From ba6f80d2728834948a52e133c65884d7ae3a3b81 Mon Sep 17 00:00:00 2001 From: Elvira Zinnurova Date: Sun, 3 Jun 2018 22:39:58 +0300 Subject: [PATCH] Bonus practice homework on glm --- .../homework-practice-06/data.csv | 50965 ++++++++++++++++ .../homework-practice-06.ipynb | 768 + 2 files changed, 51733 insertions(+) create mode 100644 2017-spring/homeworks-practice/homework-practice-06/data.csv create mode 100644 2017-spring/homeworks-practice/homework-practice-06/homework-practice-06.ipynb diff --git a/2017-spring/homeworks-practice/homework-practice-06/data.csv b/2017-spring/homeworks-practice/homework-practice-06/data.csv new file mode 100644 index 00000000..efede4da --- /dev/null +++ b/2017-spring/homeworks-practice/homework-practice-06/data.csv @@ -0,0 +1,50965 @@ +Id,Hazard,T1_V1,T1_V2,T1_V3,T1_V4,T1_V5,T1_V6,T1_V7,T1_V8,T1_V9,T1_V10,T1_V11,T1_V12,T1_V13,T1_V14,T1_V15,T1_V16,T1_V17,T2_V1,T2_V2,T2_V3,T2_V4,T2_V5,T2_V6,T2_V7,T2_V8,T2_V9,T2_V10,T2_V11,T2_V12,T2_V13,T2_V14,T2_V15 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+101994,3,18,7,5,W,B,Y,B,B,D,8,B,B,20,2,A,D,N,33,13,N,3,A,2,28,1,1,2,N,N,E,1,1 +101998,14,18,17,5,B,A,N,B,D,D,8,B,B,10,1,A,I,N,35,11,N,18,A,1,40,1,7,4,Y,N,C,2,6 +101999,9,5,15,3,B,I,Y,B,B,E,8,H,B,15,3,A,R,N,49,10,N,6,A,2,40,1,16,1,Y,N,E,5,4 diff --git a/2017-spring/homeworks-practice/homework-practice-06/homework-practice-06.ipynb b/2017-spring/homeworks-practice/homework-practice-06/homework-practice-06.ipynb new file mode 100644 index 00000000..c75e00d9 --- /dev/null +++ b/2017-spring/homeworks-practice/homework-practice-06/homework-practice-06.ipynb @@ -0,0 +1,768 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "run_control": { + "frozen": false, + "read_only": false + } + }, + "source": [ + "# Машинное обучение, ФКН ВШЭ\n", + "\n", + "## Практическое задание 6\n", + "\n", + "### Общая информация\n", + "Дата выдачи: 4 июня 2018\n", + "\n", + "Жёсткий дедлайн: 23:59MSK 14 июня" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### О задании\n", + "\n", + "Мы будем решать задачу предсказания опасных событий для страховой компании: [Liberty Mutual Group: Property Inspection Prediction](https://www.kaggle.com/c/liberty-mutual-group-property-inspection-prediction). Обучающая выборка состоит из засекреченных признаков целого и строкового типов. Целевой переменной являются счётчики $y \\in \\mathbb{Z}_+$.\n", + "\n", + "Работа состоит из следующих пунктов:\n", + "* Предобработать данные [1 балл]\n", + "* Написать свой алгоритм прогнозирования событий [2 балла]\n", + "* Настроить линейные методы из библиотеки StatsModels для решения задачи [1 балл]\n", + "* Настроить бустинг из библиотеки lightgbm для решения задачи [1 балл]\n", + "\n", + "Задания является дополнительным, то есть само по себе не учитывается в накопленной оценке. Все полученные за задание баллы являются бонусными, то есть их можно прибавить к оценке за любое теоретическое или практическое домашнее задание из курса.\n", + "\n", + "\n", + "### Оценивание и штрафы\n", + "Каждая из задач имеет определенную «стоимость» (указана в скобках около задачи). Максимально допустимая оценка за работу — 5 баллов.\n", + "\n", + "Сдавать задание после указанного срока сдачи нельзя. При выставлении неполного балла за задание в связи с наличием ошибок на усмотрение проверяющего предусмотрена возможность исправить работу на указанных в ответном письме условиях.\n", + "\n", + "Задание выполняется самостоятельно. «Похожие» решения считаются плагиатом и все задействованные студенты (в том числе те, у кого списали) не могут получить за него больше 0 баллов (подробнее о плагиате см. на странице курса). Если вы нашли решение какого-то из заданий (или его часть) в открытом источнике, необходимо указать ссылку на этот источник в отдельном блоке в конце вашей работы (скорее всего вы будете не единственным, кто это нашел, поэтому чтобы исключить подозрение в плагиате, необходима ссылка на источник).\n", + "\n", + "Неэффективная реализация кода может негативно отразиться на оценке.\n", + "\n", + "\n", + "### Формат сдачи\n", + "Для сдачи задания переименуйте получившийся файл *.ipynb в соответствии со следующим форматом: homework-practice-06-Username.ipynb, где Username — ваша фамилия и имя на латинице именно в таком порядке (например, homework-practice-06-IvanovIvan.ipynb). \n", + "\n", + "Далее отправьте этот файл в AnyTask.\n", + "\n", + "Для удобства проверки самостоятельно посчитайте свою максимальную оценку (исходя из набора решенных задач) и укажите ниже." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "** Оценка:** ..." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "import statsmodels.api as sm\n", + "\n", + "from scipy.optimize import minimize\n", + "from lightgbm import LGBMModel\n", + "from sklearn.linear_model import LinearRegression\n", + "from sklearn.preprocessing import OneHotEncoder, LabelEncoder\n", + "from sklearn.model_selection import train_test_split\n", + "\n", + "pd.set_option('max_rows', 10)\n", + "pd.set_option('max_columns', None)\n", + "plt.style.use('bmh')\n", + "\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": { + "frozen": false, + "read_only": false + } + }, + "source": [ + "__Задание 1 (1 балл).__ Загрузка и предобработка данных." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "data = pd.read_csv('data.csv', index_col='Id')\n", + "data.head()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "data.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": { + "frozen": false, + "read_only": false + } + }, + "source": [ + "Выделим категориальные и числовые признаки:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + }, + "scrolled": true + }, + "outputs": [], + "source": [ + "categorical, numerical = list(), list()\n", + "for col in data.columns[1:]:\n", + " if isinstance(data.loc[1, col], str):\n", + " categorical.append(col)\n", + " if isinstance(data.loc[1, col], np.int64):\n", + " numerical.append(col)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "data[categorical].nunique().values" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "data[numerical].nunique().values" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": { + "frozen": false, + "read_only": false + } + }, + "source": [ + "Нарисуем априорное распределение ответов $p(y)$:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "data['Hazard'].plot(kind='hist', figsize=(10, 4), bins=40, normed=True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": { + "frozen": false, + "read_only": false + } + }, + "source": [ + "В обобщённых линейных моделях, как и в машинном обучении в целом, мы проводим основную работу с апостериорным распределением $p(y|x)$, ведь именно в нём заключается информация о конкретной задаче. Здесь же мы знаем, что количество несчастных случаев во многом подчиняется распределению Пуассона, поэтому будем стараться моделировать именно его." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "В выборке могут присутствовать шумовые признаки. Попробуем простейшим способом избавиться от них.\n", + "\n", + "Исследуйте абсолютное значение корреляции:\n", + "* Признаков и отклика\n", + "* Признаков и логарифма отклика" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "corrs = [data[col].corr(data['Hazard']) for col in numerical]\n", + "corrs = pd.DataFrame(np.abs(corrs), numerical, \n", + " ['abs corr with target']).sort_values('abs corr with target')\n", + "corrs.plot(kind='bar', figsize=(10, 4))\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "# corr with log(target)\n", + "# place your code here" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": { + "frozen": false, + "read_only": false + } + }, + "source": [ + "Уберите несколько наиболее неинформативных признаков. Лучше сделать это число гиперпараметром и потом настраивать его по функционалу качества. Может быть разумно также исследовать взаимосвязь признаков с логарифмом целевой переменной, поскольку мы предполагаем, что она неотрицательна и имеет распределение Пуассона." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "# place your code here" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": { + "frozen": false, + "read_only": false + } + }, + "source": [ + "Закодируем значения категориальных признаков в числа:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "label_encoder = LabelEncoder()\n", + "data[categorical] = data[categorical].apply(label_encoder.fit_transform)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": { + "frozen": false, + "read_only": false + } + }, + "source": [ + "Выделим столбец целевой переменной из наших данных. Множество значений случайной величины с распределением Пуассона начинается с нуля $\\{0, 1, 2...\\}$, поэтому вычтем единицу из целевой переменной. На самом деле, помимо прочего это приводит к существенному росту качества на валидации." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "objects = data.loc[:, 'T1_V1':]\n", + "labels = data['Hazard'] - 1" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": { + "frozen": false, + "read_only": false + } + }, + "source": [ + "Сделаем бинарное кодирование категориальных признаков:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "mask = objects.columns.isin(categorical)\n", + "onehot_encoder = OneHotEncoder(categorical_features=mask, sparse=False)\n", + "objects_encoded = onehot_encoder.fit_transform(objects)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": { + "frozen": false, + "read_only": false + } + }, + "source": [ + "Разделим выборку на обучающую и тестовую:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "train_objects, test_objects, train_labels, test_labels = train_test_split(\n", + " objects_encoded, labels.as_matrix(), random_state=1, test_size=0.2, stratify=labels\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": { + "frozen": false, + "read_only": false + } + }, + "source": [ + "__Задание 2 (2 балла).__ Обучение регрессии с распределением Пуассона.\n", + "\n", + "Будем считать, что апостериорное распределение — это распределение Пуассона:\n", + "\n", + "$$p(y|\\lambda(x)) = \\frac{e^{-\\lambda(x)}\\lambda(x)^y}{y!}.$$\n", + "\n", + "Реализуйте функции для вычисления функционала качества (через метод максимального правдоподобия) и его градиентов — они были выведены на [семинаре](https://github.com/esokolov/ml-course-hse/blob/master/2017-spring/seminars/sem22-glm.pdf).\n", + "\n", + "Численные алгоритмы должны работать по возможности быстро, поэтому циклов быть не должно, и все операции должны быть векторными. Дальше мы будем использовать эту функцию в качестве аргумента другой функции. Можете попробовать добавить в модель регуляризатор." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "def oracle(w, X, y):\n", + " \"\"\"\n", + " :param w: weights\n", + " :param X: features\n", + " :param y: target\n", + " :yield: loss, grad\n", + " \"\"\"\n", + " \n", + " # place your code here\n", + " return loss, grad" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": { + "frozen": false, + "read_only": false + } + }, + "source": [ + "Добавьте к признакам столбец единиц, чтобы учесть вектор сдвига. Это важно. Библиотечные алгоритмы уже учитывают это внутри себя, поэтому им на вход нужно подавать исходную выборку." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "train_objects_bias = None\n", + "test_objects_bias = None" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": { + "frozen": false, + "read_only": false + } + }, + "source": [ + "Дальше воспользуйтесь функцией _scipy.optimize.minimize_, в ней реализовано множество градиентных методов оптимизации. Рекомендуется взять [L-BFGS-B](http://www.machinelearning.ru/wiki/images/6/65/MOMO17_Seminar6.pdf). Начальное приближение весов $w^{(0)}$ возьмите из стандартного нормального распределения как _np.random.randn_. Возможно, придётся запустить функцию несколько раз, прежде чем начальное приближение окажется удачным, и алгоритм покажет хороший результат. \n", + "\n", + "Сделайте прогноз для тестовых объектов. В качестве прогноза мы будем брать матожидание распределения $p(y | \\lambda(x))$ в данной точке, поэтому не забудьте взять экспоненту от выхода линейной модели, предсказывающей значение натурального параметра. Измерьте качество с помощью коэффициента Джини (чем выше – тем лучше) — именно он является целевой метрикой в соревновании." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def gini(y_true, y_pred):\n", + " # check and get number of samples\n", + " assert y_true.shape == y_pred.shape\n", + " n_samples = y_true.shape[0]\n", + " \n", + " # sort rows on prediction column \n", + " # (from largest to smallest)\n", + " arr = np.array([y_true, y_pred]).transpose()\n", + " true_order = arr[arr[:,0].argsort()][::-1,0]\n", + " pred_order = arr[arr[:,1].argsort()][::-1,0]\n", + " \n", + " # get Lorenz curves\n", + " L_true = np.cumsum(true_order) / np.sum(true_order)\n", + " L_pred = np.cumsum(pred_order) / np.sum(pred_order)\n", + " L_ones = np.linspace(1/n_samples, 1, n_samples)\n", + " \n", + " # get Gini coefficients (area between curves)\n", + " G_true = np.sum(L_ones - L_true)\n", + " G_pred = np.sum(L_ones - L_pred)\n", + " \n", + " # normalize to true Gini coefficient\n", + " return G_pred/G_true" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "# place your code here\n", + "poisson_results = minimize(oracle, None, args=(None, None), method=None, jac=True) #change parameters\n", + "pred_labels = None # w = poisson_results.x\n", + "gini(test_labels, pred_labels)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": { + "frozen": false, + "read_only": false + } + }, + "source": [ + "__Задание 3 (1 балл).__ Линейные модели из коробки.\n", + "\n", + "Запустите базовую линейную регрессию *sklearn.linear_model.LinearRegression* для предсказания логарифма целевой переменной и измерьте качество. Сравните полученный результат с работой вашего алгоритма." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "# place your code here" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": { + "frozen": false, + "read_only": false + } + }, + "source": [ + "Познакомимся теперь с библиотекой [StatsModels](http://www.statsmodels.org/dev/index.html). Она предназначена скорее для описательной статистики, проверки гипотез и построения доверительных интервалов, чем для прогнозирования, — в отличие от scikit-learn, который создан специально для решения задач машинного обучения. В то же время в StatsModels реализован очень сильный алгоритм прогнозирования временных рядов – [SARIMAX](http://www.statsmodels.org/dev/generated/statsmodels.tsa.statespace.sarimax.SARIMAX.html), который при правильной настройке работает очень хорошо и занимает первые места в конкурсах ([Запись трансляции ML тренировки 03.02.18 | TrainMyData Ascott](https://www.youtube.com/watch?v=9MQEEyYDCQc&t=1101s)). \n", + "\n", + "Мы же попробуем обучить обобщённые линейные модели (модуль [GLM](http://www.statsmodels.org/dev/glm.html)) с различными вероятностными распределениями. Запустите алгоритм _sm.GLM_ на нескольких распределениях family, посмотрите на качество и проинтерпретируйте результаты. Синтаксис StatsModels немного отличается от scikit-learn тем, что здесь объекты и метки задаются в конструкторе модели, метод _fit()_ идёт без аргументов, и после обучения сохраняется новая модель с результатами и методом _predict_." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__Gaussian__" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "#place your code here\n", + "gaussian_sm_model = None\n", + "gaussian_sm_results = None\n", + "pred_labels = gaussian_sm_results.predict(test_objects)\n", + "gini(test_labels, pred_labels)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__Poisson__" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "# place your code here" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__NegativeBinomial (Pascal)__" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "# place your code here" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "run_control": { + "frozen": false, + "read_only": false + } + }, + "source": [ + "Как видно, качество в последнем случае получилось лучше. На практике чаще используют именно отрицательное Биномиальное распределение. Оно является обобщением геометрического распределения и даёт некоторую свободу в выборе среднего и дисперсии для $p(y|x)$, тогда как в распределении Пуассона среднее и дисперсия совпадают. Если вам будет интересно, можете прочитать подробнее на вики [NegativeBinomial](https://en.m.wikipedia.org/wiki/Negative_binomial_distribution)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__Задание 4. (1 балл)__ Прогнозирование с помощью бустинга." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Что бы мы ни делали, бустинг по-прежнему остаётся лучшим подходом для широкого круга задач — особенно если мы не работаем со структурированными данными вроде последовательностей или картинок. Бустинг хоть и сложный по своей структуре алгоритм, но вероятностные распределения не чужды и ему. Запустите _LGBMModel_, используя классическую регрессию и регрессию Пуассона. Настройте параметры, чтобы добиться наилучшего качества. В особенности обратите внимание на *objective*, *n_estimators*, *num_leaves* и *colsample_bytree*." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "# objective='regression'" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true, + "run_control": { + "frozen": false, + "read_only": false + } + }, + "outputs": [], + "source": [ + "# objective='poisson'" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "hide_input": false, + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + }, + "widgets": { + "state": {}, + "version": "1.1.2" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +}