{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 베이즈정리와 정규분포의 곱\n", "\n", "

2017.08.17 조준우 metamath@gmail.com

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\n", "\n", "\n", "\n", "- 베이즈정리에 의해 사후확률분포를 구하려면 가능도likelihood와 사전확률을 곱하고 이를 데이터의 주변확률로 나눠야 한다.
\n", "\n", "- 관찰된 데이터가 정규분포를 따르고, 독립이라고 가정하면 가능도는 정규분포의 곱이된다.
\n", "\n", "- 이런 가능도에 대해 사전확률분포를 정규분포로 선택하면 사후확률분포도 정규분포를 따르게 되므로 정규분포는 정규분포의 공액사전분포이다.
\n", "\n", "- 정규분포의 곱은 어떤 상수가 곱해진 정규분포가 되므로 사후확률분포는 가능도와 사전확률분포의 곱에 비례한다.
\n", "\n", "- 사후확률분포가 정규분포가 된다는 사실을 이미 알고 있으므로 가능도와 사전확률분포의 곱을 정규화시킬 필요없이 평균과 표준편차만을 구하면 온전한 사후확률분포를 얻을 수 있다.
\n", "\n", "- 이것은 가능도와 사전확률분포의 곱에서 $\\text{exp}(\\cdot)$항 내부를 완전제곱꼴completing the square로 고치는 과정으로 구하게 된다.
\n", "\n", "- 본 문서에서는 베이즈정리에 따라 가능도와 사전확률을 곱하고, 가능도를 $\\mu$에 대해 주변화marginalizing시킨 $p(D)$로 앞의 곱을 나눠봄으로써 실제 사후확률의 분포가 완전한 정규분포 pdf가 되는것을 확인해본다.
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. 두 정규분포의 곱\n", "\n", "- 정규분포 두 개를 곱하면 정규화되지 않은 특정 상수가 곱해진 정규분포scaled gaussian가 됨을 알 수 있다. 두 정규분포가\n", "\n", "$$\n", "f(x) = \\frac{1}{ \\sqrt{2 \\pi} \\sigma_{f} } \\text{exp}\\left\\{{-\\frac{(x-\\mu_f)^2}{2 \\sigma^{2}_{f}}}\\right\\} \\tag{1.1}\\\\\n", "g(x) = \\frac{1}{ \\sqrt{2 \\pi} \\sigma_{g} } \\text{exp}\\left\\{{-\\frac{(x-\\mu_g)^2}{2 \\sigma^{2}_{g}}}\\right\\} \n", "$$\n", "\n", "일 때 두 정규분포의 곱은 다음과 같다.\n", "\n", "$$\n", "f(x)g(x) = \\frac{S_{fg}}{ \\sqrt{2 \\pi} \\sigma_{fg} } \\text{exp} \\left[ {-\\frac{(x-\\mu_{fg})^2}{2 \\sigma^{2}_{fg}}} \\right] \\tag{1.2}\n", "$$\n", "\n", "이 때 위 식에서 $S_{fg}$, $\\mu_{fg}$, $\\sigma_{fg}$는 다음과 같다.\n", "\n", "$$\n", "S_{fg} = \\frac{1}{\\sqrt{2\\pi (\\sigma^{2}_{f}+\\sigma^{2}_{g})}} \\text{exp} \\left[ -\\frac{(\\mu_{f}-\\mu_{g})^2}{2(\\sigma^{2}_{f}+\\sigma^{2}_{g})} \\right] \\tag{1.3}\n", "$$\n", "\n", "$$\n", "\\mu_{fg} = \\frac{\\mu_{f}\\sigma^{2}_{g}+\\mu_{g}\\sigma^{2}_{f}}{\\sigma^{2}_{f}+\\sigma^{2}_{g}} \\tag{1.4}\n", "$$\n", "\n", "$$\n", "\\sigma_{fg} = \\sqrt{\\frac{\\sigma^{2}_{f}\\sigma^{2}_{g}}{\\sigma^{2}_{f}+\\sigma^{2}_{g}}} \\tag{1.5}\n", "$$\n", "\n", "- 곱하는 과정은 \"Products and Convolutions of Gaussian Probability Density Functions\"[1]에 잘 나와있다.\n", "\n", "- 즉, 완전한 정규분포 pdf가 되기 위해서는 다시 정규화normalizing가 필요하다. 식(1.2)에서 보면 $S_{fg}$만 없으면 정규분포 pdf가 됨을 확인할 수 있다.\n", "\n", "- 아래 코드로 확인해본다.\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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sEcicOvUHKpWKgQMHcTEfH99a82/qc+rUSV57bQ1xcSt5773/smTJg9b3PD09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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "G_f(x)의 -inf~inf 정적분 : 1.000000\n", "G_g(x)의 -inf~inf 정적분 : 1.000000\n", "G_fg(x)의 -inf~inf 정적분 : 0.129019\n", "G_fg(x)의 -inf~inf 정적분 / S_gf : 1.000000\n" ] } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.integrate as integrate\n", "import matplotlib as mpl\n", "mpl.style.use('seaborn')\n", "\n", "x = np.linspace(-10, 10, 100)\n", "\n", "class Gaussian :\n", " def __init__(self, mu, sigma, scaled_const=1) :\n", " \"\"\"\n", " 정규분포의 파라미터 2개외에 scaled_const를 정의\n", " scaled_const는 정규화된 경우 1이다.\n", " \"\"\"\n", " self.mu = mu\n", " self.sigma = sigma\n", " self.scaled_const = scaled_const\n", " \n", " def pdf(self, x):\n", " return self.scaled_const / (np.sqrt(2*np.pi)*self.sigma) * np.exp( -((x-self.mu)**2)/(2*self.sigma**2) )\n", "\n", " def __mul__(self, other) :\n", " \"\"\"\n", " 식(1.3),(1.4),(1.5)을 이용해서 연산자 오버로딩을 한다.\n", " \"\"\"\n", " #eq 1.4\n", " mu = ((self.mu*(other.sigma**2))+(other.mu*(self.sigma**2))) / (self.sigma**2 + other.sigma**2) \n", " \n", " #eq 1.5\n", " sigma = np.sqrt( ((self.sigma**2) * (other.sigma**2)) / (self.sigma**2 + other.sigma**2) ) \n", " \n", " #eq 1.3\n", " S_fg = 1/np.sqrt(2*np.pi*(self.sigma**2 + other.sigma**2))*np.exp(-((self.mu-other.mu)**2)/(2*(self.sigma**2 + other.sigma**2))) \n", " \n", " return Gaussian(mu, sigma, S_fg)\n", " \n", "g_f = Gaussian(1.0, 1.5)\n", "g_g = Gaussian(2.0, 2.5)\n", "g_fg = g_f*g_g\n", "\n", "plt.plot(x, g_f.pdf(x), x, g_g.pdf(x), x, g_fg.pdf(x), x, g_fg.pdf(x)/g_fg.scaled_const)\n", "plt.annotate('$f(x)=\\mathcal{N}(\\mu=1.0, \\sigma=1.5)$', xy=(2.0, 0.2), xytext=(5.5, 0.25), fontsize=15, arrowprops=dict(facecolor='black', shrink=0.05))\n", "plt.annotate('$g(x)=\\mathcal{N}(\\mu=2.0, \\sigma=2.5)$', xy=(4.5, 0.1), xytext=(5.5, 0.15), fontsize=15, arrowprops=dict(facecolor='black', shrink=0.05))\n", "plt.annotate('$f(x)g(x)$', xy=(-0.1, 0.025), xytext=(-6, 0.05), fontsize=15, arrowprops=dict(facecolor='black', shrink=0.05))\n", "plt.annotate(r\"$\\frac{f(x)g(x)}{S_{fg}}$\", xy=(1.0, 0.3), xytext=(-4.5, 0.3), fontsize=20, arrowprops=dict(facecolor='black', shrink=0.05))\n", "plt.show()\n", "\n", "print(\"G_f(x)의 -inf~inf 정적분 : {:f}\".format(integrate.quad(g_f.pdf, -np.inf, np.inf)[0]))\n", "print(\"G_g(x)의 -inf~inf 정적분 : {:f}\".format(integrate.quad(g_g.pdf, -np.inf, np.inf)[0]))\n", "print(\"G_fg(x)의 -inf~inf 정적분 : {:f}\".format(integrate.quad(g_fg.pdf, -np.inf, np.inf)[0]))\n", "print(\"G_fg(x)의 -inf~inf 정적분 / S_gf : {:f}\".format(integrate.quad(g_fg.pdf, -np.inf, np.inf)[0]/g_fg.scaled_const))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. 베이즈정리와 정규분포의 곱\n", "\n", "- 데이터의 분포가 정규분포라고 가정하고 베이즈룰에 따라 데이터에 대한 파라미터의 사후확률을 계산한다.\n", "\n", "- 많은 부분 Conjugate Bayesian analysis of the Gaussian distribution[2]를 참고했다.\n", "\n", "- $D$를 $n$개의 관측 데이터, $p(\\mu \\,|\\, \\mu_0, \\sigma^2_0)$를 파라미터 $\\mu$의 사전확률라고 하면 ($\\sigma^2$, $\\sigma^2_0$ 는 알려진것으로 가정) $\\mu$에 대한 사후확률은 다음과 같다.\n", "\n", "$$\n", "p(\\mu \\,|\\, D) = \\frac{p(D \\,|\\, \\mu, \\sigma^2) \\, p(\\mu \\,|\\, \\mu_0, \\sigma^2_0)}{p(D)} \\tag{2.1}\n", "$$\n", "\n", "### 2.1 가능도Likelihood\n", "\n", "- 관측 데이터를 i.i.d로 가정하면 다음과 같이 가능도 함수는 각 데이터의 확률분포의 곱이다.\n", "\n", "$$\n", "\\begin{align*}\n", "p(D \\,|\\, \\mu, \\sigma^2) \n", "&= \\prod_{i = 1}^{n} \\left[ \\frac{1}{\\sqrt{2\\pi \\sigma^2}} \\text{exp}\\left\\{ -\\frac{1}{2\\sigma^2} (x_{i}-\\mu)^2 \\right\\} \\right] \\\\[4pt]\n", "&= \\left( \\frac{1}{\\sqrt{2\\pi \\sigma^2}} \\right)^{n} \\left[ \\text{exp}\\left\\{ -\\frac{1}{2\\sigma^2} (x_{1}-\\mu)^2 \\right\\} \\text{exp}\\left\\{ -\\frac{1}{2\\sigma^2} (x_{2}-\\mu)^2 \\right\\} \\cdots \\text{exp}\\left\\{ -\\frac{1}{2\\sigma^2} (x_{n}-\\mu)^2 \\right\\} \\right] \\\\[4pt]\n", "&= \\color{DarkOrchid}{ \\frac{1}{\\left(\\sqrt{2\\pi \\sigma^2}\\right)^{n}} } \\text{exp}\\left\\{ -\\frac{1}{2\\sigma^2} \\sum_{i=1}^{n} (x_{n}-\\mu)^2 \\right\\}\n", "\\end{align*} \\tag{2.2}\n", "$$\n", "\n", "### 2.2 사전확률Prior\n", "\n", "- 공액 사전확률로 정규분포를 파라미터 $\\mu$의 사전확률분포로 선택한다.\n", "\n", "$$\n", "p(\\mu \\,|\\, \\mu_0, \\sigma^2_0) = \\color{DarkOrchid}{ \\frac{1}{\\sqrt{2\\pi \\sigma_0^2}} } \\text{exp} \\left\\{ -\\frac{1}{2\\sigma_0^2} (\\mu-\\mu_0)^2 \\right\\} \\tag{2.3}\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.3 가능도 $\\times$ 사전확률\n", "\n", "- 식(2.1)의 분자 계산을 위해 식(2.2)와 식(2.3)을 곱한다.\n", "\n", "$$\n", "\\begin{align}\n", "p(D \\,|\\, \\mu, \\sigma^2) p(\\mu \\,|\\, \\mu_0, \\sigma^2_0) \n", "&= \\color{DarkOrchid}{ \\frac{1}{\\left(\\sqrt{2\\pi \\sigma^2}\\right)^{n}} } \\color{DarkOrchid}{ \\frac{1}{\\sqrt{2\\pi \\sigma_0^2}} } \\text{exp}\\left\\{ -\\frac{1}{2\\sigma^2} \\sum_{i=1}^{n} (x_{i}-\\mu)^2 \\right\\} \\text{exp} \\left\\{ -\\frac{1}{2\\sigma_0^2} (\\mu-\\mu_0)^2 \\right\\}\n", "\\end{align} \\tag{2.4}\n", "$$\n", "\n", "- 색깔 부분을 $ C_1 = \\color{DarkOrchid}{ \\frac{1}{\\left(\\sqrt{2\\pi \\sigma^2}\\right)^{n}} } \\color{DarkOrchid}{ \\frac{1}{\\sqrt{2\\pi \\sigma_0^2}} } $ 로 두고 계속한다.\n", "\n", "$$\n", "\\begin{align}\n", "p(D \\,|\\, \\mu, \\sigma^2) p(\\mu \\,|\\, \\mu_0, \\sigma^2_0) \n", "&= \\color{DarkOrchid}{ C_1 } \\text{exp}\\left\\{ -\\frac{1}{2\\sigma^2} \\sum_{i=1}^{n} (x_{i}-\\mu)^2 \\right\\} \\text{exp} \\left\\{ -\\frac{1}{2\\sigma_0^2} (\\mu-\\mu_0)^2 \\right\\} \\\\[4pt]\n", "&= \\color{DarkOrchid}{ C_1 } \\text{exp} \\left\\{ -\\frac{1}{2\\sigma^2} \\sum_{i=1}^{n} (x_{i}-\\mu)^2 -\\frac{1}{2\\sigma_0^2} (\\mu-\\mu_0)^2 \\right\\} \\\\[4pt]\n", "&= \\color{DarkOrchid}{ C_1 } \\text{exp} \\left\\{ -\\frac{1}{2\\sigma^2} \\sum_{i=1}^{n} (x_{i}^{2}-2x_{i}\\mu + \\mu^2) -\\frac{1}{2\\sigma_0^2} (\\mu^2 - 2\\mu_{0}\\mu + \\mu_{0}^{2}) \\right\\} \\\\[4pt]\n", "&= \\color{DarkOrchid}{ C_1 } \\text{exp} \\left\\{ -\\frac{1}{2\\sigma^2} \\sum_{i=1}^{n}x_{i}^{2} +\\frac{1}{\\sigma^2}\\sum_{i=1}^{n}x_{i}\\mu - \\frac{1}{2\\sigma^2}n\\mu^2 - \\frac{1}{2\\sigma_0^2} \\mu^2 + \\frac{1}{\\sigma_0^2}\\mu_{0}\\mu - \\frac{1}{2\\sigma_0^2}\\mu_{0}^{2} \\right\\} \\\\[4pt]\n", "\\end{align} \\tag{2.5}\n", "$$\n", "\n", "- $\\mu$에 대한 2차식으로 묶으면\n", "\n", "$$\n", "\\begin{align}\n", "&= \\color{DarkOrchid}{ C_1 } \\text{exp} \\left\\{ -\\frac{1}{2} \\left( \\frac{n}{\\sigma^2} + \\frac{1}{\\sigma_0^2} \\right) \\mu^{2} + \\left(\\frac{\\sum x_{i}}{\\sigma^2} + \\frac{\\mu_0}{\\sigma_0^2} \\right) \\mu - \\left( \\frac{\\mu_0^{2}}{2\\sigma_0^2} + \\frac{\\sum x_{i}^{2}}{2\\sigma^2} \\right) \\right\\} \\\\[4pt]\n", "&= \\color{DarkOrchid}{ C_1 } \\text{exp} \\left\\{ -\\frac{1}{2} \\left( \\frac{n}{\\sigma^2} + \\frac{1}{\\sigma_0^2} \\right) \\mu^{2} + \\left(\\frac{\\sum x_{i}}{\\sigma^2} + \\frac{\\mu_0}{\\sigma_0^2} \\right) \\mu - \\frac{1}{2} \\left( \\frac{\\mu_0^{2}}{\\sigma_0^2} - \\frac{\\sum x_{i}^{2}}{\\sigma^2} \\right) \\right\\} \\\\[4pt]\n", "&= \\color{DarkOrchid}{ C_1 } \\text{exp} \\left\\{ -\\frac{1}{2} \\left( \\frac{n\\sigma_{0}^{2}+\\sigma^2}{\\sigma^{2}\\sigma_{0}^{2}} \\right) \\mu^{2} + \\left( \\frac{\\sigma_{0}^{2} \\sum x_{i} + \\mu_{0}\\sigma^{2}}{\\sigma^{2}\\sigma_{0}^{2}} \\right) \\mu - \\frac{1}{2} \\left( \\frac{\\mu_0^{2}\\sigma^{2}-\\sigma_{0}^{2}\\sum x_{i}^{2}}{\\sigma^{2}\\sigma_{0}^{2}} \\right) \\right\\} \\\\[4pt]\n", "&= \\color{DarkOrchid}{ C_1 } \\text{exp} \\left[ -\\frac{1}{2} \\frac{1}{\\sigma^{2}\\sigma_{0}^{2}} \\left\\{ \\left( n\\sigma_{0}^{2}+\\sigma^2 \\right) \\mu^{2} - 2 \\left( \\sigma_{0}^{2} \\sum x_{i} + \\mu_{0}\\sigma^{2} \\right) \\mu + \\left( \\mu_0^{2}\\sigma^{2}+\\sigma_{0}^{2}\\sum x_{i}^{2} \\right) \\right\\} \\right] \\\\[4pt]\n", "&= \\color{DarkOrchid}{ C_1 } \\text{exp} \\left[ -\\frac{1}{2} \\frac{\\left( n\\sigma_{0}^{2}+\\sigma^2 \\right)}{\\sigma^{2}\\sigma_{0}^{2}} \\left\\{ \\mu^{2} - 2 \\left( \\frac{\\sigma_{0}^{2} \\sum x_{i} + \\mu_{0}\\sigma^{2}}{n\\sigma_{0}^{2}+\\sigma^2} \\right) \\mu + \\left( \\frac{\\sigma_{0}^{2}\\sum x_{i}^{2}+\\mu_0^{2}\\sigma^{2}}{n\\sigma_{0}^{2}+\\sigma^2} \\right) \\right\\} \\right] \\\\[4pt]\n", "\\end{align} \\tag{2.6}\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- { } 부분을 완전제곱형태로 고친다. (completing the square)\n", "\n", "$$\n", "\\begin{align}\n", "&= \\color{DarkOrchid}{ C_1 } \\text{exp} \\left[ -\\frac{1}{2} \\underbrace{\\frac{\\left( n\\sigma_{0}^{2}+\\sigma^2 \\right)}{\\sigma^{2}\\sigma_{0}^{2}}}_{\\dfrac{1}{\\sigma^{2}_{n}}} \\left\\{ \\left( \\mu - \\underbrace{\\frac{\\sigma_{0}^{2} \\sum x_{i} + \\mu_{0}\\sigma^{2}}{n\\sigma_{0}^{2}+\\sigma^2}}_{\\mu_{n}} \\right)^{2} - \\left(\\frac{\\sigma_{0}^{2} \\sum x_{i} + \\mu_{0}\\sigma^{2}}{n\\sigma_{0}^{2}+\\sigma^2} \\right)^{2} + \\underbrace{\\left( \\frac{\\sigma_{0}^{2}\\sum x_{i}^{2}+\\mu_0^{2}\\sigma^{2}}{n\\sigma_{0}^{2}+\\sigma^2} \\right)}_{C_2} \\right\\} \\right] \\\\[4pt]\n", "&= \\color{DarkOrchid}{ C_1 } \\text{exp} \\left[ -\\frac{1}{2} \\frac{1}{\\sigma^{2}_{n}} \\left\\{ (\\mu-\\mu_{n})^{2} - \\mu^{2}_{n} + C_2 \\right\\} \\right] \\\\[4pt]\n", "&= \\color{DarkOrchid}{ C_1 } \\text{exp} \\left[ -\\frac{1}{2} \\frac{1}{\\sigma^{2}_{n}} (\\mu-\\mu_{n})^{2} + \\frac{1}{2} \\frac{1}{\\sigma^{2}_{n}} \\mu^{2}_{n} -\\frac{1}{2} \\frac{1}{\\sigma^{2}_{n}} C_2 \\right] \\\\[4pt]\n", "&= \\color{DarkOrchid}{ C_1 } \\text{exp} \\left\\{ -\\frac{1}{2} \\frac{1}{\\sigma^{2}_{n}} (\\mu-\\mu_{n})^{2} \\right\\} \\text{exp} \\left\\{ \\frac{1}{2} \\frac{1}{\\sigma^{2}_{n}} \\mu^{2}_{n} \\right\\} \\text{exp} \\left\\{ -\\frac{1}{2} \\frac{1}{\\sigma^{2}_{n}} C_2 \\right\\}\n", "\\end{align} \\tag{2.7}\n", "$$\n", "\n", "- 치환을 원래 모양으로 돌리면\n", "\n", "$$\n", "\\begin{align}\n", "=&\\color{DarkOrchid}{ \\frac{1}{\\left(\\sqrt{2\\pi \\sigma^2}\\right)^{n}} }\\color{DarkOrchid}{ \\frac{1}{\\sqrt{2\\pi \\sigma_0^2}} } \n", "\\text{exp} \\left\\{ \\frac{1}{2} \\frac{ n\\sigma_{0}^{2}+\\sigma^2 }{\\sigma^{2}\\sigma_{0}^{2}} \\left( \\frac{\\sigma_{0}^{2} \\sum x_{i}+\\mu_{0}\\sigma^{2}}{n \\sigma_{0}^{2} + \\sigma^2} \\right)^{2} \\right\\}\n", "\\text{exp} \\left\\{ -\\frac{1}{2} \\frac{ n\\sigma_{0}^{2}+\\sigma^2 }{\\sigma^{2}\\sigma_{0}^{2}} \\left( \\frac{\\sigma_{0}^{2} \\sum x_{i}^{2}+ \\mu_0^{2}\\sigma^{2}}{n\\sigma_{0}^{2}+\\sigma^2} \\right) \\right\\} \\\\\n", "&\\text{exp} \\left\\{ -\\frac{1}{2} \\frac{ n\\sigma_{0}^{2}+\\sigma^2 }{\\sigma^{2}\\sigma_{0}^{2}} \\left(\\mu- \\frac{\\sigma_{0}^{2} \\sum x_{i} + \\mu_{0}\\sigma^{2}}{n\\sigma_{0}^{2}+\\sigma^2} \\right)^{2} \\right\\} \\\\[4pt]\n", "= &\\color{DarkOrchid}{ \\frac{1}{\\left(\\sqrt{2\\pi \\sigma^2}\\right)^{n}} }\\color{DarkOrchid}{ \\frac{1}{\\sqrt{2\\pi \\sigma_0^2}} } \n", "\\color{ForestGreen}{ \\text{exp} \\left\\{ \\frac{1}{2} \\frac{(\\sigma_0^2 \\sum x_{i} + \\mu_{0} \\sigma^{2})^{2}}{\\sigma^{2}\\sigma_{0}^{2}(n\\sigma_{0}^{2}+\\sigma^2)} \\right\\} }\n", "\\color{Red}{ \\text{exp} \\left\\{ -\\frac{1}{2} \\left( \\frac{\\sigma_{0}^{2} \\sum x_{i}^{2}+ \\mu_0^{2}\\sigma^{2}}{\\sigma^{2}\\sigma_{0}^{2}} \\right) \\right\\} } \\\\\n", "& \\text{exp} \\left\\{ -\\frac{1}{2} \\frac{ n\\sigma_{0}^{2}+\\sigma^2 }{\\sigma^{2}\\sigma_{0}^{2}} \\left(\\mu- \\frac{\\sigma_{0}^{2} \\sum x_{i} + \\mu_{0}\\sigma^{2}}{n\\sigma_{0}^{2}+\\sigma^2} \\right)^{2} \\right\\} \\\\[4pt]\n", "\\end{align} \\tag{2.8}\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "- 정리하면 사후확률의 분자는 아래와 같다. \n", "\n", "$$\n", "\\begin{align}\n", "&p(D \\,|\\, \\mu, \\sigma^2) p(\\mu \\,|\\, \\mu_0, \\sigma^2_0) \\\\\n", "= & \\color{DarkOrchid}{ \\frac{1}{\\left(\\sqrt{2\\pi \\sigma^2}\\right)^{n}} }\\color{DarkOrchid}{ \\frac{1}{\\sqrt{2\\pi \\sigma_0^2}} } \n", "\\color{ForestGreen}{ \\text{exp} \\left\\{ \\frac{1}{2} \\frac{(\\sigma_0^2 \\sum x_{i} + \\mu_{0} \\sigma^{2})^{2}}{\\sigma^{2}\\sigma_{0}^{2}(n\\sigma_{0}^{2}+\\sigma^2)} \\right\\} }\n", "\\color{Red}{ \\text{exp}\\left\\{ -\\frac{1}{2} \\frac{\\sigma_{0}^{2} \\sum x_{i}^{2}+ \\mu_0^{2}\\sigma^{2} }{\\sigma^2\\sigma_{0}^{2}} \\right\\} } \\\\\n", "& \\text{exp} \\left\\{ -\\frac{1}{2} \\frac{ n\\sigma_{0}^{2}+\\sigma^2 }{\\sigma^{2}\\sigma_{0}^{2}} \\left(\\mu- \\frac{\\sigma_{0}^{2} \\sum x_{i} + \\mu_{0}\\sigma^{2}}{n\\sigma_{0}^{2}+\\sigma^2} \\right)^{2} \\right\\} \n", "\\end{align} \\tag{2.9}\n", "$$\n", "\n", "- 위 식에서 색깔부분은 모두 상수이고, 식 자체는 사후확률과 비례하므로 사후확률은 평균을\n", "\n", "$$\n", "\\mu_{n}= \\frac{\\sigma_{0}^{2} \\sum x_{i} + \\mu_{0}\\sigma^{2}}{n\\sigma_{0}^{2}+\\sigma^2}\n", "$$\n", "\n", "로하고 분산의 역수를\n", "\n", "$$\n", "\\frac{1}{\\sigma^{2}_{n}} = \\frac{ n\\sigma_{0}^{2}+\\sigma^2 }{\\sigma^{2}\\sigma_{0}^{2}}\n", "$$\n", "\n", "로 가지는 정규분포가 된다.\n", "\n", "- 이를 완전히 확인하려면 식(2.1)에서 $p(D)$는 정규화 상수이므로 $p(D)$가 식(2.9)의 색깔있는 부분과 마지막 $\\text{exp}(\\cdot)$부분의 적분으로 되어있음을 확인하면 된다.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.3 Marginal Likelihood\n", "\n", "- 확률의 합법칙은 다음과 같다.\n", "\n", "$$\n", "P(X) = \\sum_{Y} P(X,Y) = \\sum_{Y} P(X|Y)P(Y) \\tag{2.11}\n", "$$\n", "\n", "- 연속확률변수에 대해서는 적분으로 바꿔 생각할 수 있고, 가능도를 파라미터 $\\mu$에 대해 주변화시키면 아래와 같다.\n", "\n", "$$\n", "p(D) = \\int_{-\\infty}^{\\infty} \\underbrace{P(D \\,|\\, \\mu, \\sigma^2)}_{likelihood} \\underbrace{P(\\mu \\,|\\, \\mu_0, \\sigma_0^2)}_{prior} \\text{d}\\mu \\tag{2.12}\n", "$$\n", "\n", "- 식(2.12)를 실제로 적분해서 식(2.9)를 나눠본다.\n", "\n", "$$\n", "\\begin{align}\n", "p(D) &= \\int_{-\\infty}^{\\infty} p(D \\,|\\, \\mu, \\sigma^2) p(\\mu \\,|\\, \\mu_0, \\sigma^2_0) d\\mu \\\\[4pt]\n", "&= \\int_{-\\infty}^{\\infty} \\color{DarkOrchid}{ \\frac{1}{\\left(\\sqrt{2\\pi \\sigma^2}\\right)^{n}} } \\color{DarkOrchid}{ \\frac{1}{\\sqrt{2\\pi \\sigma_0^2}} } \\text{exp}\\left\\{ -\\frac{1}{2\\sigma^2} \\sum_{i=1}^{n} (x_{i}-\\mu)^2 \\right\\} \\text{exp} \\left\\{ -\\frac{1}{2\\sigma_0^2} (\\mu-\\mu_0)^2 \\right\\} \\text{d}\\mu \n", "\\end{align} \\tag{2.13}\n", "$$\n", "\n", "- 식(2.13)의 피적분 함수integrand 는 식(2.4)와 같으므로 피적분함수를 2.2절의 과정을 따라 똑같이 정리하면 다음과 같다.\n", "\n", "$$\n", "\\begin{align}\n", "p(D) &= \\int_{-\\infty}^{\\infty} p(D \\,|\\, \\mu, \\sigma^2) p(\\mu \\,|\\, \\mu_0, \\sigma^2_0) d\\mu \\\\\n", "&= \\color{DarkOrchid}{ \\frac{1}{\\left(\\sqrt{2\\pi \\sigma^2}\\right)^{n}} }\\color{DarkOrchid}{ \\frac{1}{\\sqrt{2\\pi \\sigma_0^2}} } \n", "\\color{ForestGreen}{ \\text{exp} \\left\\{ \\frac{1}{2} \\frac{(\\sigma_0^2 \\sum x_{i} + \\mu_{0} \\sigma^{2})^{2}}{\\sigma^{2}\\sigma_{0}^{2}(n\\sigma_{0}^{2}+\\sigma^2)} \\right\\} }\n", "\\color{Red}{ \\text{exp}\\left\\{ -\\frac{1}{2} \\frac{\\sigma_{0}^{2} \\sum x_{i}^{2}+ \\mu_0^{2}\\sigma^{2} }{\\sigma^2\\sigma_{0}^{2}} \\right\\} } \\\\\n", "& \\int_{-\\infty}^{\\infty} \\text{exp} \\left\\{ -\\frac{1}{2} \\frac{ n\\sigma_{0}^{2}+\\sigma^2 }{\\sigma^{2}\\sigma_{0}^{2}} \\left(\\mu- \\frac{\\sigma_{0}^{2} \\sum x_{i} + \\mu_{0}\\sigma^{2}}{n\\sigma_{0}^{2}+\\sigma^2} \\right)^{2} \\right\\} \\text{d}\\mu \n", "\\end{align} \\tag{2.14}\n", "$$\n", "\n", "- 결국 색깔 부분은 모두 약분되고 사후확률은 식(2.15)처럼 된다.\n", "\n", "$$\n", "p(\\mu \\,|\\, D) = \\frac{\\text{exp} \\left\\{ -\\frac{1}{2} \\frac{ n\\sigma_{0}^{2}+\\sigma^2 }{\\sigma^{2}\\sigma_{0}^{2}} \\left(\\mu- \\frac{\\sigma_{0}^{2} \\sum x_{i} + \\mu_{0}\\sigma^{2}}{n\\sigma_{0}^{2}+\\sigma^2} \\right)^{2} \\right\\}}\n", "{\n", "\\int_{-\\infty}^{\\infty} \\text{exp} \\left\\{ -\\frac{1}{2} \\frac{ n\\sigma_{0}^{2}+\\sigma^2 }{\\sigma^{2}\\sigma_{0}^{2}} \\left(\\mu- \\frac{\\sigma_{0}^{2} \\sum x_{i} + \\mu_{0}\\sigma^{2}}{n\\sigma_{0}^{2}+\\sigma^2} \\right)^{2} \\right\\} \\text{d}\\mu \n", "}\\tag{2.15}\n", "$$\n", "\n", "- 식(2.15)는 분자를 전영역에서 정적분해서 나눔으로써 분자에 있는 지수함수를 정규화하고 있다. 그래서 $p(\\mu \\,|\\, D)$는 적분이 1이 되는 정규분포가 됨을 알 수 있다.\n", "\n", "- 실제로 적분하기 위해서 지수항을 적분해야하는데 이는 가우스 적분으로 알려져있고 아래와 같다. 극좌표계로 바꿔서 적분하는 부분은 Youtube 강의에서 많이 찾아볼 수 있다. (예 : Evaluation of the Gaussian Integral exp(-x^2) - Cool Math Trick )\n", "\n", "$$\n", "\\int_{-\\infty}^{\\infty} \\text{exp} ( -ax^2 ) dx = \\sqrt{\\frac{\\pi}{a}} \\tag{2.16}\n", "$$\n", "\n", "- 지금 적분해야하는 함수는 $\\text{exp} \\left\\{ -a(x-b)^2 \\right\\}$ 꼴로 $\\text{exp} ( -ax^2 )$가 시프트되어 있으므로 $u = x-b$로 치환하면 $du = dx$이고 결국 \n", "\n", "$$\n", "\\int_{-\\infty}^{\\infty} \\text{exp} \\left\\{ -a(x-b)^2 \\right\\} dx = \\int_{-\\infty}^{\\infty} \\text{exp} \\left\\{ -a(u)^2 \\right\\} du= \\sqrt{\\frac{\\pi}{a}} \\tag{2.17}\n", "$$\n", "\n", "같은 적분결과를 얻을 수 있다. 이 결과를 이용해서 적분해보면\n", "\n", "$$\n", "\\int_{-\\infty}^{\\infty} \\text{exp} \\left\\{ -\\frac{1}{2} \\frac{ n\\sigma_{0}^{2}+\\sigma^2 }{\\sigma^{2}\\sigma_{0}^{2}} \\left(\\mu- \\frac{\\sigma_{0}^{2} \\sum x_{i} + \\mu_{0}\\sigma^{2}}{n\\sigma_{0}^{2}+\\sigma^2} \\right)^{2} \\right\\} d\\mu \n", "= \\sqrt{\\dfrac{\\pi}{\\frac{ n\\sigma_{0}^{2}+\\sigma^2 }{2\\sigma^{2}\\sigma_{0}^{2}}}}\n", "= \\sqrt{{\\frac{2\\pi\\sigma^{2}\\sigma_{0}^{2}}{n\\sigma_{0}^{2}+\\sigma^2}}}\n", "\\tag{2.18}\n", "$$\n", "\n", "- 사후확률분포를 최종적으로 정리해보면 \n", "\n", "$$\n", "\\begin{align}\n", "p(\\mu \\,|\\, D) &= \\frac{\\text{exp} \\left\\{ -\\frac{1}{2} \\frac{ n\\sigma_{0}^{2}+\\sigma^2 }{\\sigma^{2}\\sigma_{0}^{2}} \\left(\\mu- \\frac{\\sigma_{0}^{2} \\sum x_{i} + \\mu_{0}\\sigma^{2}}{n\\sigma_{0}^{2}+\\sigma^2} \\right)^{2} \\right\\}}{\\sqrt{\\frac{2\\pi\\sigma^{2}\\sigma_{0}^{2}}{n\\sigma_{0}^{2}+\\sigma^2}}} \\\\[4pt]\n", "&= \\sqrt{\\frac{n\\sigma_{0}^{2}+\\sigma^2}{2\\pi\\sigma^{2}\\sigma_{0}^{2} }}\n", "\\text{exp} \\left\\{ -\\frac{1}{2} \\frac{ n\\sigma_{0}^{2}+\\sigma^2 }{\\sigma^{2}\\sigma_{0}^{2}} \\left(\\mu- \\frac{\\sigma_{0}^{2} \\sum x_{i} + \\mu_{0}\\sigma^{2}}{n\\sigma_{0}^{2}+\\sigma^2} \\right)^{2} \\right\\} \\\\[4pt]\n", "&= \\sqrt{\\frac{1}{2\\pi}\\frac{n\\sigma_{0}^{2}+\\sigma^2}{\\sigma^{2}\\sigma_{0}^{2}}}\n", "\\text{exp} \\left\\{ -\\frac{1}{2} \\frac{ n\\sigma_{0}^{2}+\\sigma^2 }{\\sigma^{2}\\sigma_{0}^{2}} \\left(\\mu- \\frac{\\sigma_{0}^{2} \\sum x_{i} + \\mu_{0}\\sigma^{2}}{n\\sigma_{0}^{2}+\\sigma^2} \\right)^{2} \\right\\} \\\\[4pt]\n", "&= \\sqrt{\\frac{1}{2\\pi \\sigma^{2}_{n}}} \\text{exp} \\left\\{ - \\frac{1}{2 \\sigma^{2}_{n}} \\left( \\mu - \\mu_{n} \\right)^{2} \\right\\}\n", "\\end{align}\n", "\\tag{2.19}\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 이렇게 해서 정규분포를 이용한 사후확률분포를 구해보았다.\n", "\n", "- 위 내용을 다변수 정규분포로 확장하고 싶으면 More on Multivariate Gaussians[3]와 페이스북 아이디 Yeon Woo Jeong[4]님의 정리를 보면 도움이 된다.\n", "\n", "- 같은 내용을 이항분포, 베타분포에 대해서 계산한것은 페이스북 아이디 Issac Lee님의 이항분포와 베타분포의 궁합! 켤레사전분포(Conjugate prior dist.)에 대하여[5]를 보면 된다.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. 일변수 정규분포의 곱으로써의 다변수 정규분포 (참고)\n", "\n", "\n", "- 1 장에서 두 일변수 정규분포의 곱이 정규화되지 않은 정규분포가 되는 것을 확인했었다. \n", "\n", "- 이는 곱해지는 두 정규분포의 독립변수를 같은 변수로 보고 곱했을 때 이야기다. 즉 $\\mathbb{R} \\times \\mathbb{R} \\to \\mathbb{R}$인 경우이다. \n", "\n", "- 만약 두 변수를 다른 변수로 보고 $\\mathbb{R} \\times \\mathbb{R} \\to \\mathbb{R}^2$가 되는 경우라면 어떻게 될까? \n", "\n", "- 결과만 이야기하면 두 정규분포를 곱하는것만으로도 다변수 정규분포가 된다.\n", "\n", "- 그 과정을 확인 해본다.\n", "\n", "$$\n", "f(x_1) = \\frac{1}{ \\sqrt{2 \\pi}}\\frac{1}{ \\sqrt{\\sigma_{1}^{2}} } \\exp \\left\\{{-\\frac{(x_1-\\mu_1)^2}{2 \\sigma^{2}_{1}}}\\right\\} \\tag{3.1}\n", "$$\n", "\n", "$$\n", "g(x_2) = \\frac{1}{ \\sqrt{2 \\pi}}\\frac{1}{ \\sqrt{\\sigma_{2}^{2}} } \\exp \\left\\{{-\\frac{(x_2-\\mu_2)^2}{2 \\sigma^{2}_{2}}}\\right\\} \\tag{3.2}\n", "$$\n", "\n", "식(3.1), (3.2)처럼 일변수 정규분포의 변수를 각가 다른 변수로 보고 서로 곱하면\n", "\n", "$$\n", "\\begin{align}\n", "f(x_1, x_2) \n", "&= \\frac{1}{ \\sqrt{2 \\pi}}\\frac{1}{ \\sqrt{\\sigma_{1}^{2}} } \\exp \\left\\{{-\\frac{(x_1-\\mu_1)^2}{2 \\sigma^{2}_{1}}}\\right\\} \\frac{1}{ \\sqrt{2 \\pi}}\\frac{1}{ \\sqrt{\\sigma_{2}^{2}} } \\exp \\left\\{{-\\frac{(x_2-\\mu_2)^2}{2 \\sigma^{2}_{2}}}\\right\\} \\\\[5pt]\n", "&= \\frac{1}{ (2 \\pi)^{2/2} } \\frac{1}{ (\\sigma_{1}^{2})^{1/2} } \\frac{1}{ (\\sigma_{2}^{2})^{1/2} } \\exp \\left\\{-\\frac{1}{2} \\left( \\frac{(x_1-\\mu_1)^2}{ \\sigma^{2}_{1}} + \\frac{(x_2-\\mu_2)^2}{ \\sigma^{2}_{2}}\\right)\\right\\} \n", "\\end{align} \\tag{3.3}\n", "$$\n", "\n", "가 된다. 지수항 부분을 행렬-벡터형태로 바꿀 수 있다. $\\mathbf{x} = (x_1, x_2)^{\\text{T}}$, $\\boldsymbol{\\mu} = (\\mu_1, \\mu_2)^{\\text{T}}$로 두면\n", "\n", "$$\n", "f(\\mathbf{x}) = \\frac{1}{ (2 \\pi)^{2/2} } \\frac{1}{ \\left(\\sigma_{1}^{2} \\sigma_{2}^{2} \\right)^{1/2} }\\exp \\left\\{ -\\frac{1}{2} \\begin{Bmatrix} x_1-\\mu_1 \\\\ x_2-\\mu_2 \\end{Bmatrix}^{\\text{T}} \\begin{bmatrix}\n", "\\frac{1}{\\sigma_1^2} & 0 \\\\\n", "0 & \\frac{1}{\\sigma_2^2}\n", "\\end{bmatrix} \\begin{Bmatrix} x_1-\\mu_1 \\\\ x_2-\\mu_2 \\end{Bmatrix} \\right\\} \\tag{3.4}\n", "$$\n", "\n", "로 행렬-벡터 형태로 쓸 수 있다. 곱하기 전 각 함수의 분산 $\\sigma^2_1$, $\\sigma^2_2$를 주대각 요소로 가지는 대각 행렬을 \n", "\n", "$$\n", "\\Sigma = \\begin{bmatrix}\n", "\\sigma_1^2 & 0 \\\\\n", "0 & \\sigma_2^2\n", "\\end{bmatrix}\n", "$$\n", "\n", "로 두면 이 행렬의 역행렬과 행렬식은 \n", "\n", "$$\n", "\\Sigma^{-1}= \\begin{bmatrix}\n", "\\dfrac{1}{\\sigma_1^2} & 0 \\\\\n", "0 & \\dfrac{1}{\\sigma_2^2}\n", "\\end{bmatrix} \n", "$$\n", "\n", "$$\n", "\\det(\\Sigma) = \\sigma_1^2 \\sigma_2^2\n", "$$\n", "\n", "위 결과를 이용하고 이변수라서 $D$=2로 놓고 식(3.4)를 다시 써보면\n", "\n", "$$\n", "f(\\mathbf{x}) = \\frac{1}{ (2 \\pi)^{2/2} } \\frac{1}{ \\det(\\Sigma)^{1/2} }\\exp \\left\\{ -\\frac{1}{2} (\\mathbf{x}-\\boldsymbol{\\mu})^{\\text{T}} \\Sigma^{-1} (\\mathbf{x}-\\boldsymbol{\\mu}) \\right\\} \\tag{3.5}\n", "$$\n", "\n", "가 되어 완전한 2변수 정규분포함수가 됨을 알 수 있다." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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nzVS2ikJjjZ1HxFYzMgJDDJomovR1bjq2Ff3FX9U4kumpvPhc9GzZiY5N76Pm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A6vdR/8ij1OZy5C/oInP9lQzEREZjp48JgJpqk5a6dJZ2MUpbtZ18Pl/4XWZyDP/kEZL9w+RV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\nZafpH54ra2QQFo98zZ44z6nTRxnX24h1dBCuqubj4XCxg6gMDyKA2LnLTP7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QQBCENZlK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\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FxK/dga608IjHvWPHDlKpFAUFBdTV1aGSRAqMGiY69OStfRdVXz8htcQBQUFvL8Ynmmjs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DEyXs+2UjsnrS7yKpuYlGIkTNl9C+S+RjDHmSQK9U0kUUgiWPTUZjIvL4+tW7fy0ksvMXz4cJ5+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\nz7Bt39fxuTrGTMq9N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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from mpl_toolkits.mplot3d import Axes3D\n", "\n", "mpl.style.use('bmh')\n", "plt.rcParams[\"figure.figsize\"] = (20,10)\n", "fig = plt.figure()\n", "\n", "g_1 = Gaussian(0.0, 2.0)\n", "g_2 = Gaussian(0.0, 1.5)\n", "g_12 = g_1*g_2\n", "\n", "# 그냥 곱한 경우\n", "x = np.linspace(-6, 6, 100)\n", "g_x1 = g_1.pdf(x)\n", "g_x2 = g_2.pdf(x)\n", "\n", "ax1 = fig.add_subplot(1, 2, 1)\n", "ax1.plot(x, g_1.pdf(x), label=r'$f(x_1)$')\n", "ax1.plot(x, g_2.pdf(x), label=r'$f(x_2)$')\n", "ax1.plot(x, g_12.pdf(x), label=r'$f(x_1)f(x_2)$')\n", "legend = ax1.legend(loc='upper right',fontsize=20)\n", "\n", "# 2변수로 곱한 경우\n", "g_x1m = np.tile(g_x1, (100, 1))\n", "g_x2m = np.tile(g_x2, (100, 1))\n", "\n", "xx1, xx2 = np.meshgrid(x, x)\n", "G = np.dot(g_2.pdf(x).reshape(-1,1), g_1.pdf(x).reshape(1,-1))\n", "\n", "#plt3d = plt.figure().gca(projection='3d')\n", "ax2 = fig.add_subplot(1, 2, 2, projection='3d')\n", "\n", "ax2.plot_wireframe(xx1, xx2, G, rstride=0, cstride=6, alpha=0.6, colors=\"#A60628\")\n", "ax2.plot_wireframe(xx1, xx2, G, rstride=6, cstride=0, alpha=0.6, colors=\"#348ABD\")\n", "\n", "#파란 그래프\n", "ax2.contourf(xx1, xx2, G, zdir='y', offset=ax2.get_ylim()[1])\n", "ax2.contour(xx1, xx2, g_x1m, zdir='y', colors='#348ABD', alpha=0.7, offset=ax2.get_ylim()[1])\n", "\n", "#빨간 그래프\n", "ax2.contourf(xx1, xx2, G, zdir='x', offset=ax2.get_xlim()[0])\n", "ax2.contour(xx1, xx2, g_x2m.T, zdir='x', colors='#A60628', alpha=0.7, offset=ax2.get_xlim()[0])\n", "\n", "ax2.contour(xx1, xx2, G, zdir='z', offset=-0.05)\n", "\n", "ax2.text(3, 6, 0.15, r'$f(x_1)$', color='#348ABD', zdir='x', fontsize=20)\n", "ax2.text(-6.8, -6, 0.20, r'$f(x_2)$', color='#A60628', zdir='y', fontsize=20)\n", "\n", "ax2.set_xlabel(r'$x_1$ axis',fontsize=20)\n", "ax2.set_ylabel(r'$x_2$ axis',fontsize=20)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 위 코드는 지금까지 내용을 실험한 것이다. 두 정규분포 함수 $f(x_1)=\\mathcal{N}(x_1 \\mid \\mu_1 = 0.0, \\sigma^2_1=2.0)$, $f(x_2)=\\mathcal{N}(x_2 \\mid \\mu_2= 0.0, \\sigma_2^2=1.5)$가 있을 때 이를 그냥 일변수 상태에서 곱해서 그린것이 왼쪽 보라색 그래프이다. \n", "그림에서 붉은색과 파란색 그래프 아래 넓이가 1이기 때문에 키가 작은 보라색 그래프 아래 넓이는 1이 아님을 알 수 있다. \n", "\n", "- 이 두 함수를 $x_1$과 $x_2$를 두 축으로 하는 이차원 평면에 그려보면 오른쪽 그림처럼 언덕 모양의 함수가 된다. \n", "이 경우에도 $f(x_1)$과 $f(x_2)$의 두 값이 곱해져서 함수값이 결정되므로 언덕의 키는 원래 두 함수 보다 작아졌다. 하지만 적분값이 1이 됨을 식(3.5)를 유도하면서 간접적으로 확인해보았다. 직관적으로는 키는 작아졌지만 적분값이 그래프 아래 부피가 되기 때문에 키가 작아진 만큼 충분히 커져서 1이 된다고 이해할 수 있다. \n", "\n", "- 그래프에서 회색 그림자는 언덕을 $x_1z$, $x_2 z$평면으로 투영 시킨 그림자이다. 그림자를 보면 파란색 그래프 아래 그림자가 붉은색 그래프 아래 그림자 보다 넓게 퍼져있는 것을 확인할 수 있다.\n", "\n", "- 이 상태에서 $x_2$의 값을 하나로 고정시킨 $f(x_1, x_2=-2)$ 그래프를 그려보고 이 그래프 아래의 넓이가 얼마가 되는지 알아보자. 해당 그래프는 위 오른쪽 그래프에서 $x_2=-2$에 해당하는 파란색 와이어 프레임 그래프가 되므로 키가 0.05보다 작은 종모양 그래프가 될것이다. (가장 높은 $x_2=0$에서의 키가 0.05이므로)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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XltiHi4iIiNLFuI7hmgq07s2RaZinPGYqi3nKY6bymKksrfNkwQXte3NkGuYp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\nudPjv1wz4VgPIrrBqNclT1k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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "0.10934004978399578" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import scipy.integrate as integrate\n", "\n", "def mvn(x1):\n", " return (g_1.pdf(x1)*g_2.pdf(-2))\n", "\n", "plt.rcParams[\"figure.figsize\"] = (10, 5)\n", "\n", "# mvn(x) = p(x1, x2=-2) != p(x1|x2=-2)\n", "plt.plot(x, mvn(x))\n", "#plt.plot(x, mvn(x), x, mvn(x)/g_2.pdf(-2))\n", "plt.ylim(0, 0.2)\n", "plt.show()\n", "\n", "# integral\n", "integrate.quad(mvn, -np.inf, np.inf)[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 위 그래프의 적분값은 0.109정도가 되어 정규화되지 않은 상태임을 알 수 있다. 위에 보이는 그래프는 두 확률변수의 결합확률분포 $f(x_1,x_2)$를 나타내는 그래프에서 $x_2$를 한 값으로 고정시켰을때 그래프가 된다. \n", "\n", "- 이를 $x_2$를 조건으로하는 $x_1$의 확률분포로 나타내려면 베이즈정리에 의해\n", "\n", "$$\n", "f(x_1 \\mid x_2=-2) = \\frac{f(x_1, x_2=-2)}{f(x_2=-2)} \\tag{3.6}\n", "$$\n", "\n", "처럼 $f(x_2=-2)$로 정규화 시켜주면 " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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t8p6/Nw/79+/nxRdfBCAvLw8XF5c6H7Om/Q0cOJDS0lIAkpKSCAsLq7J9bS4p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\ncE4Kg3MOvbC3PxiirtV3SGt3bfQArckdiLaSeQ57P60COVYDvVIN9LI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SUgoKCqTYOkVj\nxoxh/vz53HTTTTgcDlwu1yFDCzqLFFzA2WefzQcffMD06dMBeOCBB1SOSIhDvfHGGzQ3N3PzzTfH\nlq1YsQKDwaBiVMln+PDhDB06lBkzZqAoCgsXLlQ7pKT317/+laamJm6//fbYsscee4zevXurGJUQ\nB+Tl5XHRRRdx9dVXA3D//fej0XT+EHYlLIMYhBBCCCESSs5SFEIIIYRIMCm4hBBCCCESTAouIYQQ\nQogEk4JLCCGEECLBpOASQgghhEgwKbiEEEIIIRJMCi4hhBBCiASTgksIIYQQIsH+P2SD+UZzc2QY\nAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(x, mvn(x), label=r'$f(x_1, x_2=-2)$')\n", "plt.plot(x, mvn(x)/g_2.pdf(-2), label=r'$\\frac{f(x_1, x_2=-2)}{f(x_2=-2)}$')\n", "legend = plt.legend(loc='upper right',fontsize=20)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 위 그래프처럼 붉은색 그래프가 되어 다시 $f(x_1)$으로 돌아오게 된다. 이는 \n", "\n", "$$\n", "f(x_1 \\mid x_2=-2) = \\frac{f(x_1, x_2=-2)}{f(x_2=-2)} = \\frac{f(x_1)f(x_2=-2)}{f(x_2=-2)}=f(x_1) \\tag{3.7}\n", "$$\n", "\n", "이 되는 것으로 당연한 결과이며 식(3.7)은 두 변수가 서로 독립임을 의미한다. \n", "\n", "- 이 결과는 $f(x_1, x_2)=f(x_1)f(x_2)$인 정의와도 잘 합치한다." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. 참고문헌\n", "\n", "\n", "1. Products and Convolutions of Gaussian Probability Density Functions, P.A. Bromiley, http://www.tina-vision.net/docs/memos/2003-003.pdf\n", "\n", "2. Conjugate Bayesian analysis of the Gaussian distribution, Kevin P. Murphy, https://www.cs.ubc.ca/~murphyk/Papers/bayesGauss.pdf\n", "\n", "3. More on Multivariate Gaussians, Chuong B. Do, http://cs229.stanford.edu/section/more_on_gaussians.pdf?fref=gc\n", "\n", "4. Gaussian_Process, Yeon Woo Jeong, http://nbviewer.jupyter.org/github/maestrojeong/Machine_learning/blob/master/Gaussian_Process/gaussian_process_theory.ipynb?fref=gc\n", "\n", "5. 이항분포와 베타분포의 궁합! 켤레사전분포(Conjugate prior dist.)에 대하여, Issac Lee, http://issactoast.com/116\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%html\n", "\n", "\n", "\n", "\n", "\n", "" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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" } }, "nbformat": 4, "nbformat_minor": 2 }