GAN/change_of_variable.ipynb

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   "source": [
    "# Change of continuous random variable\n",
    "\n",
    "<p style=\"text-align: right;\">2017.06.09 조준우 metamath@gmail.com</p>\n",
    "\n",
    "<hr/>\n",
    "\n",
    "어떤 확률 변수 $Z$가 있고 $X=g(Z)$관계에 의해 정의되는 확률변수 $X$가 있다. \n",
    "이때 확률 변수 $Z$가 $z_{1} \\le z \\le z_{2}$의 값을 가질 때 발생하는 사건을 A라 하자. 예를 들어  $z_{1} \\le z \\le z_{2}$이면 우리는 오늘 저녁에 피자를 먹는다. 즉, 피자를 먹는 사건이 A이다. 그렇다면 오늘 저녁 피자를 먹을 수 있을 확률은 다음과 같다.\n",
    "\n",
    "$$P(A) = P(z_{1} \\le z \\le z_{2}) =\\int _{z_{1}} ^{z_{2}} p_{Z}(z) dz \\tag{1}$$\n",
    "\n",
    "이제 같은 사건 A가 일어날 확률을 $X=g(Z)$로 변환된 확률변수 $X$로 표현하면 다음과 같을 것이다.\n",
    "\n",
    "$$P(A) = P(x_{1} \\le x \\le x_{2}) = \\int _{g(z_{1})} ^{g(z_{2})} p_{X}(x) dx \\tag{2}$$\n",
    "\n",
    "아직 변환된 $X$에 대한 확률분포 $p_{X}(x)$를 모르는데 두 경우 사건 A가 일어날 확률을 동일하므로 $X=g(Z)$관계에 의해 적당히 잘 변환된 $p_X(x)$를 다음과 같은 관계식으로부터 찾을 수 있다.<sup>[1]</sup>\n",
    "\n",
    "$$\n",
    "P(z_{1} \\le z \\le z_{2}) = \\int _{z_{1}} ^{z_{2}} p_{Z}(z) dz = \\int _{x_{1}=g(z_{1})} ^{x_{2}=g(z_{2})} p_{X}(x) dx = P(x_{1} \\le x \\le x_{2}) \n",
    "\\tag{3}\n",
    "$$\n",
    "\n",
    "일단 $z_{1} \\le z \\le z_{2}$ 전구간에서 $X=g(Z)$의 역함수 $Z=g^{-1}(X)$가 존재한다고 가정하면 다음처럼 변수를 바꿔서 적분할 수 있다.\n",
    "\n",
    "$$\n",
    "\\int _{z_{1}} ^{z_{2}} p_{Z}(z) dz = \\int _{x_{1}=g(z_{1})} ^{x_{2}=g(z_{2})} p_{Z}(g^{-1}(x)) \\frac{d g^{-1}(x)}{dx} dx \\tag{4}\n",
    "$$\n",
    "\n",
    "확률변수 $Z$와 $X$의 도메인이 모두 1차원이라면 식(4)와 같으나 2차원 이상이 되어 적분의 경계가 영역이 되면 다음처럼 Jacobian에 절대값을 적용해야한다. 확률변수 $Z$와 $X$의 특정 영역을 $\\hat{Z}$, $\\hat{X}$라 하면\n",
    "\n",
    "$$\n",
    "\\int _{z \\in \\hat{Z}} p_{Z}(z) dz = \\int _{x \\in \\hat{X}} p_{Z}(g^{-1}(x)) \\left| \\frac{d g^{-1}(x)}{dx} \\right| dx \\tag{5}\n",
    "$$\n",
    "\n",
    "1차원에서 절대값이 필요없는 이유는 적분구간 양끝의 순서를 바꿀 수 있기 때문이다.\n",
    "예를 들어\n",
    "\n",
    "$$\n",
    "\\int_{1}^{2} (3x+1)^3 dx = \\frac{715}{4}\n",
    "$$\n",
    "\n",
    "에서 $x = g(t)= -\\frac{t+1}{3}$으로 치환한다고 하면 $t = -3x-1$ 이므로 \n",
    "\n",
    "$$\n",
    "\\int_{1}^{2} (3x+1)^3 dx=\\int_{-3(1)-1}^{-3(2)-1} \\left(3g(t) +1\\right)^3 \\frac{dg(t)}{dt} dt = \\int_{-4}^{-7} (-t)^3 \\left(-\\frac{1}{3}\\right) dt = \\frac{715}{4}\n",
    "$$\n",
    "\n",
    "가 되는데 변수를 바꾸고 나서 적분의 경계를 보면 큰수가 아래오고 작은 수가 위로 가 있다. 이는 $g(t)$를 감소함수로 선택했기 때문에 일어나는 현상인데 이때 적분의 경계의 위치를 바꾸어 작은수가 밑으로 오고 큰수가 위로 가게 하면\n",
    "\n",
    "$$\n",
    "\\int_{-4}^{-7} (-t)^3 \\left(-\\frac{1}{3}\\right) dt = -\\int_{-7}^{-4} (-t)^3 \\left(-\\frac{1}{3}\\right) dt = \\int_{-7}^{-4} (-t)^3 \\left(\\frac{1}{3}\\right) dt=\\frac{715}{4}\n",
    "$$\n",
    "\n",
    "가 되어 경계를 바꾸는것으로 인해 $dg(t) / dt$의 음의 부호가 사라진다. 그래서 항상 작은 수를 아래쪽 경계로 쓰기로 하고, $g(t)$가 증가함수든 감소함수든 상관이 없으려면 식(5)와 같이 절대값을 써준다. 하지만 1차원에서는 경계의 아래쪽이 크든 작든 상관없으므로 $g(t)$가 어떤 함수라하더라도 절대값을 안써도 상관없다. \n",
    "\n",
    "어쨋거나 식(5)의 우변은 식(3)에 의해 아래와 같으므로\n",
    "\n",
    "$$\n",
    "\\int _{x \\in \\hat{X}} p_{Z}(g^{-1}(x)) \\left| \\frac{d g^{-1}(x)}{dx} \\right| dx \n",
    "= \\int _{x \\in \\hat{X}} p_{X}(x) dx   \\tag{6}\n",
    "$$\n",
    "\n",
    "결과적으로 $p_X(x)$는 다음과 같다.\n",
    "\n",
    "$$p_X(x) = p_Z (g^{-1}(x)) \\left|\\frac{d g^{-1}(x) }{d x}\\right| \\tag{7}$$\n",
    "\n",
    "$p_X(x)$를 교재에 따라 다음처럼 다르게 표현하기도 하는데 다 같은 표현이다. <sup>[2][3]</sup>\n",
    "\n",
    "$$\n",
    "p_X(x) \n",
    "= p_Z (g^{-1}(x)) \\left|\\frac{d g^{-1}(x) }{d x}\\right| \n",
    "= p_Z (g^{-1}(x)) \\left|\\frac{dz }{d g(z)}\\right| \n",
    "= \\frac{p_Z (g^{-1}(x))}{\\left|\\frac{d g(z)}{dz}\\right|}\n",
    "= \\frac{p_Z (z)}{\\left|\\frac{d g(z)}{dz}\\right|} \n",
    "\\tag{8}\n",
    "$$\n",
    "\n",
    "반대로 $p_X(x)$로 부터 $p_Z(z)$는 다음과 같이 구해진다.\n",
    "\n",
    "$$\n",
    "p_Z(z) = p_X(x)\\left|\\frac{dg(z)}{dz}\\right|=p_X(g(z))\\left|\\frac{d g(z)}{dz}\\right| \\tag{9}\n",
    "$$\n",
    "\n",
    "여기서 알 수 있는 점은 $p_X(x)$가 $Z=g^{-1}(X)$ 관계에 의해 단순히 합성함수인 $p_Z(g^{-1}(x))$ 와 같지 않다는 점이다. $X=g(Z)$이니까  $p_X(x)$는  $p_Z(z)$에서 $z$를 모두 $g^{-1}(x)$로 대체한 합성함수  $p_Z(g^{-1}(x))$가 아닐까 생각할 수 도 있는데 아니라는 것이다. 마찬가지로 $p_Z(z)$도 $X=g(Z)$ 관계에 의한 합성함수 $p_X(g(z))$ 와 같지 않다. 실제 코딩 실습으로 알아보면 다음과 같다. 아래 실습예제는 PRML<sup>[4]</sup>의 연습문제 1.4번을 살짝 거꾸로 바꾼것이다.\n",
    "\n",
    "확률변수 $Z$의 확률밀도함수는 평균이 6, 분산이 1.0인 정규 분포이다. \n",
    "\n",
    "$$\n",
    "p_{Z}(z) = \\mathcal{N}(z \\, | \\, \\mu = 6, \\sigma^{2}=1.0) \\tag{10}\n",
    "$$\n",
    "\n",
    "$Z$를 $X$로 매핑하는 매핑함수 $g(z)$는 다음과 같다. 흔히 쓰는 시그모이드 함수이다.\n",
    "\n",
    "$$\n",
    "x = g(z)= \\frac{1}{1+\\exp (-z +5) } \\tag{11}\n",
    "$$\n",
    "\n",
    "역함수 $g^{-1}(x)$는 다음과 같다.\n",
    "\n",
    "$$\n",
    "z = g^{-1}(x)= \\log(x)-\\log(1-x)+5 \\tag{12}\n",
    "$$\n",
    "\n",
    "이를 바탕으로 식(7)에 의해 $X$의 pdf를 구할 수 있다.\n",
    "다음에 실습코드가 있고 class pz_gen으로 연속확률변수 $Z$를 class px_gen로 확률변수 $X$를 구현했다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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BG+A8zmMmMzmbs/Hjb8XEx5mvNhIrjntDB873NmAbDvy/9KR7Di2OmXF4Uls2fbBKooiI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\nknJMEiVJkiRJOf8fxliZe9YWn5IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f50ce93e470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "우리가 저녁으로 피자를 먹을 확률은\n",
      "integral from 5.5     to 6.5    p_Z(z) dz = 0.382925\n",
      "integral from g(5.5)  to g(6.5) p_X(x) dx = 0.382925\n",
      "동일하다.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.integrate as integrate\n",
    "from scipy.stats import rv_continuous\n",
    "from matplotlib.patches import Polygon\n",
    "\n",
    "def g(z) :\n",
    "    return 1.0 / (1.0+np.exp(-z+5))\n",
    "\n",
    "def g_inv(x) :    \n",
    "    return np.log(x)-np.log(1-x)+5\n",
    "\n",
    "class pz_gen(rv_continuous):\n",
    "    \"P_Z(z) distribution for R.V. Z\"\n",
    "    \n",
    "    mu = 6\n",
    "    sigma = 1.0\n",
    "    \n",
    "    def Normal(self, z) :\n",
    "        return (1 / np.sqrt(2*np.pi*(self.sigma**2)))*np.exp( -(1/2*(self.sigma**2))*(z-self.mu)**2 )\n",
    "\n",
    "    def _pdf(self, z) :\n",
    "        return self.Normal(z)\n",
    "\n",
    "        \n",
    "class px_gen(rv_continuous):\n",
    "    \"P_X(x)  distribution for R.V. X\"\n",
    "\n",
    "    mu = 6\n",
    "    sigma = 1.0\n",
    "    \n",
    "    def __init__(self):\n",
    "        \"\"\"\n",
    "        확률 변수 X는 범위가 0~1사이에 있다.\n",
    "        \"\"\"\n",
    "        rv_continuous.__init__(self, a=0.0, b=1.0)\n",
    "        \n",
    "    def Normal(self, z) :\n",
    "        return (1 / np.sqrt(2*np.pi*(self.sigma**2)))*np.exp( -(1/2*(self.sigma**2))*(z-self.mu)**2 )\n",
    "    \n",
    "    def g(self, z) :\n",
    "        return 1.0 / (1.0+np.exp(-z+5))\n",
    "\n",
    "    def g_prime(self, z):\n",
    "        return self.g(z)*(1-self.g(z))\n",
    "    \n",
    "    def g_inv(self, x) :    \n",
    "        return np.log(x)-np.log(1-x)+5\n",
    "\n",
    "    def g_inv_prime(self, x):\n",
    "        return (1/x)+(1/(1-x))\n",
    "        \n",
    "    def _pdf(self, x) :\n",
    "        #아래 두 표현 모두 동일하다. EQ.(8)\n",
    "        #return np.multiply( self.Normal(self.g_inv(x)) , np.abs(1/self.g_prime(self.g_inv(x))) )\n",
    "        return np.multiply( self.Normal(self.g_inv(x)) , np.abs(self.g_inv_prime(x)) )\n",
    "    \n",
    "# Get current size\n",
    "fig_size = plt.rcParams[\"figure.figsize\"]\n",
    "fig_size = (15,10)\n",
    "plt.rcParams[\"figure.figsize\"] = fig_size\n",
    "font = { 'size': 20, }\n",
    "\n",
    "#각 확률변수의 샘플 개수\n",
    "nos = 5000\n",
    "\n",
    "Z = pz_gen()\n",
    "X = px_gen()\n",
    "z = np.linspace(0, 10, 100)\n",
    "x = g(z)\n",
    "z_hat = 6\n",
    "x_hat = g(z_hat)\n",
    "\n",
    "Z_sample = Z.rvs(size=nos)\n",
    "X_sample = X.rvs(size=nos)\n",
    "\n",
    "fig, ax2 = plt.subplots(1, 1)\n",
    "\n",
    "ax2.plot(z, Z._pdf(z), 'r')\n",
    "ax2.plot(z, x)\n",
    "ax2.plot(X._pdf(x), x, 'm')\n",
    "ax2.text(7.5, 0.85, r'$x=g(z)$', color='orange', fontdict=font)\n",
    "ax2.text(1.8, 0.65, r'$p_X(x)$', color='m', fontdict=font)\n",
    "ax2.text(2.0, 0.4,  r'$p_Z(g^{-1}(x))$', color='green', fontdict=font)\n",
    "ax2.text(7.3, 0.2,  r'$p_Z(z)$', color='r', fontdict=font)\n",
    "#극점 잇는 점선 그리기\n",
    "ax2.plot( (z_hat, z_hat) , (Z.Normal(z_hat),x_hat), 'y--' )\n",
    "ax2.plot( (4 , z_hat),     (  x_hat , x_hat  ), 'y--')\n",
    "#극점 그리기\n",
    "ax2.plot(z_hat, Z.Normal(z_hat), 'ro')\n",
    "ax2.plot(z_hat, x_hat, 'ro')\n",
    "ax2.hist(Z_sample, 40, normed=1, facecolor='r', alpha=0.5, edgecolor='r')\n",
    "ax2.hist(X_sample, 40, normed=1, facecolor='m', alpha=0.5, edgecolor='m', orientation='horizontal')\n",
    "ax2.set_xlim([0, 10])\n",
    "ax2.set_xlabel('z', fontsize=20)\n",
    "\n",
    "# Make the shaded integral region P_z(z)\n",
    "ix = np.linspace(5.5, 6.5)\n",
    "iy = Z._pdf(ix)\n",
    "verts = [(5.5, 0)] + list(zip(ix, iy)) + [(6.5, 0)]\n",
    "poly = Polygon(verts, facecolor='0.9', edgecolor='0.6', alpha=0.5)\n",
    "ax2.add_patch(poly)\n",
    "\n",
    "# Make the shaded integral region P_x(x)\n",
    "ix = np.linspace(g(5.5), g(6.5))\n",
    "iy = X._pdf(ix)\n",
    "verts = [(0,g(5.5))] + list(zip(iy, ix)) + [(0,g(6.5))]\n",
    "poly = Polygon(verts, facecolor='0.9', edgecolor='0.6', alpha=0.5)\n",
    "ax2.add_patch(poly)\n",
    "\n",
    "ax3 = ax2.twiny()\n",
    "ax3.plot(Z.Normal(g_inv(x)),   x, 'g') \n",
    "ax3.plot(X.Normal(g_inv(x_hat)), x_hat, 'ro') #극점 그리기\n",
    "ax3.set_xlim([0, 1])\n",
    "ax2.set_ylabel('x', fontsize=20)\n",
    "\n",
    "plt.show()\n",
    "\n",
    "#print(\"dx[p_x(x)]=0 at x=6 , dz[p_x(g(z))]=0 at g_inv(6)={:f}\".format(z_hat))\n",
    "\n",
    "#구간 적분을 해본다.\n",
    "print(\"우리가 저녁으로 피자를 먹을 확률은\")\n",
    "print(\"integral from 5.5     to 6.5    p_Z(z) dz = {:f}\".format(  integrate.quad(Z._pdf, 5.5, 6.5)[0]   ) )\n",
    "print(\"integral from g(5.5)  to g(6.5) p_X(x) dx = {:f}\".format(  integrate.quad(X._pdf, g(5.5), g(6.5))[0]   ) )\n",
    "print(\"동일하다.\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "결과로 나온 그래프는 가로축을 $z$로 하여 $p_{Z}(z)$와 $X=g(Z)$를 그리고 세로축에 매핑된 $X$에 대한 확률밀도함수를 그린것이다. $Z$가 $X=g(Z)$의해 변환될 때 $p_{X}(x)$는 그림에서 마젠타색 그래프가 된다. $p_{Z}(z)$에서 $X=g(Z)$를 이용하여 만든 합성함수 $p_{Z}(g^{-1}(x))$는 녹색으로 표시되었는데 실제 $p_{X}(x)$와는 다름을 확인 할 수 있다. $p_{Z}(z)$의 극점은 합성함수 $p_{Z}(g^{-1}(x))$의 극점과 일치하나 실제 $p_{X}(x)$의 극점과는 일치하지 않음을 알 수 있다. 마지막으로 음영처리된 부분이 우리가 저녁으로 피자를 먹을 확률에 해당하는 부분인데 두 확률분포에서 음영처리된 부분의 면적은 같으므로 변환된 확률변수상에서 사건 A가 일어날 확률은 동일하다는 전재가 깨어지지 않았음을 확인할 수 있다.\n",
    "\n",
    "머신러닝<sup>[5]</sup>책에 나오는 간단한 예제 하나를 더 정리해 본다.\n",
    "\n",
    "$X \\sim Unif(-1,1)$인 확률변수에 대해 $Y = X^2$인 관계에 있는 확률변수 $Y$의 확률밀도함수를 구하라.\n",
    "\n",
    "변환 관계는 다음과 같다.\n",
    "\n",
    "$$\n",
    "y = f(x) = x^2 \\\\[5pt]\n",
    "x = f^-1 (y) = \\sqrt{y}\n",
    "$$\n",
    "\n",
    "그리고 논의한바와 같이 확률밀도함수의 변환은 다음과 같다.\n",
    "\n",
    "$$\n",
    "p_y(y) = p_x(x) \\left| \\frac{dx}{dy} \\right| = p_x(f^{-1}(y)) \\left| \\frac{df^{-1}(y)}{dy} \\right|\n",
    "$$\n",
    "\n",
    "\n",
    "- 균등분포의 확률밀도함수의 정의는 $\\frac{1}{b-a}$이므로 확률변수 $X$의 확률밀도함수는 \n",
    "\n",
    "$$\n",
    "p_x(x) = \\frac{1}{b-a} = \\frac{1}{1-(-1)} = \\frac{1}{2}\n",
    "$$\n",
    "\n",
    "- 확률변수 $Y$의 도메인은 $Y = X^2$에 의해 (0,1)이다.\n",
    "\n",
    "- $p_x(f^{-1}(y))$는 $p_x(x)$의 $x$를 $x=f^{-1}(y)$에 의해 $y$로 바꾼 합성함수이다. 따라서 변환된 도메인 (0,1)에 의해 \n",
    "\n",
    "\n",
    "$$\n",
    "p_x(f^{-1}(y)) = \\frac{1}{b-a} = \\frac{1}{1-0} = 1\n",
    "$$\n",
    "\n",
    "이고, 최종적으로 다음과 같이 $Y$의 확률밀도함수를 구할 수 있다.\n",
    "\n",
    "$$\n",
    "p_y(y) = p_x(f^{-1}(y)) \\left| \\frac{df^{-1}(y)}{dy} \\right| = 1 \\frac{d \\sqrt{y}}{dy} = \\frac{1}{2} y^{\\frac{1}{2}}\n",
    "$$"
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    "## 참고문헌\n",
    "<hr/>\n",
    "\n",
    "1. EC 2019 Sampling and Inference, Department of Economics, The University of Leicester, http://www.le.ac.uk/users/dsgp1/COURSES/LEISTATS/Lecture4.pdf \n",
    "\n",
    "2. Introduction to Probability, Statistics, and Random Processes, Hossein Pishro-Nik, https://www.probabilitycourse.com/ \n",
    "\n",
    "3. PennState, STAT 414 / 415 Intro Probability Theory, https://onlinecourses.science.psu.edu/stat414/node/157 \n",
    "\n",
    "4. Pattern Recognition and Machine Learning, Christopher M. Bishop, Springer \n",
    "\n",
    "5. 머신러닝Machine Learning: A Probabilistic Perspective, Kevin P. Murphy,노영찬,김기성(옮김), The MIT Press, 에이콘\n"
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