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@ferrine
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"# PyMC3 - МСМС и не только\n",
"\n",
"Привет, Хабрахабр!\n",
"\n",
"В [этом](https://habrahabr.ru/company/wunderfund/blog/279545/) посте уже упомянался PyMC3. Там можно почитать про основы MCMC-сэмплирования. Здесь я расскажу про то, зачем все это нужно и чем это может быть полезно на довольно простых примерах из галлереи PyMC3. Одним из таких примеров будет байесовская нейронная сеть для задачи классификации, но это в самом конце. Кому интересно - добро пожаловать!"
]
},
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"source": [
"# Введение\n",
"Прежде чем переходить к основной части, считаю необходимым освежить терминологию байесовского анализа. То, чем занимается этот подраздел теории вероятности - вывод апостериорного распределения. Задача выглядит следующим образом:\n",
"Аналитик хочет что-то узнать о ненаблюдаемых параметрах модели $z$ и у него есть некие соображения на счет того, какими они могут быть $p(z)$. Кроме того, он может судить о том, как хорошо его данные $D$ ложатся в модель с параметрами $z$. Выражается это через правдоподобие $p(D|z)$, вероятность наблюдать данные при заданных параметрах.\n",
"$$\\large p(z|D) = \\frac{p(z, D)}{p(D)} = \\frac{p(D|z)p(z)}{p(D)}$$\n",
"Где \n",
" * $p(z)$ - априорное распределение, предположения насчет предполагаемых результатов.\n",
" Когда подходишь к решению задачи, очень часто есть представление о том явлении, который исследуется. \n",
" * Например возьмем область физики. Там есть законы и механизмы взаимодействия, о них мы имеем хорошее представление за исключением некоторых величин, как например коэффициент трения какого-то вещества с поверхностью. Мы примерно предполагаем, какой он должен быть на основе прошлого опыта и накопленных знаний. Хотя бы то, что он больше нуля. Мы можем построить эксперимент, составив физическую модель с неизвестным параметром, который хочется оценить.\n",
" * **Важное замечание:** Иногда возникает соблазн подстраивать априорное распределение под наблюдаемые данные. Скажем, например, что мы прикинули на даннных, что искомый $z$ где-то около $3$ и начинаем выводить апостериорное. Постойте, но когда вы, например, доказываете теорему, вы же не пользуетесь ее результатами для ее же доказательства? Так же и здесь, априорное распределение не должно опираться на *изучаемый* набор данных.\n",
"\n",
" * $p(D|z)$ - правдоподобие, оценка адекватности предполагаетмого $z$. Выражается в вероятности наблюдать данные при условии выбранной гипотезы на $z$. \n",
" * У нас есть результаты эксперимента, для каждого набора параметров мы можем оценивать \"как хорошо модель описывает мир\". Эту идею используют классические статистики при MLE оценке.\n",
" * $p(z|D)$ - апостериорное распределение, выводы, которые мы хотим получить. \n",
" * По сути это те представления о неизвестных параметрах модели (коэф. трения), которые сложились у нас в ходе проведения эксперимента. Можно считать это компромисом между старыми знаниями и новыми, выраженными через $p(z)$ и $p(D|z)$ соответственно.\n",
" * $p(D)$ - Evidence, вероятность получить такие данные вообще, на русский переводится скверно.\n",
" \n",
"\n",
"# Байесовский вывод\n",
"На первый взгляд ничего особенного: у нас есть формулы плотностей $p(D|z)$, $p(z)$, искомая плотность выглядит следующим образом: \n",
"$$\\large p(z|D) = \\frac{p(D|z)p(z)}{p(D)} = \\frac{p(D|z)p(z)}{\\int p(D|z)p(z) dz}$$\n",
"\n",
"Перемножить две плотности не проблема. Посчитать интеграл снизу, хм, ну можно вспомнить университетский курс матанализа... В общем берем, подставляем все в формулу и готово. Вооружившись этим знанием можно смело отправляться исследовать простые модели с простыми распределениями. Однако в более менее приближенных к жизни примерах, даже такое знание не спасет и взять интеграл аналитически бывает не под силу."
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"source": [
"# Зачем все это?\n",
"Ну раз мы не можем вывести распределение $p(z|D)$, почему бы не ограничиться тогда просто точечной оценкой, скажем, где плотность распределения максимальна? Ну или в крайнем случае, даже этого не делать и искать максимум $p(D|z)$, мы же как никак хотим построить модель, которая объясняет наши данные. Первый подход называется __MAP__ (maximum a posterior) оценкой $z^{map} = argmax_z p(z|D) $, а второй __ML__ (maximum likelihood) $z^{ml} = argmax_z p(D|z)$. Второй способ почти каждый студент технического вуза проходил в курсе теории вероятности. \n",
"\n",
"У ML оценки есть ряд недостатков. Самый интуитивно понятный из них это тот, что даже сложная модель может казаться привлекательной с точки зрения этого критерия. Ведь чем больше вероятность, тем лучше, но с увеличением параметров модель может просто повторять даннные. Этот факт вводит в заблуждение и заставляет обосновывать, почему модель адекватная. С точки зрения байесовского вывода можно предствить себе ML оценку, как MAP с $p(z) = Uniform[-\\infty, \\infty]$. Да, интеграл не берется, но у нас точечная оценка и нам это не помешает, считаем плотность $p(z)$ постоянной. \n",
"\n",
"__Доказательство__\n",
"$$\\large p(z|D) = \\frac{p(z, D)}{p(D)} = \\frac{p(D|z)p(z)}{p(D)} \\rightarrow max$$\n",
"\n",
"$$\\large \\log p(z|D) = \\log \\frac{p(z, D)}{p(D)} = \\log \\frac{p(D|z)p(z)}{p(D)} \\rightarrow max$$\n",
"\n",
"$$\\large \\sim \\log {p(D|z)p(z)} - \\log{p(D)} \\rightarrow max$$\n",
"\n",
"$$\\large \\sim \\log {p(D|z)} + \\log{p(z)} \\rightarrow max$$\n",
"\n",
"$$\\large \\sim \\log {p(D|z)} \\rightarrow max$$\n",
"\n",
"Такого рода априорные распределения называются __Improper Priors__, а конкретно это еще и __Uninformative__ (неинформативное).\n",
"Иными словами, мы не имеем представления о том, каким должно быть $z$ на самом деле. Теряется возможность использовать всю доступную информацию. К примеру:\n",
" \n",
" 1. Для какой-то задачи из теории достоверно известно, что $z$ строго больше нуля. Это можно исправить преобразованием, но если поменять постановку на *\"скорее больше, чем меньше нуля\"*, то ML это не сможет учесть. \n",
" 2. Для случая линейной регрессии, когда регрессоров большое количество и есть вера в то, что не все они важны. Тогда в векторе $z$ (коэффициенты) много нулевых компонент. \n",
"\n",
"Стандартный подход хорош его простотой реализации и изученными асимптотическими свойствами, но MAP более осмысленен в ряде ситуаций."
]
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"source": [
"# Импорт всего необходимого\n",
"from theano import theano, tensor as tt\n",
"import pymc3 as pm\n",
"import pandas as pd\n",
"from sklearn import datasets\n",
"import numpy as np\n",
"from numpy import random\n",
"import pylab as plt\n",
"import seaborn as sns\n",
"import warnings\n",
"import scipy.stats as stats\n",
"warnings.filterwarnings('ignore')\n",
"%matplotlib inline\n",
"plt.mpl.style.use('ggplot')"
]
},
{
"cell_type": "markdown",
"metadata": {
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"source": [
"# Пример с монеткой\n",
"Давайте посмотрим, что происходит с апостериорным распределением, когда мы получаем новые наблюдения. Это очень похоже на изменение уверенности в самом обычном ее понимании. Сначала мы ничего не знаем, но когда получаем примеры, наше представление о ненаблюдаемых факторах меняется. Для наглядной репрезентации я буду использовать честный вывод апостериорного распределения.\n",
"\n",
"Имея prior $Uniform[0, 1]$(равносильно $Beta[\\alpha=1, \\beta=1]$) для вероятности получить \"орла\" $r$ и имея наблюдения \"орел\" $t$ и \"решка\" $f$, всего $N$ наблюдений, получим апостериорное распределение на вероятность $Beta[\\alpha=t+1, \\beta=f+1]$.\n",
"\n",
"$$\\large p(r|T=t, F=f) = \\frac{p(T=t, F=f|r)p(r)}{\\int p(T=t, F=f|r)p(r)dr}$$\n",
"\n",
"$$\\large = \\frac{C_N^k r^t(1-r)^f}{\\int_0^1 C_N^k r^t(1-r)^fdf}= \\frac{r^t(1-r)^f}{B(t+1, f+1)}$$\n",
"\n",
"$$\\large = Beta(r\\;|\\alpha=t+1, \\beta=f+1)$$"
]
},
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"source": [
"Для наглядной иллюстрации потребуется несколько вспомогательных функции и синтетические данные"
]
},
{
"cell_type": "code",
"execution_count": 2,
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{
"data": {
"text/plain": [
"array([[0, 1],\n",
" [0, 2],\n",
" [0, 3],\n",
" [0, 4],\n",
" [1, 4],\n",
" [2, 4]])"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# первая составляет нужное распределение\n",
"def posterior(t, f):\n",
" \"\"\"\n",
" t : орел\n",
" f : решка\n",
" \"\"\"\n",
" return stats.beta(a=t+1, b=f+1)\n",
"\n",
"# вторая рисует график плотности\n",
"def plot_pdf(dist, ax, c):\n",
" space = np.linspace(0, 1)\n",
" pdf = dist.pdf(space)\n",
" ax.plot(space, pdf, c=c, alpha=.5)\n",
" return ax\n",
"# Данные\n",
"true_p = .3 # Истинная вероятность получить \"Орла\"\n",
"random.seed(42) # для воспроизводимости данных\n",
"trials = np.random.uniform(size=100) < true_p # Бинарная переменная, где 1 это орел\n",
"# Составляем пары [t, f]\n",
"observed = np.array(list(zip(np.cumsum(trials), np.arange(1, trials.size+1) - np.cumsum(trials))))\n",
"observed[:6]"
]
},
{
"cell_type": "code",
"execution_count": 3,
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{
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CCCG2kSGIQogvnxTEX0tAoDCVGhUp9EqFqfTQWxX1V9ThCt3O9w3Bn+cT+zCG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RY/Rqzd6+9PHzrE6n24N3xYD0Y9FGCzul9/CT/p+9oR4Y/zLhMxfL2d8mS4/8TX7bmut23G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\n3H333YfV1MwxxXtPs9nc9bHjts6/o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"text/plain": [
"<matplotlib.figure.Figure at 0x7f76bd6e5f60>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(15, 5))\n",
"cmap = plt.get_cmap('cool')\n",
"plot_pdf(posterior(0, 0), ax, cmap(0))\n",
"for (t, f), c in zip(observed, np.linspace(0, 1, num=observed.shape[0])):\n",
" plot_pdf(posterior(t, f), ax, cmap(c))\n",
"plt.title('Эволюция апостериорного распределения вероятности выпадения орла')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Чем больше примеров мы видим, тем более узким становится апостериорное распределение, это проявление уверенности в новых знаниях. Что более интересно, так это поведение распределения при малом количестве наблюдений: оно адекватно отражает неуверенность. Этого не происходит, если пользоваться методами классической статистики и искать MLE оценку. Мы бы получали вероятность 0 для орла при малом количестве наблюдений, что, конечно, не так."
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"# Мотивация"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"**PyMC3** позволяет выводить апостериорное распределение без непосредственного вывода формул. Это делает возможным байесовский вероятностный вывод практически на любых адекватных моделях. Более того, с его помощью можно строить вероятностные нейронные сети, в которых вместо параметров распределения и предсказания тоже являются распределениями.\n",
"![](https://ai2-s2-public.s3.amazonaws.com/figures/2016-11-08/da6057368920585bcf2443295b98418840f1fc80/1-Figure1-1.png)"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"source": [
"# Начало работы с PyMC3\n",
"Библиотека *PyMC3* написана поверх *[Theano](http://deeplearning.net/software/theano/)* и поэтому может быть использована вместе с ней. *Theano* - библиотека для тензорной алгебры и широко используется для глубокого обучения. Она поддерживает символьные операции и дифференцирование, что и делает возможным не только обучать нейросети с помощью *backprop*, но и производить приближенный вариационный баесовский вывод. \n",
"\n",
"Работа с *PyMC3* по большей части напоминает работу с *Theano*, в одном из наших предыдущих [постов](https://habrahabr.ru/company/ods/blog/323272/) про нее хорошо написано.\n",
"\n",
"Базовой частью библиотеки является модель(`pm.Model`), она позволяет на лету составлять апостериорную плотность (точнее ее неотнормированную часть). Для того, чтобы это работало с приятным интерфейсом, применена небольшая магия с контекстным менеджером. Случайные переменные в *PyMC3* объявляются внутри контекста `with model: ...`.\n",
"\n",
"Сами случайные переменные являются переменными в смысле `Theano`, для них верно все то, что верно для обычных тензоров в `Theano`. Это полезно помнить, чтобы не бояться экспериментировать и строить более сложные модели."
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Будем строить модель последовательно, чтобы на наглядном примере показать, что методы MCMC с увеличением сложности модели могут ухудшать свой результат, ну или, по крайней мере, становиться непозволительно медленными.\n",
"\n",
"Сэмплировать можно с помощью вспомогательной функции `pm.sample`, она хорошо работает на настройках по умолчанию, но в целях демонстрации они изменены. По умолчанию для MCMC метода заранее подбираются подходящие параметры, что сейчас как раз не нужно."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING (theano.tensor.blas): We did not found a dynamic library into the library_dir of the library we use for blas. If you use ATLAS, make sure to compile it with dynamics library.\n",
"100%|██████████| 1000/1000 [00:00<00:00, 1368.27it/s]\n"
]
}
],
"source": [
"# выше сделан import pymc3 as pm\n",
"\n",
"with pm.Model() as simple_model:\n",
" # По соглашению все случайные переменные должны иметь уникальные имена\n",
" # Параметры распределения надо передавать после строкового имени\n",
" norm = pm.Normal('norm', 0, 1)\n",
" \n",
" # не подбирать параметры для MCMC метода NUTS\n",
" step = pm.NUTS()\n",
" trace = pm.sample(1000, step=step)\n",
" # Обратите внимание на количество итераций в секунду: оно будет уменьшаться по мере усложнения модели"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"## Trace Plot\n",
"Для визуализации результатов есть замечательные утилиты. Например, **TracePlot**. Это график истории марковской цепи. Анализируя ее, можно понять, насколько хорошо отработал алгоритм и требует ли он дополнительной настройки. Визуальными критериями качества являются:\n",
"\n",
"1. Стационарность. Сэмплы должны образовывать шум вогруг какого-то значения.\n",
"2. Не имеют сильно выраженной автокорреляции. Иногда это может быть и ожидаемо(увидим ниже), но лучше чтобы ее не было\n",
"3. Вся история не может стостоять из одной и той же повторяющейся точки. Если какая-то переменная оставалась константой, то скорее всего что-то пошло не так в коде самой модели."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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HloH18ssvY86cORgyZEjvmAnkHNUwTzvE5/8mNUMs6Qvhhj+B+g9OtVjHJMK0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\nQgghxACRBEsIIYQQQgghBsj/AyWXsmnHAVRwAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f76bd539fd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.traceplot(trace);"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Немного усложним модель"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████| 1000/1000 [00:36<00:00, 27.10it/s]\n"
]
}
],
"source": [
"with pm.Model() as simple_model:\n",
" norm = pm.Normal('norm', 0, 1)\n",
" # В качестве параметров допускается использовать уже объявленные случайные переменные\n",
" laplace = pm.Laplace('lap', mu=norm, b=3)\n",
" step = pm.NUTS()\n",
" trace = pm.sample(1000, step=step)"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Стала заметна турбулентность в марковской цепи для нормального распределения"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"image/png": 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RwVREJPTphy46YtqLNzSY+kiXE+V0gj8Blqf7H+DTfu9UUtPMbFZjgzl2aBvq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\nl6BC2hnK73cghdV3z7zTAdjaAJcLLDPb/1BXtD1YPYeoKPbyseVyAka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H9n4n1V1q8E8Y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\nEEI4yP8HyeICJgTzkgwAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f7696133710>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.traceplot(trace);"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Вот что случается, когда модель становится нетривиальной, хотя должна была быть с независимой нормально распределенной первой переменой. Для таких случаев можно сначала затюнить ADVI и использовать ковариационную матрицу и средние оттуда для инициализации NUTS. Но для начала подробнее про ADVI."
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"## ADVI\n",
"ADVI расшифровывается как *Automatic Differentiation Variational Inference* ([ссылка на статью](https://arxiv.org/abs/1603.00788)). Это, пожалуй, один из самых простых и часто используемых алгоритмов для приближенного байесовского вывода. Когда размерность латентного пространства растет, то MCMC методы становятся либо достаточно сложными в настройке (дефолтные параметры не подходят), либо итерации занимают огромное количество времени. В том, что дефолтные параметры могут не подойти, мы убедились выше. Вот тогда и встает необходимость хотя бы приблизить целевое распределение тем, с которым мы умеем работать.\n",
"\n",
"### Теория\n",
"Суть метода заключается в том, что он приближает апостериорное распределение $p(z|D)$ другим распределением $q(z)$, для которого мы умеем считать плотность и сэмплировать. В классической постановке таким распределением является многомерное нормальное с диагональной ковариационной матрицей $\\mathcal{N}(\\bar{0}, diag(\\bar{\\sigma}^2))$. Это является основным его недостатком: делается предположение, что латентные переменные независимы, но это, конечно же, не всегда так. Тем не менее, даже с такой сильной предпосылкой можно добиваться неплохих результатов. Далее мы увидим, как подобное упрощение позволяет экономить вычислительные ресурсы.\n",
"\n",
"#### Постановка задачи\n",
"Пусть есть наблюдения $\\mathcal{D}$, параметрическая модель с параметрами $z \\in \\mathcal{R}^n$ и функция ее правдоподобия $p(D|z)$. Помимо этого, байесовский подход требует наличия априорного распределения на параметры модели $p(z)$. По правилу Байеса выводим апостериорное распределение на параметры:\n",
"\n",
"$$\\large p(z|D) = \\frac{p(D|z)p(z)}{\\int{p(D|z)p(z)dz}}$$\n",
"\n",
"Часть без нормализующей константы посчитать обычно не составляет труда\n",
"\n",
"$$\\large p(z|D) \\propto p(D|z)p(z)$$\n",
"\n",
"Зададим параметрическое семейство распределений $q_{\\theta} \\in Q$, с которым будем работать.\n",
"\n",
"Метрика. Стандартным выбором для метрики в пространстве распределений является дивергенция Кульбака-Лейблера\n",
"$$\\large KL(q||p) = \\mathbb{E}_{q(z)}[log q(z)-logp(z|D)]$$\n",
"Если распределния совпадают, то матожидание равняется нулю, в противном случае матожидание больше нуля. Таким образом, задача байесовского вывода сводится к задаче оптимизации\n",
"$$\\large q_{\\theta^*} = \\underset{q_{\\theta} \\in Q}{argmin}\\; KL(q_\\theta||p)$$\n",
"\n",
"#### Решение задачи\n",
"Эта задача решается стохастическим градиентным спуском. Для этого необходимо взять производную по $\\theta$.\n",
"$$\\large \\mathbb{E}_{q_{\\theta}(z)}[log q_{\\theta}(z)-logp(z|D)]$$ \n",
"\n",
"$$\\large =\\mathbb{E}_{q_{\\theta}(z)}[log q_{\\theta}(z)]-\\mathbb{E}_{q_{\\theta}(z)}[logp(z|D)]$$\n",
"\n",
"$$\\large =\\mathbb{E}_{q_{\\theta}(z)}[log q_{\\theta}(z)]-\\mathbb{E}_{q_{\\theta}(z)}[logp(D|z)] - \\mathbb{E}_{q_{\\theta}(z)}[logp(z)] + \\mathbb{E}_{q_{\\theta}(z)}[logp(D)]$$\n",
"\n",
"Мы полностью разложили KL дивергенцию, поскольку ее надо минимизировать, то $\\mathbb{E}_{q_{\\theta}(z)}[logp(D)]$ все равно константа, и считать ее нет необходимости. Так мы избавляемся от основной проблемы аналитического вывода апостериорного распределения: неберущегося интеграла. Все, что осталось, равняется $-ELBO$ (_Evidence Lower BOund_).\n",
"\n",
"Казалось бы, дальше все задано аналитически и хорошо считается, но есть одно но. Чтобы взять производную по параметрам, придется взять производную по интегралу, который, в свою очередь, зависит от этих самых параметров. Если мы будем делать это методами MC и аппроксимировать интеграл несколькими сэмплами, то столкнемся с тем, что градиенты имеют большую дисперсию. Этого можно избежать, и выбранное нами семейство апостериорных распределений это позволяет сделать. Следующая теорема продемонстерирует условия, когда производную можно внести под знак интеграла.\n",
"\n",
"__Теорема__\n",
"\n",
"Пусть $\\epsilon$ случайная величина с плотностью распределения $q(\\epsilon)$ и пусть $z = t(\\theta, \\epsilon)$, где $t$ - детерминистская обратимая функция. Пусть плотность распределения случайной величины $z$ это $q(z|\\theta)$. Предположим далее, что $q(\\epsilon)d\\epsilon = q(z|\\theta)dz$.\n",
"Тогда для функции $f$ с производной по $z$ выполнено\n",
"\n",
"$$\\large \\frac{\\partial}{\\partial\\theta} \\mathbb{E}_{q(z|\\theta)}[f(z, \\theta)] = \\mathbb{E}_{q(\\epsilon)}[\\frac{\\partial f(z, \\theta)}{\\partial z}\\frac{\\partial z}{\\partial \\theta} + \\frac{f(z, \\theta)}{\\partial \\theta}] $$\n",
"\n",
"Это и понадобится для оптимизации. Поскольку $z \\sim \\mathcal{N}(\\mu, exp(w)^2)$ представима в виде $z = t(\\mu, w, \\epsilon) = \\epsilon*exp(w) + \\mu$, где $\\epsilon \\sim \\mathcal{N}(0, 1)$. Пусть $\\theta = (\\mu, w)$\n",
"\n",
"Это называется _Reparametrization Trick_. Используя его, уже гораздо проще взять производную от $ELBO$.\n",
"\n",
"$$\\large -\\nabla ELBO = \\mathbb{E}_{\\mathcal{N}(0, 1)}[\\nabla_{\\theta}log q_{\\theta}(t(\\theta, \\epsilon))-\\nabla_{\\theta}logp(D|t(\\theta, \\epsilon)) - \\nabla_{\\theta}logp(t(\\theta, \\epsilon))] $$\n",
"\n",
"Cделав соответствующую репараметризацию, будет достаточно вызвать `theano.grad` на выражение и получить градиент выше, точнее его единственоый сэмпл, которого вполне достаточно. После этого можно использовать любимый оптимизатор."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using advi...\n",
"Average ELBO = -0.11837: 100%|██████████| 10000/10000 [00:00<00:00, 13764.87it/s]\n",
"Finished [100%]: Average ELBO = -0.1085\n",
"Evidence of divergence detected, inspect ELBO.\n",
"100%|██████████| 1000/1000 [00:01<00:00, 974.36it/s]\n"
]
}
],
"source": [
"with pm.Model() as simple_model:\n",
" norm = pm.Normal('norm', 0, 1)\n",
" laplace = pm.Laplace('lap', mu=norm, b=3)\n",
" trace = pm.sample(1000, init='advi', n_init=10000)"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Уже гораздо лучше.\n",
"\n",
"**HINT:** на трейсплоте важно смотреть на марковскую цепь, в идеале она должна быть стационарной, примерно как здесь, и не сильно турбулентной, как выше"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"image/png": 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10Je+BUoTX10C52zfvh0PP/wwAEStTDNnzsTzzz+f0LgbNmzASy+9hF/84hfIyenbmA9u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twT3PH8EQS3BjGvKANS0ttLmCv0xrGYGO9hab72rXrOlfN/LiXTzkV0RRHYtc29eq0s6eN2O1ht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\nTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f769873cac8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pm.traceplot(trace);"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using advi...\n",
"Average ELBO = -7.4197e+05: 100%|██████████| 40000/40000 [00:03<00:00, 11614.15it/s]\n",
"Finished [100%]: Average ELBO = -1.221e+08\n",
"Evidence of divergence detected, inspect ELBO.\n",
"100%|██████████| 10000/10000 [01:06<00:00, 150.87it/s]\n"
]
}
],
"source": [
"with pm.Model() as simple_model:\n",
" norm = pm.Normal('norm', 0, 1)\n",
" laplace = pm.Laplace('lap', mu=norm, b=3)\n",
" # использование произвольных выражений (даже таких экзотических) тоже допустимо\n",
" lognorm = pm.Lognormal('lognorm', sd=norm**2 + 1e-7, testval=1)\n",
" trace = pm.sample(10000, n_init=40000)"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Здесь видно, что есть заметная автокорреляция в первой марковской цепи. На самом деле неудивительно, ведь из-за того, что мы использовали квадрат нормального распределения как стандартное отклонение, NUTS застревал в локальных максимумах плотности."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"image/png": 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kdwwlVtNuXVUrIxNN9ea0oLti9frrr+OGG27A8OHDe9WqIMOEE5Jl4KftkD/9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Jkzh507d3LjjTfy8ccfo7VmyZIlbtf90Y9+ZPd49OjR1p+zs7Ptyq8DxMXF8dBDD/kTrhBhQZ84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\nhgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f76b12d6160>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# первые 100 итераций портят картинку\n",
"pm.traceplot(trace[100:]);"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Модель можно составлять последовательно, необязательно сразу в одном контексте:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using advi...\n",
"Average ELBO = -1,954.7: 100%|██████████| 1000/1000 [00:00<00:00, 8967.46it/s]\n",
"Finished [100%]: Average ELBO = -1,402.2\n",
"100%|██████████| 1000/1000 [00:00<00:00, 1464.22it/s]\n"
]
},
{
"data": {
"image/png": 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Caeo50TaLYZgYp6mpCR988AEqKyshuweSLS0t2LFjB2bNmhVw28LCQk/fx+TkZLS2tmLn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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f76839726d8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"random.seed(42)\n",
"obs = random.normal(0, 1, size=10) + random.normal(0, 10, size=10)\n",
"with pm.Model() as model:\n",
" hc = pm.HalfCauchy('hc', beta=1)\n",
"# your code\n",
"with model:\n",
" # если есть наблюдаемые переменные, то они указываются через ключевое слово\n",
" norm = pm.Normal('norm', 0, hc, observed=obs)\n",
"\n",
"with model:\n",
" trace = pm.sample(1000, tune=200, n_init=1000)\n",
"pm.traceplot(trace[10:]);"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Идеология PyMC3 предусматривает проверку модели на валидность по ходу построения: так избегаются ошибки на раннем этапе. Это достигается принудительным использованием `test_value`"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"array([ -4.13746262, -4.79556179, 3.06731129, -17.60977173,\n",
" -17.48333168, -5.85701227, -8.54909801, 3.90990806,\n",
" -9.54971504, -13.58047676], dtype=float32)"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"norm.tag.test_value"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"`Theano` идеально подходит для векторизованных операций. Поэтому, если перед вами стоит выбор, как задавать модель: через цикл или через создание веторной случайной переменной, лучше выбрать второй вариант. В этом случае создаются независимые случайные переменные, к которым можно впоследствии обращаться по индексам."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0.5, 0.5, 0.5, 0.5], dtype=float32)"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"with pm.Model() as model:\n",
" vectorized_p = pm.Uniform('p', shape=(4,))\n",
"vectorized_p.tag.test_value"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Если вам не нравится инициализация по умолчанию, вы можете указать свою.\n"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0.3, 0.3, 0.3, 0.3])"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"with pm.Model() as model:\n",
" vectorized_p = pm.Uniform('p', \n",
" shape=(4,), \n",
" testval=np.ones((4,), 'float64') * .3, \n",
" dtype='float64')\n",
"vectorized_p.tag.test_value"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"# Байесовская линейная регрессия"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Первый более менее большой и осмысленый пример будет про цены на бостонские квартиры"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"data_ = datasets.load_boston()\n",
"data = pd.DataFrame(data=data_['data'], columns=data_['feature_names'])\n",
"y = data_['target']"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" :Attribute Information (in order):\n",
" - CRIM per capita crime rate by town\n",
" - ZN proportion of residential land zoned for lots over 25,000 sq.ft.\n",
" - INDUS proportion of non-retail business acres per town\n",
" - CHAS Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\n",
" - NOX nitric oxides concentration (parts per 10 million)\n",
" - RM average number of rooms per dwelling\n",
" - AGE proportion of owner-occupied units built prior to 1940\n",
" - DIS weighted distances to five Boston employment centres\n",
" - RAD index of accessibility to radial highways\n",
" - TAX full-value property-tax rate per $10,000\n",
" - PTRATIO pupil-teacher ratio by town\n",
" - B 1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town\n",
" - LSTAT % lower status of the population\n",
" - MEDV Median value of owner-occupied homes in $1000's\n"
]
}
],
"source": [
"print('\\n'.join(data_.DESCR.splitlines()[13:28]))"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>CRIM</th>\n",
" <th>ZN</th>\n",
" <th>INDUS</th>\n",
" <th>CHAS</th>\n",
" <th>NOX</th>\n",
" <th>RM</th>\n",
" <th>AGE</th>\n",
" <th>DIS</th>\n",
" <th>RAD</th>\n",
" <th>TAX</th>\n",
" <th>PTRATIO</th>\n",
" <th>B</th>\n",
" <th>LSTAT</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.00632</td>\n",
" <td>18.0</td>\n",
" <td>2.31</td>\n",
" <td>0.0</td>\n",
" <td>0.538</td>\n",
" <td>6.575</td>\n",
" <td>65.2</td>\n",
" <td>4.0900</td>\n",
" <td>1.0</td>\n",
" <td>296.0</td>\n",
" <td>15.3</td>\n",
" <td>396.90</td>\n",
" <td>4.98</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.02731</td>\n",
" <td>0.0</td>\n",
" <td>7.07</td>\n",
" <td>0.0</td>\n",
" <td>0.469</td>\n",
" <td>6.421</td>\n",
" <td>78.9</td>\n",
" <td>4.9671</td>\n",
" <td>2.0</td>\n",
" <td>242.0</td>\n",
" <td>17.8</td>\n",
" <td>396.90</td>\n",
" <td>9.14</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.02729</td>\n",
" <td>0.0</td>\n",
" <td>7.07</td>\n",
" <td>0.0</td>\n",
" <td>0.469</td>\n",
" <td>7.185</td>\n",
" <td>61.1</td>\n",
" <td>4.9671</td>\n",
" <td>2.0</td>\n",
" <td>242.0</td>\n",
" <td>17.8</td>\n",
" <td>392.83</td>\n",
" <td>4.03</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0.03237</td>\n",
" <td>0.0</td>\n",
" <td>2.18</td>\n",
" <td>0.0</td>\n",
" <td>0.458</td>\n",
" <td>6.998</td>\n",
" <td>45.8</td>\n",
" <td>6.0622</td>\n",
" <td>3.0</td>\n",
" <td>222.0</td>\n",
" <td>18.7</td>\n",
" <td>394.63</td>\n",
" <td>2.94</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0.06905</td>\n",
" <td>0.0</td>\n",
" <td>2.18</td>\n",
" <td>0.0</td>\n",
" <td>0.458</td>\n",
" <td>7.147</td>\n",
" <td>54.2</td>\n",
" <td>6.0622</td>\n",
" <td>3.0</td>\n",
" <td>222.0</td>\n",
" <td>18.7</td>\n",
" <td>396.90</td>\n",
" <td>5.33</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX \\\n",
"0 0.00632 18.0 2.31 0.0 0.538 6.575 65.2 4.0900 1.0 296.0 \n",
"1 0.02731 0.0 7.07 0.0 0.469 6.421 78.9 4.9671 2.0 242.0 \n",
"2 0.02729 0.0 7.07 0.0 0.469 7.185 61.1 4.9671 2.0 242.0 \n",
"3 0.03237 0.0 2.18 0.0 0.458 6.998 45.8 6.0622 3.0 222.0 \n",
"4 0.06905 0.0 2.18 0.0 0.458 7.147 54.2 6.0622 3.0 222.0 \n",
"\n",
" PTRATIO B LSTAT \n",
"0 15.3 396.90 4.98 \n",
"1 17.8 396.90 9.14 \n",
"2 17.8 392.83 4.03 \n",
"3 18.7 394.63 2.94 \n",
"4 18.7 396.90 5.33 "
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data.head()"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Создадим простую байесовскую линейную модель.\n",
"\n",
"\n",
"$$ PRICE \\sim CRIM+ZN+INDUS+CHAS+NOX+RM+AGE+DIS+RAD+TAX+PTRATIO+B+LSTAT$$\n",
"\n",
"Дефолтными приорами на коэффициенты являюстя\n",
"`Normal(mu=0, tau=1.0E-6)` и на константу `Flat`.\n",
"Оценивать модель будем с помощью [SVGD](https://arxiv.org/abs/1608.04471) для разнообразия."
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"100%|██████████| 200/200 [00:05<00:00, 35.31it/s]\n"
]
}
],
"source": [
"from functools import partial\n",
"with pm.Model() as lm_model: \n",
" lm_model = pm.GLM(x=data, y=y)\n",
" # для вариационных методов есть унифициорванный интерфейс через pm.fit\n",
" histogram = pm.fit(200, method='svgd', obj_optimizer=partial(pm.adagrad, learning_rate=.7))"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"И вот, мы получили распределение! По нему теперь можно строить доверительные интервалы, что мы и сделаем для коэффициентов при наших регрессорах."
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"scrolled": true
},
"outputs": [
{
"data": {
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9+vV07tyZTZs2VStDaGjoOa2+PaGiew0q0rYtZGdXvkxaWhAREf/bbps2sHXr70n3P6e7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\nImIaKloiImIa/w9GWYfafpYL1wAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f76a0f6ca58>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# sample_vp создает аналогичный объект, что мы получали с помощью pn.sample. \n",
"# Это просто набор случайных реализаций из приближенного распределения\n",
"pm.forestplot(histogram.sample_vp(300), varnames=data.columns);"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"# Байесовские нейронные сети\n",
"![](https://ai2-s2-public.s3.amazonaws.com/figures/2016-11-08/da6057368920585bcf2443295b98418840f1fc80/1-Figure1-1.png)"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Поскольку бэкенд `PyMC3` - `Theano`, то совершенно естественным желанием будет использовать вариационный байесовский вывод для нейронных сетей. Это довольно легко и прозрачно получается с помощью `Lasagne`.\n",
"\n",
"Отличительной особеностью байесовской нейронной сети от обычной является то, как моделируются веса. В привычном случае в качестве весов берутся конкретные значения и оптимизируются с помощь градиентного спуска. \n",
"\n",
"В случае с байесовской нейронной сетью все иначе. Веса сети воспринимаются как ненаблюдаемые случайные переменные с априорным распределением. В идеале на них надо сделать честный байесовский вывод, но мы видели, что сэмплирование тормозит уже на простых задачах, а тут совершенно иной уровень. Обычной практикой при обучении байесовских сетей является приближенный вариационный вывод этого самого распределения. Наиболее быстрым из вариационных методов является вышеупомянутый ADVI. Им и будем пользоваться тут."
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"from lasagne.layers import *\n",
"import lasagne\n",
"from sklearn import datasets\n",
"from sklearn.preprocessing import scale\n",
"from sklearn.cross_validation import train_test_split\n",
"from sklearn.datasets import make_moons"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Сгенерируем синтетические данные с помощью утилит `sklearn`"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"X, Y = make_moons(noise=0.2, random_state=0, n_samples=1000)\n",
"X = scale(X)\n",
"# дополнительно надо поменять тип, иначе X и Y float64\n",
"X = X.astype(theano.config.floatX)\n",
"Y = Y.astype(theano.config.floatX)\n",
"X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=.5)"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"image/png": 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xfn0t+vWzuX3u2jUgL0+NwEBGNEU2MpJBdTXt5BITj3W0PpYiIyMF2fh3EaQE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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f7665531128>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"ax.scatter(X[Y==0, 0], X[Y==0, 1], color='b', label='Class 0')\n",
"ax.scatter(X[Y==1, 0], X[Y==1, 1], color='r', label='Class 1')\n",
"sns.despine(); ax.legend()\n",
"ax.set(xlabel='X', ylabel='Y', title='Toy binary classification data set');"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Для `Lasagne` в качестве инициализации можно передавать функцию, возвращающую символьную переменную `theano`. Инициализация сильно отличается от `PyMC3`, поэтому придется написать свой адаптер."
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"import itertools\n",
"class RandomWeight(object):\n",
" counter = itertools.count(0)\n",
" def __init__(self, mu=0, sd=1):\n",
" self.mu = mu\n",
" self.sd = sd\n",
" \n",
" def __call__(self, shape):\n",
" name = 'auto_%s' % next(self.counter)\n",
" return pm.Normal(name, self.mu, self.sd, \n",
" testval=lasagne.init.GlorotUniform()(shape),\n",
" shape=shape, dtype=theano.config.floatX)"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Создавать нейронную сеть необходимо в контексте модели, чтобы веса инициализировались корректно"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"input_var = theano.shared(X_train)\n",
"out_var = theano.shared(Y_train)\n",
"with pm.Model() as nnet:\n",
" inp = InputLayer((None, 2), input_var)\n",
" # без констант сеть работает неплохо, можно на нее тут забить\n",
" z = DenseLayer(inp, 5, W=RandomWeight(), b=None, nonlinearity=tt.tanh)\n",
" z = DenseLayer(z, 5, W=RandomWeight(), b=None, nonlinearity=tt.tanh)\n",
" p = DenseLayer(z, 1, W=RandomWeight(), b=None, nonlinearity=tt.nnet.sigmoid)\n",
" # вместо функции потерь тепеть наблюдаемая случайная величина, ее -p(D|z) будет играть роль потерь\n",
" pm.Bernoulli('observed', p=get_output(p).flatten(), observed=out_var)"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Приближенный байесовский вывод для такой модели можно делать с помощью выше описанного ADVI"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Average Loss = 132.78: 100%|██████████| 30000/30000 [00:35<00:00, 847.38it/s] \n",
"Finished [100%]: Average Loss = 132.78\n"
]
}
],
"source": [
"with nnet:\n",
" inference = pm.ADVI()\n",
" approx = inference.fit(30000)"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
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c9jYOAMCC4WlP9g9/+EM1NjZKkl577TU99NBD+uY3v6nVq1fr7bffViKR0Ouv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\nIiIiImIwhWwREREREYP9BxlHxSpo7omzAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f76bd61a4e0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(12, 6))\n",
"plt.plot(inference.hist, alpha=.3)\n",
"plt.legend()\n",
"plt.ylabel('-ELBO')\n",
"plt.xlabel('iteration');"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Результаты можно с легкостью переиспользовать для другой задачи, например, использовать их, чтобы делать предсказания"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"# Создаем символьный вход\n",
"x = tt.matrix('X')\n",
"# Переменную количества сэмплов\n",
"n = tt.iscalar('n')\n",
"# В конфиге теано стоит compute_test_value='raise', чтобы он не ругался, зададим тестовые значения в переменные\n",
"x.tag.test_value = np.empty_like(X_train[:10])\n",
"n.tag.test_value = 100\n",
"# У любого класса аппроксимации есть меоды sample_node и apply_replacements\n",
"# Они убирают зависимость графа от латентных переменных pymc3 и заменяют их аппроксимацией\n",
"_sample_proba = approx.sample_node(get_output(p).flatten(), size=n,\n",
" more_replacements={input_var:x})\n",
"# Вот теперь можно скомпилировать функцию\n",
"# У аппроксимаций нет апдейтов генератора случайных чисел, это удобно \n",
"sample_proba = theano.function([x, n], _sample_proba)"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"Собственно сами предсказания можно получить, вызвав функцию на тест сет"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"pred = sample_proba(X_test, 500).mean(0) > 0.5"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"image/png": 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9vbJhFQTggw/MyM/3hHVdInGRxCIhTQ6bTcCYMcoRVkNF1kFnYKIb/wgIp1yf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\nMmrrxiM/UgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f76654e5860>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"ax.scatter(X_test[pred==0, 0], X_test[pred==0, 1], color='b')\n",
"ax.scatter(X_test[pred==1, 0], X_test[pred==1, 1], color='r')\n",
"sns.despine()\n",
"ax.set(title='Predicted labels in testing set', xlabel='X', ylabel='Y');"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"# Разделяющая граница\n",
"Посмотреть и разделяющую границу для классов, для этого можно подставить туда все точки на плоскости и усреднить"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"grid = np.mgrid[-3:3:100j,-3:3:100j].astype('float32')\n",
"grid_2d = grid.reshape(2, -1).T\n",
"ppc = sample_proba(grid_2d ,500)"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"image/png": 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5P1erckyZb3cF4D3pQ4Y0IgNgyyMR6YUVNSKSJbeiZHWEAJhgAhCPuqt6UWYpU+YzTBEZ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mW3I+l2wyJi9MIT6+jA0OHDwOHDmlr4y51DfJ80y+AgGn/0I9hOnIA5GMxqbF2seZa7YaJVqq4n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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f7653549c50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cmap = sns.diverging_palette(250, 12, s=85, l=25, as_cmap=True)\n",
"fig, ax = plt.subplots(figsize=(16, 9))\n",
"contour = ax.contourf(grid[0], grid[1], ppc.mean(axis=0).reshape(100, 100), cmap=cmap)\n",
"ax.scatter(X_test[pred==0, 0], X_test[pred==0, 1], color='b')\n",
"ax.scatter(X_test[pred==1, 0], X_test[pred==1, 1], color='r')\n",
"cbar = plt.colorbar(contour, ax=ax)\n",
"_ = ax.set(xlim=(-3, 3), ylim=(-3, 3), xlabel='X', ylabel='Y');\n",
"cbar.ax.set_ylabel('Posterior predictive mean probability of class label = 0');"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"# Уверенность модели\n",
"Уверенность модели в предсказаниях - очень интересная штука. Обычно в моделях мы можем получить только точечную оценку на интересующее нас значение. Она сама по себе не несет в себе информации о том, как хорошо модель понимает окружающий мир: об этом может сказать только распределение оценки. С помощью байесовских методов это делается очень интуитивно, и, более того, довольно неплохо реализовано в `PyMC3`."
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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rRkT2gwmJroy5Wzsn/hfxy5Vv4ivzjsBZfhRmcxDO8qP4yrwj+OXKNycdp2WX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\nrkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f7656fbdb00>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cmap = sns.cubehelix_palette(light=1, as_cmap=True)\n",
"fig, ax = plt.subplots(figsize=(16, 9))\n",
"contour = ax.contourf(grid[0], grid[1], ppc.std(axis=0).reshape(100, 100), cmap=cmap)\n",
"ax.scatter(X_test[pred==0, 0], X_test[pred==0, 1], color='b')\n",
"ax.scatter(X_test[pred==1, 0], X_test[pred==1, 1], color='r')\n",
"cbar = plt.colorbar(contour, ax=ax)\n",
"_ = ax.set(xlim=(-3, 3), ylim=(-3, 3), xlabel='X', ylabel='Y');\n",
"cbar.ax.set_ylabel('Uncertainty (posterior predictive standard deviation)');"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"source": [
"Это далеко не все вещи, которые можно делать с помощью PyMC3. За кадром остались байесовская оптимизация, гауссовские процессы, LDA и многое другое.\n",
"\n",
"В репозитории PyMC3 есть огромное количество примеров, которые можно запустить у себя. Они в виде _jupyter_ тетрадок [вот здесь](https://github.com/pymc-devs/pymc3/blob/master/docs/source/notebooks/)"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"# Ссылки на используемые источники"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"* [Bayesian Methods for Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers)\n",
"* [Weight Uncertainty in Neural Networks](https://arxiv.org/abs/1505.05424)\n",
"* [Пример с монеткой](https://en.wikipedia.org/wiki/Checking_whether_a_coin_is_fair)\n",
"* [Automatic Differentiation Variational Inference](https://arxiv.org/abs/1603.00788)\n",
"* [Operator Variational Inference](https://arxiv.org/abs/1610.09033)\n",
"* [Stein Variational Gradient Descent](https://arxiv.org/abs/1608.04471)\n",
"* [Полная тетрадка с нейронной сетью](https://github.com/ferrine/pymc3/blob/master/docs/source/notebooks/bayesian_neural_network_opvi-advi.ipynb)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.4.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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