{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "sTB50uLM0a9o" }, "source": [ "# \n", "\n", "# Машинное обучение. ВМК МГУ" ] }, { "cell_type": "markdown", "metadata": { "id": "0xg3G6bd0a9s" }, "source": [ "# Практическое задание 3: Линейные модели: регрессия\n", "\n", "## Уровень: **Исследовательский (Research)**" ] }, { "cell_type": "markdown", "source": [ "# О формате сдачи\n", "\n", "🔷 **При решении ноутбука используйте данный шаблон**\n", "\n", " ✅ Можно добавлять новые ячейки любых типов\n", " ❌ Не нужно удалять текстовые ячейки c разметкой частей ноутбука и формулировками заданий\n", "\n", "\n", "🔷 **При оценивании задач учитывается код**\n", "\n", " ✅ Задания, в которых необходим код, обычно помечаются фразами \"Your code here\"/\"Ваш код\" и аналогичными\n", " ❌ Ответы на вопросы без сопутствующего кода оцениваются в 0 баллов\n", " ❌ Наличе работоспособного кода в ноутбуке, если на сказано иного, обязательно\n", "\n", "🔷 **При оценивании задач учитываются выводы**\n", "\n", " ✅ Задания, в которых необходимы выводы, обычно помечаются фразами Вывод\"/\"Ответ на вопрос\"/\"Ваш текст\" и аналогичными\n", " ✅ Обычно выводы подразумевают под собой текстовый ответ (можно писать markdown, latex).\n", " ✅ Сопутствующие изображения, графики, таблички - приветствуются!\n", " ❌ При отсутствии выводов задание не засчитается на полный балл\n", "\n", "-----------\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "metadata": { "id": "6ODl7_-1JoHQ" } }, { "cell_type": "markdown", "source": [ "Цель данного задания:\n", "\n", "* Узнать, что такое переобучение и как с ним бороться в линейных моделях;\n", "* Понять, чем отличаются разные регуляризаторы;\n", "* Научиться решать задачу регрессии линейными моделями.\n", "-------\n", "**Примерное время выполнения (execution time/время выполнения, если нажать run all) всех ячеек ноутбука при правильной реализации: 7 минут **" ], "metadata": { "id": "H0Lj_c63lrku" } }, { "cell_type": "markdown", "source": [ "# Подготовка рабочей среды\n", "\n", "Сначала установим нужные нам версии библиотек. Мы гарантируем, что в данных версиях задание будет корректно отрабатывать.\n", "\n", "После установки нужных версий, **возможно,** нужно перезагрузить среду (runtime), но скорее всего вам это не понадобится\n", "\n", "\n", "На скачивание файла и установку понадобится не более 5 минут.\n", "\n", "**Важно!**\n", "\n", "Устанавливать нужные версии нужно каждый раз, когда создается новый рантайм. Например, если вы 2 часа подряд делаете это задание, то подготовить библиотеки достаточно 1 раз. Но если вы, например, начали в понедельник, затем закрыли/выключили ноутбук, то при продолжении в среду, вам нужно будет запустить рантайм заново и следовательно заново установить библиотеки.\n", "\n", "**Важно!**\n", "Если вы предпочитаете делать практические задания на своем личном ноутбуке, то проверьте, что вы установили рабочее окружение в [соответствии с гайдом](https://github.com/MSU-ML-COURSE/ML-COURSE-24-25/blob/main/tutorials/%D0%A2%D1%83%D1%82%D0%BE%D1%80%D0%B8%D0%B0%D0%BB%20%D0%BF%D0%BE%20%D1%83%D1%81%D1%82%D0%B0%D0%BD%D0%BE%D0%B2%D0%BA%D0%B5%20%D1%80%D0%B0%D0%B1%D0%BE%D1%87%D0%B5%D0%B3%D0%BE%20%D0%BE%D0%BA%D1%80%D1%83%D0%B6%D0%B5%D0%BD%D0%B8%D1%8F%20%D0%B2%20Python%20%D0%B4%D0%BB%D1%8F%20%D1%80%D0%B5%D1%88%D0%B5%D0%BD%D0%B8%D1%8F%20%D0%B7%D0%B0%D0%B4%D0%B0%D1%87%20(2).pdf)\n" ], "metadata": { "id": "d4sbAeC--5gV" } }, { "cell_type": "code", "source": [ "from sklearn.metrics import mean_squared_error\n", "# !!! Данный блок будет работать только в Google-Colab !!!\n", "! gdown 10k8Hwn9kpK9SpK4IEj4-EaWQZqgYT5-Q\n", "! pip install -r /content/requirements_2024_25_for_colab_small.txt" ], "metadata": { "id": "hQLVkvfL-5gW" }, "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "source": [ "Проверим версию библиотеки:" ], "metadata": { "id": "vUCY0KLD7VmA" } }, { "cell_type": "code", "source": [ "import catboost\n", "\n", "assert (catboost.__version__ == '1.2.7')" ], "metadata": { "id": "CIWS5lZ3-5gX", "jupyter": { "is_executing": true } }, "outputs": [], "execution_count": null }, { "cell_type": "markdown", "source": [ "Теперь можно приступать к выполнению задания! :)" ], "metadata": { "id": "eC9VrV8G-5gX" } }, { "cell_type": "markdown", "source": [ "-----------\n", "" ], "metadata": { "id": "y39N4E_B-5gX" } }, { "cell_type": "code", "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "import warnings\n", "\n", "warnings.simplefilter(\"ignore\")\n", "sns.set(style=\"darkgrid\")\n", "%matplotlib inline" ], "metadata": { "id": "Gc3xTMopl8c1", "ExecuteTime": { "end_time": "2024-11-15T17:40:36.846900Z", "start_time": "2024-11-15T17:40:36.821616Z" } }, "outputs": [], "execution_count": 2 }, { "cell_type": "markdown", "metadata": { "id": "cLTHFUz40a9w" }, "source": [ "## Линейная регрессия и регуляризация" ] }, { "cell_type": "markdown", "metadata": { "id": "PGuTcL0H0a9w" }, "source": [ "Напомним, что линейная регрессия — это модель следующего вида: $$a(x) = \\langle w, x \\rangle + b$$ где $w \\in \\mathbb{R}^d$, $b \\in \\mathbb{R}$. Обучить линейную регрессию — значит найти $w$ и $b$." ] }, { "cell_type": "markdown", "source": [ "В модели линейной регрессии с $l_2$ регуляризацией мы оптимизируем следующий функционал:\n", "\n", "$\\frac{1}{N} \\cdot ∑_{i=1}^M (w_1 \\cdot x_{i1} + \\dots w_n \\cdot x_{in} + b - y_i)^2 + \\frac{\\alpha}{2} \\cdot \\left( w_1^2 + \\dots + w_n^2 \\right) \\rightarrow \\min_{w_1, \\dots, w_n, b}$\n", "\n", "В модели линейной регрессии с $l_1$ регуляризацией мы оптимизируем следующий функционал:\n", "\n", "$\\frac{1}{N} \\cdot ∑_{i=1}^M (w_1 \\cdot x_{i1} + \\dots w_n \\cdot x_{in} + b - y_i)^2 + \\alpha \\cdot \\left( |w_1| + \\dots + |w_n| \\right) \\rightarrow \\min_{w_1, \\dots, w_n, b}$" ], "metadata": { "id": "7ee6L2lk4dBV" } }, { "cell_type": "markdown", "source": [ "### **Задание 1 [1 балл]**\n", "\n", "Почему при обучении линейных моделей, коэффициент $b$ не регуляризуется? Дайте ответ с опорой на лекции. Возможно вам также поможет картика из базовой части" ], "metadata": { "id": "yBXvREbq6J33" } }, { "cell_type": "markdown", "source": [ "**Ваши выводы тут:**\n", "\n", "Потому что в случае, если бы коэффициент $b$ также регуляризовывался, то модели было бы сложно подстраиваться под новые данные, так как они могут быть смещены относительно оси Y на другое значение\n", "\n", "Если говорить конкретнее, то:\n", "1. Смещение $b$ независимо от значений признаков и добавляется отдельно ==> его резуляризация не несёт пользы\n", "2. Регуляризация применяется, чтобы снизить сложность модели и избежать переобучения, однако $b$ не влияет на сложность модели, а значит не требует регуляризации" ], "metadata": { "id": "Iqj_cwbV_vEL" } }, { "cell_type": "markdown", "source": [ "-----\n", "" ], "metadata": { "id": "Md8-JjM68ZUe" } }, { "cell_type": "markdown", "source": [ "Рассмотрим модель линейной регрессии с $l_2$ регуляризацией. В sklearn эта модель реализована посредством класса Ridge. В нём есть методы fit и predict. Первый принимает на вход обучающую выборку и вектор целевых переменных и обучает модель, второй, будучи вызванным после обучения модели, возвращает предсказание на выборке." ], "metadata": { "id": "HND8s6ee6h0P" } }, { "cell_type": "markdown", "metadata": { "id": "oMjk5Dty0a92" }, "source": [ "Сгенерируем случайные данные. Пусть $x$ будет обычным числом из равномерного распределения, а $𝑦=0.5 \\cdot x + 0.1$ — целевая переменная. При этом наблюдаем мы $\\overline{y} = y + \\varepsilon,~\\varepsilon \\sim N(0, 0.01)$. Добавим в данные к переменной $x$ её же умноженную на $3$. То есть, теперь у нас два признака $x_1$ и $x_2 = 3 \\cdot x_1$." ] }, { "cell_type": "markdown", "source": [ "Поскольку $y = c \\cdot 0.5 \\cdot x_1 + \\frac{1 - c}{6} \\cdot x_2 + 0.1$, где $c$ любое сколь угодно большое вещественное число. То, как мы могли убедиться в базовой части, без регуляризации есть риск выучить очень большие веса." ], "metadata": { "id": "X66mK63v-BI0" } }, { "cell_type": "markdown", "source": [ "Посмотрим, как меняется значения весов, в зависимости от значения коэффициента регуляризации." ], "metadata": { "id": "O1ogDSg798EZ" } }, { "cell_type": "code", "source": [ "from sklearn.linear_model import Ridge" ], "metadata": { "id": "icTp30Uj7pJn", "ExecuteTime": { "end_time": "2024-11-15T17:40:37.237981Z", "start_time": "2024-11-15T17:40:37.021547Z" } }, "outputs": [], "execution_count": 3 }, { "cell_type": "code", "source": [ "np.random.seed(1)\n", "X = np.random.uniform(0, 1, 100)\n", "Y = X * 0.5 + 0.1 + np.random.randn(100) * 0.1\n", "\n", "X3 = np.hstack((X[:, None], 3 * X[:, None]))\n", "Y3 = X3[:, 0] * 0.5 + 0.1 + np.random.randn(100) * 0.1" ], "metadata": { "id": "cidgDWJf7o83", "ExecuteTime": { "end_time": "2024-11-15T17:40:37.284590Z", "start_time": "2024-11-15T17:40:37.276157Z" } }, "outputs": [], "execution_count": 4 }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 653 }, "id": "7YIxYW8T0a92", "outputId": "17c380cc-7cb6-460f-fd7f-c7332a1cdb31", "ExecuteTime": { "end_time": "2024-11-15T17:40:39.786740Z", "start_time": "2024-11-15T17:40:38.430509Z" } }, "source": [ "w1 = []\n", "w2 = []\n", "\n", "alphas = [0.01, 0.1, 1, 10, 100, 1000]\n", "\n", "for alpha in alphas:\n", " reg = Ridge(alpha=alpha)\n", " reg.fit(X3, Y3)\n", " w1.append(reg.coef_[0])\n", " w2.append(reg.coef_[1])\n", "\n", "w1 = np.array(w1)\n", "w2 = np.array(w2)\n", "\n", "fig, axs = plt.subplots(figsize=(14, 7), ncols=2)\n", "axs[0].plot(alphas, w1, label=\"w1\")\n", "axs[0].plot(alphas, w2, label=\"w2\")\n", "axs[0].set_xscale(\"log\")\n", "axs[0].set_title(\"Веса регрессии при разных alpha\")\n", "axs[0].set_xlabel(\"alpha\")\n", "axs[0].set_ylabel(\"Значение весов\")\n", "axs[0].legend()\n", "axs[1].plot(alphas, w2 / w1, label=\"отношение w2 к w1\", linewidth=10)\n", "axs[1].plot([0.01, 1000], [3, 3], label=\"отношение x2 к x1\", linestyle=\"--\", linewidth=8)\n", "axs[1].set_xscale(\"log\")\n", "axs[1].set_ylim(2, 4)\n", "axs[1].set_xlabel(\"alpha\")\n", "axs[1].set_ylabel(\"Значение отношения\")\n", "axs[1].set_title(\"Отношение весов\")\n", "axs[1].legend()\n", "plt.show()" ], "outputs": [ { "data": { "text/plain": [ "
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}, "metadata": {}, "output_type": "display_data" } ], "execution_count": 5 }, { "cell_type": "markdown", "metadata": { "id": "C9EKJVTi0a92" }, "source": [ "### **Задание 2 [2 баллa]**\n", "\n", "Как думаете, почему отношение между весами постоянно? (подсказка, необходимо выписать функцию потерь и посчитать производные по весам)" ] }, { "cell_type": "markdown", "metadata": { "id": "oqvdO95D0a93" }, "source": [ "Функция потерь имеет следующий вид:\n", "$J(w) = \\sum_{i=1}^{n} (y_i - (w_1 x_{1i} + w_2 x_{2i}))^2 + \\alpha (w_1^2 + w_2^2)$\n", "\n", "Считая производные, получим:\n", "1. $\\frac{\\partial J}{\\partial w_1} = -2 \\sum_{i=1}^{n} x_{1i} (y_i - (w_1 x_{1i} + w_2 x_{2i})) + 2 \\alpha w_1 = 0$\n", "2. $\\frac{\\partial J}{\\partial w_2} = -2 \\sum_{i=1}^{n} x_{2i} (y_i - (w_1 x_{1i} + w_2 x_{2i})) + 2 \\alpha w_2 = 0$\n", "\n", "Если рассматривать конкретно наши данные ($x_2=3*x_1$), то получим:\n", "1. $\\frac{\\partial J}{\\partial w_1} = -2 \\sum_{i=1}^{n} x_{1i} (y_i - (w_1 x_{1i} + 3 w_2 x_{1i})) + 2 \\alpha w_1 = 0$\n", "2. $\\frac{\\partial J}{\\partial w_2} = -2 \\sum_{i=1}^{n} 3 x_{1i} (y_i - (w_1 x_{1i} + 3 w_2 x_{1i})) + 2 \\alpha w_2 = 0$\n", "\n", "Если произвести следующие вычисления: $3\\frac{\\partial J}{\\partial w_1} -\\frac{\\partial J}{\\partial w_2}=6 \\alpha w_1- 2\\alpha w_2$\n", "\n", "Получаем, что веса зависят друг от друга также, как и коэффициенты, т.е. 1 к 3.\n", "\n", "Это объясняет постоянство отношения весов с ростом $\\alpha$" ] }, { "cell_type": "markdown", "source": [ "-----\n", "" ], "metadata": { "id": "49ZLe4IeK5WE" } }, { "cell_type": "markdown", "metadata": { "id": "hhiWDj0P0a93" }, "source": [ "Заметим, что при $l_2$ регуляризации в данном примере веса получились пропорциональны значениям признаков. При этом, мы знаем, что оба признака взаимно однозначны, и прогноз можно делать только по одному из них. Для этого придумана $l_1$ регуляризация. В билиотеке sklearn линейная регрессия с $l_1$ регуляризацией реализована в классе Lasso" ] }, { "cell_type": "markdown", "metadata": { "id": "MLs7j7dL0a93" }, "source": [ "### **Задание 3 [2 баллa]**\n", "\n", "Почему в нашем примере $l_1$ регуляризация приведёт к разреживанию весов? (подсказка, нужно опять подсчитать производную, но обратите внимание на дифференцируемость модуля)." ] }, { "cell_type": "markdown", "metadata": { "id": "se90tJIm0a93" }, "source": [ "**Ваши выводы тут:**\n", "\n", "Изначальная функция имеет вид: $J(w) = \\sum_{i=1}^{n} (y_i - (w_1 x_{1i} + w_2 x_{2i}))^2 + \\alpha (|w_1| + |w_2|)$\n", "\n", "Снова возьмём производную:\n", "1. $\\frac{\\partial J}{\\partial w_1} = -2 \\sum_{i=1}^{n} x_{1i} \\left( y_i - (w_1 + 3w_2) x_{1i} \\right) + \\alpha \\cdot \\text{sign}(w_1)$\n", "2. $\\frac{\\partial J}{\\partial w_2} = -2 \\sum_{i=1}^{n} 3x_{1i} \\left( y_i - (w_1 + 3w_2) x_{1i} \\right) + \\alpha \\cdot \\text{sign}(w_2)$\n", " * $\\text{sign}(w_i)$ - знак $i-го$ веса\n", "\n", "\n", "Почему у нас зануляются веса:\n", "1. Во всех точках, кроме $w_i=0$ у нас идёт постоянное стремление к уменьшению весов\n", "2. Так как в точке 0 у нас не определена производная, то это потенциальная точка для остановки\n", "3. Так как веса получаются линейно зависимыми, то вес может занулится, а весь вклад, который он вносил,перейдёт на первый вес\n", "\n", "\n" ] }, { "cell_type": "markdown", "source": [ "-----" ], "metadata": { "id": "WJMbvsfFK8pc" } }, { "cell_type": "markdown", "metadata": { "id": "gGRzji4H0a93" }, "source": [ "Добавим $l_1$ регуляризацию и посмотрим, как меняется значения весов, в зависимости от значения коэффициента регуляризации." ] }, { "cell_type": "code", "source": [ "from sklearn.linear_model import Lasso" ], "metadata": { "id": "wwHDV57OFYWc", "ExecuteTime": { "end_time": "2024-11-15T17:40:42.290351Z", "start_time": "2024-11-15T17:40:42.281571Z" } }, "outputs": [], "execution_count": 6 }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "bLRyD9MJ0a93", "outputId": "6e6345ec-4810-412c-e79a-596d07b7812c", "ExecuteTime": { "end_time": "2024-11-15T17:40:46.915130Z", "start_time": "2024-11-15T17:40:46.899051Z" } }, "source": [ "reg = Lasso(alpha=1., max_iter=1000, tol=1e-4)\n", "reg.fit(X3, Y3)\n", "print(\"Веса, при alpha = 1.\")\n", "print(\"w1:\", reg.coef_[0], \"\\tw2:\", reg.coef_[1])\n", "print()\n", "\n", "reg = Lasso(alpha=0.1, max_iter=1000, tol=1e-4)\n", "reg.fit(X3, Y3)\n", "print(\"Веса, при alpha = 0.1\")\n", "print(\"w1:\", reg.coef_[0], \"\\tw2:\", reg.coef_[1])\n", "print()\n", "\n", "reg = Lasso(alpha=0.01, max_iter=1000, tol=1e-4)\n", "reg.fit(X3, Y3)\n", "print(\"Веса, при alpha = 0.01\")\n", "print(\"w1:\", reg.coef_[0], \"\\tw2:\", reg.coef_[1])\n", "print()\n", "\n", "reg = Lasso(alpha=0.001, max_iter=1000, tol=1e-4)\n", "reg.fit(X3, Y3)\n", "print(\"Веса, при alpha = 0.001\")\n", "print(\"w1:\", reg.coef_[0], \"\\tw2:\", reg.coef_[1])\n", "print()\n", "\n", "reg = Lasso(alpha=0.0001, max_iter=1000, tol=1e-4)\n", "reg.fit(X3, Y3)\n", "print(\"Веса, при alpha = 0.0001\")\n", "print(\"w1:\", reg.coef_[0], \"\\tw2:\", reg.coef_[1])\n", "print()\n", "\n", "reg = Lasso(alpha=0.00001, max_iter=1000, tol=1e-4)\n", "reg.fit(X3, Y3)\n", "print(\"Веса, при alpha = 0.00001\")\n", "print(\"w1:\", reg.coef_[0], \"\\tw2:\", reg.coef_[1])\n", "print()" ], "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Веса, при alpha = 1.\n", "w1: 0.0 \tw2: 0.0\n", "\n", "Веса, при alpha = 0.1\n", "w1: 0.0 \tw2: 0.029684463509327023\n", "\n", "Веса, при alpha = 0.01\n", "w1: 0.0 \tw2: 0.14506160917248503\n", "\n", "Веса, при alpha = 0.001\n", "w1: 0.0 \tw2: 0.1565993237388008\n", "\n", "Веса, при alpha = 0.0001\n", "w1: 0.0 \tw2: 0.15775309519543243\n", "\n", "Веса, при alpha = 0.00001\n", "w1: 0.39668731991454986 \tw2: 0.025639365702912618\n", "\n" ] } ], "execution_count": 7 }, { "cell_type": "markdown", "metadata": { "id": "sVlEPN8M0a94" }, "source": [ "### **Задание 4 [2 баллa]**\n", "\n", "Почему в итоге при $\\alpha = 0.00001$ получились веса не равные нулю?" ] }, { "cell_type": "markdown", "metadata": { "id": "gG3RGBp90a94" }, "source": [ "**Подсказка**\n", "\n", " Обратите внимание на то, каким странным получился вес $w_2$" ] }, { "cell_type": "markdown", "source": [ "**Ваши выводы тут:**\n", "\n", "Так как штраф за наличие весов (коэф. $\\alpha$) весьма низок, то модель не считает его значительным, чтобы занулять. \n", "\n", "Пояснение:\n", "1. Оба веса вносят некоторый вклад в улучшение качества модели\n", "2. Если коэффициент $\\alpha$ не вносит достаточного штрафа, то модель не будет искать имеющуюся зависимость между весами, предпочитая оставить вес ненулевым\n", "3. Хоть вес $w_2$ и не ноль, он всё равно весьма мал, так что основной вклад, как и раньше, вносится вторым весов\n", "4. При увеличении числа итераций, веса могут занулиться, так как даже с практически отсутствующей регуляризацией модель сможет найти зависимость.\n", " * При выполнении приведённого ниже кода видно, что при увеличении числа итераций модель всё-таки зануляет один из весов ==> она дообучилась.\n", " * Изначально кол-ва итераций не хватило, так как модель была слишком сложной для таких простых данных (из-за малого $\\alpha$ и слабой регуляризации, которая как раз и уменьшает сложность модели)" ], "metadata": { "id": "EgY01lIqALZO" } }, { "cell_type": "code", "metadata": { "id": "XHeValDp0a94", "ExecuteTime": { "end_time": "2024-11-15T17:47:20.498210Z", "start_time": "2024-11-15T17:47:20.479209Z" } }, "source": [ "reg = Lasso(alpha=0.00001, max_iter=10000, tol=1e-4)\n", "reg.fit(X3, Y3)\n", "print(\"Веса, при alpha = 0.00001\")\n", "print(\"w1:\", reg.coef_[0], \"\\tw2:\", reg.coef_[1])\n", "print()" ], "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Веса, при alpha = 0.00001\n", "w1: 0.0 \tw2: 0.15786847234109586\n", "\n" ] } ], "execution_count": 8 }, { "cell_type": "markdown", "source": [ "-----" ], "metadata": { "id": "O6QiwnxuLBLL" } }, { "cell_type": "markdown", "source": [ "В предущих блоках мы использовали модельные примеры, в которых $y$ зависел от $x$ линейно. Но так бывает далеко не всегда.\n", "\n", "### **Задание 5 [1 баллa]**\n", "\n", " Придумайте, сгенерируйте и визуализируйте пример, в котором линейная регрессия будет плохо классифицировать данные." ], "metadata": { "id": "KgKtO4HPLPsh" } }, { "cell_type": "code", "source": [ "from sklearn.model_selection import train_test_split\n", "from sklearn.metrics import mean_squared_error\n", "\n", "\n", "def generate_polynomial_data(n_samples):\n", " X = np.linspace(-10, 10, n_samples)\n", " coeffs = [-1, 3, 2] # Коэффициенты для x^2, x^1, x^0\n", " y = np.polyval(coeffs, X) + np.random.uniform(0, 1, n_samples)\n", " X = X.reshape(-1, 1)\n", " return X, y\n", "\n", "\n", "# Генерация 500 образцов\n", "X4, Y4 = generate_polynomial_data(500)\n", "X4_train, X4_test, Y4_train, Y4_test = train_test_split(X4, Y4, test_size=0.2, random_state=50)\n", "\n", "reg = Ridge(alpha=0.1)\n", "reg.fit(X4_train, Y4_train)\n", "Y4_pred = reg.predict(X4_test)\n", "print(\"MSE для нашей модели: \", mean_squared_error(Y4_test, Y4_pred))\n", "\n", "plt.figure(figsize=(18, 6))\n", "\n", "# Линейная регрессия без полинома\n", "plt.subplot(1, 3, 1)\n", "plt.scatter(X4, Y4, color='blue', label='Данные')\n", "plt.scatter(X4_test, Y4_pred, color='red', label='Предсказание модели')\n", "plt.xlabel('Признак X')\n", "plt.ylabel('Целевая переменная y')\n", "plt.title('Данные с полиномиальной зависимостью')\n", "plt.legend()\n", "plt.grid(True)\n", "plt.tight_layout()\n", "plt.show()" ], "metadata": { "id": "gT9UwrRHMVmW", "ExecuteTime": { "end_time": "2024-11-15T19:24:07.968389Z", "start_time": "2024-11-15T19:24:07.431850Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MSE для нашей модели: 805.0142195307291\n" ] }, { "data": { "text/plain": [ "
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" }, "metadata": {}, "output_type": "display_data" } ], "execution_count": 69 }, { "cell_type": "markdown", "source": [ "### **Задание 6 [2 баллa]**\n", "\n", "Приведите искусственный пример (можно даже очень неправдоподобный), когда линейная регрессия с $l_2$ регуляризацией гарантированно занулит какой-нибудь признак? Покажите (теоретически или программно), что признак действительно зануляется\n" ], "metadata": { "id": "RayRFAUQ8_im" } }, { "cell_type": "code", "source": [ "X1 = np.random.randn(100, 1)\n", "X2 = np.ones((100, 1))*10\n", "Y = 3 * X1\n", "X = np.hstack((X1, X2))\n", "ridge = Ridge(alpha=0.5)\n", "ridge.fit(X, Y)\n", "\n", "print(\"Коэффициенты Ridge-регрессии:\")\n", "print(f\"w1 (X1): {ridge.coef_[0][0]:.4f}\")\n", "print(f\"w2 (X2): {ridge.coef_[0][1]}\")" ], "metadata": { "id": "Gw3c956KAdel", "ExecuteTime": { "end_time": "2024-11-15T19:18:54.506544Z", "start_time": "2024-11-15T19:18:54.486775Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Коэффициенты Ridge-регрессии:\n", "w1 (X1): 2.9841\n", "w2 (X2): 0.0\n" ] } ], "execution_count": 67 }, { "cell_type": "markdown", "source": [ "**Ваши выводы тут:**\n", "\n", "В случае, если один из признаков является константным, то модель занулит его.\n", "\n", "Это связано с тем, что при взятии производной, мы будем получать 0, что и приведёт к занулению признака." ], "metadata": { "id": "6zxO0gPaAWyl" } }, { "cell_type": "markdown", "source": [ "**Выводы** В первой части задания по линейным моделям мы должны были узнать:\n", ".\n", "\n", "1. Зачем нужна регуляризация.\n", "2. Как отбирать значащие признаки.\n", "3. Когда линейные модели работают хорошо, а когда плохо\n", "\n", "-----\n", "\n", "\n", "Во **второй части** мы будем применять линейные модели для классификации реальных данных, где мы сможем проверить наши выводы, полученные на искуственных примерах. А также убедимся в полезности нормировки и научимся работать с разными видами данных.\n" ], "metadata": { "id": "QU7Z9Ku8ycY_" } } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" }, "colab": { "provenance": [] } }, "nbformat": 4, "nbformat_minor": 0 }