{ "cells": [ { "cell_type": "markdown", "metadata": { "id": "sTB50uLM0a9o" }, "source": [ "# \n", "\n", "# Машинное обучение. ВМК МГУ" ] }, { "cell_type": "markdown", "metadata": { "id": "0xg3G6bd0a9s" }, "source": [ "\n", "# Практическое задание 5: Линейные модели: регрессия\n", "\n", "## Уровень: **Базовый (Base)**" ] }, { "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 регуляризация, зачем она нужна, и чем отличаются разные регуляризаторы.\n", "* Научиться решать задачу регрессии линейными моделями.\n", "-------\n", "\n", "**Примерное время выполнения (execution time/время выполнения, если нажать run all) всех ячеек ноутбука при правильной реализации: 5 минут **" ] }, { "cell_type": "markdown", "metadata": { "id": "CTmlafz7W04M" }, "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": "UodfS2cpXMUd" }, "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": 3, "metadata": { "id": "zyRnTYF5X37Y" }, "outputs": [], "source": [ "import catboost\n", "assert(catboost.__version__ == '1.2.8')" ] }, { "cell_type": "markdown", "metadata": { "id": "UShU_WkjlqrP" }, "source": [ "Теперь можно приступать к выполнению задания! :)" ] }, { "cell_type": "markdown", "metadata": { "id": "GLIQiUj6KNYj" }, "source": [ "-----------\n", "" ] }, { "cell_type": "code", "execution_count": 31, "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": "1oms7GV80a9x" }, "source": [ "Для обучения линейной регрессии, равно как и для обучения остальных простых моделей (линейные модели, решающие деревья, knn и т.д.) отлично подходит библиотека `scikit-learn` (sklearn): в ней очень понятный и простой интерфейс.\n", "\n", "Однако для обучения более сложных моделей вроде бустинга и нейронных сетей всё же нужно пользоваться специализированными библиотеками: XGBoost, LightGBM, CatBoost и пр. для градиентного бустинга над деревьями, PyTorch, Tensorflow и пр. для нейронных сетей.\n", "\n", "---\n", "Напомним, что линейная регрессия — это модель вида\n", "\n", "$$a(x) = \\langle w, x \\rangle + b$$ где $w \\in \\mathbb{R}^d$, $b \\in \\mathbb{R}$. Для обучения параметров $w$ решается оптимизационная задача следующего вида:\n", "\n", "$$\\frac{1}{M} ∑_{i=1}^M (w_1 \\cdot x_{i1} + \\dots + w_n \\cdot x_{in} + b - y_i)^2 + \\alpha \\cdot R(w) \\rightarrow \\min_{w_1, \\dots, w_n, b}$$\n", "\n", "Здесь $R(w)$ — это регуляризация параметров модели, $\\alpha$ — коэффициент регуляризации, задаваемый перед началом обучения.\n", "\n", "Для обучения линейной регрессии, нам подойдет реализация из sklearn. В sklearn есть несколько классов, реализующих линейную регрессию. Основные это:\n", "\n", "- `LinearRegression` — линейная регрессия без регуляризации $R(w) = 0$ (метод наименьших квадратов)\n", "- `Ridge` — линейная регрессия с оптимизацией MSE и $\\ell_2$-регуляризацией $R(w) = \\frac{1}{2} \\cdot \\left( w_1^2 + \\dots + w_n^2 \\right)$\n", "- `Lasso` — линейная регрессия с оптимизацией MSE и $\\ell_1$-регуляризацией $R(w) = |w_1| + \\dots + |w_n|$\n", "\n", "Также есть SVR, ElasticNet и пр., но не будем сегодня о них\n", "\n", "У моделей из sklearn 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": "cbSs0Vyv7siW" }, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": { "id": "X7WovweT0a9x" }, "source": [ "Рассмотрим, модельные данные для задачи регрессии. Пусть $x$ будет обычным числом из равномерного распределения, а $y = 0.5 \\cdot x + 0.1$ — целевая переменная. При этом наблюдаем мы $\\overline{y} = y + \\varepsilon,~\\varepsilon \\sim N(0, 0.01)$." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 731 }, "id": "qVGiym5s0a9y", "outputId": "ce3215df-d8c5-4371-f796-0e55074f0222" }, "outputs": [ { "data": { "image/png": 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Xm5tIGESTZHVhrwsCXfjoOVLQrL9HQReP6dr6emgPJSSUsNDx6uf7dyqQPATKQDM0qUWBhILMlgJlvblrwocyRcoo+X9oddtU2aIgmjCWHnAqwNMbpWb4601XQY3e/DKzLZrgpsyl3lD1RqNAUhlNZY81scenoEJBpDJMCvZ061O3sf0AXrP407sb+PSm4GfD/umf/inwdn16Bj2fb8h33323FywpKFZrPr256nlUFk4T9zKzdMcdd5w3oVDBdWZHgtbyJ/PpeVN2UmOvQEyTeDInPGoylMZB+yoDr4sU7afJf82dK/o9FCirhCAooE0/H/yANjO76PO/7l9s+ZoLFPz9MwM4lR7oudYteV0o6Ln0g0ede7oAUVCjchGd2yqL8Mfbv1vRGrqroZ+rsVJAqRIb/b+Ouy2PlT6ZTxeCem4VdGqRH31/ermHKNhWZlAXVbowzexWIf5dAQVn/mvTp4tXBYn+3SKffo6Cc52vKrVqiSacaew0eU+BsiZcKogMmmzpPwe5ngv+8fulY+mUkdex+n+jWktdKzReOl8U4LYmUBaNlS4m1VHE7/Kj8o2W2me29jnIB/1tVZCsn6mM9i233OIlMJA81CgDzfC7KCh4ULarOXqT1x9RUacBn1oeSVBLJGV6dZtQb8TpmQrdnhQF57q9r6DltNNOa/L9yiTr1q1KDnT7XLV5qkVNt2bNGi9IVrZQnSF0m9QPkpW98tu7ZcsI6va0ApugN0S/dEPlD/mi38mva9WteD03fjmASgeC6Na16hx1waDWUXpO/GNr7XirflPBm7JlGne1g9KbemYrPJ+CJmW5FNjpgkbPqzovBMl2Puh4FUQrc64xV5Cn30djGJSx99tbZT732j+oflbPj4IR/T7ptE3nkoJTlTj8/Oc/T31NZQw6T3VOaoEUXQD4AYsCUr9mONv5o2BTGVy/flbPl8ZLHQsUoGtM9Xu39bEUKGvM9KHvU7CqrgV6TaqONpPfllHt+ZqjAE7S5wr49DrTsfklA+kXeOog8x//8R859UzXRbHOGWWU9RzookwXakH8EpKg80b8kiT/XMh2/LrQVJa0uW4f2egujZ5fBfO6m9UW+lumIN3/+5ZrN5+2vh7aShet+l1VE62VWXVnSWMcdNcO7iNQBpqh7JsCTAWKyrYpu5hJE+1U56hAWpkkBaU+vQHoZ6iMQH/gfXqz15u5slPK9KZnp/QmpIBKtcpqp6RgMb2FVGv4WSMFIOmZM2WVNMHPf8MJyqr5/FZRquNMD1KUCdPzoYydstn54tcf6nlN518MSHq/YQU9atWlTJPGSs9XW7NlmdIzhy1NnlQQ4V9MNHfbXcGFgmAFa+m/n84DZdH9fUSPq7sL+v00uTF9jHQXwO9/rBZf6bS/vpY+Vqqx1Pmn56a5Y9OdB5U5/PKXv0z18m5uLHTnRAGhX96S7fzRRc5//ud/encH0n+OAl89jgJGZUDz8Vg+f/z92/U+lSSo3EF1wNlq6v1+vjrn0+8G6efdc8893u+kevR0usDQeLWm/lftAfW3xV+QKOiC2K+VVqCoix0dfzpdYKg+WRfAfu20jkM/T3930u8Y6TzTBajOjZZKHYKo1EjnkcYjM6OeKx2nzkNdTCrzr6A9l/aSbX09tIWeH2WONd7KnOsuk+4g6e+B+kUHZerhNkovgCxUeiB6M1NQq6ysMkp6I1Ltskok9AakYNlfdMSnTKPqg9XbU7fp9Uam2++awKcMot5U1Tc26Pak3oza2jvZp0lxqkVWQKtMnd7cFWQqAFeGVNls3erO1vVCQYNuCysDpN9B3TOUOVM2SJlBBUCZ9CaYPkHKz+4qG5O+3Z90pP31Zq/fVR/KrqkkQM+9LhJ0u14BgSZJqm45/Xj1BqbacAUZuSxY0FI2W8GI6A1ZGVYdiwJIZT+DJvPpDVsXHMr2KTOo2+d6joIyT3rDVbmB6suVPdRMfwWuCkD0nCqzmz7eKuXQ4+u49Bzq5ypg10WU3sTVOSWzJ62CRGXC9X0ae02K0zmqzLw6NjRH36fHU823alBVaqJzXeeQzhfdrVDApsdXFlRZYI2HAkmNh7J9QXSO6BxXIKPfWWPqZxT1s3QHRpnjtj6WMn/+OaWx0EWhnh/JnHSnoFuvv6DXXDo9z7pg0cQzlSupTEMXOLo41M/XazN9QqT4Nbutodejzm9lfjVhNLPMw6fAXN1AVJqi80cBprLMeg2rN7KeT114+/W7unDVsehiWIGjngc9jp5LfY/+VvmThVtDQb2C+8yLhNbS3zfNw9DYtTQW6dryemgLXQzpb7TKffw7fEpeqD+5vqYLv2x9suEeAmWgBXpzV1CrbI7+KPst3XTbV4GNan2bm2GvhSoUuGgSk4Ip/WFXDbDeIJQJDcrMqGZRNZaagNWWOtD0N2+VIqh7g265KrOoyYLK4CjwV9ChN1QFas1lwnRBoElP+lDArNvZCmz0nOiNKSgbpMA3qPxAwWNQAKl9FQz4z6X+X0GKHk8BigJVPZbeqBRQ6HdRVlwTpxRgaxz0fLWX3xZMNC6qwdQbpcYqc5zSJ/PpaxpTBVcttd7SxYaCNWX29Hso+FAQq3FQIJROgY/axSkzqEUZdP4p+6ogUivGBWUFVSqkoFSBk847BZg6Lk0AbWmCmcZUi5Ko1ETnqoIO1currEj/1oWDzkndRVBWVsGEAmo9D+klR5n0/Cmw1PHo99DYKZjT+a/xFgW/bXksBVvpZQTKWPqBYmYrNVFGMKhrQiZdzOixVRev81AZbV0s6XXjXzyn0/nZ2kUodG4rCNd5p2xpNroA098ddZvQxYQu6DSeuvjQRWXm61DnkiZL6jnV60QXCcpK68JWZS9toTFqaQW+XCjQ1kWBLkZ1cZirtrweWkt3Bm+++Wbv56r0Ip1Ke3SBrL85uvjwu7TAfR3UTLnYBwGgceCorJoCCb8/qMv8cgMFx2g7dX9In4gJRJHKaxRo6i6QLuiAqKNGGYgQZaqVNVJWsq2ZHwCIIuXlVCqjDH22uxBAlFB6AUTAq6++6t3u1SQnTUxTmUFzPXEBIE40t0ATotWNRAvJqOQkaEEXIIoIlIEIUD2mJitpRrUyyZptnRT5mKkOILpUT606aQXMmhCoSbhAXFCjDAAAAASgRhkAAAAIQKAMAAAABCBQBgAAAAIwmS/PVPJdXx9e2XdJSYdQHw+FwTi6gXF0A+PoBsbRDSUFGEf9TC3KlQsC5TzTYFZW1oTyWB07lljv3t2tunq77dlTH8pjIv8YRzcwjm5gHN3AOLqhY4HGsby8u5WW5hYoU3oBAAAABCBQBgAAAAIQKAMAAAABCJQBAACAAATKAAAAQAACZQAAACAAgTIAAADgeqBcX19vc+bMsXHjxtmwYcNs6tSptn79+sB9b731VquoqAj8uOqqq0I/dgAAAESLU4Hy3LlzbeHChTZz5kxbtGiRFzhPmTLFdu3a1WTfb3zjG/bMM880+vjmN79pe+21l51zzjlFOX4AAABEhzOBsoLhBQsW2PTp0238+PE2ePBgmz17tm3cuNGWLFnSZP/u3bvbvvvum/rYvHmz3XPPPXb11Vd7WWUAAAAkmzOB8urVq62mpsbGjBmT2lZWVmZDhgyxFStWtPj91113nR1zzDF25plnFvhIAQAAEAcdzRHKHEu/fv0abe/Tp0/qa8156qmn7MUXX7SHH364oMcIAACA+HAmUN6xY4f3uXPnzo22d+nSxbZu3Zr1e++880478cQT7fDDD8/LsXTsGE6ivrS0pNFnxBPj6AbG0Q2MoxsYRzeURmAcnQmUu3btmqpV9v9famtrrVu3bs1+3wcffGDLly+3O+64Iy/HUVLSwXr37m5hKitr/vdDfDCObmAc3cA4uoFxdENZEcfRmUDZL7nYtGmTDRw4MLVd/842OW/p0qVWXl5uxx9/fF6Oo76+waqrt1sYdIWlk6e6eofV1dWH8pjIP8bRDYyjGxhHNzCObigt0DjqZ+aapXYmUFaXix49enjZYT9Qrq6utlWrVtnkyZOb/b4XXnjBRo0aZR075u+p2LMn3BelTp6wHxP5xzi6gXF0A+PoBsbRDXVFHEdnAmXVJisgnjVrlpch7t+/v910003Wt29fmzBhgtXV1VllZaX17NmzUWmGAul//dd/LeqxAwAAIHqcqnJXD+WJEyfajBkzbNKkSVZaWmrz58+3Tp062YYNG2zs2LG2ePHiRt+j/sm9evUq2jEDAAAgmjo0NDQ0FPsgXLs9UFlZE8pjqbuGJg5WVdVwaynGGEc3MI5uYBzdwDi6oWOBxrG8vHvONcpOZZQBAACAfCFQBgAAAFyezAcAAApH7U/fWL/FttTUWq/uXeywAb28tQMAlxEoAwCArFau2WQLl661qm21qW29e3axs08eZCMq+hT12IBCovQCAABkDZJve+jVRkGy6N/arq8DriJQBgAAzZZbKJOczX1L13r7AS4iUAYAAIFUk5yZSc5Uua3W2w9wEYEyAAAIpIl7+dwPiBsCZQAAEEjdLfK5HxA3BMoAACCQWsCpu0U25T0/bRUHuIhAGQAABFKfZLWAy2bSyYPopwxnESgDAIBmqU/ytDOHNsksK5Os7fRRhstYcAQAAGSlYHj4oH1ZmQ+JQ6AMAABapKB48IG9i30YQKgovQAAAAACECgDAAAAAQiUAQAAgAAEygAAAEAAAmUAAAAgAF0vAAAA0ER9fUPiWwISKAMAAKCRlWs22cKla61qW21qmxad0UqNSVpkhtILAAAANAqSb3vo1UZBsujf2q6vJwWBMgAAAFLlFsokZ3Pf0rXefklA6QUAAAA8qknOzCRnqtxWa6vfq7KSDh2cr18mUAYAAIBHgW8u5j38qtXs3ON8/TKlFwAAAPAoO5yLmrQg2eX6ZQJlAAAAeFRCoexwW93nWP0ygTIAAAA8qjNWCUVbVW6r9eqcXUGgDAAAgBTVGU87c2iTzHL3rh3zWuccB0zmAwAAQJNgefigfRutzKeSilm/+Vve6pzjgEAZAAAAgWUYgw/snfq3AmVlmbO1jyvv+WmrOFdQegEAAIC81C9POnmQU/2UCZQBAADQrvrl8p5dvO2u9VGm9AIAAADtql8+jJX5AAAAAGtSv+wqSi8AAACAAATKAAAAQAACZQAAACAAgTIAAAAQgEAZAAAACECgDAAAAASgPRwAAACKor6+IdL9mAmUAQAAELqVazbZwqVrrWpbbWqbVvzTMtlRWeGP0gsAAACEHiTf9tCrjYJk0b+1XV+PAgJlAAAAhFpusXDp2qz73Ld0rbdfsREoAwAAIDRvrN/SJJOcqXJbra15r8qKjUAZAAAAodlSU5vbfp/ssmIjUAYAAEBoenXvktt+PTpbsREoAwAAIDSHDejldbfIprxnF6sY2NuKjUAZAAAAoSkp6eC1gMtm0smDItFPmUAZAAAg4tQBYvW6Klu2aqP3OQodIdpDfZKnnTm0SWZZmWRtj0ofZRYcAQAAiLA4LMzRFjr24YP2ZWU+AAAAtH1hjkz+whxRyr62hYLiwQcWvxa5OZReAAAARFCcFuZwFYEyAABAjBfm0H4oDAJlAACAOC/MkeN+aD0CZQAAgDgvzJHjfmg9AmUAAIAYL8yh/VAYBMoAAAARFKeFOVxFoAwAABDDhTkuOOMI6961kzOLkEQRfZQBAABitjDHth27bdGT7i1CEjVklAEAAGKyMMfoIX2tZudum/fwq01ax/mLkGiREuSHU4FyfX29zZkzx8aNG2fDhg2zqVOn2vr165vdf/fu3XbzzTen9p88ebK9/vrroR4zAABArliEJFxOBcpz5861hQsX2syZM23RokVe4DxlyhTbtWtX4P7XXHONPfjgg3bDDTfYAw88YOXl5V5wvW3bttCPHQAAoCUsQhIuZwJlBcMLFiyw6dOn2/jx423w4ME2e/Zs27hxoy1ZsqTJ/so0Kzj+z//8Ty+jfMghh9j1119vnTt3tldfbbqmOgAAQCEo+6vJeLlMymMRknA5M5lv9erVVlNTY2PGjEltKysrsyFDhtiKFSvstNNOa7T/s88+az179rQTTjih0f5/+tOfQj1uAACQXKonVilFrpPyWIQkXM5klJU5ln79+jXa3qdPn9TX0r3zzjs2YMAAL9v85S9/2Y4//niv7OKtt94K7ZgBAECyg2RNvmvNpDwWIQmXMxnlHTt2eJ9VOpGuS5cutnXr1ib7f/LJJ7Zu3TqvrvmKK67wssnz5s2zs88+2xYvXmz77LNPm4+lY8dwrj9KS0safUY8MY5uYBzdwDi6IQ7jqPIKTbrL5r4n19rIw/drsqDI5FMq7Nb7X272+756SoV17lxqcVcagXF0JlDu2rVrqlbZ/3+pra21bt26Ndm/Y8eOXrCsOmbVJ4v+//Of/7w99NBD3iTAttDJ3Lt3dwtTWVnT3w/xwzi6gXF0A+PohiiP4ytvfuRNusumsrrWPqjaaUce+plG2yeMOdh6dO9idzz8in28dWdq+2d6dbOppw+1447a31xSVsRxdCZQ9ksuNm3aZAMHDkxt178rKiqa7N+3b18vWPaDZFGArXKM999/v11XiNXV2y0MusLSyVNdvcPq6upDeUzkH+PoBsbRDYyjG+Iwjus3bM15vwP2aRooHj5gb7t52vG25r0q2/LJLuvVo7NVDOztJeyqqmqsWOrrGwKPKUrjqJ+Za5bamUBZXS569Ohhy5cvTwXK1dXVtmrVKq8/cqaRI0fanj177JVXXrEjjzzS27Zz506vG8YXv/jFdh3Lnj3hvih18oT9mMg/xtENjKMbGEc3RHkce3brlPN+2X6HQQf0ahSkFrN/8spWTkyMwzhGt3inlVSbrIB41qxZ9uSTT3pdMC655BIvczxhwgSrq6uzzZs3e8GwHHPMMXbcccfZlVdeaS+88IK9+eabXq1yaWmpnX766cX+dQAAgMNcm5S3sg0TE+PAmUBZ1EN54sSJNmPGDJs0aZIX9M6fP986depkGzZssLFjx3oT9Xy33nqrjRo1yi666CLv+1SzfM8993gLjwAAABSKyhGUac1m0smD2ly2EKZ6h1cL7NDQ0BC/o44w3R6orAynNkjdNTRxULVIUb21hJYxjm5gHN3AOLohTuMYVK6gcovRR+xnwwft62WUox4sr15XZTfe92KL+10xabgNPrB30cexvLx78mqUAQAA4ka1uwqIteT0i2s327LXPrRtO3bbH1943/vIR41voW1xeLVAp0ovAAAA4kYZ45qdnwbHCpLjVuPby+HVAgmUAQAAiijuNb6HOTYxMR2BMgAAQBGp7CKzW0QmLU6i/aKoxKGJiZkIlAEAQMEoC6rJXstWbfQ+RzUrWkwu1PiOqOhj084c2iSzrEyytke5xjobJvMBAIBYLUDhGldqfEekTUxUUK/jjUPXjmzIKAMAgLxzdQGKQji0/94trtQXlxrfkpIOXgu40UP6ep/jHCQLgTIAAMiruE9OC5MuGK68/S9Nul24UuMbdwTKAAAgr+I+Oa3YWXeXanzjjhplAACQVy5MTotC1l3lGD8+f4y3Qh2Kg2ceAADklSuT04qddVc5xpt/3xraMaEpAmUAAJBXLi9AkS9k3eOBQBkAAOSVywtQ5AtZ93ggUAYAAHnn6gIU+ULWPR6YzAcAAJxegEIT54p9DM1l3dX1ojlJz7pHAYEyAAAo+AIUxRLl1QH9rHvm8SmTPCkCxwcCZQAAYiuKmdIoWbH60z7FmfzVAaNQAhKVrDuCESgDABBDUc6URkFdfYP9+g9rWlwdUEFqsYPSYmfd0Twm8wEA4MiKbn6mVF9PulVvf+yt/pcNqwOiJQTKAAA4tqKbMqXaL8kqq3fmtB99ipENgTIAAI6t6Eam1Ky8rGtO+9GnODf19Q22el2VLVu10fuclAsxapQBAIgRVnTLzZDP7uN1j8hWfkGf4tysTHA9PBllAABihBXdclNa0sG+ekpF1n3oU9yylQmvhydQBgAgRljRLXcjB7M6YHvUUw9P6QUAAHHCim6tk5Q+xYXoqf1GK+rhXW1vR6AMAEDMsKJb67jep7hQNcRbqIcnUAYAII6SkikttqivfujXEBdi9cFe1MMTKAMAEOegzeVMabFFvdtDrjXEbV198LD/rYfPVn7hej08gTIAADEQ9aDNNYXM1OZLoWuIS6iHp+sFAABRl/QWXWGLS7eHMGqIR1Qku3MIGWUAACKs0LfXEd9uD2HVEI9IcD08gTIAABEWl6AtahcXr7z5ka3fsNV6duvU6qAuLt0ewqwhLnG8c0hzCJQBAIiwuARtUaEyFGXYK9tRyx2Xbg/UEBceNcoAAERYXIK2KNVypwfJbanljtPqh0mvIS40MsoAAEQYLbrCr+WOW6Y2yTXEhUZGGQCACPODtmyiFLTFoZbbxUytX0M8ekhf73PSz4d8IaMMAEDEsWR1cWq5ydSCQBkAgBggaCtOLXdSuz3gUwTKAADEBEFb86jlbt9S6FxwBSNQBgAAsRe3CXjFwlLorcNkPgAA4FQttzLHcZiAFzaWQm89MsoAAMAZCoZHHr6ffVC1s80r87mIpdDbhkAZAAA4RYHekYd+xg7Yp5vt2VNf7MOJBJZCbxtKLwAAABzHUuhtQ6AMAADgOJZCbxtKLwCgAGi/BCBKaJ/XNgTKAJBntF8CEDW0z2sbSi8AII9WrKb9EoBot8/ThXs62uc1j4wyAORJXX2D/foPa7LuQ/slAMXEUuitQ6AMAHmy6u2PvfZK2dB+CUCxsRR67ii9AIA8qazemdN+tF8CgHggUAaAPCkv65rTfrRfAoB4IFAGgDwZ8tl9vEkx2dB+CQDig0AZAPKktKSDffWUiqz70H4JAOKDQBkA8mjkYNovAYAr6HoBAHlG+yUAcAOBMgAUAO2XACD+KL0AAAAAAhAoAwAAAAEovQAAICHq6xuonQdagUAZAIAEWLlmky1cutaq0pZZV3eWs08eRDcWoBmUXgAAkIAg+baHXm0UJIv+re36OoAEBMr19fU2Z84cGzdunA0bNsymTp1q69evb3b/Rx991CoqKpp8vP/++6EeNwAAhSq3UCY5m/uWrvX2A+B4oDx37lxbuHChzZw50xYtWuQFzlOmTLFdu3YF7r9mzRobNWqUPfPMM40++vXrF/qxAwCQb6vXVTXJJGeq3Fbr1S4DcDhQVjC8YMECmz59uo0fP94GDx5ss2fPto0bN9qSJUsCv+eNN97wMsj77rtvo4/S0tLQjx8AgHxSScW8R17NaV9N8APgcKC8evVqq6mpsTFjxqS2lZWV2ZAhQ2zFihXNZpQPOeSQEI8SAIDw6pJrdu7JaX91wQDgcKCszLFklk306dMn9bV0W7dutQ8//NBeeOEF+5d/+RcbO3asXXjhhfbOO++EdswAABSjLjldec9PW8UBcLg93I4dO7zPnTt3brS9S5cuXlCcae3aT/+INDQ02I9+9CPbuXOnzZs3z84++2x77LHH7DOf+UybjqNjx3CuP0pLSxp9Rjwxjm5gHN3gyji+/m5li3XJ6b56SoV17uxOyaEr45h0pREYR6cC5a5du6Zqlf3/l9raWuvWrVuT/Y855hj7y1/+Yr1797YOHT5tuP6zn/3Mq29+8MEH7bzzzmv1Mahxe+/e3S1MZWVNfzfED+PoBsbRDXEfx93vVOW0X8+9OtlF/zbMjjtqf3NR3McRxR9HpwJlv+Ri06ZNNnDgwNR2/VsT9oKUl5c3+rcC6gMOOMAryWjr7a7q6u0WBl1h6eSprt5hdXX1oTwm8o9xdAPj6AZXxrFTh9xavV145pF2+IC9raqqxlziyjgmXWmBxlE/M9cstVOBsrpc9OjRw5YvX54KlKurq23VqlU2efLkJvv/5je/sVtuucWeeuop22uvvbxtn3zyib377rs2ceLENh/Hnj3hvih18oT9mMg/xtENjKMb4j6Oh+y/t7fqXrbyC9UlD+q/d6x/T9fHEcUfR6eKd1SbrIB41qxZ9uSTT3pdMC655BLr27evTZgwwerq6mzz5s1eLbKccMIJXp/lK664wqtXfuWVV+ziiy/2ssxf/vKXi/3rAADQJioD1NLU2Uw6eZC3H4CEBMqiHsrKBs+YMcMmTZrk9UOeP3++derUyTZs2OB1tli8eHGqVOOuu+6y7du3e/uec8451rNnT7vnnnu8CYAAAMTViIo+Nu3MoV5mOTOTrO36OuJN5Z5aUGbZqo3eZ1ZXzL8ODWr5gLzeHqisDKfWS901NHFQtWXcWoovxtENjKMbXBxHBU9adU8LiqhXstrAuZ5JdnEcg/pkqwVgenmNLop0J8GVi6COBRrH8vLuyaxRBgAAjSkoHnxg72IfBgqwmEwmBc3azh2D/HGu9AIAACDJi8nct3Rt6GUY9Y6WgZBRBgAAiAmV0bS0mEzltlpvv7DuJKx0uAyEjDIAAEBMqNY8n/vlqwykKiN498tA9PU4I1AGAACICU3IzOd+LpaB5BOBMgAAQEyoa0lmy79MagGo/aJUBhJXBMoAAGe4OqEI7mrtORulxWS2RKwMpBCYzAcAcILLE4rgpraes/5iMpnfq0zypBDP914RKgMpFAJlAEDs0VcWSTtn9bXhg/Yt6mIyh/1vGUi28ouwykAKhdILAECsJWFCEdySr3PWX0xm9JC+3uewV1wsiVAZSKEQKAMAYi0JE4rgFpfO2RH/WwaSOcFQmWQX7uRQegEAiLUkTCiCW1w7Z0dEoAykUAiUAQCx1poJRbqV7eKbOeLFxUlwJf9bBuIaAmUAQKzlOqFo245ddvm85+iKgaJLwiQ4V1CjDACItVwmFI06vI/Ne/g1Z5fZRbwkYRKcKwiUAQCxl21C0QVnDLXlr2cPhOmKgbC5PgnOFZReAACc0NyEotZ0GBh6yD6hHS/g8iQ4VxAoAwCcETShyLUOA3HEJMrkTYJzBYEyAMBpLnYYiBOWFkecUaMMAEhEh4Fs6DBQ2GWamUSJuCJQBgA4jQ4DxcHS4nABgTIAwHlx7TCgIHL1uipbtmqj9zlOQaVLyzQjuahRBgAkQtw6DLSltjdKk+aYRAkXECgDABIjLh0G/NreTH5tb1AWPGqT5phECRdQegEAQMxre6M4aY5JlHABgTIAADGu7c0lsL7r96tt1buVodY4M4kSLiBQBgAgQlpb25tLYF2zc4/NWvQ3u3zec6Fml+M6iRLwUaMMAECEtLa2tzWT4bLVOBdK3CZRAukIlAEAiBC/tjdblji9trctk+FU46zgNaxgNS6TKIFMlF4AABAhra3tzWXSXCb6FwO5IVAGACBiWlPbm0tgHYT+xUDLKL0AACCCWlPb6wfWmX2Us6F/MdAyAmUAACKqNbW9fmCtpa7nPfKq1+miOfQvBnJD6QUAAA4F1kMOLrdz/mlw1v3oXwzkhkAZAADH0L8YyA9KLwAAcBD9i4H2I1AGAMBR9C92i5Yg58InXATKAAAAEaelxzO7mqi0Rq0BKaUpHGqUAQAAIh4ka+nxzNZ//pLk+joKg0AZAAAgwuUWyiS3tCS59kP+ESgDAABElGqSW1pEhiXJC4caZQAICRNxABRqqXGWJC8MAmUACAETcQC0Ra5LjbMkeWFQegEABcZEHABtpTtPmQvHZGJJ8sIhUAaAAmIiDoD2UHmW7jxlw5LkhUOgDAAxnIijwHr1uipbtmqj95lAG3AXS5IXDzXKABCziTjUOwPJw5LkxUGgDAAxmojj1ztn8uudyS4B7mJJ8vBRegEAMZmIQ70zWosSHaB9yCgDQAgTcYKywK2diNOaemeyTqBEB2g/MsoAEJOJOCw8gFzRkhDIDzLKABCTiTgsPIBc5Fqio/ORiWBAdgTKABCTiTh+vXO28gsWHgAlOkD+UHoBADHBwgPJ05bJeJToAPlDRhkAYljvnDlJS5lkBclM0nJHWyfjUaID5A+BMgDEjGsLDyhLWojfpVA/Nwzt6ZdNiQ6QPwTKABBDriw8UKgWZnFujdbeyXj5bEkIJB01ygAAp1qYxb01Wmsm4xW6JSGQdGSUAQDOtDBzoTVavibjuVaiAxQDgTIAwJkWZi60RsvnZDxXSnSAYqH0AgAQukK1MHOhNZo/GS8bJuMB4SBQBgCErlAtzIrRGq0tvY6zoV82EB3OBcr19fU2Z84cGzdunA0bNsymTp1q69evz+l7H330UauoqLD333+/4McJAElWqKxp2NlYTQy8fN5zduN9L9odj67yPuvf7Z0wyGQ8IBqcq1GeO3euLVy40H784x9b37597aabbrIpU6bYY489Zp07d272+/7+97/bddddF+qxAkBSFaqFWZit0drT6zgXTMYDis+pjPKuXbtswYIFNn36dBs/frwNHjzYZs+ebRs3brQlS5ZkzUJffvnldsQRR4R6vACQZG3JmuZS5hBGNjbX7hr5KMPQZLzRQ/p6nwmSgXA5lVFevXq11dTU2JgxY1LbysrKbMiQIbZixQo77bTTAr/v5z//ue3evdsuuugiW7ZsWYhHDADJ1pqsaWsWESl0NtaF7hoAEhYoK3Ms/fr1a7S9T58+qa9levnll70s9P33328ffvhhXo6jY8dwEvWlpSWNPiOeGEc3MI7tM/SQfbJ+fcXq7GUOF088ykYO7tPqn9vWcdy2Y3dOP0/7hfWegH/g9eiG0giMo1OB8o4dO7zPmbXIXbp0sa1btzbZf/v27XbZZZd5HwcddFBeAmVlK3r37m5hKivrFurjoTAYRzcwjvlXpzKHP77RYpnDScceZKV5yhi3NI4D+u2d08/RfmG/J+AfeD26oayI4+hUoNy1a9dUrbL//1JbW2vdujV9kq+//no7+OCD7ayzzsrbMagerbp6u4VBV1g6eaqrd1hdXX0oj4n8YxzdwDgWzuvvVtrHW3dm3eejLTts+Uvv2+EHlYcyjvv37urVPKu8ojnlZV28/aqqatp1TGg9Xo9uKC3QOOpn5pqldipQ9ksuNm3aZAMHDkxt17/V9i3TAw884GWfhw8f7v27rq7O+6xa5m9961veR1vs2RPui1InT9iPifxjHN3AOObfx9U7c94vX899LuM4qaXuGicN8pIn7Z3Qh7bj9eiGuiKOo1OBsrpc9OjRw5YvX54KlKurq23VqlU2efLkJvtndsJ46aWXvO4Xd9xxhx122GGhHTcAIFqLiOTC766ROcFQmWYF0fQ6/pQuFGhxh7hyKlBWdlgB8axZs6y8vNz69+/v9VFWP+UJEyZ4GePKykrr2bOnV5px4IEHNvp+f8Lf/vvvb716sTQoAESBv4hIti4TxVrSmV7H2bWmUwkQRc5NB1UP5YkTJ9qMGTNs0qRJVlpaavPnz7dOnTrZhg0bbOzYsbZ48eJiHyYAwJElnel1nH1BlswLHL9TSXtXLwTC0KGhoYHiqTzX0VRWhjNxQy2HNJtaE0WowYovxtENjGNxspP5LnNgHPNXbqGlvFu6C3DjBccV5MKCcXRDxwKNY3l592RO5gMAuCsqZQ7U3LaMBVngCgJlAEBs+GUOxULNbW50EZHP/YBica5GGQCAYtTcPvrMO7SCi3inEqC1CJQBAGiBAmBlkrN5+Jl37LK5zzJJLa1TSTbF6lQCtAaBMgAAeai5lS2f7KKjQww6lQC5IlAGACDPtbT3LV2b+DIMf0GWzMyyMsnaTk034oDJfAAA5LmWlo4O0epUArQVgTIAAHlYHTATHR2i0akEaA9KLwAAyEPNbSY6OgDxR6AMACgK1fCuXldly1Zt9D5Hvaa3uZrbIHR0ANxA6QWAdmOlMiRl4Q6/5vbx596xh595t9n96OgAuIFAGUAiAx4Uf+GOTP7CHe3tiFDoCzf9rC+N/az137dHk3NfmWQFyZz7gBsIlIGIikOWttABD5K5cIdaqylr25bzPcwLNzo6AO4jUAYiKA5Z2kIHPEjuwh1tba1WjAs3OjoAbmMyHxAx/pt9ZjDhv9lHZcWv1gQ8SPYkuLa0TGtta7VcL9zi9FwBKD4yykCExClLW6iAB/G/25CPlmmtba1WyEw1gOQiowxESJyytIUKeBD/uw25LNyR79ZqXLgBKAQCZTgvTrep4/RmX6iAB26XFuSycEdbWqtx4QagECi9gNPidps6Tm/2fsATNHnKRy/Z/HGptMBfuCOfrdVyWWKaCzcArUWgDGfFsXVZ3N7sCxHwIP53G4rRWo0LNwCFQKAMJ8VpUlzc3+zpJRuOON1tKFZrNS7cAOQbgTKcFOfb1HF8s6eXbOHF7W5DsXDhBiCfCJRjrq6+wV5/t9I+rt7JG4JDt6l5s4cLdxuKhQs3APlCoBxjK1ZvsoV/fMM+3rozFhPVwuTCbWre7OHC3QYAiDMC5ZiK40S1MHGbGq7ibgMAhIc+yjHkSj/VOPZqBaJ0t2H0kL7eZ85jACgMAuUYitPqbVG4TZ25KIYyyUnPuAMAgJZRehFDcZ+oFiZuUwPh0V0sXmsAXEKgHEMuTFQLE5PigMKL2yqYAJALSi9iPFEtGyaqAQh7cnFmSZg/uVhfB4A4IlCOISaqAYgKJhcDcBmBckzpVubFE4+yffbu2mg7E9UAhInJxchGF0ir11XZslUbvc9cMCFuqFGOsZGD+9hJxx5ky196n5X5ABQFk4vRHOrW4QIC5ZgrLelghx9Ubnv21Bf7UAAksCsEk4sRhEWx4AoCZQAIgavZNVbBRFvr1tW6M+4XinAfNcoAUGAud4VgcjEyUbcOlxAoA0ABJaErBKtgIh1163AJpRcAQuFifW6+s2txXhiHVTDho24dLiFQBlBwrtbn5iJJ2TVWwUSYdetJvfhGuAiUARRU0me/k11D0vh160Gv+3zVrSf54hvhokYZQMEkoT63JSw5jyQqZN26y5NjET1klAEUTFLqc4udXQOSUree68X3yMP3a/NjAOnIKAMomCTV5+aSXevetWluomunEqtvcDejjmTz69ZHD+nrfW7vBWGuF99r3qtq1+MAPgJlAAVDfW5jNTv3NNm2c3e9zXv4Nfvtn7JnyQC04uL7k10FPxYkA4EygIKhPjf328VPPL/eVqymthLIy8V3j84FPxYkA4EygIJh1bbcbxfLvUvWOD2xEQjr4rtioJtzHhA+AmUABeX6qm0KbFevq7K/vLrRXnnzo8BAN9fbxdu272ZZXyALLr4RNrpeACg4V1dtC+rlqgsAvVGnXwC0pgbb9YmNQL4uvnN57QHtRaAMIBSurdrW3EIqlQELqeiioEe3TvbJjt0t/tykTGwE2sPVi29ED6UXAFDghVT05v21Uw5r8ecmYWIjENXWc0AQAmUAKOBCKr6Rg/ezU0cNyPo91FYCQLQQKANASAupfOULg+yCM4Zaz26dnJzYCACuoUYZAEJcSGXk4D424jBqKwEgDgiUAaCVDu2/t3XoYJZt5Wl9XfslYWIjALiK0gsAaKU3/741a5As+rr2AwDEF4EyAIRUowwAiBcCZQAIsUYZABAfBMoA0EqafJe5JHcmeiIDQPwRKANAK2ky3tknD8q6Dz2RUSxa6Gb1uipbtmqj99lf+AZAgbteHH744fb666+34WEAwC3qeazex1qhL33xkfKyLjbppEH0REbRllbPPCd190MXdpyTQIED5YaMad7/8z//Y+PHj2/DwwJA/CnwGD7o057I23bstgH99rb9e3clg4eiBcm3PfRqk+0KmrWdRW2AApdedFBj0DTf+ta37Pzzz7d169a14aEBIP78nshjhva1Iw/9DOUWKApdnCmTnM19S9dyEQeEWaM8YcIEe/rpp+20006zWbNm2fbt263Y6uvrbc6cOTZu3DgbNmyYTZ061davX9/s/q+99pp9/etft+HDh9vo0aPt6quvtm3btoV6zAAAtIfuaqSXWwSp3Fbr7QcgpEBZAemdd95pBx54oP3yl7+0U0891R555BErprlz59rChQtt5syZtmjRIi9wnjJliu3atavJvh999JGde+651r9/f3vwwQe97125cqV973vfK8qxAwDQFvT2BiLa9WLMmDFecKzgcseOHd7nSZMmeZnasCkYXrBggU2fPt2rnR48eLDNnj3bNm7caEuWLGmy/9///ncbO3asXXfddXbwwQfb5z73OfvKV75izz77bOjHDgBAW9HbG4hwe7jS0lI755xz7A9/+IOdccYZ9re//c3+7d/+zf7jP/7DKisrLSyrV6+2mpoaL3j3lZWV2ZAhQ2zFihVN9j/66KPtlltusY4dP53T+NZbb3lB//HHHx/aMQMA0F709gYi0PWiJeXl5fajH/3IyygrS/vf//3fXvB80UUX2eTJk62kpLBtm5U5ln79+jXa3qdPn9TXmnPKKafYu+++65Vh/OxnP2vXcXTsGE576tLSkkafEU+MoxsYRzfEeRwnn1Jht97/crNf/+opFda5c6klQZzHEdEaxw4NmT3f8tRHefPmzXbNNdfYk08+6XXLOPTQQ+373/9+o2xvvikbfMUVV3jHmB6Ua9umTZvsrrvuavZ7X3nlFa905KabbrKqqirvZ3Xv3r3Vx6CnM7M7CAAAYXju5Q/sjodfsY+37kxt+0yvbjb19KF23FH7F/XYgDjqmK/aYNUkv/TSS/byyy97nz/44INGwePatWvtG9/4hv3zP/+zV5LRq1f+b/907do1dTz+/0ttba1169Yt6/ceeeSR3mdlkz//+c/bH//4R6+MpLXUeqe6OpzuH7rCKivrZtXVO6yurj6Ux0T+MY5uYBzdEPdxPHzA3nbztONtzXtVtuWTXdarR2erGNjba1tYVVVjSRH3cURhx1E/M9csdbsC5WuvvdYLjNesWWN1dXWpoFg1v8o+a3Kc2q7pQ9naG2+80X73u995NczK7g4YMMDyyS+5UPZ44MCBqe36d0VFRZP93377bXvvvfcaLZqy3377eUH8hx9+2Obj2LMn3BelTp6wHxP5xzi6gXF0Q9zHcdABvRolcJLaPznu44jij2O7AuX77rvP+7z33nt7PYv9oPioo44KzODefvvtdv/993sZ5Z/85CftrgXOpC4XPXr0sOXLl6cC5erqalu1apVXI53pueee84L3Z555xpv0JwqcVXpxyCGH5PXYAAAAEC/tCpSvv/56LzBuTVA5ceJE+/3vf2/PP/+85Vvnzp29gFiLn2hioSbmqea4b9++3uIoynqrC0fPnj290gwtlHLHHXfY5Zdfbpdddplt3brV+50U6J944ol5Pz4AAADER6umEWbO+1PQ25bMqwLXQq1+px7KOq4ZM2Z43TfUum7+/PnWqVMn27Bhg9c3efHixd6+KrG4++67vf/XvtOmTfNayWl/fR8AAACSq1VdL/JF/YqXLVtmX/3qV83FOprKynAmTKgNXe/e3b0JGtRgxRfj6AbG0Q2MoxsYRzd0LNA4lpd3D2cyX1spC00NMAAAAKKMTtwAAABAAAJlAAAAIACBMgAAABCAQBkAAAAIQKAMAAAABCBQBgAAAAIQKAMAAAABCJQBAACAqCw4AgBAsdTXN9gb67fYlppa69W9ix02oJeVlHQo9mEBiCACZQBAYgLVlWs22cKla61qW21qW++eXezskwfZiIo+oRwDgPggUAYAhKaYgaoe+7aHXm2yXcei7dPOHGrHHtG3oMcAIF6oUQYAhMIPVNOD5PRAVV8vZBZbAXo29y1d6+0HAD4CZQBNKFhYva7Klq3a6H0meEDcA1WVemQG6Jkqt9XamveqCvL4AOKJ0gsAjVDDiWIGqtpv8IG98/74qofOab9PduX9sQHEFxllRB7ZzWTcGofbcg5Uc9yvtTRpMKf9enQuyOMDiCcyyog0spvRuzU+fNC+kW6lFcfWX3E85oIFqjnu11p6TvW3I1tWu7xnF6sYmP9sNoD4IlBGZOUyQ51g2Y1b4/kKFON4YRXHYy5koKr9CkHnk57ToL8pvkknD3LuAgVA+1B6gUgq9sSfJCrWrXEFipfPe85uvO9Fu+PRVd5n/bu1ZR5xLBuJ4zG3N1DNptCBqi48dIGtgD0zQOfCG0AQMsqIpGJP/EmiYtwaz9ddgziWjcTxmPMVqGZm0BWoKkgOI1DVY+g5db3UJV+SUBYEZEOgjEgq9sSfJAr71ng+A8U4XljF8ZhdCVT1WC49p4WSlLIgIBtKLxBJxZ74k0Rh3xpvTaDo4oVVHI8534Hq6CF9vc9kKKMnSWVBQDYEyoh0djObQk78SaowazjzGSjG8cIqjseMZGCOCPAPlF4gkpih7v6t8XwGisXuqNAWcTxmJENSy4KAIGSUEVnMUHf71ng+7xq8uHaz7dpdl3WfqF1YRaELBBAkyWVBQCYyyoi0KEz8ycQs8GjdNWiuc4avR7dO9vVTKyJ5YRWFLhBAJsqCgH8gUEbkRWmGOrPAoxUo5lJL2am0g3exFVVRvBhEslEWBPwDgTKQI1YKjF6gmEstZdUnuyJfSxmli0GAOSLAP1CjDOSAWeCF1daaaGopgcJgjgjwKTLKQA6YBR5NcamlpK4dcURZEECgDOSEzGU0xaGWkrp2xBllQUg6Si8QmP1ava7Klq3a6H2mnCA+mcukiXqLNVY3A4B4I6OMRsh+xTdzmVRRbbGWa127bm1zKxsAoolAGSl0dWges8CjLYq1lNS1A0D8UXoBD10dWsYs8GgLYzXB1qCuHQDij4wyPGS/4pu5LEa3Bro4tIy6dgCIPwJleMh+5S4ps8Cbq1c/9vA+tvz1TdSxt4C6dgCIP0ov4CH7hVy7NTzx/Hq6ODjQkQMA0DICZTTKfmVD9isZcqlXb07S69gzUdcOAPFG6QU8dHVAa+rVm0Mde1NJq2sHAJcQKCMW/WgJMsLT3jp06tiTW9cOAK4hUEaks18sgBK+9tahU8cOAHAFNcqIbD9alv+Nbr16c6hjBwC4hEAZkcQCKNHu1tAc6tjdodfW6nVVtmzVRu8zrzUASUTpBSIpDguguFw7na1efVRAH+Vi17Ejvyh5AoBPESgjkqK+AEoSAols9eoTxx/q7EVC0vklT5n8kifa2gFIEgJlREZ6hrb6k12RnTiWpECiuW4N+ezi4HJm3tWSJ11AMUYAkoBAGZEQlKHt0MGsoSFaE8cIJPIrCZn5OIlDyRMAhInJfCi65rpbZAuSizVxrDWBBLKjq0n0RL3kCQDCRqCMosolQ6vMclSW/yWQyA+6mkRTrqVM9MoGkBSUXqCocsnQKrN81hcOtbIenYtew0ogkR/c4o92D+1sY0OvbABJQkYZRZVr5lVBcrEXQMl1MQ4CiZaRmY9vD216ZQNIEgJlFFXcMrQEEskc9yTxe2hnXhAWs+QJAIqF0gsUtZ1XHG/1ZluMg0U33B33JMnWQxsAkoRAGUVt5+VnaIP6Ekc5Q0sg0T5xHfckyWevbACIK0ovUPR2XnG91esHElGonY6juI47ACA5yCgjEgttkKFNJsYdABBlBMqITDuvttzqZfnj+OMWPwAgqgiUEdt2Xix/DAAACokaZeRkU+WOSLXzYvljAABQaATKaJGCzoefeafF/cJq58XyxwAAIAwEymh3UBp2O6/W1EsDAAC0lXOBcn19vc2ZM8fGjRtnw4YNs6lTp9r69eub3X/t2rV23nnn2bHHHmtjxoyx6dOn2wcffBDqMUdZLkGpnDH2oNDqgqNYLw0AANzjXKA8d+5cW7hwoc2cOdMWLVrkBc5TpkyxXbt2Ndm3qqrKzj33XOvatav96le/sl/84hdWWVnp7V9bS5DVmmCzT/leFhaWPwYAAGFwKlBWMLxgwQIvKzx+/HgbPHiwzZ492zZu3GhLlixpsv/SpUtt+/btduONN9phhx1mQ4cOtZtuusneeust++tf/1qU3yFqohiU+ssfZ8PyxwAAoL2cCpRXr15tNTU1XgmFr6yszIYMGWIrVqxosr/2UwZaGWVfScmnT0l1dXVIRx1tUQxK/eWP81kvrVrs1euqbNmqjd5nJgICAACn+igrcyz9+vVrtL1Pnz6pr6U74IADvI90d9xxhxc4jxw5ss3H0bFjONcfpaUljT4XyuRTKuzW+19u9utfPaXCOncutTAde0RfKyktsV//YY03cc9XXtbFvjqhwkYOzr1eesXqTU1/Ts8u3u/Vmp8T9XFEYTGObmAc3cA4uqE0AuPoVKC8Y8envX47d+7caHuXLl1s69atLX6/6pTvvfdemzFjhpWXl7fpGJTF7N27u4WprKxb1q/X1TfYqrc/tsrqnVZe1tWGfHYfK21FtnXCmIOtR/cudsfDr9jHW3emtn+mVzebevpQO+6o/a0YdFwnHXtQu363517+IPAiQEGztl/19ZGh/X4tjSPigXF0A+PoBsbRDWVFHEenAmW/hEK1yunlFJqY161b809yQ0OD/fSnP7V58+bZBRdcYF/72tfafAy6ZV9dvd3CoCssnTzV1Tusrq6+oNnSwwfsbTdPO97WvFdlWz7ZZb16dLaKgb29C4OqqhorpgP26eZ9SPXW7a0aq9sfbD5TLrc/9LJV9C8raNu7XMYR0dfSOOp8C3r9IFp4PbqBcXRDaYHGUT8z1yy1U4GyX3KxadMmGzhwYGq7/l1RURH4Pbt377arrrrKHn/8ce/zOeec0+7j2LMn3BelTp6gx/RXr2suWzrtzKGtbuk26IBejd7441zLq1rk9AuIIJXVtbbqnUobfGDvoo0j4iVoHFluPX54PbqBcXRDXRHH0aniHXW56NGjhy1fvjy1TZPyVq1a1WzN8RVXXGFPPPGE3XzzzXkJkqOC1etaRj9mhIHl1gEgvpzKKKs2efLkyTZr1iyvxrh///5eu7e+ffvahAkTrK6uzuuT3LNnT68048EHH7TFixd7wfKoUaNs8+bNqZ/l7xNXrVm9LoxsaRRFsfUd3JLrBevwQftShgEAEeRURlnUQ3nixInehLxJkyZZaWmpzZ8/3zp16mQbNmywsWPHesGxqNxC1EdZ29M//H3iimxpPFvfwS0stw4A8eZURlkUGF9++eXeRya1gluzZk3q31qcxFVkS3PvxxxUx93WfsxAOi5YASDenMso41NkS3OjiVSa1Jj5XOm5actkRyAdF6wAEG/OZZTxKbKl2etGdatbWTwFKKoP1Uf6Nl1AJPG5QWEuWLOVX3DBCgDRRaCcgGxpZlsqvTErSE5itpQ2XQgTF6wAEG8Eyo5T8Ee2NHtfab9NF6UWKAQuWAEgvgiUE0BBcVJbwPlo04Vi4oIVAOKJQBmJQF9pFBsXrAAQP3S9QCLQpgsAALQWgTISIdf2W5sqdxT8WAAAQDwQKCMRVA/aq0fnFvd7+qUPvHpmAAAAAmUkpj50/LD9W9xPdcwsJwwAAITJfEiMPuV7FaVOOXOBE7odAAAQDwTKSIxiLCec1AVOuDgAALiAQBmJEfZywkld4CSpFwcAAPdQo4zELSecTb6WE851gRPXJg76FweZFyP+xYG+DgBAXBAoI5HLCSvDmZlJzmeGtzULnLgiqRcHAAB3UXqBxAljOeEkLnDC6ocAANcQKCORCr2ccDEmDhZbEi8OAABuo/QCKODEwWzyOXEwCpJ4cQAAcBuBMhDziYNRkcSLAwCA2wiUgZhPHIyKJF4cAADcRo0yEPOJg1G8OMjso6yLAwXJrl0cAADcRqAMxHziYNQk7eIAAOAuAmUAeZe0iwMAgJuoUQYAAAACECgDAAAAAQiUAQAAgAAEygAAAEAAAmUAAAAgAIEyAAAAEIBAGQAAAAhAoAwAAAAEIFAGAAAAAhAoAwAAAAEIlAEAAIAABMoAAABAAAJlAAAAIEDHoI0ACq++vsHeWL/Ftu3YbQP67W199+5iq9dV2ZaaWuvVvYsdNqCXlZR0KPZhAgCQWATKQBGsXLPJFi5da1XbalPbOnQwa2j4xz69e3axs08eZCMq+hTnIAEASDhKL5DYbK6yt8tWbfQ+699hBsm3PfRqoyBZ0oNk0de1n/YHAADhI6OMxAnK5oaVvVVArsdujfuWrrXhg/alDAMAgJCRUUaiNJfNDSt7q5rkzMduSeW2Wu/7AABAuAiUkRi5ZHOVvS1kGYYm6oX5fQAAoO0IlJEYuWRzC529VTeLML8PAAC0HTXKCW9NlqRWZLlmZQuZvdXzrHro1pRflPf8dHwAAEC4CJQTqJiT2Yop16xsIbO3uhjR86x66FxNOnmQ8xcxAABEEaUXCVPsyWzF5Gdzi5291cXItDOHNjkW9VHOPBbt5/LFCwAAUUZGOUFynczmaiuyXLK5YWVvFfzqeWZlPgAAootAOUFaM5lt8IG9zUV+Njez9ETZWwXJYWZvFQTree7YscR69+5uVVU1zj7vAADEEYFygkRhMlsUpGdzyd4CAIDmECgnSBQms0WFn80FAABoDpP5EiQqk9kAAADigEA5QfzJbNnQigwAAOBTBMoJ01xrMlqRAQAANEaNcgIxma2pJK5UCAAAsiNQTigms/1DUlcqBAAA2VF6gURL8kqFAAAgOwJlJFauKxVqPwAAkDwEykis1qxUCAAAkodAGYnFSoUAACAbAmUkFisVAgCAbAiUkVisVAgAALIhUEZisVIhAABIVKBcX19vc+bMsXHjxtmwYcNs6tSptn79+py+b8qUKXbrrbeGcpyIBlYqBAAAiVlwZO7cubZw4UL78Y9/bH379rWbbrrJC4Afe+wx69y5c+D37Nq1y66++mr785//bEcffXTox4ziYqVCAADgfKCsgHfBggV22WWX2fjx471ts2fP9rLLS5YssdNOO63J9/z1r3/1guSdO3daWVlZEY46uaK0bDQrFQIAAKcD5dWrV1tNTY2NGTMmtU3B75AhQ2zFihWBgfLTTz/tBdLTpk2zL33pSyEfcXKxbDQAAIg6pwLljRs3ep/79evXaHufPn1SX8t0ySWX5P04OnYMp/S7tLSk0ee4WLH602WjM/nLRl888SgbOTg5wXJcxxGNMY5uYBzdwDi6oTQC4+hUoLxjxw7vc2YtcpcuXWzr1q2h3cLv3bu7hamsrJvFRZ2Wjf7jGy0uG33SsQdZacJqhOM0jmge4+gGxtENjKMbyoo4jk4Fyl27dk3VKvv/L7W1tdatW7fQ6m6rq7eH8li6wtLJU129w+rq6i0OXn+30j7eujPrPh9t2WHLX3rfDj+o3JIgjuOIphhHNzCObmAc3VBaoHHUz8w1S+1UoOyXXGzatMkGDhyY2q5/V1RUhHYce/aE+6LUyRP2Y7bVx9U7c94vLr9TEscRzWMc3cA4uoFxdENdEcfRqeKdwYMHW48ePWz58uWpbdXV1bZq1SobOXJkUY8Nn2LZaAAAEBdOZZRVmzx58mSbNWuWlZeXW//+/b0+yuqnPGHCBKurq7PKykrr2bNno9IMhL9sdHq3i0wsGw0AAKLAqYyyTJ8+3SZOnGgzZsywSZMmWWlpqc2fP986depkGzZssLFjx9rixYuLfZiJxbLRAAAgLjo0NDQ0FPsgXKujqaysCeWx1IZOHTaqqmpiV4MV1EdZmeRJCeyjHOdxxD8wjm5gHN3AOLqhY4HGsby8ezIn8yE+WDYaAABEHYEyioZlowEAQJQ5V6MMAAAA5AOBMgAAABCAQBkAAAAIQKAMAAAABCBQBgAAAAIQKAMAAAABCJQBAACAAATKAAAAQAACZQAAACAAK/PFWH19g73y5ke2fsNW69mtE0tAAwAA5BGBckytXLPJ7lu61iq31aa29e7Zxc4+eZCNqOhT1GMDAABwAaUXMQ2Sb3vo1UZBslRtq/W26+sAAABoHwLlGJZbLFy6Nus+yjRrPwAAALQdgXLMvLF+i5c5zkaZZu0HAACAtiNQjpktNbV53Q8AAADBCJRjplf3LnndDwAAAMEIlGNGLeDU3SKb8p5dvP0AAADQdgTKMaM+yWoBl82kkwfRTxkAAKCdCJRjSH2Sp5051Mscp9O/tZ0+ygAAAO3HgiMxpWB45OH72QdVO1mZDwAAoAAIlGNMQfGRh37GDtinm+3ZU1/swwEAAHAKpRcAAABAAAJlAAAAIACBMgAAABCAQBkAAAAIQKAMAAAABCBQBgAAAAIQKAMAAAABCJQBAACAAATKAAAAQAACZQAAACAAS1gjsurrG+yN9VtsS02t9erexQ4b0MtbthsAACAMBMqIpJVrNtnCpWutalttalvvnl3s7JMH2YiKPkU9NgAAkAyUXiCSQfJtD73aKEgW/Vvb9XUAAIBCI1BG5MotlEnO5r6la739AAAAColAGZGimuTMTHKmym213n4AAACFRKCMSNHEvXzuBwAA0FYEyogUdbfI534AAABtRdcLRIpawKm7Rbbyi/Ken7aKA4LQVhAAkC8EyogUBTRqAafuFs2ZdPIgAp8WJDVYpK0gACCfCJQROQpopp05tEnAo0yygmQCnuySGiz6bQUz+W0FdU65/PsDAPKPQBmRpIBm+KB9E5kVbY+kBou5thXUOcU5BADIFYEyIksBzeADexf7MGIjycFia9oKck4BAHJF1wvAEUnuQU1bQQBAIRAoA45IcrBIW0EAQCEQKAOOSHKw6LcVzIa2ggCA1iJQBhyR5GDRbyuYDW0FAQCtRaAMOCLpwaLfVjDzYkEXB652+wAAFBZdLwCHJL0HNW0FAQD5RKAMOCbpwSJtBQEA+UKgDDiIYBEAgPajRhkAAAAIQKAMAAAABCBQBgAAAAIQKAMAAAABCJQBAACAAATKAAAAQAACZQAAACAAgTIAAAAQgEAZAAAASEKgXF9fb3PmzLFx48bZsGHDbOrUqbZ+/fpm96+qqrJLL73URo4caaNGjbJrr73WduzYEeoxAwAAIHqcC5Tnzp1rCxcutJkzZ9qiRYu8wHnKlCm2a9euwP2nT59u69ats7vuust++tOf2tNPP23XXHNN6McNAACAaHEqUFYwvGDBAi/4HT9+vA0ePNhmz55tGzdutCVLljTZ/8UXX7Tnn3/efvKTn9gRRxxhY8aMseuuu84eeeQR+/DDD4vyOwAAACAanAqUV69ebTU1NV7A6ysrK7MhQ4bYihUrmuz/wgsv2L777muHHHJIapvKLzp06GArV64M7bgBAAAQPR3NIcocS79+/Rpt79OnT+pr6ZQ1zty3c+fO1qtXL9uwYUObj6Njx3CuP0pLSxp9Rjwxjm5gHN3AOLqBcXRDaQTG0alA2Z+Ep2A3XZcuXWzr1q2B+2fu6+9fW1vbpmMoKelgvXt3tzCVlXUL9fFQGIyjGxhHNzCObmAc3VBWxHF0KlDu2rVrqlbZ/39R0NutW9MnWfsETfLT/nvttVebjqG+vsGqq7dbGHSFpZOnunqH1dXVh/KYyD/G0Q2MoxsYRzcwjm4oLdA46mfmmqV2KlD2yyg2bdpkAwcOTG3XvysqKprs37dvX1u6dGmjbQqct2zZ4pVrtNWePeG+KHXyhP2YyD/G0Q2MoxsYRzcwjm6oK+I4OlW8oy4XPXr0sOXLl6e2VVdX26pVq7w+yZm0TbXLag/nUxcMGTFiREhHDQAAgChyKqOseuPJkyfbrFmzrLy83Pr372833XSTlzmeMGGC1dXVWWVlpfXs2dMruzj66KPtc5/7nF1yySVe7+Tt27fb1VdfbWeccYbtt99+xf51AAAAUEROZZRFPZQnTpxoM2bMsEmTJllpaanNnz/fOnXq5HWyGDt2rC1evNjbV23gfvazn9kBBxxgX//61+073/mOnXDCCSw4AgAAAOvQ0NDQUOyDcK2OprKyJpTHUhs6ddioqqqhBivGGEc3MI5uYBzdwDi6oWOBxrG8vHvOk/mcyygDAAAA+UCgDAAAAAQgUAYAAAACECgDAAAAAQiUAQAAgAAEygAAAEAAAmUAAAAgAIEyAAAAEIBAGQAAAAhAoAwAAAAEIFAGAAAAAhAoAwAAAAEIlAEAAIAABMoAAABAAAJlAAAAIACBMgAAABCAQBkAAAAIQKAMAAAABCBQBgAAAAIQKAMAAAABCJQBAACAAATKAAAAQAACZQAAACAAgTIAAAAQgEAZAAAACECgDAAAAAQgUAYAAAACECgDAAAAAQiUAQAAgAAEygAAAEAAAmUAAAAgAIEyAAAAEIBAGQAAAAhAoAwAAAAEIFAGAAAAAhAoAwAAAAEIlAEAAIAABMoAAABAAAJlAAAAIACBMgAAABCAQBkAAAAIQKAMAAAABCBQBgAAAAIQKAMAAAABOgZthFvq6xvsjfVbbEtNrfXq3sUOG9DLSko6FPuwAAAAIo1A2XEr12yyhUvXWtW22tS23j272NknD7IRFX2KemwAAABRRumF40HybQ+92ihIFv1b2/V1AAAABCNQdrjcQpnkbO5butbbDwAAAE0RKDtKNcmZmeRMldtqvf0AAADQFIGyozRxL5/7AQAAJA2BsqPU3SKf+wEAACQNgbKj1AJO3S2yKe/5aas4AAAANEWg7Cj1SVYLuGwmnTyIfsoAAADNIFB2mPokTztzaJPMsjLJ2k4fZQAAgOax4IjjFAwPH7QvK/MBAAC0EoFyAigoHnxg72IfBgAAQKxQegEAAAAEIFAGAAAAAhAoAwAAAAEIlAEAAIAABMoAAACA64FybW2tXXvttTZmzBgbPny4XXrppVZZWZnz937pS1+yBx98sODHCQAAgOhzKlC+5ppr7JlnnrFbb73V7r77bnv77bdt+vTpLX7ftm3b7MILL7Q1a9aEcpwAAACIPmcC5Q8//NAefvhhmzFjhh1zzDF21FFH2S233GIrVqywF198sdnv+9Of/uRlkquqqkI9XgAAAESbM4HyypUrvc+jR49ObTv44INtv/3284Ll5ixdutTOOussW7RoUSjHCQAAgHjo6FJGuXfv3talS5dG2/v06WMbN25s9vtuuOGGEI4OAAAAcRObQPn999+3k046qdmvf/vb37bOnTs32a7AWRP1wtSxYziJ+tLSkkafEU+MoxsYRzcwjm5gHN1QGoFxjE2grBKKxYsXN/v1p59+2nbt2tVku4Lkbt26WVhKSjpY797dLUxlZeH9figcxtENjKMbGEc3MI5uKCviOMYmUO7UqZMdcsghzX5dHSu2bNniBcvpmeVNmzZ5QXZY6usbrLp6eyiPpSssnTzV1Tusrq4+lMdE/jGObmAc3cA4uoFxdENpgcZRPzPXLHVsAuWWjBgxwurr671JfeqjLO+8845Xuzxy5MhQj2XPnnBflDp5wn5M5B/j6AbG0Q2MoxsYRzfUFXEcnSneUdb4i1/8otcebvny5fbyyy/bd7/7XRs1apQNGzbM20fZ5s2bNweWaAAAAABOBsoyc+ZML5t80UUX2Te/+U377Gc/a3PmzEl9Xf2Ux44dm7WvMgAAACAdGhoaGngq8nt7oLKyJrTuGpo4WFVVw62lGGMc3cA4uoFxdAPj6IaOBRrH8vLuOdcoO5VRBgAAAPKFQBkAAAAIQKAMAAAABKBGOc/0dKqXclhUY0OPyPhjHN3AOLqBcXQD4+iG0gKMoxaH69ChQ077EigDAAAAASi9AAAAAAIQKAMAAAABCJQBAACAAATKAAAAQAACZQAAACAAgTIAAAAQgEAZAAAACECgDAAAAAQgUAYAAAACECgDAAAAAQiUAQAAgAAEygAAAEAAAmUAAAAgAIFyhNXX19ucOXNs3LhxNmzYMJs6daqtX7++2f2rqqrs0ksvtZEjR9qoUaPs2muvtR07doR6zMjPWK5du9bOO+88O/bYY23MmDE2ffp0++CDD0I9ZrRvDNM9+uijVlFRYe+//37BjxP5Hcfdu3fbzTffnNp/8uTJ9vrrr4d6zGj/OH788cfe++Po0aO9v6uXXHKJffjhh6EeM1p2++2329e+9rWs+4Qd6xAoR9jcuXNt4cKFNnPmTFu0aJH3h2HKlCm2a9euwP0VTK1bt87uuusu++lPf2pPP/20XXPNNaEfN9o3lvojcO6551rXrl3tV7/6lf3iF7+wyspKb//a2tqiHD9a/3r0/f3vf7frrrsutONEfsdRf0MffPBBu+GGG+yBBx6w8vJyLyjbtm1b6MeOto/jd77zHS/ZcOedd3of+v9p06aFftxo3q9//Wv7r//6L2tJ6LFOAyKptra2Yfjw4Q2//vWvU9u2bt3acNRRRzU89thjTfb/61//2nDYYYc1vPnmm6ltf/7znxsqKioaNm7cGNpxo/1j+dvf/tbbf8eOHaltH3zwgTe+zz33XGjHjbaPoa+urq5h0qRJDf/+7//ujd/69etDOmLkYxzfe+8972/oU0891Wj/E088kddijMZRX9Pr78knn0xtW7p0qbetqqoqtONGMMUo559/fsOwYcMaTj311IbJkyc3s2dxYh0yyhG1evVqq6mp8W67+8rKymzIkCG2YsWKJvu/8MILtu+++9ohhxyS2qZbEh06dLCVK1eGdtxo/1hqP2VLlFH2lZR8+lKtrq4O6ajRnjH0/fznP/du3Z9//vkhHSnyOY7PPvus9ezZ00444YRG+//pT39q9DMQ7XHU39Lu3bvbww8/bJ988on38cgjj9jBBx/sfR+K67XXXrNOnTp5JWpHH3101n2LEet0LMhPRbtt3LjR+9yvX79G2/v06ZP6WjrVWmXu27lzZ+vVq5dt2LChwEeLfI7lAQcc4H2ku+OOO7w/9qrJQvTHUF5++WVbsGCB3X///dRCxnQc33nnHRswYIAtWbLEew1qHBWMfe9732v0Ro1oj6PeC3/84x/b1Vdfbcccc4wXVGnfe++9N5WEQPF84Qtf8D5yUYxYhzMkovzCdJ0A6bp06RJYp6r9M/fNtj+iO5aZVKesP+iXXXaZVx+J6I/h9u3bvfHSx0EHHRTacSK/46jMo2ohdYfnu9/9rs2bN886duxoZ599tjc5DPEYx4aGBm8C5vDhw7062Lvvvtv2339/u/DCC70xRnzsKEKsQ6AcUf5t98yJCToRunXrFrh/0CQG7b/XXnsV8EiR77FM/+OuiQ3XX3+9XXDBBS3OBEZ0xlBjptu6Z511VmjHiPyPo4JiBVKzZ8+2sWPH2lFHHeX9vzz00EMhHTXaO46///3vvWTDTTfdZCNGjPBu1assShNtdccH8dG1CLEOgXJE+bcWNm3a1Gi7/r3ffvs12b9v375N9tXJtGXLFu8WE+IzlqK61ssvv9z7Y37VVVd5M7YRnzFUd4TnnnvOy2DpQ10S5LTTTvPGFPH5u6pgOb3MQm/UKseg1V98xlF1rbpw7dGjR2rb3nvv7W3THQPER98ixDoEyhE1ePBg70W9fPny1DZN5Fq1alVgnaq2qTYr/UX//PPPe591BY34jKVcccUV9sQTT3j9W88555wQjxb5GEPVtD7++OPe5CF9KMMsqnMlyxyvv6t79uyxV155JbVt586dXr/eAw88MLTjRvvGUcGV3hvTb82rPEoXO5RGxcvIIsQ6TOaLKNXgqLH9rFmzvLrU/v37e7eN9IKfMGGC1dXVeb11NSNbGQ7NFP3c5z7nNVFXP0H9EdDEhTPOOKPZrCWiOZbq2bp48WIvWNYtws2bN6d+lr8Poj2GmUGUP8FIdZGadIJ4jKMmfh133HF25ZVXer2wNXZa5KK0tNROP/30Yv86idXacdT74Pz58707c9/+9re9n6GyNtW1fvnLXy72r4MsIhHrFKTpHPJiz549DTfeeGPD6NGjvf6CU6dOTfVh1Wf1EnzggQdS+3/00UcNF198sbfvscce2/DDH/6wYefOnUX8DdCWsTz33HO9fwd9pI83ov16TLds2TL6KMd0HLdt2+b9LdXf1KOPPtp7fa5du7aIvwHaMo7qu6tevaNGjfK+56KLLuL1GEFXXnlloz7KUYh1Oug/hQnBAQAAgPiiRhkAAAAIQKAMAAAABCBQBgAAAAIQKAMAAAABCJQBAACAAATKAAAAQAACZQAAACAAgTIAAAAQgEAZAAAACECgDAAAAAQgUAYAAAACECgDAFJeeuklGzJkiA0fPtw++OCDRl+78cYbraKiwi6//PKiHR8AhIlAGQCQcvTRR9v5559v27dvt2uuuSa1/fnnn7c777zTBgwYYD/84Q+LeowAEBYCZQBAIxdeeKEdccQR9vTTT9vjjz9u27ZtsyuvvNJKSkrslltusR49ehT7EAEgFB0aGhoawnkoAEBcvPXWW3bmmWdaWVmZjRgxwp544gm79NJL7bzzziv2oQFAaAiUAQCB7r77brvhhhu8/x89erRXeqGsMgAkBX/xAACBJkyYYB07dvT+X5P7CJIBJA1/9QAATehm4/e//33bs2eP9erVy375y1/aa6+9VuzDAoBQESgDAJq499577bnnnrNTTz3VbrvtNi9gvuKKK6y2trbYhwYAoSFQBgA08vbbb9usWbO8TPLVV19txxxzjE2aNMnefPNNr+sFACQFgTIAIMXPHO/cudN+8IMf2D777ONtV8eLfv36eRP8li9fXuzDBIBQECgDAFLmzZtnr7zyip144on2pS99KbVdvZO1AIlql6+66ir75JNPinqcABAG2sMBAAAAAcgoAwAAAAEIlAEAAIAABMoAAABAAAJlAAAAIACBMgAAABCAQBkAAAAIQKAMAAAABCBQBgAAAAIQKAMAAAABCJQBAACAAATKAAAAQAACZQAAACAAgTIAAABgTf1/KIslTBI+zQoAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "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", "plt.figure(figsize=(8, 8))\n", "plt.scatter(X, Y)\n", "plt.title(\"Обучающая выборка зависимости y от x\", size=15)\n", "plt.xlabel(\"x\", size=15)\n", "plt.ylabel(r'$\\overline{y}$', size=15)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "t0cYZCLC0a9z" }, "source": [ "**Обучим** линейную регрессию с $l_2$ регуляризацией, и посмотрим как регуляризация влияет на качество модели. В реализации библиотеки `sklearn` (класс Ridge) коэффициент регуляризации задаётся параметром `alpha`" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "id": "CA4ewkpWFcBe" }, "outputs": [], "source": [ "from sklearn.linear_model import Ridge" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 655 }, "id": "g09w5dAO0a9z", "outputId": "1b330e33-5d9e-40af-de18-f42ba332f2a0" }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x_axis = np.linspace(0, 1, 200)\n", "fig, axs = plt.subplots(figsize=(14, 7), ncols=2)\n", "axs[0].scatter(X, Y)\n", "\n", "w = []\n", "b = []\n", "\n", "alphas = [0.0, 0.1, 1.0, 10.0, 100.0, 1000.0]\n", "\n", "for alpha in alphas:\n", " reg = Ridge(alpha=alpha) # Задаем параметр alpha\n", " reg.fit(X[:, None], Y)\n", " pred = reg.predict(x_axis[:, None])\n", " w.append(reg.coef_[0])\n", " b.append(reg.intercept_)\n", " axs[0].plot(x_axis, pred, label=\"alpha=\" + str(alpha))\n", "\n", "axs[0].legend()\n", "axs[0].set_xlabel(\"x\", size=15)\n", "axs[0].set_ylabel(\"y\", size=15)\n", "axs[0].set_title(\"Ridge регрессия с разными коэффициентами регуляризации\")\n", "axs[1].plot(alphas, w, label=\"w\")\n", "axs[1].plot(alphas, b, label=\"b\")\n", "axs[1].set_xlabel(\"alpha\", size=15)\n", "axs[1].set_ylabel(\"Значение параметров\", size=15)\n", "axs[1].set_title(\"Значение параметров w и b при разных значениях регуляризации\")\n", "axs[1].set_xscale(\"symlog\", linthresh=0.01)\n", "axs[1].legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "351BHRAS0a9z" }, "source": [ "### **Задание 1 [2 баллa]**\n", "\n", "Как зависят параметры модели от константы регуляризации? А качество?\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "id": "u9XL2W5JKd3J" }, "source": [ "**Ваши выводы тут:**\n", "\n", "Зависимость параметров:\n", "- С увеличением константы веса модели начинают уменьшаться. При очень больших значениях они становятся практически нулевыми\n", "- При больших значениях alpha практически весь вклад вносится за счёт коэффициента смещения\n", "- С увеличением значений alpha возникает высокий риск недообучения\n", "\n", "Качество модели:\n", "- При значительном увеличении alpha качество модели сильно падает " ] }, { "cell_type": "markdown", "metadata": { "id": "wx3R5ed38SwQ" }, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": { "id": "Y7z1NWrn0a90" }, "source": [ "Казалось бы, зачем нам **регуляризация**?\n", "\n", "Давайте рассмотрим ещё один модельный пример. Представим, что кто-то добавил в данные к переменной $x$ её же умноженную на $2$. То есть, теперь у нас два признака $x_1$ и $x_2 = 2 \\cdot x_1$. Тогда, $y = c \\cdot 0.5 \\cdot x_1 + \\frac{1 - c}{4} \\cdot x_2 + 0.1$, где $c$ любое сколь угодно большое вещественное число. Это может привести к тому, что без регуляризации мы рискуем выучить очень большие веса!" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "lgeNX7GW0a90", "outputId": "7229cd0e-6a0e-40db-ed5b-78a78a3f151b" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "w1: 0.003110369132959204 \tw2: 0.24999999999999994\n" ] } ], "source": [ "np.random.seed(1)\n", "X2 = np.hstack((X[:, None], 2 * X[:, None]))\n", "Y2 = X2[:, 0] * 0.5 + 0.1 + np.random.randn(100) * 0.1\n", "\n", "reg = Ridge(alpha=0.0)\n", "reg.fit(X2, Y2)\n", "print(\"w1:\", reg.coef_[0], \"\\tw2:\", reg.coef_[1])" ] }, { "cell_type": "markdown", "metadata": { "id": "fMvEEVdd0a90" }, "source": [ "Коэффициенты адекватные, хотя и не похожи на изначальную зависимость. Но что, если $x_2$ будет равняться $3 \\cdot x_1$?" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "TwlR5M8l0a90", "outputId": "25056e2e-8fe7-4eb7-979a-8504d50b3ef9" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "w1: 9734611262837.348 \tw2: -3244870420945.615\n" ] } ], "source": [ "np.random.seed(1)\n", "X3 = np.hstack((X[:, None], 3 * X[:, None]))\n", "Y3 = X3[:, 0] * 0.5 + 0.1 + np.random.randn(100) * 0.1\n", "\n", "reg = Ridge(alpha=0.0)\n", "reg.fit(X3, Y3)\n", "print(\"w1:\", reg.coef_[0], \"\\tw2:\", reg.coef_[1])" ] }, { "cell_type": "markdown", "metadata": { "id": "aESDtjM40a91" }, "source": [ "Тут вот уже не повезло. Коэффициенты случайно выучились неадекватно большими.\n", "\n", "Создадим обучающую выборку из того же распределения и посмотрим на качество:" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "zKEqSVP-0a91", "outputId": "dac0ffc4-ea77-4665-c89b-91cea4a39ada" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MSE loss: 0.0219\n" ] } ], "source": [ "np.random.seed(2)\n", "X3_test = np.random.uniform(0, 1, 100)\n", "X3_test = np.hstack((X3_test[:, None], 3 * X3_test[:, None]))\n", "Y3_test = X3_test[:, 0] * 0.5 + 0.1 + np.random.randn(100) * 0.1\n", "\n", "Y3_test_pred = np.sum(reg.coef_[None] * X3_test + reg.intercept_, axis=1)\n", "print(\"MSE loss: %.4f\" % np.mean((Y3_test_pred - Y3_test) ** 2))" ] }, { "cell_type": "markdown", "metadata": { "id": "o3h2jGLt0a91" }, "source": [ "Вроде бы неплохое, но что если мы добавим ко второму признаку одного из объектов небольшой шум?" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "K2_S39zx0a91", "outputId": "e87fdd60-16cc-4ee4-b575-57a96a5c40b3" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MSE loss: 1051.9490520394384\n", "Предсказание для первого с шумом: -324.0625\n", "Предсказание для первого без шума: 0.4248046875\n" ] } ], "source": [ "X3_test[0, 1] = X3_test[0, 1] + 1e-10\n", "Y3_test_pred_noisy = np.sum(reg.coef_[None] * X3_test + reg.intercept_, axis=1)\n", "print(\"MSE loss:\", np.mean((Y3_test_pred_noisy - Y3_test) ** 2))\n", "print(\"Предсказание для первого с шумом: \", Y3_test_pred_noisy[0])\n", "print(\"Предсказание для первого без шума: \", Y3_test_pred[0])" ] }, { "cell_type": "markdown", "metadata": { "id": "mb8h28NH0a92" }, "source": [ "Как видим, даже небольшое изменение в данных, приводит к резкому падению качества." ] }, { "cell_type": "markdown", "metadata": { "id": "JO03NCnf0a92" }, "source": [ "### **Задание 2 [2 баллa]**\n", "Рассмотрите больше примеров (хотя бы два) с двумя признаками $x_1$ и $x_2$, где $x_2$ линейно зависит от $x_1$. Убедитесь, что линейная модель без регуляризации крайне неустойчива." ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "id": "4fYvzntu0a92" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "w1: 1696626244189.3145 \n", "w2: -113108416279.25912\n", "-----\n", "w1: -0.24676691369166734 \n", "w2: -0.5\n" ] } ], "source": [ "X_4 = np.random.uniform(0, 1, 100)\n", "X_4 = np.hstack((X_4[:, None], 15 * X_4[:, None]))\n", "Y_4 = X_4[:, 0] * 0.5 + 0.1 + np.random.randn(100) * 0.1\n", "\n", "reg = Ridge(alpha=0.0)\n", "reg.fit(X_4, Y_4)\n", "print(\"w1:\", reg.coef_[0], \"\\nw2:\", reg.coef_[1])\n", "print(\"-----\")\n", "\n", "X_5 = np.random.uniform(0, 1, 100)\n", "X_5 = np.hstack((X_5[:, None], -19 / 13 * X_5[:, None]))\n", "Y_5 = X_5[:, 0] * 0.5 + 0.1 + np.random.randn(100) * 0.1\n", "\n", "reg = Ridge(alpha=0.0)\n", "reg.fit(X_5, Y_5)\n", "print(\"w1:\", reg.coef_[0], \"\\nw2:\", reg.coef_[1])" ] }, { "cell_type": "markdown", "metadata": { "id": "RayRFAUQ8_im" }, "source": [ "-------------" ] }, { "cell_type": "markdown", "metadata": { "id": "QntGTsze_FPB" }, "source": [ "## Масштабирование данных" ] }, { "cell_type": "markdown", "metadata": { "id": "qFrLJkwU0a95" }, "source": [ "Попробуем обучить линейную регрессию уже c $l_1$ регуляризацией (Lasso) на специальном датасете из sklearn" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "id": "6Wz-2yw70a95" }, "outputs": [], "source": [ "from sklearn.datasets import fetch_california_housing\n", "from sklearn.model_selection import train_test_split\n", "\n", "X, y = fetch_california_housing(return_X_y=True)\n", "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=2024)" ] }, { "cell_type": "markdown", "metadata": { "id": "H_nI4pA4so5t" }, "source": [ "Взглянем немножко на данные. Выведем средние значения каждого признака" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "VJxbObHelbzz", "outputId": "fd0843bc-44f8-42bf-9618-5f70d6784947" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 3.868 28.712 5.411 1.093 1416.185 3.109 35.637 -119.583]\n" ] } ], "source": [ "with np.printoptions(formatter={'float': '{: 0.3f}'.format}):\n", " print(X_train.mean(axis=0))" ] }, { "cell_type": "markdown", "metadata": { "id": "0FqB2pnvtRAG" }, "source": [ "Нетрудно видеть, что масштаб у разных признаков сильно отличается. Это может приводить к разным неприятным эффектам. Подробнее эту проблему мы разберём в следующем задании." ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "id": "xDqH8v2BmF4G" }, "outputs": [], "source": [ "from sklearn.preprocessing import StandardScaler" ] }, { "cell_type": "markdown", "metadata": { "id": "keUMYxF5tjXH" }, "source": [ "### **Задание 3 [1 балл]**\n", "\n", "Отмасштабируйте данные при помощи класса `StandardScaler`. Выведите средние значения и дисперсии признаков на обучающей и тестовой выборках.\n", "\n", "**Примечание** Результат положите в переменные X_train_scaled и X_test_scaled , чтобы последующий код был рабочим" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "id": "m0j2RZhmmgPY" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "X_train_scaled:\n", "Среднее значение = -1.5276078667068268e-14\n", "дисперсия = 1.0000000000000033\n", "\n", "X_train_scaled:\n", "Среднее значение = 0.009713241824084506\n", "дисперсия = 1.2685666097336883\n" ] } ], "source": [ "scaler = StandardScaler()\n", "\n", "X_train_scaled = scaler.fit_transform(X_train)\n", "X_test_scaled = scaler.transform(X_test)\n", "\n", "print(f\"X_train_scaled:\\nСреднее значение = {X_train_scaled.mean()}\\nдисперсия = {X_train_scaled.var()}\\n\")\n", "print(f\"X_train_scaled:\\nСреднее значение = {X_test_scaled.mean()}\\nдисперсия = {X_test_scaled.var()}\")" ] }, { "cell_type": "markdown", "metadata": { "id": "76eKB65uuK0i" }, "source": [ "Измерим качество прогнозатора. Будем использовать метрику RMSE." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "id": "t6yAIUIFujHO" }, "outputs": [], "source": [ "from sklearn.metrics import mean_squared_error, root_mean_squared_error\n", "from sklearn.linear_model import Lasso" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "ObS-2QbA0a95", "outputId": "a8fe0587-c74b-4575-d697-e5dd1a6b8e9c" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Test RMSE = 0.9798\n" ] } ], "source": [ "reg = Lasso(alpha=0.5)\n", "reg.fit(X_train_scaled, y_train)\n", "y_pred = reg.predict(X_test_scaled)\n", "print(\"Test RMSE = %.4f\" % root_mean_squared_error(y_test, y_pred))" ] }, { "cell_type": "markdown", "metadata": { "id": "WOczQNKBvAY-" }, "source": [ "### **Задание 4 [2 баллa]**\n", "\n", "В чем плюсы RMSE по сравнению с MSE?" ] }, { "cell_type": "markdown", "metadata": { "id": "qOHAhn1S9K8i" }, "source": [ "**Ваши выводы тут:**\n", "\n", "Плюсы:\n", "- `RMSE`, за счёт извлечения квадратного корня, выражается в тех же единицах измерения, что и оригинальные данные.\n", " - `MSE` же, напротив, имеет в качестве единиц измерения квадрат исходных е.и.\n", " - В целом `RMSE` чаще используется для прикладных задач за счёт удобства оценки данных в тех же единицах измерения, в то время как `MSE` применяется в математических задачах, так как более явно учитывает влияние больших выбросов\n", "- Несмотря на то, что обе приведённые метрики весьма чувствительны к большим значениям ошибки (так как все ошибки вносят квадратичный вклад), `RMSE` несколько сглаживает их влияние за счёт извлечения корня\n", " - Это может быть полезно, когда влияние подобных ошибок не столь важно для модели\n", "- При равномерном распределении ошибок `RMSE` можно использовать как среднеквадратичное отклонения" ] }, { "cell_type": "markdown", "metadata": { "id": "zJ1M29rY89m5" }, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": { "id": "0NVSmCoL0a96" }, "source": [ "Обратим внимание на веса модели. Почти все из них занулились! Это большое преимущество, так как разреживание весов позволяет отбирать нужные признаки, делая модель более лёгкой." ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "id": "pVFBOLvf0a96" }, "outputs": [ { "data": { "text/plain": [ "array([ 0.28811554, 0. , 0. , -0. , -0. ,\n", " -0. , -0. , -0. ])" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "reg.coef_" ] }, { "cell_type": "markdown", "metadata": { "id": "RuP2oVgo0a96" }, "source": [ "А теперь обучим с $l_2$ регуляризацией." ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "id": "3TJN4CGY0a96" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 8.50854581e-01 1.25545440e-01 -2.78892640e-01 3.08812622e-01\n", " -1.99686054e-04 -4.12942247e-02 -8.88296917e-01 -8.60046905e-01]\n" ] } ], "source": [ "reg = Ridge(alpha=0.5)\n", "reg.fit(X_train_scaled, y_train)\n", "print(reg.coef_)" ] }, { "cell_type": "markdown", "metadata": { "id": "OImrNXyD0a97" }, "source": [ "Как видим, веса не разрежены, хотя и есть очень маленькие значения" ] }, { "cell_type": "markdown", "metadata": { "id": "TLMmhppM9AVY" }, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": { "id": "3Np7mCO7_iwz" }, "source": [ "## Подбор гиперпараметра при регуляризации" ] }, { "cell_type": "markdown", "metadata": { "id": "QSvWWyfWeBaz" }, "source": [ "При обучении мы заранее не знаем, какое значение параметра регуляризации даст наилучшие результаты. Подобрать оптимальные параметры можно с помощью **кросс-валидации**. В sklearn есть несколько классов со встроенной кросс-валидацией" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "id": "pdsMzMTvd_6K" }, "outputs": [], "source": [ "from sklearn.model_selection import GridSearchCV\n", "from sklearn.pipeline import Pipeline" ] }, { "cell_type": "markdown", "metadata": { "id": "m9ZE2NxwfOJo" }, "source": [ "Воспользуемся классом GridSearch для перебора параметров по сетке.\n", "\n", "* Для линейных регрессий перебирается параметр $\\alpha$ - сила регуляризации. Обычно важнее перебирать порядок этого параметра, а не точное его значение. В силу этого сетку перебора будет удобно сделать через функцию np.logspace, например np.logspace(-3, 3, 10).\n", "\n", "### **Задание 5 [3 баллa]**\n", "\n", "Воспользуйтесь классом [GridSearch](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html) и подберите константы регуляризации для Lasso и Ridge регрессий. Измерьте качество обученных моделей. Сетка перебора должна быть логарифмической, из хотя бы 10 значений\n" ] }, { "cell_type": "markdown", "metadata": { "id": "6VHlyE8vLWrc" }, "source": [ "**Подсказка**\n", "\n", "* Пример, как можно перебирать параметры в GridSearch у вложенных [Pipeline](https://scikit-learn.org/stable/modules/generated/sklearn.pipeline.Pipeline.html#sklearn.pipeline.Pipeline) можно [найти вот тут](https://www.kaggle.com/code/ilnazsalimov/gridsearch-with-pipeline)\n", "* Обратите внимание, что сейчас мы сразу заносим масштабирование в Pipeline - чтобы иметь возможность сразу вызываться от оригинальных X_train, а также чтобы не было утечки данных при использовании GridSearch\n", "* В GridSearch в качестве скоринговой функции можно подавать строковое описание функции из sklearn, которое [можно посмотреть вот тут](https://scikit-learn.org/stable/modules/model_evaluation.html), а также саму скоринговую функцию из sklearn или собственную функцию, сделанную [через make_scorer](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.make_scorer.html#sklearn.metrics.make_scorer)\n", "\n", "**Примечание** Итоговое качество должно быть не больше 0.75 RMSE. За меньшее качество балл будет снижаться" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "id": "AcwCrIunwoxK" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2 0.72237\n", "Name: mean_test_score, dtype: float64\n", "5 0.722382\n", "Name: mean_test_score, dtype: float64\n" ] } ], "source": [ "model_lasso = Pipeline([\n", " (\"scaler\", StandardScaler()),\n", " (\"regr\", Lasso())\n", "])\n", "\n", "model_ridge = Pipeline([\n", " (\"scaler\", StandardScaler()),\n", " (\"regr\", Ridge())\n", "])\n", "\n", "parametrs = {\n", " 'regr__alpha': list(np.logspace(-5, 6, 12)),\n", "}\n", "\n", "lasso_cv = GridSearchCV(\n", " model_lasso,\n", " cv=5,\n", " scoring=\"neg_root_mean_squared_error\",\n", " param_grid = parametrs\n", ")\n", "\n", "ridge_cv = GridSearchCV(\n", " model_ridge,\n", " cv=5,\n", " scoring=\"neg_root_mean_squared_error\",\n", " param_grid = parametrs\n", ")\n", "\n", "lasso_cv.fit(X_train, y_train)\n", "ridge_cv.fit(X_train, y_train)\n", "lasso_res = pd.DataFrame(lasso_cv.cv_results_)\n", "ridge_res = pd.DataFrame(ridge_cv.cv_results_)\n", "\n", "print(-lasso_res['mean_test_score'].sort_values(ascending=False).head(1))\n", "print(-ridge_res['mean_test_score'].sort_values(ascending=False).head(1))" ] }, { "cell_type": "markdown", "metadata": { "id": "AjG4DjsE5VOd" }, "source": [ "Убедимся, что Lasso всё ещё зануляет признаки (скорее всего модель Lasso занулила хотя бы один)." ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "id": "NIvVQE2bQfid" }, "outputs": [ { "data": { "text/plain": [ "array([ 0.84604739, 0.12597833, -0.26816238, 0.29792527, 0. ,\n", " -0.04027369, -0.87740579, -0.84850035])" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lasso_cv.best_estimator_.named_steps[\"regr\"].coef_" ] }, { "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. Кaк подбирать параметры линейной модели.\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 }