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@tanutarou
Last active November 25, 2017 06:49
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ベルヌーイ試行のMAP推定、ベイズ推定の例:きのこ傘投げ問題
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from IPython.core.pylabtools import figsize\n",
"from matplotlib import pyplot as plt\n",
"%matplotlib inline\n",
"import numpy as np\n",
"figsize(12.5, 12)\n",
"import seaborn as sns\n",
"sns.set(context='paper', style='darkgrid', rc={'figure.facecolor':'white'}, font_scale=1.2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# きのこの傘投げ問題\n",
"やんてね君はきのこの傘を投げました。\n",
"\n",
"きのこの傘は、確率$\\lambda$で表向きになります。\n",
"\n",
"やんてね君はこの$\\lambda$がどんな値か分かりません。 \n",
"\n",
"やんてね君は$10$回きのこを投げることで、この$\\lambda$を推定したいです。 \n",
"\n",
"ベイズ的アプローチで推定してみましょう。"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# モデルを定義しよう\n",
"\n",
"やんてね君は、これはコイン投げに近いぞと考え、きのこの傘が表になる確率はベルヌーイ分布に従うと考えました。\n",
"$$\n",
"p(x|\\lambda) = Bern(\\lambda) = \\lambda^x (1 - \\lambda)^{1-x}\n",
"$$\n",
"そして、きのこの傘が表になる確率$\\lambda$の事前分布として、ベルヌーイ分布の共役分布であるベータ分布を仮定しました。\n",
"$$\n",
"p(\\lambda; \\alpha, \\beta) = Beta(\\alpha, \\beta) = \\frac{1}{B(\\alpha, \\beta)} \\lambda^{\\alpha-1} (1 - \\lambda)^{\\beta - 1}\n",
"$$\n",
"ここで、$\\alpha, \\beta$はハイパパラメータです。$B(\\alpha, \\beta)$はベータ関数と呼ばれる関数です。\n",
"$\\alpha=1, \\beta=1$とおくと、$\\lambda$の分布として$[0, 1]$の範囲の一様分布を仮定したのと等価(以下にプロットしてある)になるので、情報のないはじめの段階ではこのパラメータで設定しておくのが無難と思い、そのように設定しました。"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f130a3bfe48>]"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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AFBDiAABQQIgDAEABIQ4AAAWEOAAAFBDiAABQQIgDAEABIQ4AAAWEOAAAFBDiAABQQIgD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\nbdR1lOWRAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f130cb5a9b0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Beta(1, 1)のプロット\n",
"from scipy.stats import beta\n",
"a = 1.0\n",
"b = 1.0\n",
"x = np.linspace(beta.ppf(0.01, a, b), beta.ppf(0.99, a, b), 100)\n",
"plt.plot(x, beta.pdf(x, a, b), 'r-', lw=5, alpha=0.6)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 事後確率分布の計算\n",
"今回、事前分布に共役分布であるベータ分布を選んだので、事後確率分布もベータ分布になります。\n",
"\n",
"実際に計算してみると以下のようになります。\n",
"\n",
"$$\n",
"\\begin{eqnarray}\n",
"p(\\lambda | x) &=& \\frac{p(x | \\lambda) p(\\lambda)}{p(x)} \\\\\n",
" &=& \\frac{\\lambda^x (1 - \\lambda)^{1-x} \\frac{1}{B(\\alpha, \\beta)} \\lambda^{\\alpha-1} (1 - \\lambda)^{\\beta-1}}{p(x)} \\\\\n",
" &=& \\frac{\\frac{1}{B(\\alpha, \\beta)} \\lambda^{x+\\alpha-1} (1 - \\lambda)^{1 - x + \\beta - 1}}{p(x)}\\\\\n",
" &=& \\frac{\\frac{B(x+\\alpha, 1-x+\\beta)}{B(\\alpha, \\beta)} Beta(x+\\alpha, 1-x+\\beta)}{p(x)}\\\\\n",
" &=& Beta(x+\\alpha, 1-x+\\beta)\n",
"\\end{eqnarray}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# データを用いて事後確率分布を求めよう\n",
"やんてね君は$10$回きのこの傘を投げました。\n",
"\n",
"その結果、[表、表、裏、表、表、表、裏、裏、表、表]という結果が得られました。\n",
"\n",
"この結果をもとに事後確率分布を更新していきましょう。"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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+Ctr0tygxD+lvvfWW3nnnHVVWVuqFF16QJK1Zs0aFhYV65ZVX5Ha79cADD6iw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vfJuteHiI8/gq1gGzzXfgfa5Cn8Wx7EmKQTEdHg4/NBqaz4MjHv68JCkgQ9ZSy07MnQsnMgEhIQ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\neye0L3ZAqqkJaB/Rsyd8kybDlz0RIrZHB1dIdjLSh6Dphy8h4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E5EFE4aGqCeKoFyohhK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\ncqP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A1qxZg29961vo1q0b+vTpg0WLFl07R5Zl3HnnnYiLi0OXLl3wzW9+E7t27WryPj74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\nZcgAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f130a0976d8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"figsize(12.5, 25)\n",
"ts = [1, 1, 0, 1, 1, 1, 0, 0, 1, 1]\n",
"# 事前分布のパラメータ\n",
"a = 1.0\n",
"b = 1.0\n",
"plt.subplot(11, 1, 1)\n",
"x = np.linspace(0, 1, 100)\n",
"plt.plot(x, beta.pdf(x, a, b), 'r-', lw=5, alpha=0.6)\n",
"plt.title('init')\n",
"for i, t in enumerate(ts):\n",
" plt.subplot(11, 1, i+2)\n",
" a = t + a\n",
" b = 1 - t + b\n",
" plt.plot(x, beta.pdf(x, a, b), 'r-', lw=5, alpha=0.6)\n",
" plt.title('update {}'.format(i))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# MAP推定をしてみよう\n",
"事後確率分布を見る限り、大体$\\lambda$は0.7ぐらいかなということが分かります。\n",
"\n",
"最後の事後確率分布を使ってMAP推定をしてみましょう。\n",
"\n",
"今回、事前分布として一様分布を仮定しているので10回中7回表がでたことから、$\\lambda=0.7$だろうという最尤推定の結果とほぼ等しくなっています。\n",
"\n",
"今回はしませんでしたが、あらかじめきのこの形状を見て表が出やすそうとか裏が出やすそうとかいう事前知識があればそれを取り入れられるのが、今回のベイズ的アプローチのメリットです。"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"MAP estimation: lambda = 0.6996996996996997\n"
]
}
],
"source": [
"xs = np.linspace(0, 1, 1000)\n",
"ma = -1\n",
"for x in xs:\n",
" if beta.pdf(x, a, b) > ma:\n",
" ma = beta.pdf(x, a, b)\n",
" map_lam = x\n",
"print(\"MAP estimation: lambda = {}\".format(map_lam))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# ベイズ推定をしてみよう\n",
"MAP推定により今回解きたい問題は解けました。\n",
"\n",
"MAP推定によりパラメータの値を推定できたので、もうきのこを投げなくても次きのこを投げたら表になるか、裏になるかをシミュレーションできるようになりました。\n",
"\n",
"しかし、MAP推定はあくまで事後確率分布が最大となるような$\\lambda$しか考えていません。\n",
"実際の事後確率分布はその一点しか確率をもたないわけではなく、幅を持っています。\n",
"\n",
"これらの情報をすべて活用して未来にきのこを投げたときの表裏のシミュレーションをしたいときに使うのが、ベイズ推定です。\n",
"\n",
"ベイズ推定では、以下の式で予測分布を計算します。共役分布なので、積分が解析的に行なえます。\n",
"$$\n",
"\\begin{eqnarray}\n",
"p^*(y) &=& \\int p(y|\\lambda) p(\\lambda|x) d\\lambda \\\\\n",
" &=& \\int p(y|\\lambda) Beta[x+\\alpha, 1-x+\\beta] d\\lambda \\\\\n",
" &=& \\int \\lambda^y (1 - \\lambda)^{1-y} \\frac{1}{B(x+\\alpha, 1-x+\\beta)} \\lambda^{x+\\alpha-1} (1-\\lambda)^{1-x+\\beta-1} d\\lambda \\\\\n",
" &=& \\frac{1}{B(x+\\alpha, 1-x+\\beta)} \\int \\lambda^{x+y+\\alpha-1} (1-\\lambda)^{2-x-y+\\beta-1} d\\lambda \\\\\n",
" &=& \\frac{B(x+y+\\alpha, 2-x-y+\\beta)}{B(x+\\alpha, 1-x+\\beta)}\n",
"\\end{eqnarray}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"p[0] = 0.30030030030030025\n",
"p[1] = 0.6996996996996997\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.collections.LineCollection at 0x7f130a3f9080>"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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"text/plain": [
"<matplotlib.figure.Figure at 0x7f130a097898>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"figsize(12.5, 4)\n",
"from scipy.stats import bernoulli\n",
"# まずはMAP推定での予測分布を見てみる\n",
"x = [0, 1]\n",
"y = bernoulli.pmf(x, map_lam)\n",
"print(\"p[0] = {}\".format(y[0]))\n",
"print(\"p[1] = {}\".format(y[1]))\n",
"plt.plot(x, y, 'bo', ms=8)\n",
"plt.vlines(x, 0, y, colors='b', lw=5, alpha=0.5)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"p[0] = 0.3333333333333333\n",
"p[1] = 0.6666666666666666\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.collections.LineCollection at 0x7f1309d9e978>"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x7f1309d9ea58>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from scipy.special import beta\n",
"# ベイズ推定での予測分布を見てみる\n",
"x = np.array([0, 1])\n",
"y = beta(a+x, b+1-x) / beta(a, b)\n",
"print(\"p[0] = {}\".format(y[0]))\n",
"print(\"p[1] = {}\".format(y[1]))\n",
"plt.plot(x, y, 'bo', ms=8)\n",
"plt.vlines(x, 0, y, colors='b', lw=5, alpha=0.5)"
]
}
],
"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": "3.5.2"
},
"toc": {
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"toc_cell": false,
"toc_position": {},
"toc_section_display": "block",
"toc_window_display": false
},
"varInspector": {
"cols": {
"lenName": 16,
"lenType": 16,
"lenVar": 40
},
"kernels_config": {
"python": {
"delete_cmd_postfix": "",
"delete_cmd_prefix": "del ",
"library": "var_list.py",
"varRefreshCmd": "print(var_dic_list())"
},
"r": {
"delete_cmd_postfix": ") ",
"delete_cmd_prefix": "rm(",
"library": "var_list.r",
"varRefreshCmd": "cat(var_dic_list()) "
}
},
"types_to_exclude": [
"module",
"function",
"builtin_function_or_method",
"instance",
"_Feature"
],
"window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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