors for train is: 0.718\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-5-69205c5bbb3e>:10: FutureWarning: Support for multi-dimensional indexing (e.g. `obj[:, None]`) is deprecated and will be removed in a future version.  Convert to a numpy array before indexing instead.\n",
      "  return (X - self.mu[np.newaxis, :]) / self.sigma[np.newaxis, :]\n"
     ]
    }
   ],
   "source": [
    "'''StandartScaler почему-то не импортируется, поэтому я просто напишу самостоятельно'''\n",
    "# Предупреждение о будущей поддержке, поэтому на решение оно не влияет и это не ошибка\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "class Scaler:\n",
    "    def fit(self, X: np.array) -> None:\n",
    "        self.mu = X.mean(axis=0)\n",
    "        self.sigma = X.std(axis=0)\n",
    "        \n",
    "    def transform(self, X: np.array) -> np.array:\n",
    "        return (X - self.mu[np.newaxis, :]) / self.sigma[np.newaxis, :]\n",
    "    \n",
    "scaler = Scaler()\n",
    "scaler.fit(x_train)\n",
    "x_train_transformed = scaler.transform(x_train)\n",
    "scaler.fit(x_test)\n",
    "x_test_transformed = scaler.transform(x_test)\n",
    "neighbours = [1, 3, 5, 10, 15, 25]\n",
    "clfs = []\n",
    "for k in neighbours:\n",
    "    y_predicted_test = KNeighborsClassifier(n_neighbors=k, metric='euclidean').fit(x_train_transformed[['alcohol', 'magnesium']], y_train).predict(x_test_transformed[['alcohol', 'magnesium']])\n",
    "    y_predicted_train = KNeighborsClassifier(n_neighbors=k, metric='euclidean').fit(x_train_transformed[['alcohol', 'magnesium']], y_train).predict(x_train_transformed[['alcohol', 'magnesium']])\n",
    "    knn = KNeighborsClassifier(n_neighbors = k, metric='euclidean')\n",
    "    clfs.append(knn)\n",
    "    print(f'Accuracy for {k} neighbors for test is: {np.mean(y_predicted_test==y_test):.3f}', \n",
    "            f'Accuracy for {k} neighbors for train is: {np.mean(y_predicted_train==y_train):.3f}')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 1.4 (0 баллов)** Установите библиотеку `mlxtend` командой ниже. Библиотеку также можно установить из терминала при помощи `pip` или `conda`, как указано [здесь](http://rasbt.github.io/mlxtend/installation/). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: mlxtend in /Users/andreydyadyunov/Downloads/anaconda3/lib/python3.8/site-packages (0.18.0)\n",
      "Requirement already satisfied: pandas>=0.24.2 in /Users/andreydyadyunov/Downloads/anaconda3/lib/python3.8/site-packages (from mlxtend) (1.1.3)\n",
      "Requirement already satisfied: scikit-learn>=0.20.3 in /Users/andreydyadyunov/Downloads/anaconda3/lib/python3.8/site-packages (from mlxtend) (0.23.2)\n",
      "Requirement already satisfied: numpy>=1.16.2 in /Users/andreydyadyunov/Downloads/anaconda3/lib/python3.8/site-packages (from mlxtend) (1.19.2)\n",
      "Requirement already satisfied: joblib>=0.13.2 in /Users/andreydyadyunov/Downloads/anaconda3/lib/python3.8/site-packages (from mlxtend) (0.17.0)\n",
      "Requirement already satisfied: matplotlib>=3.0.0 in /Users/andreydyadyunov/Downloads/anaconda3/lib/python3.8/site-packages (from mlxtend) (3.3.2)\n",
      "Requirement already satisfied: setuptools in /Users/andreydyadyunov/Downloads/anaconda3/lib/python3.8/site-packages (from mlxtend) (50.3.1.post20201107)\n",
      "Requirement already satisfied: scipy>=1.2.1 in /Users/andreydyadyunov/Downloads/anaconda3/lib/python3.8/site-packages (from mlxtend) (1.5.2)\n",
      "Requirement already satisfied: python-dateutil>=2.7.3 in /Users/andreydyadyunov/Downloads/anaconda3/lib/python3.8/site-packages (from pandas>=0.24.2->mlxtend) (2.8.1)\n",
      "Requirement already satisfied: pytz>=2017.2 in /Users/andreydyadyunov/Downloads/anaconda3/lib/python3.8/site-packages (from pandas>=0.24.2->mlxtend) (2020.1)\n",
      "Requirement already satisfied: threadpoolctl>=2.0.0 in /Users/andreydyadyunov/Downloads/anaconda3/lib/python3.8/site-packages (from scikit-learn>=0.20.3->mlxtend) (2.1.0)\n",
      "Requirement already satisfied: pillow>=6.2.0 in /Users/andreydyadyunov/Downloads/anaconda3/lib/python3.8/site-packages (from matplotlib>=3.0.0->mlxtend) (8.0.1)\n",
      "Requirement already satisfied: kiwisolver>=1.0.1 in /Users/andreydyadyunov/Downloads/anaconda3/lib/python3.8/site-packages (from matplotlib>=3.0.0->mlxtend) (1.3.0)\n",
      "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.3 in /Users/andreydyadyunov/Downloads/anaconda3/lib/python3.8/site-packages (from matplotlib>=3.0.0->mlxtend) (2.4.7)\n",
      "Requirement already satisfied: certifi>=2020.06.20 in /Users/andreydyadyunov/Downloads/anaconda3/lib/python3.8/site-packages (from matplotlib>=3.0.0->mlxtend) (2020.6.20)\n",
      "Requirement already satisfied: cycler>=0.10 in /Users/andreydyadyunov/Downloads/anaconda3/lib/python3.8/site-packages (from matplotlib>=3.0.0->mlxtend) (0.10.0)\n",
      "Requirement already satisfied: six>=1.5 in /Users/andreydyadyunov/Downloads/anaconda3/lib/python3.8/site-packages (from python-dateutil>=2.7.3->pandas>=0.24.2->mlxtend) (1.15.0)\n"
     ]
    }
   ],
   "source": [
    "!pip install mlxtend"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Если всё прошло успешно, то в выводе команды выше вы увидите сообщение вроде \"successfully installed\", а следующая ячейка выполнится без ошибок."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import mlxtend"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 1.5 (1 балл)** Библиотека `mlxtend` позволяет достаточно просто визуализировать решающие поверхности обученных классификаторов. Изучите [документацию](http://rasbt.github.io/mlxtend/user_guide/plotting/plot_decision_regions/) библиотеки и найдите, как можно построить несколько графиков решающих поверхностей на сетке (decision regions grid). Постройте такую сетку графиков для обученных выше классификаторов.\n",
    "\n",
    "**Подсказки:**\n",
    "1. Вы можете использовать готовый код, приведённый в документации, и адаптировать его для нашего случая.\n",
    "2. Вам могут понадобиться дополнительные библиотеки, которые используются в примере из документации.\n",
    "3. Обратите внимание на то, как нужно изменить параметры `gridspec.GridSpec()` и `itertools.product()` для нашего числа классификаторов. \n",
    "4. В функции `plot_decision_region()` используйте `y_train` и нужные столбцы из `X_train`. Возможно, их придётся перевести в формат массива `numpy`.\n",
    "5. Если в задаче 1.3 вы сохраните обученные классификаторы в список, то не будет необходимости обучать их заново. \n",
    "6. Построение графика может занять некоторое время – придётся немного подождать!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 936x576 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mlxtend.plotting import plot_decision_regions\n",
    "import itertools\n",
    "import matplotlib.gridspec as gridspec\n",
    "gs = gridspec.GridSpec(2, 3)\n",
    "fig = plt.figure(figsize=(13,8))\n",
    "labels = ['neighbors = 1', 'neighbors = 3', 'neighbors = 5', 'neighbors = 10', 'neighbors = 15', 'neighbors = 25']\n",
    "for clf, lab, grd in zip(clfs,\n",
    "                         labels,\n",
    "                         itertools.product([0, 1, 2], repeat=2)):\n",
    "\n",
    "    clf.fit(x_train_transformed[['alcohol', 'magnesium']], y_train)\n",
    "    ax = plt.subplot(gs[grd[0], grd[1]])\n",
    "    fig = plot_decision_regions(X=pd.DataFrame.to_numpy(x_train_transformed[['alcohol', 'magnesium']]), y=y_train, clf=clf, legend=2)\n",
    "    plt.title(lab)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 1.6 (0.5 балла)** Прокомментируйте результаты, полученные в задачах 1.3 и 1.5. Какое число соседей оптимально использовать для обучения классификатора? Поясните ваш выбор при помощи описания геометрии данных и получаемой решающей поверхности."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " По моему отнюдь не скромному мнению, оптимальное число соседей - 5 \n",
    " По той простой причине, что экьюреси там достойное, но переобучения не наблюдается, и на графиках прослеживается допустимый (по субъективной оценке) объем ошибок\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задание 2: Обученная машина."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В этом задании мы рассмотрим упрощённую идею того, как метод ближайших соседей можно применить при моделировании движения робота. \n",
    "\n",
    "Рассмотрим робота на дискретной двумерной плоскости, который за каждый момент дискретного времени может передвинуться на одну позицию вправо, влево, вверх или вниз. На плоскости разбросаны метки одного из четырёх классов, анализируя которые робот может (но не обязан) корректировать своё перемещение. Пусть метки класса 0 соответствуют сигналу переместиться вправо, метки класса 1 – влево, класса 2 – вверх, класса 3 – вниз. \n",
    "\n",
    "Передвижение робота осуществляется по следующему правилу: с вероятностью 0.2 робот передвинется вправо, и с вероятностью 0.8 – оценит, метки какого класса преобладают среди `k` его ближайших соседей, и передвинется в направлении этого доминирующего класса. \n",
    "\n",
    "Для лучшего понимания происходящего изобразим возможное положение робота и меток:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(12345)\n",
    "x = np.arange(20)\n",
    "landmarks = x + np.round(np.random.normal(2, 8, 20)) # сгенерируем случайные метки\n",
    "random_classes = np.random.randint(0, 4, 20)\n",
    "\n",
    "fig, ax = plt.subplots(figsize = (10, 7))\n",
    "scatter = ax.scatter(x, landmarks, c = random_classes)\n",
    "ax.scatter(4, 7, c = 'r', marker = 'o', label = 'robot position')\n",
    "legend1 = ax.legend(*scatter.legend_elements(),\n",
    "                    loc = \"lower left\", title = \"Classes\")\n",
    "ax.add_artist(legend1)\n",
    "\n",
    "plt.plot()\n",
    "_ = plt.legend()\n",
    "_ = plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "На следующем шаге робот передвинется на 1 либо вправо, либо в направлении, которое указывают ближайшие соседи."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 2.1 (1.5 балла)** Реализуйте класс, который задаёт описанное поведение робота, используя шаблон ниже:\n",
    "1. Определите атрибуты `trajectory` (переменная для хранения истории перемещения робота в виде последовательности точек с двумя координатами) и `knn` (обученный kNN классификатор, который по позиции метки предсказывает её класс).\n",
    "2. Определите метод `move()`: рассчитайте новое положение робота по правилам выше и добавьте её в историю перемещений. Подсказка: исходы можно интерпретировать как результаты подбрасывания монетки с вероятностью орла, равной 0.2. Для моделирования такого подбрасывания можно использовать, например, `np.random.binomial()` с правильными параметрами. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MobileRobot():\n",
    "    \n",
    "    def __init__(self, k, initial_position, landmarks, classes):\n",
    "        '''\n",
    "        Attributes:\n",
    "        ------\n",
    "        k: int\n",
    "            Number of neighbours\n",
    "            \n",
    "        initial_position: ndarray\n",
    "            Initial position of the robot as a point, e.g. (-1, 1)\n",
    "            \n",
    "        landmarks: ndarray\n",
    "            numpy array of shape (n_landmarks, 2) with the euclidean positions of points\n",
    "        \n",
    "        classes: ndarray\n",
    "            numpy array of shape (n_landmarks, ) with class of landmark for each point in landmarks\n",
    "        \n",
    "        '''\n",
    "        # Store the history of movements\n",
    "        self.trajectory = initial_position\n",
    "        \n",
    "        # kNN Classifier for determining the classes of landmarks\n",
    "        self.knn = KNeighborsClassifier(n_neighbors=k)\n",
    "        \n",
    "        # Mapping between classes of points and movements\n",
    "        self.mapping = {0: np.array([1, 0]), \n",
    "                        1: np.array([-1, 0]),\n",
    "                        2: np.array([0, 1]),\n",
    "                        3: np.array([0, -1])}\n",
    "        \n",
    "        self.landmark = landmarks\n",
    "        self.classes = classes\n",
    "        self.initial_position = initial_position\n",
    "        \n",
    "    def move(self):\n",
    "        '''\n",
    "        Calculate new position of the robot and add it to the history\n",
    "        '''\n",
    "        \n",
    "        self.knn.fit(self.landmark, self.classes)\n",
    "        prediction = self.knn.predict([self.initial_position])\n",
    "        if np.random.binomial(1, 0.8, 1) == 1:\n",
    "            self.initial_position = self.initial_position + self.mapping[prediction.sum()]\n",
    "            self.trajectory = np.vstack((self.trajectory, self.initial_position))\n",
    "        else:\n",
    "            self.initial_position = self.initial_position + self.mapping[0]\n",
    "            self.trajectory = np.vstack((self.trajectory, self.initial_position))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 2.2 (0.5 балла)** Дополните функцию `conduct_experiment`: определите переменную `traj` так, чтобы она содержала историю перемещения робота в виде двумерного массива numpy, в котором столбцы соответствуют координатам x и y соответствующей позиции."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def conduct_experiment(x,\n",
    "                       mean = 0,\n",
    "                       std = 2, \n",
    "                       n_movements = 10, \n",
    "                       k = 3, \n",
    "                       initial_position = np.array([10, 20])):\n",
    "    \n",
    "    np.random.seed(12345)\n",
    "    # Generate random landmarks\n",
    "    landmarks = np.vstack((x, x + np.round(np.random.normal(mean, std, len(x))))).T\n",
    "    \n",
    "    # Generate random classes of landmarks\n",
    "    classes = np.random.randint(0, 4, size = len(x))\n",
    "    \n",
    "    # Conduct experiment\n",
    "    robot = MobileRobot(k, initial_position, landmarks, classes)\n",
    "    \n",
    "    for n in range(n_movements):\n",
    "        robot.move()\n",
    "    \n",
    "    fig, ax = plt.subplots(figsize = (10, 8))\n",
    "    scatter = ax.scatter(landmarks[:, 0], landmarks[:, 1], c = classes)\n",
    "    legend1 = ax.legend(*scatter.legend_elements(),\n",
    "                        loc=\"lower left\", title=\"classes\")\n",
    "    ax.add_artist(legend1)\n",
    "    \n",
    "    traj = robot.trajectory\n",
    "    ax.plot(traj[:, 0], traj[:, 1], \n",
    "               c = 'r', marker = 'o', label = 'robot position')\n",
    "\n",
    "    plt.plot()\n",
    "    _ = plt.legend()\n",
    "    _ = plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(30)\n",
    "conduct_experiment(x, mean = 3, std = 10, k = 5, n_movements = 50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 2.3 (1 балл)** Как число соседей влияет на траекторию движения робота в нашем эксперименте? Постройте четыре графика с различным числом соседей на ваш выбор. А что было бы в случае, если классы назначаются меткам не случайно, а осмысленно? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Количество соседей относительно несильно влияет на нашу траекторию (все равно прослеживается движение вправо) \n",
    "Однако, стоит заметить, что траектории не идентичны, потому что разное количество соседей выдает нам разный класс из-за различной концентрации точек"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "conduct_experiment(x, mean = 3, std = 10, k = 3, n_movements = 50)\n",
    "conduct_experiment(x, mean = 3, std = 10, k = 4, n_movements = 50)\n",
    "conduct_experiment(x, mean = 3, std = 10, k = 6, n_movements = 50)\n",
    "conduct_experiment(x, mean = 3, std = 10, k = 9, n_movements = 50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Задание 3: Линейная регрессия."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В этом задании мы рассмотрим различные аспекты построения линейной модели. Мы будем работать с одним из классических наборов данных в статистике, содержащим информацию о бриллиантах. Описание можно посмотреть [здесь](https://www.kaggle.com/shivam2503/diamonds)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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>Unnamed: 0</th>\n",
       "      <th>carat</th>\n",
       "      <th>cut</th>\n",
       "      <th>color</th>\n",
       "      <th>clarity</th>\n",
       "      <th>depth</th>\n",
       "      <th>table</th>\n",
       "      <th>price</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>z</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0.23</td>\n",
       "      <td>Ideal</td>\n",
       "      <td>E</td>\n",
       "      <td>SI2</td>\n",
       "      <td>61.5</td>\n",
       "      <td>55.0</td>\n",
       "      <td>326</td>\n",
       "      <td>3.95</td>\n",
       "      <td>3.98</td>\n",
       "      <td>2.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>0.21</td>\n",
       "      <td>Premium</td>\n",
       "      <td>E</td>\n",
       "      <td>SI1</td>\n",
       "      <td>59.8</td>\n",
       "      <td>61.0</td>\n",
       "      <td>326</td>\n",
       "      <td>3.89</td>\n",
       "      <td>3.84</td>\n",
       "      <td>2.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>0.23</td>\n",
       "      <td>Good</td>\n",
       "      <td>E</td>\n",
       "      <td>VS1</td>\n",
       "      <td>56.9</td>\n",
       "      <td>65.0</td>\n",
       "      <td>327</td>\n",
       "      <td>4.05</td>\n",
       "      <td>4.07</td>\n",
       "      <td>2.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>0.29</td>\n",
       "      <td>Premium</td>\n",
       "      <td>I</td>\n",
       "      <td>VS2</td>\n",
       "      <td>62.4</td>\n",
       "      <td>58.0</td>\n",
       "      <td>334</td>\n",
       "      <td>4.20</td>\n",
       "      <td>4.23</td>\n",
       "      <td>2.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>0.31</td>\n",
       "      <td>Good</td>\n",
       "      <td>J</td>\n",
       "      <td>SI2</td>\n",
       "      <td>63.3</td>\n",
       "      <td>58.0</td>\n",
       "      <td>335</td>\n",
       "      <td>4.34</td>\n",
       "      <td>4.35</td>\n",
       "      <td>2.75</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0  carat      cut color clarity  depth  table  price     x     y  \\\n",
       "0           1   0.23    Ideal     E     SI2   61.5   55.0    326  3.95  3.98   \n",
       "1           2   0.21  Premium     E     SI1   59.8   61.0    326  3.89  3.84   \n",
       "2           3   0.23     Good     E     VS1   56.9   65.0    327  4.05  4.07   \n",
       "3           4   0.29  Premium     I     VS2   62.4   58.0    334  4.20  4.23   \n",
       "4           5   0.31     Good     J     SI2   63.3   58.0    335  4.34  4.35   \n",
       "\n",
       "      z  \n",
       "0  2.43  \n",
       "1  2.31  \n",
       "2  2.31  \n",
       "3  2.63  \n",
       "4  2.75  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('/Users/andreydyadyunov/Downloads/diamonds.csv')\n",
    "data.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Мы будем решать задачу предсказания цены бриллианта `price` в зависимости от его характеристик."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 3.1 (0.1 балла)** Есть ли в наборе данных пропущенные значения? Если да, удалите их. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Unnamed: 0    0\n",
       "carat         0\n",
       "cut           0\n",
       "color         0\n",
       "clarity       0\n",
       "depth         0\n",
       "table         0\n",
       "price         0\n",
       "x             0\n",
       "y             0\n",
       "z             0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.isnull().sum()\n",
    "# Пропущенных значений нет"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 3.2 (0.1 балла)** Есть ли в наборе данных бессмысленные столбцы (признаки, не несущие дополнительной информации)? Если да, то удалите их."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>carat</th>\n",
       "      <th>cut</th>\n",
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      "text/plain": [
       "       carat        cut color clarity  depth  table  price     x     y     z\n",
       "0       0.23      Ideal     E     SI2   61.5   55.0    326  3.95  3.98  2.43\n",
       "1       0.21    Premium     E     SI1   59.8   61.0    326  3.89  3.84  2.31\n",
       "2       0.23       Good     E     VS1   56.9   65.0    327  4.05  4.07  2.31\n",
       "3       0.29    Premium     I     VS2   62.4   58.0    334  4.20  4.23  2.63\n",
       "4       0.31       Good     J     SI2   63.3   58.0    335  4.34  4.35  2.75\n",
       "...      ...        ...   ...     ...    ...    ...    ...   ...   ...   ...\n",
       "53935   0.72      Ideal     D     SI1   60.8   57.0   2757  5.75  5.76  3.50\n",
       "53936   0.72       Good     D     SI1   63.1   55.0   2757  5.69  5.75  3.61\n",
       "53937   0.70  Very Good     D     SI1   62.8   60.0   2757  5.66  5.68  3.56\n",
       "53938   0.86    Premium     H     SI2   61.0   58.0   2757  6.15  6.12  3.74\n",
       "53939   0.75      Ideal     D     SI2   62.2   55.0   2757  5.83  5.87  3.64\n",
       "\n",
       "[53940 rows x 10 columns]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Бессмысленный столбец unnamed\n",
    "data = data.drop('Unnamed: 0', axis=1)\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 3.3 (0.1 балла)** Линейная регрессия основана на предположении о линейной связи между признаками и целевой переменной, а потому перед выбором переменных для включения в модель имеет смысл проверить, насколько эта связь выполняется. Для следующих пунктов нам также потребуются выборочные корреляции между признаками. Выведите матрицу выборочных корреляций между всеми вещественными признаками и целевой переменной (то есть в этой матрице будет $k+1$ строка, где $k$ – количество вещественных признаков).\n",
    "\n",
    "Какие вещественные признаки коррелируют с целевой переменной больше всего?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "carat    0.921591\n",
       "depth   -0.010647\n",
       "table    0.127134\n",
       "price    1.000000\n",
       "x        0.884435\n",
       "y        0.865421\n",
       "z        0.861249\n",
       "dtype: float64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matcorr = data.corrwith(data['price'])\n",
    "matcorr\n",
    "# По матрице корреляций видно, что меньше всего коррелируют с целевой переменной признаки\n",
    "# depth, table\n",
    "# Остальные признаки коррелируют сильно"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 3.4 (0.1 балла)** Так как линейная модель складывает значения признаков с некоторыми весами, нам нужно аккуратно обработать категориальные признаки. Закодируйте категориальные переменные при помощи OneHot-кодирования."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
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       "      <td>0.75</td>\n",
       "      <td>62.2</td>\n",
       "      <td>55.0</td>\n",
       "      <td>2757</td>\n",
       "      <td>5.83</td>\n",
       "      <td>5.87</td>\n",
       "      <td>3.64</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>53940 rows × 27 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       carat  depth  table  price     x     y     z  cut_Fair  cut_Good  \\\n",
       "0       0.23   61.5   55.0    326  3.95  3.98  2.43         0         0   \n",
       "1       0.21   59.8   61.0    326  3.89  3.84  2.31         0         0   \n",
       "2       0.23   56.9   65.0    327  4.05  4.07  2.31         0         1   \n",
       "3       0.29   62.4   58.0    334  4.20  4.23  2.63         0         0   \n",
       "4       0.31   63.3   58.0    335  4.34  4.35  2.75         0         1   \n",
       "...      ...    ...    ...    ...   ...   ...   ...       ...       ...   \n",
       "53935   0.72   60.8   57.0   2757  5.75  5.76  3.50         0         0   \n",
       "53936   0.72   63.1   55.0   2757  5.69  5.75  3.61         0         1   \n",
       "53937   0.70   62.8   60.0   2757  5.66  5.68  3.56         0         0   \n",
       "53938   0.86   61.0   58.0   2757  6.15  6.12  3.74         0         0   \n",
       "53939   0.75   62.2   55.0   2757  5.83  5.87  3.64         0         0   \n",
       "\n",
       "       cut_Ideal  ...  color_I  color_J  clarity_I1  clarity_IF  clarity_SI1  \\\n",
       "0              1  ...        0        0           0           0            0   \n",
       "1              0  ...        0        0           0           0            1   \n",
       "2              0  ...        0        0           0           0            0   \n",
       "3              0  ...        1        0           0           0            0   \n",
       "4              0  ...        0        1           0           0            0   \n",
       "...          ...  ...      ...      ...         ...         ...          ...   \n",
       "53935          1  ...        0        0           0           0            1   \n",
       "53936          0  ...        0        0           0           0            1   \n",
       "53937          0  ...        0        0           0           0            1   \n",
       "53938          0  ...        0        0           0           0            0   \n",
       "53939          1  ...        0        0           0           0            0   \n",
       "\n",
       "       clarity_SI2  clarity_VS1  clarity_VS2  clarity_VVS1  clarity_VVS2  \n",
       "0                1            0            0             0             0  \n",
       "1                0            0            0             0             0  \n",
       "2                0            1            0             0             0  \n",
       "3                0            0            1             0             0  \n",
       "4                1            0            0             0             0  \n",
       "...            ...          ...          ...           ...           ...  \n",
       "53935            0            0            0             0             0  \n",
       "53936            0            0            0             0             0  \n",
       "53937            0            0            0             0             0  \n",
       "53938            1            0            0             0             0  \n",
       "53939            1            0            0             0             0  \n",
       "\n",
       "[53940 rows x 27 columns]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features = ['cut', 'color', 'clarity']\n",
    "data = pd.get_dummies(data, prefix=features)\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 3.5 (0.2 балла)** Разделите выборку на тренировочную и тестовую. Долю тестовой выборки укажите равной 0.3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "F = data.drop('price', axis=1)\n",
    "A = data['price']\n",
    "f_train, f_test, a_train, a_test = train_test_split(F, A, test_size = 0.3, random_state=6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 3.6 (0.3 балла)** Зачастую при использовании линейных моделей вещественные признаки масштабируются. При этом оценки коэффициентов теряют прямую статистическую интерпретацию (\"при увеличении $X_1$ на 1, $y$ увеличивается на $w_1$\"), но приобретают свойства, полезные в задачах машинного обучения. В этой задаче масштабируйте вещественные признаки тренировочной и тестовой выборок при помощи модуля `StandardScaler`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-5-69205c5bbb3e>:10: FutureWarning: Support for multi-dimensional indexing (e.g. `obj[:, None]`) is deprecated and will be removed in a future version.  Convert to a numpy array before indexing instead.\n",
      "  return (X - self.mu[np.newaxis, :]) / self.sigma[np.newaxis, :]\n"
     ]
    },
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>carat</th>\n",
       "      <th>depth</th>\n",
       "      <th>table</th>\n",
       "      <th>x</th>\n",
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       "      <th>z</th>\n",
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       "      <th>cut_Premium</th>\n",
       "      <th>...</th>\n",
       "      <th>color_I</th>\n",
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       "      <th>clarity_I1</th>\n",
       "      <th>clarity_IF</th>\n",
       "      <th>clarity_SI1</th>\n",
       "      <th>clarity_SI2</th>\n",
       "      <th>clarity_VS1</th>\n",
       "      <th>clarity_VS2</th>\n",
       "      <th>clarity_VVS1</th>\n",
       "      <th>clarity_VVS2</th>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>7743</th>\n",
       "      <td>0.937313</td>\n",
       "      <td>-0.654231</td>\n",
       "      <td>-0.211031</td>\n",
       "      <td>1.119121</td>\n",
       "      <td>1.089451</td>\n",
       "      <td>0.950349</td>\n",
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       "      <td>-0.057499</td>\n",
       "      <td>-0.376909</td>\n",
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       "      <td>0.169016</td>\n",
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       "      <td>-1.238215</td>\n",
       "      <td>-1.222383</td>\n",
       "      <td>-1.198056</td>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>1896</th>\n",
       "      <td>-0.184496</td>\n",
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       "      <td>-0.108845</td>\n",
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       "      <td>-0.655877</td>\n",
       "      <td>-1.157545</td>\n",
       "      <td>-1.159168</td>\n",
       "      <td>-1.115425</td>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>15950</th>\n",
       "      <td>0.937313</td>\n",
       "      <td>-0.792892</td>\n",
       "      <td>0.678661</td>\n",
       "      <td>1.110158</td>\n",
       "      <td>1.170726</td>\n",
       "      <td>0.964121</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>16182 rows × 26 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          carat     depth     table         x         y         z  cut_Fair  \\\n",
       "9359   0.429324  1.287023  2.013199  0.509620  0.457309  0.619825         0   \n",
       "9490   0.640986 -1.139544  2.013199  0.823334  0.863686  0.647369         0   \n",
       "27    -1.052311  0.316396 -0.211031 -1.300957 -1.294627 -1.198056         0   \n",
       "7743   0.937313 -0.654231 -0.211031  1.119121  1.089451  0.950349         0   \n",
       "48686 -0.057499 -0.376909  3.792584  0.169016  0.087054  0.082724         1   \n",
       "...         ...       ...       ...       ...       ...       ...       ...   \n",
       "36921 -0.819483 -1.208875  1.568353 -0.781089 -0.870189 -0.895076         0   \n",
       "35809 -1.031145 -0.376909 -0.211031 -1.238215 -1.222383 -1.198056         0   \n",
       "1896  -0.184496  2.049658  0.233815 -0.108845 -0.138711  0.110267         1   \n",
       "36599 -1.009979 -0.168918 -0.655877 -1.157545 -1.159168 -1.115425         0   \n",
       "15950  0.937313 -0.792892  0.678661  1.110158  1.170726  0.964121         0   \n",
       "\n",
       "       cut_Good  cut_Ideal  cut_Premium  ...  color_I  color_J  clarity_I1  \\\n",
       "9359          1          0            0  ...        0        0           0   \n",
       "9490          0          0            0  ...        0        0           0   \n",
       "27            0          0            0  ...        0        1           0   \n",
       "7743          0          0            1  ...        0        0           0   \n",
       "48686         0          0            0  ...        0        1           0   \n",
       "...         ...        ...          ...  ...      ...      ...         ...   \n",
       "36921         0          0            1  ...        0        0           0   \n",
       "35809         0          1            0  ...        0        0           0   \n",
       "1896          0          0            0  ...        0        0           0   \n",
       "36599         0          1            0  ...        0        0           0   \n",
       "15950         0          1            0  ...        1        0           0   \n",
       "\n",
       "       clarity_IF  clarity_SI1  clarity_SI2  clarity_VS1  clarity_VS2  \\\n",
       "9359            0            1            0            0            0   \n",
       "9490            0            0            1            0            0   \n",
       "27              0            0            0            0            1   \n",
       "7743            0            0            1            0            0   \n",
       "48686           0            0            0            1            0   \n",
       "...           ...          ...          ...          ...          ...   \n",
       "36921           0            0            0            1            0   \n",
       "35809           1            0            0            0            0   \n",
       "1896            0            0            0            0            1   \n",
       "36599           0            0            0            0            0   \n",
       "15950           0            1            0            0            0   \n",
       "\n",
       "       clarity_VVS1  clarity_VVS2  \n",
       "9359              0             0  \n",
       "9490              0             0  \n",
       "27                0             0  \n",
       "7743              0             0  \n",
       "48686             0             0  \n",
       "...             ...           ...  \n",
       "36921             0             0  \n",
       "35809             0             0  \n",
       "1896              0             0  \n",
       "36599             1             0  \n",
       "15950             0             0  \n",
       "\n",
       "[16182 rows x 26 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#from sklearn.preprocessing import StandardScaler \n",
    "# Все равно не импортируется, воспользуемся прошлым\n",
    "# Вылезает предупреждение, но это не страшно, в этой версии все еще работает\n",
    "scaler = Scaler() \n",
    "f_train_transformed = f_train[['carat', 'depth', 'table', 'x', 'y', 'z']]\n",
    "f_train = f_train.drop(['carat', 'depth', 'table', 'x', 'y', 'z'], axis=1)\n",
    "scaler.fit(f_train_transformed)\n",
    "f_train_transformed = scaler.transform(f_train_transformed)\n",
    "f_train_transformed = f_train_transformed.merge(f_train, left_index=True, right_index=True)\n",
    "f_test_transformed = f_test[['carat', 'depth', 'table', 'x', 'y', 'z']]\n",
    "f_test = f_test.drop(['carat', 'depth', 'table', 'x', 'y', 'z'], axis=1)\n",
    "scaler.fit(f_test_transformed)\n",
    "f_test_transformed = scaler.transform(f_test_transformed)\n",
    "f_test_transformed = f_test_transformed.merge(f_test, left_index=True, right_index=True)\n",
    "f_test_transformed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 3.7 (0.2 балла)** Оцените линейную регрессию на тренировочной выборке. Выведите среднеквадратичную ошибку на тренировочной и тестовой выборках."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE train: 1252396.340, test: 1333133.347\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error\n",
    "slr = LinearRegression()\n",
    "slr.fit(f_train_transformed, a_train)\n",
    "a_train_pred = slr.predict(f_train_transformed)\n",
    "a_test_pred = slr.predict(f_test_transformed)\n",
    "print('MSE train: {:.3f}, test: {:.3f}'.format(\n",
    "        mean_squared_error(a_train, a_train_pred),\n",
    "        mean_squared_error(a_test, a_test_pred)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 3.8 (0.2 балла)** Изучите документацию модуля `LinearRegression` и выведите полученные оценки коэффициентов. Назовите вещественные переменные, оценки коэффициентов которых по модулю на порядок превышают оценки прочих вещественных переменных."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>carat</th>\n",
       "      <td>5336.214293</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>depth</th>\n",
       "      <td>-85.408844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>table</th>\n",
       "      <td>-52.489234</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x</th>\n",
       "      <td>-1118.251404</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>7.261476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>z</th>\n",
       "      <td>-53.559838</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cut_Fair</th>\n",
       "      <td>-570.898195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cut_Good</th>\n",
       "      <td>1.245224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cut_Ideal</th>\n",
       "      <td>253.768268</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cut_Premium</th>\n",
       "      <td>179.068038</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cut_Very Good</th>\n",
       "      <td>136.816664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>color_D</th>\n",
       "      <td>807.999226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>color_E</th>\n",
       "      <td>623.224880</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>color_F</th>\n",
       "      <td>549.305564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>color_G</th>\n",
       "      <td>348.334323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>color_H</th>\n",
       "      <td>-139.685381</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>color_I</th>\n",
       "      <td>-646.587938</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>color_J</th>\n",
       "      <td>-1542.590675</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>clarity_I1</th>\n",
       "      <td>-3809.545877</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>clarity_IF</th>\n",
       "      <td>1483.645165</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>clarity_SI1</th>\n",
       "      <td>-132.881954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>clarity_SI2</th>\n",
       "      <td>-1099.188946</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>clarity_VS1</th>\n",
       "      <td>766.593674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>clarity_VS2</th>\n",
       "      <td>462.923236</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>clarity_VVS1</th>\n",
       "      <td>1195.427391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>clarity_VVS2</th>\n",
       "      <td>1133.027311</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         0\n",
       "carat          5336.214293\n",
       "depth           -85.408844\n",
       "table           -52.489234\n",
       "x             -1118.251404\n",
       "y                 7.261476\n",
       "z               -53.559838\n",
       "cut_Fair       -570.898195\n",
       "cut_Good          1.245224\n",
       "cut_Ideal       253.768268\n",
       "cut_Premium     179.068038\n",
       "cut_Very Good   136.816664\n",
       "color_D         807.999226\n",
       "color_E         623.224880\n",
       "color_F         549.305564\n",
       "color_G         348.334323\n",
       "color_H        -139.685381\n",
       "color_I        -646.587938\n",
       "color_J       -1542.590675\n",
       "clarity_I1    -3809.545877\n",
       "clarity_IF     1483.645165\n",
       "clarity_SI1    -132.881954\n",
       "clarity_SI2   -1099.188946\n",
       "clarity_VS1     766.593674\n",
       "clarity_VS2     462.923236\n",
       "clarity_VVS1   1195.427391\n",
       "clarity_VVS2   1133.027311"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(columns=f_test_transformed.columns, data=slr.coef_.reshape(1, 26)).T\n",
    "# Вещественные переменные, которые по модулю на порядок превышают прочие по кф. - carat, x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 3.9 (0.4 балла)** Как можно заметить из анализа корреляционной матрицы в задаче 3.3, между некоторыми признаками имеется сильная корреляция, что может быть индикатором проблемы *мультиколлинеарности*. Различия в порядке коэффициентов, выявленные в предыдущей задаче также намекают на её присутствие. Как известно, для решения этой проблемы можно либо исключить некоторые признаки из модели, либо использовать регуляризацию. Мы воспользуемся вторым вариантом. \n",
    "\n",
    "Вспомним, что смысл регуляризации заключается в том, чтобы изменить функцию потерь так, чтобы устранить проблемы, появляющиеся из-за мультиколлинеарности. При L1-регуляризации предлагается минимизировать следующую функцию потерь:\n",
    "\n",
    "$$\n",
    "\\|y - X\\hat{w}\\|^2 + \\alpha\\sum_{i=1}^k|w_i|\n",
    "$$\n",
    "\n",
    "Такая модель называется Lasso-регрессией.\n",
    "\n",
    "При L2-регуляризации предлагается минимизировать следующую функцию потерь:\n",
    "\n",
    "$$\n",
    "\\|y - X\\hat{w}\\|^2 + \\frac{1}{2}\\alpha\\|w\\|^2\n",
    "$$\n",
    "\n",
    "Такая модель называется Ridge-регрессией. \n",
    "\n",
    "Обучите Lasso-регрессию и Ridge-регрессию, уставновив гиперпараметр регуляризации равным 10. Для этого используйте модули `Lasso` и `Ridge` из `sklearn`. Сильно ли уменьшились веса? Сделайте вывод о том, насколько сильно проблема мультиколлинеарности проявлялась в изначальной регрессии."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ОТВЕТ:\n",
    "\n",
    "У регрессии Лассо коэффициенты на порядок ниже, чем у изначальной и ниже, чем у Риджа \n",
    "Про проблему мультиколлинеарности можно сказать, что ее влияние на изначальную регрессию есть, однако замечу, что не катастрофическое, потому что даже с регуляризацией данных коэффициенты остались довольно большими, хоть и сократились на какую-то величину\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                         0\n",
      "carat          4872.112367\n",
      "depth           -95.976359\n",
      "table           -70.573546\n",
      "x              -708.584857\n",
      "y                -0.000000\n",
      "z               -66.881035\n",
      "cut_Fair       -420.513774\n",
      "cut_Good        -26.171312\n",
      "cut_Ideal        95.161620\n",
      "cut_Premium       0.000000\n",
      "cut_Very Good     0.000000\n",
      "color_D         310.826854\n",
      "color_E         167.532876\n",
      "color_F         105.642647\n",
      "color_G           0.000000\n",
      "color_H        -426.522470\n",
      "color_I        -866.466423\n",
      "color_J       -1657.271976\n",
      "clarity_I1    -3560.963644\n",
      "clarity_IF      628.533610\n",
      "clarity_SI1    -617.587947\n",
      "clarity_SI2   -1523.438987\n",
      "clarity_VS1     151.311810\n",
      "clarity_VS2     -15.676016\n",
      "clarity_VVS1    512.314915\n",
      "clarity_VVS2    501.095863\n",
      "MSE Lasso train: 1289325.599, test: 1378958.462\n",
      "                         0\n",
      "carat          5297.595346\n",
      "depth           -82.469340\n",
      "table           -52.842644\n",
      "x             -1066.575865\n",
      "y                 6.820501\n",
      "z               -69.915476\n",
      "cut_Fair       -573.321560\n",
      "cut_Good          1.145734\n",
      "cut_Ideal       254.737965\n",
      "cut_Premium     179.143684\n",
      "cut_Very Good   138.294177\n",
      "color_D         803.169031\n",
      "color_E         619.593090\n",
      "color_F         545.713190\n",
      "color_G         346.569440\n",
      "color_H        -140.012502\n",
      "color_I        -643.287628\n",
      "color_J       -1531.744622\n",
      "clarity_I1    -3737.115306\n",
      "clarity_IF     1464.316963\n",
      "clarity_SI1    -140.954113\n",
      "clarity_SI2   -1102.936163\n",
      "clarity_VS1     756.509647\n",
      "clarity_VS2     454.388277\n",
      "clarity_VVS1   1183.534595\n",
      "clarity_VVS2   1122.256100\n",
      "MSE Ridge train: 1252559.407, test: 1333588.235\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "lasso = Lasso(alpha=10)\n",
    "lasso.fit(f_train_transformed, a_train)\n",
    "a_train_pred = lasso.predict(f_train_transformed)\n",
    "a_test_pred = lasso.predict(f_test_transformed)\n",
    "print(pd.DataFrame(columns=f_test_transformed.columns, data=lasso.coef_.reshape(1, 26)).T)\n",
    "print('MSE Lasso train: {:.3f}, test: {:.3f}'.format(\n",
    "        mean_squared_error(a_train, a_train_pred),\n",
    "        mean_squared_error(a_test, a_test_pred)))\n",
    "\n",
    "ridge = Ridge(alpha=10)\n",
    "ridge.fit(f_train_transformed, a_train)\n",
    "a_r_train_pred = ridge.predict(f_train_transformed)\n",
    "a_r_test_pred = ridge.predict(f_test_transformed)\n",
    "print(pd.DataFrame(columns=f_test_transformed.columns, data=ridge.coef_.reshape(1, 26)).T)\n",
    "print('MSE Ridge train: {:.3f}, test: {:.3f}'.format(\n",
    "        mean_squared_error(a_train, a_r_train_pred),\n",
    "        mean_squared_error(a_test, a_r_test_pred)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 3.10 (0.4 балла)** Как обсуждалось на семинарах, Lasso-регрессию можно использовать для отбора наиболее информативных признаков. Для следующих значений параметра регуляриазции $\\alpha$: 0.1, 1, 10, 100, 200 –  обучите Lasso- и Ridge-регрессии и постройте график измненения евклидовой нормы весов (`np.linalg.norm()` от вектора оценок коэффициентов) в зависимости от параметра $\\alpha$. Как известно, норма является численной характеристикой величины вектора, а потому по норме можно судить о том, насколько большие элементы содержит вектор оценок коэффициентов. \n",
    "\n",
    "Какой метод агрессивнее уменьшает веса? Поясните, почему Lasso-регрессию часто используют для отбора признаков."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ОТВЕТ:\n",
    "Регрессия Лассо более агрессивно занижает веса, поэтому ее и используют чаще для отбора признаков \n",
    "Особенно когда это необходимо, потому что количество признаков огромно, а цена ошибки позволяет избавиться \n",
    "от части признаков"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/andreydyadyunov/Downloads/anaconda3/lib/python3.8/site-packages/sklearn/linear_model/_coordinate_descent.py:529: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 74529523.96990967, tolerance: 59753000.79383364\n",
      "  model = cd_fast.enet_coordinate_descent(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fda819495b0>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1800x792 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "w_lasso = []\n",
    "w_ridge = []\n",
    "alphas = [0.1, 1, 10, 100, 200]\n",
    "for each in alphas:\n",
    "    lasso = Lasso(alpha=each)\n",
    "    lasso.fit(f_train_transformed, a_train)\n",
    "    w_lasso.append(np.linalg.norm(lasso.coef_))\n",
    "    ridge = Ridge(alpha=each)\n",
    "    ridge.fit(f_train_transformed, a_train)\n",
    "    w_ridge.append(np.linalg.norm(ridge.coef_))\n",
    "plt.figure(figsize=(25,11))\n",
    "plt.plot(alphas, w_lasso, c='r', linewidth=5, label='Lasso')\n",
    "plt.plot(alphas, w_ridge, c='b', linewidth=5, label='Ridge')\n",
    "plt.legend(fontsize=25)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 3.11 (0.5 балла)** \n",
    "В зависимости от значения параметра $\\alpha$ в Lasso-регрессии зануляются разные оценки коэффициентов. Оптимальное значение $\\alpha$ можно подобрать, например, при помощи кросс-валидации по тренировочной выборке. \n",
    "\n",
    "Для проведения кросс-валидации можно использовать модуль `LassoCV`. Этот модуль принимает список значений $\\alpha$ (параметр `alphas`) и при обучении проводит кросс-валидацию для каждого значения из этого списка, сохраняя MSE на каждом участке кросс-валидации (количество участков – параметр `cv`) в матрицу ошибок (то есть итоговая матрица будет иметь размер `len(alphas)` $\\times$ `cv`). После обучения модели матрицу ошибок можно получить, обратившись к атрибуту `.mse_path_`. \n",
    "\n",
    "Заметим, что модель может использовать $\\alpha$ не в том порядке, в котором вы подаёте их в функцию: для определения порядка используйте атрибут `.alphas_` Установите количество участков для кросс-валидации (параметр `cv`) равным 5.\n",
    "\n",
    "Усредните ошибки для каждого значения $\\alpha$ (то есть по строкам матрицы ошибок) и выберите то значение, которое даёт наибольшее качество. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>200.0</th>\n",
       "      <td>1.660507e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100.0</th>\n",
       "      <td>1.675401e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10.0</th>\n",
       "      <td>1.563782e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>1.716003e+06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.1</th>\n",
       "      <td>1.790584e+06</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  0\n",
       "200.0  1.660507e+06\n",
       "100.0  1.675401e+06\n",
       "10.0   1.563782e+06\n",
       "1.0    1.716003e+06\n",
       "0.1    1.790584e+06"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LassoCV\n",
    "lscv = LassoCV(alphas=np.array([0.1, 1, 10, 100, 200]), cv=5)\n",
    "lscv.fit(f_train_transformed, a_train)\n",
    "mn = lscv.mse_path_.mean(axis=0)\n",
    "mat_means = pd.DataFrame(columns=lscv.alphas_, data=mn.reshape(1, 5))\n",
    "mat_means.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 3.12 (0.5 балла)** Обучите итоговую Lasso-регрессию с выбранным параметром $\\alpha$ на тренировочной выборке. Выведите полученные коэффициенты и прокомментируйте, какие признаки оказались неинформативными, а какие – наиболее информативными. Приведите возможное смысловое объяснение этого результата."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В регрессии Лассо оказалось, что есть абсолютно не информативные признаки: \n",
    "у, cut_Premium, cut_Very Good, color_G \n",
    "К тому же некоторые признаки имеют очень низкие коэффициенты относительно большинства, например, зет \n",
    "Это могло произойти потому что не смотря на наличие этих признаков, они не сказываются на цене бриллиантов"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                         0\n",
      "carat          4872.112367\n",
      "depth           -95.976359\n",
      "table           -70.573546\n",
      "x              -708.584857\n",
      "y                -0.000000\n",
      "z               -66.881035\n",
      "cut_Fair       -420.513774\n",
      "cut_Good        -26.171312\n",
      "cut_Ideal        95.161620\n",
      "cut_Premium       0.000000\n",
      "cut_Very Good     0.000000\n",
      "color_D         310.826854\n",
      "color_E         167.532876\n",
      "color_F         105.642647\n",
      "color_G           0.000000\n",
      "color_H        -426.522470\n",
      "color_I        -866.466423\n",
      "color_J       -1657.271976\n",
      "clarity_I1    -3560.963644\n",
      "clarity_IF      628.533610\n",
      "clarity_SI1    -617.587947\n",
      "clarity_SI2   -1523.438987\n",
      "clarity_VS1     151.311810\n",
      "clarity_VS2     -15.676016\n",
      "clarity_VVS1    512.314915\n",
      "clarity_VVS2    501.095863\n"
     ]
    }
   ],
   "source": [
    "lasso = Lasso(alpha=10)\n",
    "lasso.fit(f_train_transformed, a_train)\n",
    "\n",
    "print(pd.DataFrame(lasso.coef_, F.columns))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Задача 3.13 (0.4 балла)** Сделайте предсказания обученной Lasso-регрессии на тестовой выборке и сравните среднеквадратичную ошибку с ошибкой обычной линейной регрессии из задачи 3.7. Какую модель лучше использовать для предсказаний? Приведите возможное объяснение, почему одна модель оказалась лучше другой."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE test: 1378958.462\n"
     ]
    }
   ],
   "source": [
    "a_test_pred = lasso.predict(f_test_transformed)\n",
    "print('MSE test: {:.3f}'.format(\n",
    "        mean_squared_error(a_test, a_test_pred)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "ОТВЕТ:\n",
    "Среднеквадратичная ошибка снизилась, поэтому эту модель использовать лучше, чем обычную \n",
    "Это происходит потому что обычная модель учитывает признаки, которые не влияют на цену, а также потому что\n",
    "кроссвалидация помогает еще снизить уровень ошибок."
   ]
  }
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