{ "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", "metadata": { "id": "6ODl7_-1JoHQ" }, "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" ] }, { "cell_type": "markdown", "metadata": { "id": "H0Lj_c63lrku" }, "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 **" ] }, { "cell_type": "markdown", "metadata": { "id": "d4sbAeC--5gV" }, "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" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "hQLVkvfL-5gW" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m A new release of pip is available: \u001b[0m\u001b[31;49m25.2\u001b[0m\u001b[39;49m -> \u001b[0m\u001b[32;49m25.3\u001b[0m\n", "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m To update, run: \u001b[0m\u001b[32;49mpip install --upgrade pip\u001b[0m\n" ] } ], "source": [ "! curl https://raw.githubusercontent.com/MSU-ML-COURSE/ML-COURSE-25-26/refs/heads/master/requirements/requirements.txt -o ./requirements_2025_26_for_colab_small.txt\n", "! pip install -q -r ./requirements_2025_26_for_colab_small.txt" ] }, { "cell_type": "markdown", "metadata": { "id": "vUCY0KLD7VmA" }, "source": [ "Проверим версию библиотеки:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "CIWS5lZ3-5gX" }, "outputs": [], "source": [ "import catboost\n", "assert(catboost.__version__ == '1.2.8')" ] }, { "cell_type": "markdown", "metadata": { "id": "eC9VrV8G-5gX" }, "source": [ "Теперь можно приступать к выполнению задания! :)" ] }, { "cell_type": "markdown", "metadata": { "id": "y39N4E_B-5gX" }, "source": [ "-----------\n", "" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "id": "Gc3xTMopl8c1" }, "outputs": [], "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", "warnings.simplefilter(\"ignore\")\n", "sns.set(style=\"darkgrid\")\n", "%matplotlib inline" ] }, { "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", "metadata": { "id": "7ee6L2lk4dBV" }, "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", "$\\frac{1}{N} \\cdot ∑_{i=1}^M (w_1 \\cdot x_{i1} + \\dots w_n \\cdot x_{in} + b - y_i)^2 + \\alpha \\cdot \\left( |w_1| + \\dots + |w_n| \\right) \\rightarrow \\min_{w_1, \\dots, w_n, b}$" ] }, { "cell_type": "markdown", "metadata": { "id": "yBXvREbq6J33" }, "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" ] }, { "cell_type": "markdown", "metadata": { "id": "Iqj_cwbV_vEL" }, "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", "Конкретнее:\n", "- Смещение b независимо от значений признаков и добавляется отдельно ==> его резуляризация не несёт пользы\n", "- Регуляризация применяется, чтобы снизить сложность модели и избежать переобучения, однако b не влияет на сложность модели, а значит не требует регуляризации" ] }, { "cell_type": "markdown", "metadata": { "id": "Md8-JjM68ZUe" }, "source": [ "-----\n", "" ] }, { "cell_type": "markdown", "metadata": { "id": "HND8s6ee6h0P" }, "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." ] }, { "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", "metadata": { "id": "X66mK63v-BI0" }, "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." ] }, { "cell_type": "markdown", "metadata": { "id": "O1ogDSg798EZ" }, "source": [ "Посмотрим, как меняется значения весов, в зависимости от значения коэффициента регуляризации." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "id": "icTp30Uj7pJn" }, "outputs": [], "source": [ "from sklearn.linear_model import Ridge" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "id": "cidgDWJf7o83" }, "outputs": [], "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" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 653 }, "id": "7YIxYW8T0a92", "outputId": "17c380cc-7cb6-460f-fd7f-c7332a1cdb31" }, "outputs": [ { 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "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()" ] }, { "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": [ "**Ваши выводы тут:**\n", "\n", "Функция потерь имеет 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:\n", "- $\\frac{\\partial J}{\\partial w_1} = -2 \\sum_{i=1}^{n} x_{1i} (y_i - (w_1 x_{1i} + w_2 x_{2i})) + 2 \\alpha w_1 = 0$\n", "- $\\frac{\\partial J}{\\partial w_2} = -2 \\sum_{i=1}^{n} x_{2i} (y_i - (w_1 x_{1i} + w_2 x_{2i})) + 2 \\alpha w_2 = 0$\n", "\n", "Если рассматривать конкретно наши данные ($x_2=3*x_1$):\n", "- $\\frac{\\partial J}{\\partial w_1} = -2 \\sum_{i=1}^{n} x_{1i} (y_i - (w_1 x_{1i} + 3 w_2 x_{1i})) + 2 \\alpha w_1 = 0$\n", "- $\\frac{\\partial J}{\\partial w_2} = -2 \\sum_{i=1}^{n} 3 x_{1i} (y_i - (w_1 x_{1i} + 3 w_2 x_{1i})) + 2 \\alpha w_2 = 0$\n", "\n", "Если произвести 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", "metadata": { "id": "49ZLe4IeK5WE" }, "source": [ "-----\n", "" ] }, { "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", "- $\\frac{\\partial J}{\\partial w_1} = -2 \\sum_{i=1}^{n} x_{1i} \\left( y_i - (w_1 + 3w_2) x_{1i} \\right) + \\alpha \\cdot \\text{sign}(w_1)$\n", "- $\\frac{\\partial J}{\\partial w_2} = -2 \\sum_{i=1}^{n} 3x_{1i} \\left( y_i - (w_1 + 3w_2) x_{1i} \\right) + \\alpha \\cdot \\text{sign}(w_2)$\n", " * $\\text{sign}(w_i)$ - знак $i-го$ веса\n", "\n", "\n", "Почему у нас зануляются веса:\n", "- Во всех точках, кроме $w_i=0$ у нас идёт постоянное стремление к уменьшению весов\n", "- Т.к. в точке 0 у нас не определена производная, то это потенциальная точка для остановки\n", "- Т.к. веса получаются линейно зависимыми, то вес может занулится, а весь вклад, который он вносил,перейдёт на первый вес\n" ] }, { "cell_type": "markdown", "metadata": { "id": "WJMbvsfFK8pc" }, "source": [ "-----" ] }, { "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", "execution_count": 8, "metadata": { "id": "wwHDV57OFYWc" }, "outputs": [], "source": [ "from sklearn.linear_model import Lasso" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "bLRyD9MJ0a93", "outputId": "6e6345ec-4810-412c-e79a-596d07b7812c" }, "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: 0.15659932373880084\n", "\n", "Веса, при alpha = 0.0001\n", "w1: 0.0 \tw2: 0.1577530951954324\n", "\n", "Веса, при alpha = 0.00001\n", "w1: 0.3966873199145487 \tw2: 0.025639365702912757\n", "\n" ] } ], "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()" ] }, { "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", "metadata": { "id": "EgY01lIqALZO" }, "source": [ "**Ваши выводы тут:**\n", "\n", "Т.к. штраф за наличие весов (коэф. $\\alpha$) весьма низок, то модель не считает его значительным, чтобы занулять. \n", "\n", "Пояснение:\n", "- Оба веса вносят некоторый вклад в улучшение качества модели\n", "- Если коэффициент $\\alpha$ не вносит достаточного штрафа, то модель не будет искать имеющуюся зависимость между весами, предпочитая оставить вес ненулевым\n", "- Хоть вес $w_2$ и не ноль, он всё равно весьма мал, так что основной вклад, как и раньше, вносится вторым весов\n", "- 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)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "id": "XHeValDp0a94" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Веса, при alpha = 0.00001\n", "w1: 0.0 \tw2: 0.15786847234109574\n" ] } ], "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])" ] }, { "cell_type": "markdown", "metadata": { "id": "O6QiwnxuLBLL" }, "source": [ "-----" ] }, { "cell_type": "markdown", "metadata": { "id": "KgKtO4HPLPsh" }, "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." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "id": "gT9UwrRHMVmW" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MSE для модели: 810.5074902548056\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "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]\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", "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 модели: \", mean_squared_error(Y4_test, Y4_pred))\n", "\n", "plt.figure(figsize=(18, 6))\n", "\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')\n", "plt.xlabel('Признак X')\n", "plt.ylabel('Целевая y')\n", "plt.title('Данные с пол зависимостью')\n", "plt.legend()\n", "plt.grid(True)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "RayRFAUQ8_im" }, "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" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "id": "Gw3c956KAdel" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Коэфф Ridge-регрессии:\n", "w1 (X1): 2.9883\n", "w2 (X2): 0.0\n" ] } ], "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(\"Коэфф Ridge-регрессии:\")\n", "print(f\"w1 (X1): {ridge.coef_[0]:.4f}\")\n", "print(f\"w2 (X2): {ridge.coef_[1]}\")" ] }, { "cell_type": "markdown", "metadata": { "id": "6zxO0gPaAWyl" }, "source": [ "**Ваши выводы тут:**\n", "\n", "В случае, если один из признаков константа, то модель занулит его.\n", "\n", "Это связано с тем, что при взятии производной, мы будем получать 0, что и приведёт к занулению признака." ] }, { "cell_type": "markdown", "metadata": { "id": "QU7Z9Ku8ycY_" }, "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": { "colab": { "provenance": [] }, "kernelspec": { "display_name": ".venv", "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": "3.13.7" } }, "nbformat": 4, "nbformat_minor": 0 }