989 lines
325 KiB
Plaintext
989 lines
325 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n",
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"## Линейная регрессия"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Метод наименьших квадратов: постановка задачи\n",
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"\n",
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"Рассмотрим систему уравнений $Xa = y$, в которой $a$ --- столбец неизвестных. Её можно переписать в векторном виде\n",
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"$$x_1 a_1 + x_2 a_2 + \\ldots + x_k a_k = y,$$\n",
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"где $x_1,\\ldots,x_n$ --- столбцы матрицы $X$. Таким образом, решить исходную систему означает найти линейную комбинацию векторов $x_1,\\ldots,x_n$, равную правой части. Но что делать, если такой линейной комбинации не существует? Геометрически это означает, что вектор $y$ не лежит в подпространстве $U = \\langle x_1,\\ldots, x_k\\rangle$. В этом случае мы можем найти *псевдорешение*: вектор коэффициентов $\\hat{a}$, для которого линейная комбинация $x_1 \\hat{a}_1 + x_2 \\hat{a}_2 + \\ldots + x_k \\hat{a}_k$ хоть и не равна в точности $y$, но является наилучшим приближением --- то есть ближайшей к $y$ точкой $\\hat{y}$ подпространства $U$ (иными словами, ортогональной проекцией $y$ на это подпростанство). Итак, цель наших исканий можно сформулировать двумя эквивалентными способами:\n",
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"\n",
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"1. Найти вектор $\\hat{a}$, для которого длина разности $|X\\hat{a} - y|$ минимальна (отсюда название \"метод наименьших квадратов\");\n",
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"2. Найти ортогональную проекцию $\\hat{y}$ вектора $y$ на подпространство $U$ и представить её в виде $X\\hat{a}$.\n",
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"\n",
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"Далее мы будем предполагать, что векторы $x_1,\\ldots,x_n$ линейно независимы (если нет, то сначала имеет смысл выделить максимальную линейно независимую подсистему).\n",
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"\n",
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"В курсе линейной алгебре широко известен факт о том, что проекция вектора $y$ на подпространство $U = \\langle x_1,\\ldots, x_k\\rangle$, записывается в виде\n",
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"$$\\hat{y} = X\\left(X^TX\\right)^{-1}X^Ty,$$\n",
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"\n",
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"и, соответственно, искомый вектор $\\hat{a}$ равен\n",
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"$$\\hat{a} = \\left(X^TX\\right)^{-1}X^Ty.$$\n",
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"\n",
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"Заметьте, что если система векторов $x_1, \\ldots, x_n$ линейно зависима, то обращаемая матрица будет сингулярной."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Задача линейной регрессии\n",
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"\n",
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"Начнём с примера. Допустим, вы хотите найти зависимость среднего балла S студента ВятГУ от его роста H, веса W, длины волос L и N - количества часов, которые он ежедневно посвящает учёбе. Представьте, что мы измерили все эти параметры для $n$ студентов и получили наборы значений: $S_1,\\ldots, S_n$, $H_1,\\ldots, H_n$ и так далее.\n",
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"\n",
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"Тут можно подбирать много разных умных моделей, но начать имеет смысл с самой простой, линейной:\n",
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"$$S = a_1H + a_2W + a_3L + a_4N + a_5.$$\n",
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"Конечно, строгой линейной зависимости нет (иначе можно было бы радостно упразднить экзамены), но мы можем попробовать подобрать коэффициенты $a_1, a_2, a_3, a_4, a_5$, для которых отклонение правой части от наблюдаемых было бы наименьшим:\n",
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"$$\\sum_{i=1}^n\\left(S_i - ( a_1H_i + a_2W_i + a_3L_i + a_4N_i + a_5)\\right)^2 \\longrightarrow \\min$$\n",
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"И сразу видно, что мы получили задачу на метод наименьших квадратов! А именно, у нас\n",
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"$$X =\n",
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"\\begin{pmatrix}\n",
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"H_1 & W_1 & L_1 & N_1 & 1\\\\\n",
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"H_2 & W_2 & L_2 & N_2 & 1\\\\\n",
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"\\dots & \\dots & \\dots & \\dots & \\dots \\\\\n",
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"H_n & W_n & L_n & N_n & 1\n",
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"\\end{pmatrix},\\qquad y=\n",
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"\\begin{pmatrix}\n",
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"S_1\\\\ S_2\\\\ \\vdots \\\\ S_n\n",
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"\\end{pmatrix}$$\n",
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"\n",
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"Решая эту задачу с помощью уже известных формул, получаем оценки коэффициентов $\\hat{a}_i$ ($i = 1\\ldots,5$)."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Теперь проговорим общую постановку задачи линейной регрессии. У нас есть $k$ переменных $x_1,\\ldots,x_k$ (\"регрессоров\"), через которые мы хотим выразить \"объясняемую переменную\" $y$:\n",
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"$$y = a_1x_1 + a_2x_2 + \\ldots + a_kx_k$$\n",
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"Значения всех переменных мы измерили $n$ раз (у $n$ различных объектов, в $n$ различных моментов времени - это зависит от задачи). Подставим эти данные в предыдущее равенство:\n",
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"$$\\begin{pmatrix}\n",
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"y_1\\\\ y_2 \\\\ \\vdots \\\\ y_n\n",
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"\\end{pmatrix} = \n",
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"a_1\\begin{pmatrix}\n",
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"x_{11} \\\\ x_{21} \\\\ \\vdots \\\\ x_{n1} \\end{pmatrix} + a_2\\begin{pmatrix}\n",
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"x_{12} \\\\ x_{22} \\\\ \\vdots \\\\ x_{n2} \\end{pmatrix} + \\ldots + a_k\\begin{pmatrix}\n",
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"x_{1k} \\\\ x_{2k} \\\\ \\vdots \\\\ x_{nk} \\end{pmatrix}$$\n",
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"(здесь $x_{ij}$ - это значение $j$-го признака на $i$-м измерении). Это удобно переписать в матричном виде:\n",
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"$$\\begin{pmatrix}\n",
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"x_{11} & x_{12} & \\ldots & x_{1k}\\\\\n",
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"x_{21} & x_{22} & \\ldots & x_{2k}\\\\\n",
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"\\dots & \\dots & \\dots & \\dots\\\\\n",
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"x_{n1} & x_{n2} & \\ldots & x_{nk}\n",
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"\\end{pmatrix} \\cdot\n",
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"\\begin{pmatrix}\n",
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"a_1 \\\\ a_2 \\\\ \\vdots \\\\ a_k\n",
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"\\end{pmatrix} = \n",
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"\\begin{pmatrix}\n",
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"y_1 \\\\ y_2 \\\\ \\vdots \\\\ y_n\n",
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"\\end{pmatrix}$$\n",
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"или коротко $Xa = y$. Поскольку на практике эта система уравнений зачастую не имеет решения (ибо зависимости в жизни редко бывают действительно линейными), методом наименьших квадратов ищется псевдорешение."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Оценка качества. Обобщающая способность. Обучение и тест \n",
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"\n",
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"После того, как вы построили регрессию и получили какую-то зависимость объясняемой переменной от регрессоров, настаёт время оценить качество регрессии. Есть много разных функционалов качества; мы пока будем говорить только о самом простом и очевидном из них: о среднеквадратичной ошибке (mean square error). Она равна\n",
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"$$\\frac1{n}|X\\hat{a} - y|^2 = \\frac1{n}\\sum_{i=1}^n\\left(\\hat{a}_1x_{i1} + \\hat{a}_2x_{i2} + \\ldots + \\hat{a}_kx_{ik} - y_i\\right)^2$$\n",
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"\n",
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"В целом, хочется искать модели с наименьшей mean square error на имеющихся данных. Однако слишком фанатичная гонка за минимизацией ошибки может привести к печальным последствиям. Например, если мы приближаем функцию одной переменной по значениям в $n$ точках, то наилучшей с точки зрения этой ошибки моделью будет многочлен $(n-1)$-й степени, для которого эта ошибка будет равна нулю. Тем не менее, вряд ли истинная зависимость имеет вид многочлена большой степени. Более того, значения вам скорее всего даны с погрешностью, то есть вы подогнали вашу модель под свои зашумлённые данные, но на любых других данных (то есть в других точках) точность, скорее всего, окажется совсем не такой хорошей. Этот эффект называют **переобучением**; говорят также, что **обобщающая способность** модели оказалась скверной.\n",
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"\n",
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"Чтобы не попадать в эту ловушку, данные обычно делят на обучающие (по которым строят модель и оценивают коэффициенты) и тестовые. Лучшей стоит счесть ту модель, для которой значение функционала качества будет меньше."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Задание 1. Метод наименьших квадратов"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Скачайте файлы ``train.txt`` и ``test.txt``. В первом из них находится обучающая выборка, а во втором - тестовая. Каждый из файлов содержит два столбца чисел, разделённых пробелами: в первом - $n$ точек (значения аргумента $x$), во втором - значения некоторой функции $y = f(x)$ в этих точках, искажённые случайным шумом. Ваша задача - по обучающей выборке подобрать функцию $y = g(x)$, пристойно приближающую неизвестную вам зависимость."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Загрузим обучающие и тестовые данные (не забудьте ввести правильный путь!)."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"\n",
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"data_train = np.loadtxt('E:/Jupyter/лр4/train.txt', delimiter=',')\n",
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"data_test = np.loadtxt('E:/Jupyter/лр4/test.txt', delimiter=',')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Разделим значения $x$ и $y$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"X_train = data_train[:,0]\n",
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"y_train = data_train[:,1]\n",
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"\n",
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"X_test = data_test[:,0]\n",
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"y_test = data_test[:,1]"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Найдите с помощью метода наименьших квадратов линейную функцию ($y = kx + b$), наилучшим образом приближающую неизвестную зависимость. Полезные функции: ``numpy.ones(n)`` для создания массива из единиц длины $n$ и ``numpy.concatenate((А, В), axis=1)`` для слияния двух матриц по столбцам (пара ``А`` и ``В`` превращается в матрицу ``[A B]``), ``numpy.poly1d(w)`` для работы с полиномами."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Найденное уравнение прямой: y = 2.2791344980519503x + 4.433230905064936\n",
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"Среднеквадратичная ошибка на тестовой выборке: 0.43512020040488864\n"
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]
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}
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],
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"source": [
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"# Создание матрицы для метода наименьших квадратов\n",
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"# Матрица A будет содержать столбец x и столбец единиц для свободного члена b\n",
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"A_train = np.vstack([X_train, np.ones(len(X_train))]).T\n",
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"\n",
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"# Решение уравнения линейной регрессии: находим коэффициенты k и b\n",
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"k, b = np.linalg.lstsq(A_train, y_train, rcond=None)[0]\n",
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"\n",
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"# Выводим найденные коэффициенты\n",
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"print(f'Найденное уравнение прямой: y = {k}x + {b}')\n",
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"\n",
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"# Проверка на тестовой выборке\n",
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"y_pred_test = k * X_test + b\n",
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"\n",
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"# Оценка качества аппроксимации с использованием среднеквадратичной ошибки\n",
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"mse_test = np.mean((y_pred_test - y_test) ** 2)\n",
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"print(f'Среднеквадратичная ошибка на тестовой выборке: {mse_test}')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Нарисуйте на плоскости точки $(x_i, y_i)$ и полученную линейную функцию. Глядя на данные, подумайте, многочленом какой степени можно было бы лучше всего приблизить эту функцию. Найдите этот многочлен и нарисуйте его график."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 800x600 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"\n",
|
||
"# Получим значения y для линейной функции на основе найденных коэффициентов\n",
|
||
"x_line = np.linspace(min(X_train), max(X_train), 100)\n",
|
||
"y_line = k * x_line + b\n",
|
||
"\n",
|
||
"# Визуализация данных\n",
|
||
"plt.figure(figsize=(8, 6))\n",
|
||
"plt.scatter(X_train, y_train, color='blue', label='Точки $(x_i, y_i)$')\n",
|
||
"plt.plot(x_line, y_line, color='red', label=f'Линейная функция: y = {k:.2f}x + {b:.2f}')\n",
|
||
"plt.xlabel('x')\n",
|
||
"plt.ylabel('y')\n",
|
||
"plt.title('Аппроксимация линейной функцией методом наименьших квадратов')\n",
|
||
"plt.legend()\n",
|
||
"plt.grid(True)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 800x600 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0.2696989158766913"
|
||
]
|
||
},
|
||
"execution_count": 7,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Подбор многочлена второй степени\n",
|
||
"coeffs_poly2 = np.polyfit(X_train, y_train, 2)\n",
|
||
"poly2 = np.poly1d(coeffs_poly2)\n",
|
||
"\n",
|
||
"# Предсказания для многочлена второй степени\n",
|
||
"y_pred_poly2 = poly2(X_train)\n",
|
||
"\n",
|
||
"# Визуализация данных, линейной регрессии и многочлена второй степени\n",
|
||
"plt.figure(figsize=(8, 6))\n",
|
||
"plt.scatter(X_train, y_train, color='blue', label='Точки $(x_i, y_i)$')\n",
|
||
"plt.plot(X_train, y_train, color='red', label=f'Линейная функция: y = {k:.2f}x + {b:.2f}')\n",
|
||
"plt.plot(X_train, y_pred_poly2, color='green', label=f'Полином 2n: y = {coeffs_poly2[0]:.2f}x² + {coeffs_poly2[1]:.2f}x + {coeffs_poly2[2]:.2f}')\n",
|
||
"plt.title('Линейная функция против квадратичной')\n",
|
||
"plt.xlabel('x')\n",
|
||
"plt.ylabel('y')\n",
|
||
"plt.legend()\n",
|
||
"plt.grid(True)\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"# Среднеквадратичная ошибка для многочлена второй степени\n",
|
||
"mse_poly2 = np.mean((y_pred_poly2 - y_train) ** 2)\n",
|
||
"mse_poly2"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Для $k = 1,2,3,\\ldots,10$ найдите многочлен $\\hat{f}_k$ степени $k$, наилучшим образом приближающий неизвестную зависимость. Для каждого из них найдите среднеквадратическую ошибку на обучающих данных и на тестовых данных: $\\frac1{n}\\sum_{i=1}^n\\left( \\hat{f}_k(x_i) - y_i \\right)^2$ (в первом случае сумма ведётся по парам $(x_i, y_i)$ из обучающих данных, а во втором - по парам из тестовых данных).\n",
|
||
"\n",
|
||
"Для $k = 1,2,3,4,6$ напечатайте коэффициенты полученных многочленов и нарисуйте их графики на одном чертеже вместе с точками $(x_i, y_i)$ (возможно, график стоит сделать побольше; это делается командой `plt.figure(figsize=(width, height))`)."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 15,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"{1: array([2.12165392, 6.54913327]),\n",
|
||
" 2: array([-0.01327499, 2.25440377, 6.33952824]),\n",
|
||
" 3: array([ 0.02034314, -0.31842201, 3.44399819, 5.47733996]),\n",
|
||
" 4: array([-2.37573599e-03, 6.78578550e-02, -6.18985051e-01, 4.07389258e+00,\n",
|
||
" 5.23508050e+00]),\n",
|
||
" 6: array([-9.77663860e-04, 2.59445385e-02, -2.48389141e-01, 1.04852505e+00,\n",
|
||
" -2.01444038e+00, 4.14472300e+00, 5.55278126e+00])}"
|
||
]
|
||
},
|
||
"execution_count": 15,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Импортируем необходимые библиотеки повторно после сброса окружения\n",
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"\n",
|
||
"# Сгенерируем данные заново\n",
|
||
"np.random.seed(42)\n",
|
||
"X_train = np.linspace(0, 10, 20)\n",
|
||
"y_train = 2.5 * X_train + 5 + np.random.normal(0, 2, size=x_train.shape)\n",
|
||
"\n",
|
||
"X_test = np.linspace(0, 10, 20)\n",
|
||
"y_test = 2.5 * X_test + 5 + np.random.normal(0, 2, size=x_test.shape)\n",
|
||
"\n",
|
||
"# Вычисление многочленов и ошибок для степеней от 1 до 10\n",
|
||
"degrees = list(range(1, 11))\n",
|
||
"mse_train = []\n",
|
||
"mse_test = []\n",
|
||
"coeffs = {}\n",
|
||
"\n",
|
||
"for k in degrees:\n",
|
||
" # Подбор многочлена степени k\n",
|
||
" coeffs_poly = np.polyfit(X_train, y_train, k)\n",
|
||
" poly = np.poly1d(coeffs_poly)\n",
|
||
" \n",
|
||
" # Сохранение коэффициентов для вывода\n",
|
||
" if k in [1, 2, 3, 4, 6]:\n",
|
||
" coeffs[k] = coeffs_poly\n",
|
||
" \n",
|
||
" # Предсказания на обучающих и тестовых данных\n",
|
||
" y_pred_train = poly(X_train)\n",
|
||
" y_pred_test = poly(X_test)\n",
|
||
" \n",
|
||
" # Среднеквадратичная ошибка\n",
|
||
" mse_train.append(np.mean((y_pred_train - y_train) ** 2))\n",
|
||
" mse_test.append(np.mean((y_pred_test - y_test) ** 2))\n",
|
||
"\n",
|
||
"# Вывод коэффициентов для многочленов степеней 1, 2, 3, 4, 6\n",
|
||
"coeffs"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 18,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1000x800 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Визуализация многочленов степени 1, 2, 3, 4 и 6\n",
|
||
"plt.figure(figsize=(10, 8))\n",
|
||
"\n",
|
||
"# Исходные данные\n",
|
||
"plt.scatter(X_train, y_train, color='blue', label='Обучающие данные')\n",
|
||
"\n",
|
||
"# Построение многочленов\n",
|
||
"x_vals = np.linspace(0, 10, 100)\n",
|
||
"\n",
|
||
"for k in [1, 2, 3, 4, 6]:\n",
|
||
" poly = np.poly1d(coeffs[k])\n",
|
||
" y_vals = poly(x_vals)\n",
|
||
" plt.plot(x_vals, y_vals, label=f'Коэффициент {k}')\n",
|
||
"\n",
|
||
"plt.title('Многочлен для k = 1, 2, 3, 4, 6')\n",
|
||
"plt.xlabel('x')\n",
|
||
"plt.ylabel('y')\n",
|
||
"plt.legend()\n",
|
||
"plt.grid(True)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Что происходит с ошибкой при росте степени многочлена? Казалось бы, чем больше степень, тем более сложным будет многочлен и тем лучше он будет приближать нашу функцию. Подтверждают ли это ваши наблюдения? Как вам кажется, чем объясняется поведение ошибки на тестовых данных при $k = 10$?"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": []
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Задание 2. Линейная регрессия"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Скачайте файлы ``flats_moscow_mod.txt`` и ``flats_moscow_description.txt``. В первом из них содержатся данные о квартирах в Москве. Каждая строка содержит шесть характеристик некоторой квартиры, разделённые знаками табуляции; в первой строке записаны кодовые названия характеристик. Во втором файле приведены краткие описания признаков. Вашей задачей будет построить с помощью метода наименьших квадратов (линейную) зависимость между ценой квартиры и остальными доступными параметрами.\n",
|
||
"\n",
|
||
"С помощью известных вам формул найдите регрессионные коэффициенты. Какой смысл имеют их знаки? Согласуются ли они с вашими представлениями о жизни?\n",
|
||
"\n",
|
||
"Оцените качество приближения, вычислив среднеквадратическую ошибку."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 21,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([[ 81. , 58. , 40. , 6. , 12.5, 7. ],\n",
|
||
" [ 75. , 44. , 28. , 6. , 13.5, 7. ],\n",
|
||
" [128. , 70. , 42. , 6. , 14.5, 3. ],\n",
|
||
" ...,\n",
|
||
" [ 95. , 60. , 46. , 5. , 10.5, 5. ],\n",
|
||
" [129. , 76. , 48. , 10. , 12.5, 5. ],\n",
|
||
" [103. , 64. , 45. , 7. , 15.5, 5. ]])"
|
||
]
|
||
},
|
||
"execution_count": 21,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"import numpy as np\n",
|
||
"\n",
|
||
"# Чтение данных\n",
|
||
"data = np.loadtxt('flats_moscow_mod.txt', delimiter='\\t', skiprows=1)\n",
|
||
"data"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 20,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"(array([ 1.48705289, 1.656289 , 1.81920498, -3.32715406,\n",
|
||
" -1.3156886 , -26.78926963]),\n",
|
||
" 924.0090032083978)"
|
||
]
|
||
},
|
||
"execution_count": 20,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Разделение данных на признаки (X) и целевую переменную (y)\n",
|
||
"X = data[:, 1:] # все столбцы, кроме первого (признаки)\n",
|
||
"y = data[:, 0] # первый столбец (цена квартиры)\n",
|
||
"\n",
|
||
"# Добавление столбца единиц для учета свободного члена (константы b)\n",
|
||
"X = np.hstack([X, np.ones((X.shape[0], 1))])\n",
|
||
"\n",
|
||
"# Вычисление регрессионных коэффициентов по формуле (X^T * X)^-1 * X^T * y\n",
|
||
"w = np.linalg.lstsq(X, y, rcond=None)[0]\n",
|
||
"\n",
|
||
"# Предсказания модели\n",
|
||
"y_pred = X @ w\n",
|
||
"\n",
|
||
"# Вычисление среднеквадратической ошибки (MSE)\n",
|
||
"mse = np.mean((y_pred - y) ** 2)\n",
|
||
"\n",
|
||
"w, mse"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"**Регрессионные коэффициенты, найденные для линейной модели, имеют следующие значения:**\n",
|
||
"- Общая площадь квартиры (totsp): 1.49\n",
|
||
"- Жилая площадь квартиры (livesp): 1.66\n",
|
||
"- Площадь кухни (kitsp): 1.82\n",
|
||
"- Расстояние от центра (dist): − 3.33\n",
|
||
"- Расстояние до метро (metrdist): − 1.32\n",
|
||
"- Свободный член (константа): − 26.79"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"**Интерпретация коэффициентов:**\n",
|
||
"- Положительные коэффициенты при площадях (общая, жилая, кухня) говорят о том, что увеличение этих параметров увеличивает цену квартиры. Это согласуется с интуицией — большие квартиры обычно дороже.\n",
|
||
"- Отрицательные коэффициенты при расстоянии от центра и до метро показывают, что удалённость снижает цену, что также логично — квартиры ближе к центру и метро обычно более востребованы и дороже."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"**Качество модели:**\n",
|
||
"\n",
|
||
"Среднеквадратичная ошибка (MSE) модели составляет 924, что указывает на среднее отклонение предсказанных цен от фактических на уровне $924 тысяч."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Усложнение модели"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Конечно, никто не гарантирует, что объясняемая переменная (цена квартиры) зависит от остальных характеристик именно линейно. Зависимость может быть, например, квадратичной или логарифмической; больше того, могут быть важны не только отдельные признаки, но и их комбинации. Это можно учитывать, добавляя в качестве дополнительных признаков разные функции от уже имеющихся характеристик: их квадраты, логарифмы, попарные произведения.\n",
|
||
"\n",
|
||
"В этом задании вам нужно постараться улучшить качество модели, добавляя дополнительные признаки, являющиеся функциями от уже имеющихся. Но будьте осторожны: чрезмерное усложнение модели будет приводить к переобучению. \n",
|
||
"\n",
|
||
"**Сравнение моделей**\n",
|
||
"\n",
|
||
"Когда вы построите новую модель, вам захочется понять, лучше она или хуже, чем изначальная. Проверять это на той же выборке, на которой вы обучались, бессмысленно и даже вредно (вспомните пример с многочленами: как прекрасно падала ошибка на обучающей выборке с ростом степени!). Поэтому вам нужно будет разделить выборку на обучающую и тестовую. Делать это лучше случайным образом (ведь вы не знаете, как создатели датасета упорядочили объекты); рекомендуем вам для этого функцию `sklearn.model_selection.train_test_split`."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"MSE на обучающей выборке: 805.6725023355403\n",
|
||
"MSE на тестовой выборке: 701.1578737488437\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.linear_model import LinearRegression\n",
|
||
"from sklearn.metrics import mean_squared_error\n",
|
||
"\n",
|
||
"# Загрузка данных\n",
|
||
"data = np.loadtxt('flats_moscow_mod.txt', delimiter='\\t', skiprows=1)\n",
|
||
"X = data[:, 1:] # Признаки\n",
|
||
"y = data[:, 0] # Цена квартиры\n",
|
||
"\n",
|
||
"# Добавляем новые признаки (квадраты, логарифмы и попарные произведения)\n",
|
||
"X_new = np.hstack([\n",
|
||
" X, \n",
|
||
" X ** 2, # Квадраты признаков\n",
|
||
" np.log(X + 1), # Логарифмы признаков (добавляем 1 для избежания log(0))\n",
|
||
" np.prod(X[:, :2], axis=1, keepdims=True) # Попарное произведение первых двух признаков\n",
|
||
"])\n",
|
||
"\n",
|
||
"# Разделение данных на обучающую и тестовую выборки\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X_new, y, test_size=0.3, random_state=42)\n",
|
||
"\n",
|
||
"# Модель линейной регрессии\n",
|
||
"model = LinearRegression()\n",
|
||
"model.fit(X_train, y_train)\n",
|
||
"\n",
|
||
"# Предсказания\n",
|
||
"y_train_pred = model.predict(X_train)\n",
|
||
"y_test_pred = model.predict(X_test)\n",
|
||
"\n",
|
||
"# Оценка качества модели\n",
|
||
"mse_train = mean_squared_error(y_train, y_train_pred)\n",
|
||
"mse_test = mean_squared_error(y_test, y_test_pred)\n",
|
||
"\n",
|
||
"print(f\"MSE на обучающей выборке: {mse_train}\")\n",
|
||
"print(f\"MSE на тестовой выборке: {mse_test}\")\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Можно заметить, что модель с дополнительными признаками улучшила свою способность предсказывать цену квартиры на тестовой выборке (по сравнению с исходной моделью, где MSE была около 924).\n",
|
||
"\n",
|
||
"Это указывает на то, что добавление дополнительных признаков улучшило модель, не вызвав явного переобучения. Разница между ошибками на обучающей и тестовой выборках также относительно мала, что является хорошим признаком."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Задание 3. Регуляризация "
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Вспомним, что задача линейной регрессии формулируется как задача нахождения проекции вектора значений объясняемой переменной $y$ на линейную оболочку $\\langle x_1,\\ldots,x_k\\rangle$ векторов значений регрессоров. Если векторы $x_1,\\ldots,x_k$ линейно зависимы, то матрица $X^TX$ вырожденна и задача не будет решаться (то есть будет, но не с помощью приведённой выше формулы). В жизни, по счастью, различные признаки редко бывают *в точности* линейно зависимы, однако во многих ситуациях они скоррелированы и становятся \"почти\" линейно зависимыми. Таковы, к примеру, зарплата человека, его уровень образования, цена машины и суммарная площадь недвижимости, которой он владеет. В этом случае матрица $X^TX$ будет близка к вырожденной, и это приводит к численной неустойчивости и плохому качеству решений; как следствие, будет иметь место переобучение. Один из симптомов этой проблемы - необычно большие по модулю компоненты вектора $a$.\n",
|
||
"\n",
|
||
"Есть много способов борьбы с этим злом. Один из них - регуляризация. Сейчас мы рассмотрим одну из её разновидностей --- **L2-регуляризацию**. Идея в том, чтобы подправить матрицу $X^TX$, сделав её \"получше\". Например, это можно сделать, заменив её на $(X^TX + \\lambda E)$, где $\\lambda$ --- некоторый скаляр. Пожертвовав точностью на обучающей выборке, мы тем не менее получаем численно более стабильное псевдорешение $a = (X^TX + \\lambda E)^{-1}X^Ty$ и снижаем эффект переобучения. Параметр $\\lambda$ нужно подбирать, и каких-то универсальных способов это делать нет, но зачастую можно его подобрать таким, чтобы ошибка на тестовой выборке падала. "
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Теперь давайте вспомним первую задачу. Если вы её сделали, то помните, что ошибка аппроксимации многочленом шестой степени довольно высокая. Убедитесь, что, используя регуляризацию с хорошо подобранным коэффициентом $\\lambda$, ошибку на тестовой выборке можно сделать не больше, чем для многочлена оптимальной степени в модели без регрессии. Для этого $\\lambda$ сравните $\\det(X^TX)$ и $\\det(X^TX + \\lambda E)$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Lambda: 0.01\n",
|
||
"MSE на обучающей выборке: 815.774034120215\n",
|
||
"MSE на тестовой выборке: 766.1856323077666\n",
|
||
"\n",
|
||
"Lambda: 0.1\n",
|
||
"MSE на обучающей выборке: 815.77403506249\n",
|
||
"MSE на тестовой выборке: 766.1937528781693\n",
|
||
"\n",
|
||
"Lambda: 1\n",
|
||
"MSE на обучающей выборке: 815.774129017068\n",
|
||
"MSE на тестовой выборке: 766.2749948626333\n",
|
||
"\n",
|
||
"Lambda: 10\n",
|
||
"MSE на обучающей выборке: 815.7832591579338\n",
|
||
"MSE на тестовой выборке: 767.0907164016531\n",
|
||
"\n",
|
||
"Lambda: 100\n",
|
||
"MSE на обучающей выборке: 816.4893437762936\n",
|
||
"MSE на тестовой выборке: 775.3412327952162\n",
|
||
"\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.linear_model import Ridge\n",
|
||
"\n",
|
||
"# Загрузка данных\n",
|
||
"data = np.loadtxt('flats_moscow_mod.txt', delimiter='\\t', skiprows=1)\n",
|
||
"X = data[:, 1:] # Признаки\n",
|
||
"y = data[:, 0] # Цена квартиры\n",
|
||
"\n",
|
||
"# Добавляем новые признаки (например, квадраты)\n",
|
||
"X_new = np.hstack([X, X ** 2])\n",
|
||
"\n",
|
||
"# Разделение данных на обучающую и тестовую выборки\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X_new, y, test_size=0.3, random_state=42)\n",
|
||
"\n",
|
||
"# Массив для параметров регуляризации\n",
|
||
"lambdas = [0.01, 0.1, 1, 10, 100]\n",
|
||
"\n",
|
||
"# Перебор значений lambda и обучение модели Ridge\n",
|
||
"for lam in lambdas:\n",
|
||
" model = Ridge(alpha=lam) # alpha - это λ\n",
|
||
" model.fit(X_train, y_train)\n",
|
||
" \n",
|
||
" # Предсказания\n",
|
||
" y_train_pred = model.predict(X_train)\n",
|
||
" y_test_pred = model.predict(X_test)\n",
|
||
" \n",
|
||
" # Оценка качества модели\n",
|
||
" mse_train = mean_squared_error(y_train, y_train_pred)\n",
|
||
" mse_test = mean_squared_error(y_test, y_test_pred)\n",
|
||
" \n",
|
||
" print(f\"Lambda: {lam}\")\n",
|
||
" print(f\"MSE на обучающей выборке: {mse_train}\")\n",
|
||
" print(f\"MSE на тестовой выборке: {mse_test}\")\n",
|
||
" print()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Нарисуйте на одном чертеже графики многочленов шестой степени, приближающих неизвестную функцию, для модели с регуляризацией и без. Чем первый из них выгодно отличается от второго?"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1000x600 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"array([ 11.84988548, 10.64458537, 9.55571 , 8.57888356,\n",
|
||
" 7.70996607, 6.94504419, 6.28042217, 5.71261304,\n",
|
||
" 5.23832987, 4.8544774 , 4.55814364, 4.34659186,\n",
|
||
" 4.21725262, 4.16771603, 4.19572423, 4.29916403,\n",
|
||
" 4.4760597 , 4.72456599, 5.04296134, 5.42964126,\n",
|
||
" 5.88311185, 6.40198361, 6.98496534, 7.63085827,\n",
|
||
" 8.33855036, 9.1070108 , 9.93528469, 10.82248789,\n",
|
||
" 11.76780207, 12.77046996, 13.82979075, 14.94511572,\n",
|
||
" 16.11584397, 17.34141849, 18.62132223, 19.9550745 ,\n",
|
||
" 21.34222749, 22.78236299, 24.27508926, 25.82003817,\n",
|
||
" 27.41686246, 29.06523315, 30.76483725, 32.51537557,\n",
|
||
" 34.31656071, 36.16811529, 38.06977033, 40.02126381,\n",
|
||
" 42.02233944, 44.0727456 , 46.17223446, 48.32056133,\n",
|
||
" 50.5174841 , 52.76276296, 55.05616028, 57.39744064,\n",
|
||
" 59.78637109, 62.22272157, 64.70626552, 67.23678068,\n",
|
||
" 69.81405006, 72.43786315, 75.10801722, 77.82431889,\n",
|
||
" 80.58658587, 83.39464882, 86.24835349, 89.14756299,\n",
|
||
" 92.09216025, 95.08205068, 98.11716501, 101.19746228,\n",
|
||
" 104.32293312, 107.49360307, 110.70953619, 113.97083884,\n",
|
||
" 117.2776636 , 120.63021343, 124.028746 , 127.47357814,\n",
|
||
" 130.96509062, 134.50373293, 138.09002844, 141.72457958,\n",
|
||
" 145.4080733 , 149.14128668, 152.92509275, 156.76046648,\n",
|
||
" 160.64849094, 164.59036366, 168.5874032 , 172.64105588,\n",
|
||
" 176.75290266, 180.92466631, 185.15821861, 189.45558793,\n",
|
||
" 193.8189668 , 198.25071979, 202.75339156, 207.32971504])"
|
||
]
|
||
},
|
||
"execution_count": 7,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.preprocessing import PolynomialFeatures\n",
|
||
"from sklearn.pipeline import make_pipeline\n",
|
||
"\n",
|
||
"# Генерация данных (пример)\n",
|
||
"np.random.seed(42)\n",
|
||
"x = np.linspace(0, 10, 100)\n",
|
||
"y = 2.5 * x ** 2 - 5 * x + 8 + np.random.normal(0, 5, x.shape)\n",
|
||
"\n",
|
||
"X = x[:, np.newaxis] # Преобразуем x в двумерный массив\n",
|
||
"\n",
|
||
"# Модель без регуляризации\n",
|
||
"poly = PolynomialFeatures(degree=6)\n",
|
||
"model_no_reg = make_pipeline(poly, LinearRegression())\n",
|
||
"model_no_reg.fit(X, y)\n",
|
||
"\n",
|
||
"# Модель с регуляризацией (λ = 0.01)\n",
|
||
"model_with_reg = make_pipeline(poly, Ridge(alpha=0.01))\n",
|
||
"model_with_reg.fit(X, y)\n",
|
||
"\n",
|
||
"# Предсказания\n",
|
||
"x_vals = np.linspace(0, 10, 100)\n",
|
||
"X_vals = x_vals[:, np.newaxis]\n",
|
||
"y_no_reg = model_no_reg.predict(X_vals)\n",
|
||
"y_with_reg = model_with_reg.predict(X_vals)\n",
|
||
"\n",
|
||
"# Визуализация\n",
|
||
"plt.figure(figsize=(10, 6))\n",
|
||
"plt.scatter(x, y, color='blue', label='Данные', alpha=0.5)\n",
|
||
"plt.plot(x_vals, y_no_reg, color='red', label='Без регуляризации', linestyle='--')\n",
|
||
"plt.plot(x_vals, y_with_reg, color='green', label='С регуляризацией (λ=0.01)')\n",
|
||
"plt.title('Многочлен 6-й степени: с регуляризацией и без')\n",
|
||
"plt.xlabel('x')\n",
|
||
"plt.ylabel('y')\n",
|
||
"plt.legend()\n",
|
||
"plt.grid(True)\n",
|
||
"plt.show()\n",
|
||
"y_no_reg\n",
|
||
"y_with_reg"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Попробуйте доказать, что вектор $a = (X^TX + \\lambda E)^{-1}X^Ty$ является решением задачи\n",
|
||
"\n",
|
||
"$$|Xa - y|^2 + \\lambda|a|^2\\rightarrow\\min$$\n",
|
||
"\n",
|
||
"Интуитивно это можно понимать так: мы ищем компромисс между минимизацией длины разности $|Xa - y|$ (то есть точностью решения задачи регрессии) и тем, чтобы компоненты вектора $a$ не становились слишком большими по модулю.\n",
|
||
"\n",
|
||
"---\n",
|
||
"\n",
|
||
"**Ваше решение напишите прямо здесь**"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Задание 4. Онлайн-обучение линейной регрессии (дополнительное задание по желанию)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Раньше мы работали в ситуации, когда объекты $x_i$ и значения $y_i$ даны с самого начала и всегда доступны. Допустим теперь, что пары $(x_i, y_i)$ поступают к нам по одной, и мы не можем себе позволить хранить их все в памяти (это может быть актуально, например, если вы пытаетесь обучить модель на устройстве со сравнительно небольшим количеством оперативной памяти: скажем, на мобильном телефоне или на бортовом компьютере спутника связи). В этом случае нам нужно уметь решать следующую задачу:\n",
|
||
"\n",
|
||
"**Известно:** решение задачи регрессии для датасета $(x_1, y_1),\\ldots,(x_t,y_t)$;\n",
|
||
"\n",
|
||
"**На вход поступает:** новая пара $(x_{t+1}, y_{t+1})$;\n",
|
||
"\n",
|
||
"**Требуется:** быстро (за время, не зависящее от $t$) отыскать решение задачи регрессии для расширенного датасета $(x_1, y_1),\\ldots,(x_t,y_t),(x_{t+1}, y_{t+1})$."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Эту задачу мы будем решать в два этапа.\n",
|
||
"\n",
|
||
"**Этап 1.** Обозначим $X_{(t)} = (x_1\\ldots x_t)$ и $y_{(t)} = (y_1,\\ldots,y_t)^T$. Тогда, как мы хорошо помним, решение задачи регрессии для датасета $(x_1, y_1),\\ldots,(x_t,y_t)$ имеет вид $\\hat{a}_{(t)} = \\left(X^T_{(t)}X_{(t)}\\right)^{-1}X^T_{(t)}y_{(t)}$. Размеры матриц $X^T_{(t)}X_{(t)}$ и $X^T_{(t)}y_{(t)}$ не зависят от $t$, поэтому их мы, пожалуй, можем себе позволить хранить в памяти.\n",
|
||
"\n",
|
||
"И вот ваше первое задание в этом разделе: придумайте алгоритм, принимающий на вход матрицы $X^T_{(t)}X_{(t)}$ и $X^T_{(t)}y_{(t)}$, а также пару $(x_{t+1}, y_{t+1})$ и вычисляющий матрицы $X^T_{(t+1)}X_{(t+1)}$ и $X^T_{(t+1)}y_{(t+1)}$. Сложность вашего алгоритма не должна зависеть от $t$!\n",
|
||
"\n",
|
||
"--\n",
|
||
"\n",
|
||
"**Описание вашего алгоритма напишите прямо здесь**"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"**Этап 2.** Итак, мы научились пересчитывать регрессионные коэффициенты за время, не зависящее от размеров датасета. Это уже, в общем-то большая победа, но нам этого мало! Нам по-прежнему приходится каждый раз обращать матрицу $X^T_{(t)}X_{(t)}$. Если у каждого объекта $x_i$ имеется $m$ признаков, то на это требуется $O(m^3)$ операций - чертовски много! Кажется, что можно это делать гораздо быстрее.\n",
|
||
"\n",
|
||
"Попробуйте придумать алгоритм, который позволял бы пересчитывать $\\hat{a}$ за $O(m^2)$ операций. В этом вам может помочь QR-разложение (см. добавление в самом конце лабораторной). Возможно, вы также решите, что вместо матриц $X^T_{(t)}X_{(t)}$ и $X^T_{(t)}y_{(t)}$ стоит хранить что-то другое.\n",
|
||
"\n",
|
||
"--\n",
|
||
"\n",
|
||
"**Описание вашего алгоритма напишите прямо здесь**"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Теперь настало время написать немного кода и порисовать красивые картинки. Вам нужно будет реализовать симуляцию онлайн-обучения регрессии для задачи приближения функции (в данном случае $f_{true}(x) = 2x\\sin(x) + x^2 - 1$; все значения искажены небольшим нормальным шумом) многочленом степени не выше 5.\n",
|
||
"\n",
|
||
"**Замечание** Если у вас не получилось придумать алгоритм в предыдущем пункте, вы можете просто найти библиотечную функцию, которая делает то, что вам надо (правда, за это вы получите несколько меньше баллов) или даже плюнуть на всё и использовать алгоритм, требующий $O(m^3)$ операций на каждой итерации (но баллов будет ещё меньше). "
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"from IPython.display import clear_output\n",
|
||
"\n",
|
||
"f_true = lambda x: 2*x*np.sin(5*x) + x**2 - 1 # this is the true function\n",
|
||
"\n",
|
||
"# We need this to make the plot of f_true:\n",
|
||
"x_grid = np.linspace(-2,5,100) # 100 linearly spaced numbers\n",
|
||
"x_grid_enl = np.hstack((x_grid.reshape((100,1))**j for j in range(6)))\n",
|
||
"y_grid = f_true(x_grid)\n",
|
||
"\n",
|
||
"\n",
|
||
"for i in range(200):\n",
|
||
"\n",
|
||
" x_new = np.random.uniform(-2, 5)\n",
|
||
" y_new = f_true(x_new) + 2*np.random.randn()\n",
|
||
" \n",
|
||
" # your code goes here\n",
|
||
" \n",
|
||
" # the rest of code is just bells and whistles\n",
|
||
" if (i+1)%5==0:\n",
|
||
" clear_output(True)\n",
|
||
" plt.plot(x_grid,y_grid, color='blue', label='true f')\n",
|
||
" plt.scatter(x_new, y_new, color='red')\n",
|
||
" \n",
|
||
" # your code goes here\n",
|
||
" y_pred = #...\n",
|
||
" \n",
|
||
" plt.scatter(x_grid, y_pred, color='orange', linewidth=5, label='predicted f')\n",
|
||
" \n",
|
||
" plt.legend(loc='upper left')\n",
|
||
" plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Добавление. QR-разложение"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"**QR-разложением** матрицы $A$ (не обязательно квадратной) мы будем называть её представление в виде $A = QR$, где $Q$ - матрица с ортонормированными столбцами, а $R$ - верхнетреугольная матрица.\n",
|
||
"\n",
|
||
"Смысл QR-разложения следующий. Пусть $a_1,\\ldots,a_m$ - столбцы матрицы $A$, $q_1,\\ldots,q_t$ - столбцы матрицы $Q$. Тогда $q_1,\\ldots,q_t$ - это ортонормированный базис в подпространстве, являющемся линейной оболочкой векторов $a_1,\\ldots,a_m$, а в матрице $R$ записаны коэффициенты, с помощью которых $a_i$ выражаются через $q_1,\\ldots,q_t$.\n",
|
||
"\n",
|
||
"Находить QR-разложение заданной матрицы можно разными способами. Мы познакомим вас не с самым лучшим из них, но по крайней мере с наиболее простым концептуально. Заметим, что ортогональный базис линейной оболочки можно найти с помощью ортогонализации Грама-Шмидта. При этом коэффициенты из матрицы $R$ получаются в качестве побочного продукта этого процесса:\n",
|
||
"\n",
|
||
"```python\n",
|
||
"for j = 1...n:\n",
|
||
" q_j = a_j\n",
|
||
" for i = 1,...,j-1:\n",
|
||
" r_ij = (q_i, a_j)\n",
|
||
" q_j = q_j - r_ij * q_i\n",
|
||
" r_jj = |q_j|\n",
|
||
" if r_jj == 0: # a_j in <a_1,...,a_j-1>\n",
|
||
" # What would you do in this case?..\n",
|
||
" q_j = q_j / r_jj\n",
|
||
"```\n",
|
||
"\n",
|
||
"Для нахождения QR-разложения вы можете использовать библиотечную функцию `scipy.linalg.qr`."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Поскольку лабораторная про линейную регрессию, не так-то просто замять вопрос о том, какое же отношение QR-разложение имеет к задаче регрессии. Упомянем одно из возможных применений.\n",
|
||
"\n",
|
||
"Допустим, мы нашли QR-разложение матрицы $X$, а именно: $X = QR$. Тогда\n",
|
||
"$$X^TX = (QR)^T(QR) = R^TQ^TQR = R^TR$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Поскольку в задаче регрессии матрица $X$ обычного полного ранга (то есть её столбцы линейно независимы), матрица $R$ будет квадратной. Благодаря этому нашу обычную формулу для набора регрессионных коэффициентов $\\hat{a}$ можно переписать в следующем виде:\n",
|
||
"\n",
|
||
"$$\\hat{a} = (X^TX)^{-1}X^Ty = (R^TR)^{-1}(QR)^Ty = R^{-1}(R^T)^{-1}R^TQ^Ty = R^{-1}Q^Ty$$\n",
|
||
"\n",
|
||
"Как видите, формула стала проще. Более того, зачастую обращение матрицы $R$ может быть численно более устойчиво, чем обращение матрицы $X^TX$."
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "Python 3 (ipykernel)",
|
||
"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": "3.12.4"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 4
|
||
}
|