{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 第3部 モデリング入門" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## 3.1 確率論的プログラマの仕事\n", "\n", "![alt text](fig/infer2.png \"infer2\")\n", "\n", "結局,確率論的プログラミングにおいて,プログラマがやることは,\n", "\n", "- データを用意する\n", "- パラメータの種類を決め,確率分布を決める\n", "- パラメータ込みで事前分布を数式で表す\n", "- パラメータ込みで尤度を数式で表す\n", "- MCMCサンプリング法を選ぶ\n", "\n", "あとは計算機がMCMCサンプリングをして,パラメータの推定値を返す." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "結局,事前分布や尤度の確率分布を上手にモデリングするには,確率分布とその確率分布の関係をよく知っていなければならない.\n", "\n", "![alt text](fig/distrib.png \"distrib\") [distrib.png](fig/distrib.png)\n", "\n", "\"Univariate Distribution Relationships\" [2008amstat.pdf](doc/2008amstat.pdf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.2 コイン投げ - pymc3" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Using gpu device 0: GeForce GTX TITAN (CNMeM is disabled)\n" ] } ], "source": [ "# coding: utf-8\n", "from __future__ import division\n", "import os\n", "import sys\n", "import glob\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "%matplotlib inline\n", "%precision 4\n", "#plt.style.use('ggplot')\n", "import seaborn as sns\n", "sns.set_style('white')\n", "sns.set_context('paper')\n", "\n", "np.random.seed(1234)\n", "import pymc3 as pm\n", "import scipy.stats as stats" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\r", " [-----------------100%-----------------] 1000 of 1000 complete in 0.2 sec" ] }, { "data": { "image/png": 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OFyWSkBQNrzzYLnLRNEsyWuhZsMJhGuaEZQmKHQ8jX0SIpRCxEbjmenoD6OkN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\nOdNTMQgf4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rxwy1825YQW3L9i4Vttdf2SituStD3RfeFJGsIjjtULFLFwOiI9BjaL3uv6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\nmBRShJVAEJESZ8Oz90/Glz+cxNotlXh41XbcPWskr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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# データを用意する\n", "n = 100\n", "h = 61\n", "\n", "# パラメータをきめる\n", "alpha = 2\n", "beta = 2\n", "\n", "niter = 1000\n", "with pm.Model() as model: # context management\n", " # 事前分布をモデリング\n", " p = pm.Beta('p', alpha=alpha, beta=beta)\n", "\n", " # 尤度をモデリング\n", " y = pm.Binomial('y', n=n, p=p, observed=h)\n", "\n", " #-- パラメータ推定 --\n", " \n", " # MAP推定を使って初期値をきめる.MAP推定とMCMCは相性がいい\n", " start = pm.find_MAP() \n", " \n", " # MCMCの遷移ステップを選ぶ\n", " step = pm.NUTS(scaling=start) \n", " \n", " trace = pm.sample(niter, step, start, random_seed=123, progressbar=True)\n", " \n", " pm.traceplot(trace)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist(trace['p'], 15, histtype='step', normed=True, label='post');\n", "x = np.linspace(0, 1, 100)\n", "plt.plot(x, stats.beta.pdf(x, alpha, beta), label='prior');\n", "plt.legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.3 コイン投げ - pystan" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Inference for Stan model: anon_model_ccec8cd16799dee6754657976ed54632.\n", "1 chains, each with iter=1000; warmup=500; thin=1; \n", "post-warmup draws per chain=500, total post-warmup draws=500.\n", "\n", " mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat\n", "p 0.61 4.1e-3 0.04 0.53 0.57 0.61 0.64 0.69 116 1.0\n", "lp__ -70.17 0.05 0.53 -71.72 -70.33 -69.96 -69.79 -69.74 105 1.0\n", "\n", "Samples were drawn using NUTS(diag_e) at Mon Oct 12 17:12:11 2015.\n", "For each parameter, n_eff is a crude measure of effective sample size,\n", "and Rhat is the potential scale reduction factor on split chains (at \n", "convergence, Rhat=1).\n" ] } ], "source": [ "import pystan\n", "\n", "# pystanではstanのコードは日本語を許しません.\n", "# それはstanに渡す直前で強制的にasciiに変換しているからです.\n", "\n", "coin_code = \"\"\"\n", "// The order of following declarations matters.\n", "//\n", "// data declaration here\n", "data {\n", " int n; // number of tosses\n", " int y; // number of heads\n", "}\n", "\n", "// in case you want to tweak data...\n", "transformed data {}\n", "\n", "// parameters declaration here\n", "parameters {\n", " real p;\n", "}\n", "\n", "// in case you want to tweak parameters...\n", "transformed parameters {}\n", "\n", "// your model here\n", "model {\n", " p ~ beta(2, 2);\n", " y ~ binomial(n, p);\n", "}\n", "\n", "// tweaking samples from posterior\n", "generated quantities {}\n", "\"\"\"\n", "\n", "# データを用意\n", "coin_dat = {\n", " 'n': 100,\n", " 'y': 61,\n", " }\n", "\n", "# パラメータ推定.デフォルトでNUTSが使われる\n", "fit = pystan.stan(model_code=coin_code, data=coin_dat, iter=1000, chains=1)\n", "#fit = pystan.stan(file='coin_code.stan', data=coin_dat, iter=1000, chains=1)\n", "\n", "print(fit)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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S5VMAKMgywjxixaBF+hqMkcJvf/tb/PrXv8Zzzz0HhmEE1T41Go2w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\nq8rzQlIpK1RRvYuK0gJaNg815CkGQG1jD2L0WpQ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-69.7715, -70.3478,\n", " -69.7456, -69.9129, -69.7789, -69.7456, -70.0218, -69.7482,\n", " -69.7789, -70.5987, -70.845 , -69.7879, -70.3232, -70.2862,\n", " -70.0958, -69.7461, -69.8724, -71.0242, -69.954 , -69.7944,\n", " -69.757 , -70.5123, -69.7427, -69.8584, -69.7576, -70.014 ,\n", " -71.1048, -69.7598, -70.1258, -70.2406, -69.8941, -69.7835,\n", " -69.758 , -69.8708, -70.5917, -69.9473, -70.1031, -69.8153,\n", " -69.9279, -70.2766, -72.9958, -69.7432, -69.7909, -71.348 ,\n", " -70.1812, -71.7785, -69.7757, -70.4074, -70.4036, -69.7438,\n", " -70.0673, -69.7801, -69.8594, -71.7188, -71.1211, -69.8727,\n", " -69.7484, -70.841 , -69.7554, -69.8644, -70.8029, -71.7973,\n", " -70.6646, -69.7446, -69.8776, -69.7527, -70.6994, -69.9858,\n", " -69.7621, -70.7702, -70.2216, -69.8126, -69.9538, -69.9187,\n", " -69.7454, -71.5826, -70.234 , -70.6075, -69.7469, -70.6656,\n", " -69.9907, -69.9651, -70.4844, -69.7971, -73.6988, -69.7445,\n", " -69.7439, -70.9306, -70.3927, -70.4234, -70.4077, -70.3063,\n", " -69.7494, -70.0104, -69.7427, -69.9808, -70.0218, -70.5706,\n", " -69.9905, -70.0725, -70.0425, -70.0287, -69.7913, -69.9155,\n", " -69.7477, -70.0051, -69.8548, -70.1338, -69.8909, -69.92 ,\n", " -70.7394, -70.8725]))]))" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "coin_dict = fit.extract()\n", "coin_dict.keys()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3.4 モデリングの素振り練習\n", "\n", "- 正規分布 [normal_pymc](normal_pymc.ipynb) [normal_pystan](normal_pystan.ipynb)\n", "- 線形回帰 [linreg_pymc](linreg_pymc.ipynb) [linreg_pystan](linreg_pystan.ipynb)\n", "- ロジステック回帰 [gender_pymc](gender_pymc.ipynb) [gender_pystan](gender_pystan.ipynb)\n", "- 階層ベイズ [gelmanradon_pymc](gelmanradon_pymc.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": 0 }