ee046202_tutorial_00_probability_optimization.ipynb

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    "# <img src=\"https://img.icons8.com/dusk/64/000000/artificial-intelligence.png\" style=\"height:50px;display:inline\"> EE 046202 - Technion - Unsupervised Learning & Data Analysis\n",
    "---\n",
    "\n",
    "#### <a href=\"https://taldatech.github.io\">Tal Daniel</a>\n",
    "\n",
    "## Tutorial 00 - Probability, Optimization and Inequalities  Refresher\n",
    "---"
   ]
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    "### <img src=\"https://img.icons8.com/bubbles/50/000000/checklist.png\" style=\"height:50px;display:inline\"> Agenda\n",
    "---\n",
    "* [Probability Basics](#-Probability-Basics)\n",
    "    * [Bayes Rule](#-Bayes-Rule)\n",
    "    * [Expectation & Variance](#-Mean-(Expectation)-&-Variance)\n",
    "* [Vectors of Random Variables](#-Vectors-of-Random-Variables)\n",
    "* [Lagrange Multipliers](#-Lagrange-Multipliers)\n",
    "    * [Maximum Entropy Exercise](#-Exercise---Max-Entropy-Distribution)\n",
    "* [Useful Inequalities](#-Useful-Inequalities)\n",
    "* [Recommended Videos](#-Recommended-Videos)\n",
    "* [Credits](#-Credits)"
   ]
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   "source": [
    "# imports for the tutorial\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from scipy.stats import multivariate_normal\n",
    "%matplotlib notebook"
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    "## <img src=\"https://img.icons8.com/office/80/000000/dice.png\" style=\"height:50px;display:inline\"> Probability Basics\n",
    "---\n",
    "| Term | Usually denoted by | Definition | Example  |\n",
    "| --- | --- | --- | --- |\n",
    "| **Experiment** | | <center>any procedure that can be infinitely repeated and has a well-defined set of possible outcomes </center>|<center> toss a coin twice </center> |\n",
    "| **Sample** | $\\omega$ |<center> A single outcome of an experiment </center>|<center>  A single outcome. For example: HH </center>|\n",
    "| **Sample Space** | $\\Omega$ | <center>The set of all possible outcomes </center>| <center> The set of all possible outcomes, for example: {HH, HT, TH, TT} </center>|\n",
    "| **Event** | $A$ | <center>a subset of possible outcomes </center>| <center>A = {HH} , B= {HT, TH}  <br> An empty set  $\\emptyset$ <br> The entire set (any outcome): $\\Omega$ </center>|\n",
    "| **Event Space** | $\\mathcal{F}$ | <center>The space of all possible events </center>| <center> $\\{HH\\}, \\{HT\\}, \\{TH\\}, \\{TT\\}, \\{\\emptyset\\}, \\{\\Omega\\}$ </center> |\n",
    "| **Probability** | P, Pr |<center> A function $P:\\mathcal{F}\\rightarrow\\left[0,1\\right]$ which assigns a probability to each event </center>| <center> $P(HT) = \\frac{1}{4}$<br> $P(\\emptyset)=0$<br>$P(\\Omega)=1$ </center>|"
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    "## <img src=\"https://img.icons8.com/clouds/64/000000/handshake.png\" style=\"height:50px;display:inline\"> Joint Probability\n",
    "---\n",
    "* **Joint Probability - Pr(A,B)** - the probability that both event A and event B happen ($Pr(A,B) \\geq 0$)\n",
    "* **Marginal Distributions** -\n",
    "    * $\\sum_i Pr(A_i, B_j) = Pr(B_j)$\n",
    "    * $\\sum_j Pr(A_i, B_j) = Pr(A_i)$\n",
    "* **Law of Total Probability** - suppose the events $B_1, B_2, ..., B_k$ are mutually exclusive (intersection of all events is zero) and form a partition of the sample space (i.e. one of them must occur), then for any event $Pr(A)$: $$Pr(A) = \\sum_{j=1}^k Pr(A|B_j)P(B_j)$$"
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    "* **Conditioning** - if A and B are events and $Pr(B) > 0$, the **conditional probability of A given B** is: $Pr(A|B)$\n",
    "    * $Pr(A|B) = \\frac{P(A,B)}{P(B)}$\n",
    "    * $\\rightarrow Pr(A,B) = Pr(A|B)Pr(B)$\n",
    "    * **The chain rule** - in the general case: $$Pr(\\bigcap_i A_i) = \\prod_{i=n}^1 Pr(A_i|A_{i-1}, ..., A_1)$$\n",
    "        * $Pr(A,B,C) = P(A|B,C)P(B,C) = P(A|B,C)P(B|C)P(C)$\n",
    "        * Is that the only option? No! $Pr(A,B,C) = P(C|A,B)P(A,B) = P(C|A,B)P(B|A)P(A)$\n",
    "    \n",
    "* **Independence** - \n",
    "    * Two events A and B are independent iff (iff = \"if and only if\")\n",
    "        * $Pr(A|B) = Pr(A)$\n",
    "        * $Pr(A,B) = Pr(A)Pr(B)$\n",
    "    * For a set of events $\\{A_i\\}$, independence:\n",
    "        * $Pr(\\bigcap_i A_i) = \\prod_i Pr(A_i)$\n",
    "* **Conditional Independence** - Events A and B are conditionally independent given C:\n",
    "    * $Pr(A,B|C) = Pr(A|C)Pr(B|C)$\n",
    "    * $Pr(A|B,C) = Pr(A|C)$"
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    "## <img src=\"https://img.icons8.com/dusk/64/000000/variable.png\" style=\"height:50px;display:inline\"> Continuous Random Variables\n",
    "---\n",
    "Assume $X$ is a continuous random variable. We define the following:\n",
    "* **Cumulative Distribution Function (CDF)** - $F(x) = P(X \\leq x)$\n",
    "    * The CDF is monotonically non-decreasing\n",
    "    * $ P(a < X \\leq b) = F(b) - F(a)$\n",
    "    * $\\lim_{a\\to\\infty} F_x(a) = 1$\n",
    "    * $\\lim_{a\\to 0} F_x(a) = 0$\n",
    "* **Probability Density Function (PDF)** - $f(x) = \\frac{d}{dx}F(x)$\n",
    "    * $P(a < X \\leq b) = \\int_a^b f(x)dx $\n",
    "* All we have seen for **discrete** variables hold for **continuous** by replacing the sum with an integral."
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   "source": [
    "def plot_normal_pdf_cdf(mu=0, sigma=1):\n",
    "    x = np.linspace(-10, 10, 1000)\n",
    "    x_pdf = (1 / np.sqrt(2 * np.pi * sigma ** 2)) * np.exp(- (x - mu) ** 2 / (2 * sigma ** 2))\n",
    "    x_cdf = np.cumsum(x_pdf) / (len(x) / (np.max(x) - np.min(x))) # normalization\n",
    "    fig = plt.figure(figsize=(8,5))\n",
    "    ax = fig.add_subplot(1,1,1)\n",
    "    ax.plot(x, x_pdf, label='PDF')\n",
    "    ax.plot(x, x_cdf, label='CDF')\n",
    "    ax.grid()\n",
    "    ax.legend()\n",
    "    ax.set_xlabel('x')\n",
    "    ax.set_title('PDF and CDF of Normal Distribution')"
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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_normal_pdf_cdf(mu=0, sigma=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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e857JmdTVoDAWmQOGEklOWdg55bXe9mb1jGXOW7FiBd/5zneOe31sbKzgLRQBrr76aq6++uqK1qPsMWMzu9nMDpjZ1iLL32ZmD/tf95rZeRWtoYicsCOJFAs6p55P7PWMFcYi9SDIBK5bgItLLH8GeKVz7gXAJ4BNFaiXiFRINusYHk9NTtrK6W1vYXhcw9Qi9aBsGDvnfgUcLrH8XufcEf/pfcCqCtVNRCogkcrgHMddaau3o1k9Y5E6YUEuFG9ma4A7nHPnlFnv/cAZzrl3FVl+LXAtwLJlyzbkLj9WCfF4nO7u7oqVFya1pT41aluOjGf5H/1jXH12K32rWybbcfPWCR4ezPC5V3WWL6RONeo+KWSutWXevHmceuqpmFmNajVzmUyGWCw2q/c653j66acZGhqa8vqrXvWqB51zGwu+odwXsAbYWmadVwHbgEVBytywYYOrpLvvvrui5YVJbalPjdqWp/aPuFNuuMP9YMse59yxdnzqR4+5M/7mzhBrduIadZ8UMtfasmPHDjc4OOiy2Wz1KzRLw8PDs3pfNpt1g4ODbseOHcctAx5wBTKxIrOpzewFwL8ClzjnDlWiTBGpjNydmXrapv6497Y3M5bKkExnaW3W9X+ktlatWsXAwACDg4NhV6Wo8fFx2tvbZ/Xe9vZ2Vq0KftT2hMPYzE4G/gN4u3PuyRMtT0QqK+5P0uqaHsZ5V+HK3ThCpFZaWlpYu3Zt2NUoqb+/nxe+8IU12VbZMDazW4E+YLGZDQAfBVoAnHM3AR8BFgFf9Mf+067QeLiIhCLXM+4+rmfshfHweFphLBKysmHsnLuizPJ3AQUnbIlI+CaHqdun/rjnnmtGtUj4dKBIJOLi/lW2pg9T556PJnWusUjYFMYiEZfrGXe1TT1Fo6vVD+OJTM3rJCJTKYxFIi4+kaG1uYm25mlh7IdzQj1jkdApjEUiLj6ROm7yFhwbps71nEUkPApjkYiLj6dLhvGowlgkdApjkYiLT2QKhnFnizdMrWPGIuFTGItEXLFh6qYmo7M1pp6xSB1QGItEXHwiTXd74UsKdLU169QmkTqgMBaJuNEiw9TgXZVLw9Qi4VMYi0TcyHj6uAt+5GiYWqQ+KIxFIi4+kTruUpg5GqYWqQ8KY5EIS2eyjKeyRYepu1pjGqYWqQMKY5EIywVt0TBua9YwtUgdUBiLRNjIhHeTiJITuDRMLRI6hbFIhE32jIscM+5s1WxqkXqgMBaJsNx1pztbYwWXd7fFGE2mcc7VsloiMo3CWCTCxpJer7eztfgxY+dgLKXesUiYFMYiEZa7PWKxnnGn7twkUhcUxiIRluvxdpQYpgZI6LixSKgUxiIRdmyYunAYd7WqZyxSDxTGIhGWyIVxS/FjxqB7GouETWEsEmG5Yer21sI/6rkwzoW2iIRDYSwSYYlkmliT0RorEsb+8LWGqUXCpTAWibCxZJbOlhhmVnC5hqlF6oPCWCTCxlLpojOp4dgELg1Ti4RLYSwSYYlkpmQY544l66IfIuFSGItEWCKZoaOleBi3xpqINdnkxUFEJBwKY5EIG0tmip5jDGBmdLbEGEtma1grEZmubBib2c1mdsDMthZZbmb2eTPbbmYPm9n5la+miMzGWCpT9LrUOe2tMcZS6hmLhClIz/gW4OISyy8BTvO/rgX++cSrJSKVUO6YMXhX59IELpFwlf6TGXDO/crM1pRY5TLga867B9t9ZjbfzJY75/ZVqI4iMktjyXTJY8YAHS2xyctmnjDnIJsBl/G+r7KmTBJS41XfTi2oLfWnKZP0/h8XOTWwksqGcQArgd15zwf81xTGIiFLlDlmDF7POPBs6ok4PH4H7PoN7H8MRgdh7AikEl4IU9v7Ir8C4J6abrJq1Jb68wqAlz8L7fOqvq1KhHGhPxkK/kSa2bV4Q9ksW7aM/v7+CmzeE4/HK1pemNSW+tSIbRkZm+DQgX309x+efG16O8ZHxxgepnTbXJYVe3/Muh3foDkzSqq5m3j3OpKta0h1nUsm1o6zJqAJZ03+99XvTUwkk7S1tlZ9O7WgttSfiWSSwd/8jmys+m2pRBgPAKvznq8C9hZa0Tm3CdgEsHHjRtfX11eBzXv6+/upZHlhUlvqUyO2JfWTzZy+7hT6+s6YfG16O76x6wH2Hh2jr++iwoVk0vD9/wZPfQfW9UHfh2hZ/WIW1GDorpxG3CfFqC31p5btqMSpTbcDV/mzql8CDOl4sUj4kuks6awre8y47DD1L/4WHvkOvPpv4O3fh5NfUpNjaCJzSdmesZndCvQBi81sAPgo0ALgnLsJ2AxcCmwHEsA11aqsiASXm5TVUebUpo6WWPGLfuz+Pfzm/4cNV8Mr/meFaygiOUFmU19RZrkD/qJiNRKRikj45w6Xm8DVUezUJufgzhugZwW87lPVqKKI+HQFLpGIyvWMg8ymHi80TP3ML2HvH+CVH4C27mpUUUR8CmORiMr1doOcZ5zKOFKZaZfE/N2/QNdSWH9ltaooIj6FsUhE5SZllbsCV275lKHq0YPw1E/gvLdCc1vV6igiHoWxSEQlAg9Te1NHpgxVP/Z9yKbhvJJTRkSkQhTGIhE1OZu6pcxsav+exlN6xk/8GBaug6VnVa1+InKMwlgkosaCzqb2w3ry9KbkKDzzKzj9Yp1PLFIjCmORiJqcwBVgNjXkDVPv+i1kJuB5r61q/UTkGIWxSESNBQzj4yZw7f4dWBOsvqCq9RORYxTGIhE1eZ5xgFObID+M74Nl50BbT1XrJyLHKIxFIiqRytAaa6I5VvrHPDdMPZbMeDeFGHjQu/60iNSMwlgkosaSmbJD1HBsmHoslYH9WyE1CqtfXO3qiUgehbFIRCWS6bJX3wLonJxNnYGB+70XdbxYpKYqcT9jEalDiWSm7GlNkNczTqbh8CPQsQDmrS7zLhGpJPWMRSJqPBVsmLolZsSazBumPvAYLD1b5xeL1JjCWCSigvaMzYzOlhiJiRQc2AbLdNUtkVpTGItEVCKZoT3AMWPwhqrbR/dAMq5LYIqEQGEsElFjAXvG4IXxwvh278mys6tYKxEpRGEsElFjqczkHZnK6WiJsTjxtPdk6ZlVrJWIFKIwFomoRMDzjMG78Mey8Wdg3sm68pZICBTGIhE1lkyXvRRmTkdrjCWpPbD4eVWulYgUojAWiSDnHImApzaBdxvFkzJ7vXsYi0jNKYxFImgincW58ndsylkcG6XHxWHB2irXTEQKURiLRFDQOzblrMzu875Rz1gkFApjkQhKpPwwDjibeoXCWCRUCmORCBpLpgFoDzhMvSy9h6wzWLCmirUSkWIUxiIRlJjhMPXi5B72sZCktVazWiJShMJYJIImjxkH7BkvmBhgV3aZd7MIEak5hbFIBOWOGQedTd07todn3dLJEBeR2goUxmZ2sZk9YWbbzeyDBZbPM7MfmtlDZvaomV1T+aqKSFC5UA0UxukJOpKH2OMWk/CPNYtIbZUNYzOLAV8ALgHOAq4ws+m3dfkL4DHn3HlAH/BPZjr4JBKWY8eMA8ymHt4DwD4WaZhaJCRBesYXANudczucc0ngNuCyaes4oMfMDOgGDgP6E1skJLnZ1IF6xkMDAOxxizVMLRKSIGG8Etid93zAfy3fjcCZwF7gEeAvnXPZitRQRGZsLDWDCVx+GO91iyZ71CJSW0GuCGAFXnPTnr8e2AK8GjgV+KmZ3eOcG55SkNm1wLUAy5Yto7+/f8YVLiYej1e0vDCpLfWpkdry2PYkAL+79x6abOqP8PR2nLLzHtYCz7mF3P/Hh8juDXahkHrQSPukHLWl/tSyHUF+6gaA1XnPV+H1gPNdA3zaOeeA7Wb2DHAG8Pv8lZxzm4BNABs3bnR9fX2zrPbx+vv7qWR5YVJb6lMjteW3iW207dzJq1/1quOWHdeO279Lev8SJsZbOfX0M+l74fSBr/rVSPukHLWl/tSyHUGGqe8HTjOztf6krMuB26et8yzwGgAzWwY8H9hRyYqKSHCJZCbwOcYMDZDtXTn5PhGpvbI9Y+dc2syuB+4CYsDNzrlHzew6f/lNwCeAW8zsEbxh7RuccwerWG8RKWEslQl8XWqG9mALTwPQqU0iIQn00+qc2wxsnvbaTXnf7wVeV9mqichsjSUD3svYORgaoGndqyffJyK1pytwiURQIpmmI8h1qceOQGqU2PxVNDeZzjMWCYnCWCSCEkF7xiPPeY+9y+lojemYsUhIFMYiEeQdMw4QxnE/jLtPorM1pmFqkZAojEUiaCzobOpcz7jnJDpbmydvMCEitaUwFomgRDJDR5DrUueFcXtLbPIymiJSWwpjkQgaS2XoaA3w4x3fD6090NpFp44Zi4RGYSwSQYlkOth5xiPPQc8yAIWxSIgUxiIRk806xlPZYKc2xfdD90kAdLRoApdIWBTGIhEznp7BHZtG9kHPSZPr6zxjkXAojEUiJjfUXPY8Y+dgZP9kGHe0NmuYWiQkCmORiMkNNZcdpp4YhvQYdB87ZqzZ1CLhUBiLREyud1t2AtfIfu8xb5g6kcrg3QlVRGpJYSwSMbnjvmWPGY/s8x79nnF7SwznYCKdrWb1RKQAhbFIxORug1j2mHE81zNeDhwLbx03Fqk9hbFIxAQ+Zjx59a1jx4xB9zQWCYPCWCRijh0zDtAzbu6Atl7Am00NuqexSBgUxiIRkztmXHaYOnf1LTMAOv2etM41Fqk9hbFIxIwFnU0d3z85ectbX8eMRcKiMBaJmETQY8ajB6FryeTTXE9aw9QitacwFomYsWQaM2hvKfPjPToIXYsnn+Z60uoZi9SewlgkYkaTGTpbYph/LLigbAbGDk/tGbdoNrVIWBTGIhGTSGbobCtzvHjsCLhs4WFqTeASqTmFsUjEjCXT5U9rGh30HqcMU2sCl0hYFMYiETOazASYvJUL40LD1ApjkVpTGItEzFgyQ1e5YepcGHce6xk3NRntLU2Ma5hapOYUxiIRkwg0TH3Ie8zrGYM3o1oTuERqT2EsEjGJwMPUBp0Lp7zc0RLTMLVICBTGIhGTCDpM3bkImqaGdkdrTBf9EAlBoDA2s4vN7Akz225mHyyyTp+ZbTGzR83sl5WtpogElUhmyl+XenTwuCFq8GZUq2csUntl/nwGM4sBXwD+H2AAuN/MbnfOPZa3znzgi8DFzrlnzWxptSosIqUlkunJmz4UNXpwymlNOR0t6hmLhCFIz/gCYLtzbodzLgncBlw2bZ0rgf9wzj0L4Jw7UNlqikgQzjnGUgEu+pEoHMadrTESKU3gEqm1IGG8Etid93zAfy3f6cACM+s3swfN7KpKVVBEghtPZXEuwL2Miw5TN2uYWiQEZYepgUIXuHUFytkAvAboAH5rZvc5556cUpDZtcC1AMuWLaO/v3/GFS4mHo9XtLwwqS31qRHaMjzh/WgO7NxBv9tdcJ3R4aMwPsQzB+LsmtaeocMTHB3J1H07cxphnwSlttSfWrYjSBgPAKvznq8C9hZY56BzbhQYNbNfAecBU8LYObcJ2ASwceNG19fXN8tqH6+/v59KlhcmtaU+NUJbdh9OwN13s/6cM+nbsKrgOvfe9V0A1p7zItZu7Juy7BdDW9l6ZG/dtzOnEfZJUGpL/allO4IMU98PnGZma82sFbgcuH3aOj8ALjKzZjPrBF4MbKtsVUWknNwQc6lh6tbkkPdNZ4EJXJpNLRKKsj1j51zazK4H7gJiwM3OuUfN7Dp/+U3OuW1m9mPgYSAL/Ktzbms1Ky4ixxv1r55V6tSmlpQfxgWOGXe0xEims2SyjlhTiVswikhFBRmmxjm3Gdg87bWbpj3/B+AfKlc1EZmp3GlJXa3Ff7Qne8ZFzjMG7/SonvaWyldQRArSFbhEIiTIMPWxnnGhYWovxHWusUhtKYxFIiQRYJi6NXkUmlqgfd5xyzp1G0WRUCiMRSIkEWCYuiU17PWK7fhjwseGqRXGIrWkMBaJkFyIlp3AVWCIOv99Y7qnsUhNKYxFIiQx4Q1Tlz616WjByVve+3TMWCQMCmORCEmkMrTGmmiJFf/R9nrGxcL42GxqEakdhbFIhIwFuH1ia7J4GLe3aJhaJAwKY5EIGZ1Il75JRHKUWHYCOmqR2HoAABgMSURBVBcVXKwJXCLhUBiLREgilSkdxqMHvceyw9QKY5FaUhiLRMhYMjM5CaugsmGcm8ClY8YitaQwFomQ0Yl06WPGo4PeY5Ewbm1uoiVmjKpnLFJTCmORCBlLZegKFMaFzzMG6GprZnRCPWORWlIYi0SIN4GrxDB1IjdMXSKMW5uJK4xFakphLBIhZU9tGj1IpqkVWruKrtLVFiMxoWFqkVpSGItESCLAMHWydX7JMrramifviywitaEwFomQxERm8jaIBY0eJNVy/N2a8mmYWqT2FMYiEZHOZElmsmXOMx4sH8YaphapOYWxSEQk/EtYlrvoR7K1XBirZyxSawpjkYjI9WaLzqZ2DhLBhql1owiR2lIYi0REfCIFQHd7kTCeGIZMMlDPeFTD1CI1pTAWiYi4H6DdbUWGqf1LYaZaekuW090WI5nJkkxnK1o/ESlOYSwSEbmrZnW3tRRZIRfGpU9tyg1za6hapHYUxiIRMTLuhWdX0Z6xdynMZGu5nrEXxprEJVI7CmORiDjWMy5yzDiR6xmXP2bslafjxiK1ojAWiYh4uTD2e8blwrjT71nrKlwitaMwFomIXBh3FQ3jQ9DaQzbWWrKc7smescJYpFYUxiIRMTqRpiVmtDUX+bEeHSx5t6acrlaFsUitKYxFIiI+kaarrRkzK7xC0DDODVPrmLFIzQQKYzO72MyeMLPtZvbBEuu9yMwyZvanlauiiAQRn0hP9moLShyCriVly5mcwKVjxiI1UzaMzSwGfAG4BDgLuMLMziqy3meAuypdSREpb3QiTU+xq29B4J5xt2ZTi9RckJ7xBcB259wO51wSuA24rMB67wG+CxyoYP1EJKDcMHVB2azXM+4sH8ZtzU00mY4Zi9RSkDBeCezOez7gvzbJzFYCbwJuqlzVRGQm4hOZ4mE8fhSy6UDD1GamOzeJ1FiJMa1JhWaDuGnPPwfc4JzLFJ08ApjZtcC1AMuWLaO/vz9gNcuLx+MVLS9Makt9qve2DB5O0NrTVLCOnaMDXAA89uwB4l0nl21HCxme3jVAf/9gVepaKfW+T2ZCbak/tWxHkDAeAFbnPV8F7J22zkbgNj+IFwOXmlnaOff9/JWcc5uATQAbN250fX19s6z28fr7+6lkeWFSW+pTvbcle+/PWbtqMX195x2/cNe9cD+ctfEVHNjdVLYdCx7sp3dhL31951enshVS7/tkJtSW+lPLdgQJ4/uB08xsLbAHuBy4Mn8F59za3Pdmdgtwx/QgFpHqGi11zNi/+pY3TH2obFnd7S2MaJhapGbKhrFzLm1m1+PNko4BNzvnHjWz6/zlOk4sEjLnHPFkmp6iYexdl9qbwFU+jHvbmxkZT1WugiJSUpCeMc65zcDmaa8VDGHn3NUnXi0RmYlEMoNzpS6FmQvjRYHK62lvZt/QeIVqJyLl6ApcIhEwWva61IPQPg+aS1+XOqenrUU9Y5EaUhiLREDu+G7Ri34kDgY6rSmnp72Z4TEdMxapFYWxSARM9oyLXQ5zdGZh3NvRwlgqQyqTrUT1RKQMhbFIBJS/feLBwMeL4VgPOz6u3rFILSiMRSIgF5pFh6lHB2c4TN0CwIjCWKQmFMYiETDsh2avH6JTZDMwdjjQTSJycqE+rElcIjWhMBaJgOExLzTndRQI49GD4LLQvSxweQpjkdpSGItEwJAfxt2Fhqnj+73HGYRxr4apRWpKYSwSAcPjKXramok1FbhRi8JYpO4pjEUiYGgsRW+hIWo4FsY9Mx+m1oU/RGpDYSwSAcNj6fJh3LU0cHndk2GsnrFILSiMRSJgeDxFb7HTmkb2Q1svtHYGLq8l1kRHS2xyYpiIVJfCWCQChsdShWdSg9cznsHx4pzejmb1jEVqRGEsEgHDJY8ZH5hVGPe0tzAyoZ6xSC0ojEUiYHg8XfiCHwDx56A7+PHinJ529YxFakVhLNLg0pks8Yl0iWHqA9Bz0ozL7Wlvmbyyl4hUl8JYpMHleq+9HQUmcE3EIRmffc9YE7hEakJhLNLgclffKjhMPYsLfuT0trfocpgiNaIwFmlwucAsOEwdP+A9ziKM53e2cDSRwjl3ItUTkQAUxiINbngsN0xd2Z7xgs4W0lk3ea9kEakehbFIgxsqdcemEwrjVgCOJjRULVJtCmORBpcbpi44gSu+HywGnYtmXG4ujA+PJk+ofiJSnsJYpMENl5rANbLfm0ndNPMf9QVdXnlHEgpjkWpTGIs0uKGxFM1NRmdr7PiFI3uhd8Wsyp2vYWqRmlEYizS4I4kkC7paMStwL+Ph2YfxQg1Ti9SMwlikwR0eTU4G53GG9kDvylmV29vRghkc1TC1SNUpjEUa3JHR1OTx3SnGhyE5MuuecazJmNfRwhENU4tUncJYpMEdGp1gYVeBnvHwXu9xlj1j8IaqD6tnLFJ1gcLYzC42syfMbLuZfbDA8reZ2cP+171mdl7lqyoihRxJpCZPQ5pieI/3eAJh7F2FS2EsUm1lw9jMYsAXgEuAs4ArzOysaas9A7zSOfcC4BPApkpXVESOl8k6jiaSLCrZM57dMDV45xofGdUwtUi1BekZXwBsd87tcM4lgduAy/JXcM7d65w74j+9D1hV2WqKSCHDYymyDhYUDGO/Z9yzfNblz+9s1XnGIjUQJIxXArvzng/4rxXzTuDOE6mUiARzyD/tqPAx4z3QtRSai8y0DmBhV4vCWKQGClw/7zgFTl6k4G1czOxVeGF8YZHl1wLXAixbtoz+/v5gtQwgHo9XtLwwqS31qR7b8uSRDAC7t2+j/+hTU5adu3MrLU29/GFanWfSjiPPJRlPZbnr53fTFiv0qyBc9bhPZkttqT81bYdzruQX8FLgrrznHwI+VGC9FwBPA6eXK9M5x4YNG1wl3X333RUtL0xqS32qx7b8eOs+d8oNd7hHBo4ev/DGFzt365XHvTyTdnzzvl3ulBvucHuOJE6gltVTj/tkttSW+lONdgAPuAKZGGSY+n7gNDNba2atwOXA7fkrmNnJwH8Ab3fOPVmhvxNEpIzBkQkAFne3TV3gHBzdBfNPPqHyF3d7Q9wH4xMnVI6IlFZ2mNo5lzaz64G7gBhws3PuUTO7zl9+E/ARYBHwRf+SfGnn3MbqVVtEwAtjM1jUPe248OhBSCVgwZoTKn9JT9vkdkSkeoIcM8Y5txnYPO21m/K+fxfwrspWTUTKOTAywcLOVlpi0wa5juz0HuefckLlL+1tn9yOiFSPrsAl0sAGRyYme69THN3lPZ5gzzg3TK2esUh1KYxFGthgvEgYH3nGezzBY8ZtzTHmd7YojEWqTGEs0sAGh8eLhPEu6F4GrZ0nvI0l3W0cGBk/4XJEpDiFsUiDcs4xGJ9gaU/78QuP7DzhIeqcpb1t6hmLVJnCWKRBHU2kSGVc8WPGFQpjr2esMBapJoWxSIPa7w8dL+udFsaZFAwNnPBM6pxlve0cGJ4gmy144T0RqQCFsUiD2nNkDIAV8zumLjj8DLgsLDq1IttZMb+DZCY7eR1sEak8hbFIg9p71AvjVdPDePBx73HJ8yuynZV++Xv87YlI5SmMRRrUwNExWmNNx18K8+AT3uPi0yuynVzPe6/CWKRqFMYiDWrv0XGWz2+nqWna3ZQGn4B5J0NrV0W2s3KB3zM+ojAWqRaFsUiD2nMkwYp5HccvGHyiYkPUAL3tzXS3NWuYWqSKFMYiDWrP0bHJXuukbBYOPlXRMDYzVs7vUBiLVJHCWKQBjacyHBiZYNX0MB56FtJjFQ1jgNULO9h9OFHRMkXkGIWxSAN65uAozsG6Jd1TFxzY5j0uOaOi21u7uItnDo7qXGORKlEYizSgHYOjAKxbPG2S1t4tYE2w7JyKbm/dkm4m0lkNVYtUicJYpAE9czAOeD3WKfb+ERY/vyI3iMiXC/1nDo5WtFwR8SiMRRrQjsFRTuptp6uteeqCfVtgxfqKb2/tki5/u/GKly0iCmORhrR9MM66JdN6xUMDEN8Pyysfxku62+hpb2a7wlikKhTGIg0mlcny+HMjnL2id+qCXb/1Hk95acW3aWactbyXR/cOV7xsEVEYizSc7QfiJNNZzlk5b+qCZ++Ftt6KT97KOWflPLbtGyadyValfJG5TGEs0mC27hkC4OwV08J4529g9YuhKVaV7Z6zspfxVJYdmsQlUnEKY5EG8/DAEJ2tsamnNR3Z5d0gYt0rq7bdc/2e+EO7j1ZtGyJzlcJYpMHct+MQG9csnHqDiKd+4j2efknVtrtucTcLu1q5b8fhqm1DZK5SGIs0kAMj4zx1IM7LTl00dcHjP4KF62Dx86q27aYm46XrFnHv0wdxTlfiEqkkhbFIA7l3+yGAqWE8vBee+SWc81+qvv2XnrqIfUPjPD2o48YilaQwFmkgdzy8j5N626dO3tryLXBZOO+Kqm//NWcuxQw2P7Kv6tsSmUsUxiIN4mgiyS+fPMAbz1tOLHe8ODUOv98E6/pg0alVr8PyeR1csGYh39+yR0PVIhWkMBZpEF//7S5SGcebz1917MX7v+RddevC99WsHn+6YRU7Bkf55ZODNdumSNQpjEUawOHRJF/+zTO85oylnLncv/LW4R3Q/2k47XWw9hU1q8tl61eyYl47//unT5LRLRVFKiJQGJvZxWb2hJltN7MPFlhuZvZ5f/nDZnZ+5asqMjdlso4P/PvDjE6k+Z8XP997cWQ/3HoFxFrg0n8Es9KFVFBrcxM3XHIGDw0M8X9+8VTNtisSZWXD2MxiwBeAS4CzgCvM7Kxpq10CnOZ/XQv8c4XrKTIn7R8e57pvPMjPtu3nw5eeyRlLOmHrd2FTHxx9Fv7s67DglJrX60/OW8GbX7iSz/3sKf5u8zZGxlM1r4NIlDSXX4ULgO3OuR0AZnYbcBnwWN46lwFfc96MjvvMbL6ZLXfO1WTK5eEDexjafi9/TA7M+L2lJqEYDii+vOR7nSvxTig192Vo4FkeTDxd7J0lquTy/i1UJyhaq7KfQ6lVir93eO8eHhh+rOB7T6RcSrzX8t5XqAQr9eG74u8dfm4f9x/6Y/GalZzQ5IquZtNKS6azDI2n2Dc0zq5Do5xCitvPiPGC3d+CX98LY4dhyZlwxa1VuV1iEGbGZ/70BbS3xtj0qx18875dvPx5izl9WQ+Lu1vpbm+hJWbEmozmJsPMqEbffev+NMlHn6tCyV4ba2nrgTSpx/bXdJvVEpW2bD2Q5uWZLC2x6h/RDRLGK4Hdec8HgBcHWGclMCWMzexavJ4zy5Yto7+/f4bVLWxo1xYuG/iMt9UI2ACwN+xaVFB1fleGo9ZzlvzLTGd3NZNoX8rQvPUcWvdiDi5+ETx5FJ7sn3GR8Xi8Yj97r1sAp7+0nV/sTvPQzgP8bNt+an4Y+Y8P1niDVfSHB8KuQeVEpC3PX/BLOluq/4dZkDAuVIvpP25B1sE5twnYBLBx40bX19cXYPPlxYfP44ebuzjzzOmj53kVLPVXrpX6q8dKHo4rtcyZUbw/ULzcrY9s5Zxzzy36TleqlzFZaPGKFa2zv6DwzvSXFX9zwfc99NBDnLd+fYntlqtvbrvF61tOqe0WbE+Rcv/w4B84f8OG0qvlvXj8J2KFVjtuWUvMmNfRcqxusVaaOhbQaUYnsLxg7YLr7++nUj97OVf7j9ms43AiSWIiQzqbJZN1pLOuahO9HnzwATZs2FiVsmvtgQceYONGtaWePPDAA7z+NX3HTiWsoiBhPACsznu+iuP7bUHWqZru3gX0nHQazzvv5bXaZFXt3B9nzZkbyq/YALYPHGTVqWeHXY2K6Hx6gJNWV/9c3kbW1GQs7m6D7tps7+BTseNvJdmg1Jb6c/CpWE2CGILNpr4fOM3M1ppZK3A5cPu0dW4HrvJnVb8EGKrV8WIREZFGV7Zn7JxLm9n1wF14R7Buds49ambX+ctvAjYDlwLbgQRwTfWqLCIiEi1Bhqlxzm3GC9z8127K+94Bf1HZqomIiMwNugKXiIhIyBTGIiIiIVMYi4iIhExhLCIiEjKFsYiISMgUxiIiIiFTGIuIiITMSt15qKobNhsEdlWwyMXAwQqWFya1pT5FpS1RaQeoLfUqKm2pRjtOcc4tmf5iaGFcaWb2gHOu8a9MjtpSr6LSlqi0A9SWehWVttSyHRqmFhERCZnCWEREJGRRCuNNYVeggtSW+hSVtkSlHaC21KuotKVm7YjMMWMREZFGFaWesYiISENqqDA2s7eY2aNmljWzjdOWfcjMtpvZE2b2+iLvX2hmPzWzp/zHBbWpeWlm9m0z2+J/7TSzLUXW22lmj/jrPVDregZhZh8zsz157bm0yHoX+/tqu5l9sNb1DMLM/sHMHjezh83se2Y2v8h6dblfyn3G5vm8v/xhMzs/jHqWY2arzexuM9vm//z/ZYF1+sxsKO//3UfCqGsQ5f6/NMJ+MbPn533WW8xs2MzeO22dut0nZnazmR0ws615rwXKh6r97nLONcwXcCbwfKAf2Jj3+lnAQ0AbsBZ4GogVeP/fAx/0v/8g8Jmw21Sgjv8EfKTIsp3A4rDrWKb+HwPeX2admL+P1gGt/r47K+y6F6jn64Bm//vPFPv/Uo/7JchnDFwK3AkY8BLgd2HXu0hblgPn+9/3AE8WaEsfcEfYdQ3YnpL/Xxplv+TVNwY8h3f+bEPsE+AVwPnA1rzXyuZDNX93NVTP2Dm3zTn3RIFFlwG3OecmnHPPANuBC4qs91X/+68C/7k6NZ0dMzPgz4Bbw65LlV0AbHfO7XDOJYHb8PZNXXHO/cQ5l/af3gesCrM+MxTkM74M+Jrz3AfMN7Plta5oOc65fc65P/jfjwDbgJXh1qqqGmK/5HkN8LRzrpIXcaoq59yvgMPTXg6SD1X73dVQYVzCSmB33vMBCv+wLnPO7QPvBxxYWoO6zcRFwH7n3FNFljvgJ2b2oJldW8N6zdT1/vDazUWGeoLur3ry53i9lULqcb8E+Ywbbj+Y2RrghcDvCix+qZk9ZGZ3mtnZNa3YzJT7/9Jo++VyincgGmWfQLB8qNq+aa5EIZVkZj8DTiqw6K+dcz8o9rYCr9XVNPGA7bqC0r3ilzvn9prZUuCnZva4/xdeTZVqC/DPwCfwPv9P4A27//n0Igq8N5T9FWS/mNlfA2ngm0WKqYv9Mk2Qz7hu9kMQZtYNfBd4r3NueNriP+ANk8b9eQrfB06rdR0DKvf/pWH2i5m1An8CfKjA4kbaJ0FVbd/UXRg75147i7cNAKvznq8C9hZYb7+ZLXfO7fOHfQ7Mpo6zUa5dZtYMvBnYUKKMvf7jATP7Ht6QSc1/6QfdR2b2JeCOAouC7q+qC7Bf3gG8AXiN8w8aFSijLvbLNEE+47rZD+WYWQteEH/TOfcf05fnh7NzbrOZfdHMFjvn6u76yAH+vzTMfgEuAf7gnNs/fUEj7RNfkHyo2r6JyjD17cDlZtZmZmvx/vr6fZH13uF//w6gWE87DK8FHnfODRRaaGZdZtaT+x5vctHWQuuGadqxrTdRuI73A6eZ2Vr/L+vL8fZNXTGzi4EbgD9xziWKrFOv+yXIZ3w7cJU/e/clwFBumK6e+HMpvgxsc859tsg6J/nrYWYX4P1uO1S7WgYT8P9LQ+wXX9HRvEbZJ3mC5EP1fneFOaNtpl94v9wHgAlgP3BX3rK/xpvl9gRwSd7r/4o/8xpYBPwceMp/XBh2m/LqeQtw3bTXVgCb/e/X4c3cewh4FG8YNfR6F2jH14FHgIf9/6TLp7fFf34p3qzYp+u4Ldvxjg9t8b9uaqT9UugzBq7L/T/DG3L7gr/8EfLOUKinL+BCvKHAh/P2xaXT2nK9//k/hDfZ7mVh17tIWwr+f2nQ/dKJF67z8l5riH2C9wfEPiDlZ8o7i+VDrX536QpcIiIiIYvKMLWIiEjDUhiLiIiETGEsIiISMoWxiIhIyBTGIiIiIVMYi4iIhExhLCIiEjKFscgcYWYv8m/g0e5fCepRMzsn7HqJCLroh8hcYmafBNqBDmDAOfe/Qq6SiKAwFplT/Ovp3g+M412eMBNylUQEDVOLzDULgW6gB6+HLCJ1QD1jkTnEzG4HbgPW4t3E4/qQqyQi1OH9jEWkOszsKiDtnPuWmcWAe83s1c65X4RdN5G5Tj1jERGRkOmYsYiISMgUxiIiIiFTGIuIiIRMYSwiIhIyhbGIiEjIFMYiIiIhUxiLiIiETGEsIiISsv8LPejPF2GBUokAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_normal_pdf_cdf(mu=0, sigma=0.3)\n",
    "# notice how the pdf can be larger than 1 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## <img src=\"https://img.icons8.com/dusk/64/000000/b.png\" style=\"height:50px;display:inline\"> Bayes Rule\n",
    "---\n",
    "Suppose that the events $B_1, ..., B_k$ are mutually exclusive and form a partition of the sample space (i.e. one of them must occur), then for any event $Pr(A)$, **Bayes Rule**:\n",
    "$$Pr(B_i|A) = \\frac{Pr(A,B_i)}{Pr(A)} = \\frac{Pr(A|B_i)Pr(B_i)}{Pr(A)} = \\frac{Pr(A|B_i)Pr(B_i)}{\\sum_{j=1}^k Pr(A|B_j)Pr(B_j)}$$\n",
    "\n",
    "* **Posterior Distribution** - $Pr(B_i|A)$\n",
    "* **Liklihood Distribution** - $Pr(A|B_i)$\n",
    "* **Prior Distribution** - $Pr(B_i)$\n",
    "* **Evidence** - $Pr(A)$\n",
    "\n",
    "#### <img src=\"https://img.icons8.com/dusk/64/000000/high-priority.png\" style=\"height:50px;display:inline\"> REMEMBER THESE NAMES!\n",
    "---\n",
    "<img src=\"./assets/bayes_rule_names.jpg\" style=\"height:200px\">\n",
    "\n",
    "\n",
    "* <a href=\"https://www.analyticsvidhya.com/blog/2019/06/introduction-powerful-bayes-theorem-data-science/\">Image Source</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## <img src=\"https://img.icons8.com/dusk/64/000000/statistics.png\" style=\"height:50px;display:inline\"> Mean (Expectation) & Variance\n",
    "---\n",
    "### Mean (Expectation) - $\\mu$\n",
    "---\n",
    "The mean is the probability weighted average of all possible values.\n",
    "* Discrete Variables:\n",
    "    * $\\mathbb{E}[X] = \\sum_{x \\in X} xp(x)$\n",
    "    * $\\mathbb{E}[f(X)] = \\sum_{x \\in X} f(x)p(x)$\n",
    "* Continuous Variables:\n",
    "    * $\\mathbb{E}[X] = \\int_x xp(x)$\n",
    "    * $\\mathbb{E}[f(X)] = \\int_{x \\in X} f(x)p(x)$\n",
    "* Example: the mean of a fair six-sided dice: $$\\mathbb{E}[X] = 1*\\frac{1}{6} + 2*\\frac{1}{6} + 3*\\frac{1}{6} + 4*\\frac{1}{6} + 5*\\frac{1}{6} + 6*\\frac{1}{6} = 3.5$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* **Empirical Mean**: if $X \\sim P(x)$ and we are given $N$ i.i.d. samples of $X$, the empirical mean: $$ \\overline{X}_N = \\frac{1}{N}\\sum_{i=1}^N X_i $$\n",
    "    * The empirical mean is also **R.V.** as a sum of RVs is also an RV. \n",
    "    * It converges to the actual mean as we will see shortly.\n",
    "        * What is the meaning of \"random variable converges?\" **It is not a number! (but a random variable)**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* **The Law of Total Expectation (Smoothing Theorem)**: $$\\mathbb{E}_x[X] = \\mathbb{E}_y\\big[\\mathbb{E}_x[X|Y] \\big] $$\n",
    "    * Proof: $$\\mathbb{E}\\big[\\mathbb{E}[X|Y] \\big] = \\mathbb{E}\\big[ \\sum_x x \\cdot P(X=x|Y) \\big] = \\sum_y \\big[ \\sum_x x \\cdot P(X=x|Y) \\big] \\cdot P(Y=y)$$ $$= \\sum_y \\big[ \\sum_x x \\cdot P(X=x|Y) \\cdot P(Y=y)\\big] = \\sum_y \\big[ \\sum_x x \\cdot P(X=x, Y=y)\\big]$$ $$ = \\sum_x x\\cdot \\big[ \\sum_y \\cdot P(X=x, Y=y)\\big] = \\sum_x x\\cdot \\big[P(X=x)\\big] = \\mathbb{E}[X]$$\n",
    "    * Example: Suppose that two factories supply light bulbs to the market. Factory X's bulbs work for an average of 5000 hours, whereas factory Y's bulbs work for an average of 4000 hours. It is known that factory X supplies 60% of the total bulbs available. What is the expected length of time that a purchased bulb will work for? $$\\mathbb{E}[L] = \\mathbb{E}\\big[\\mathbb{E}[L|factory] \\big] = \\mathbb{E}[L|X] \\cdot P(X) + \\mathbb{E}[L|Y] \\cdot P(Y) = 5000 \\cdot 0.6 + 4000 \\cdot 0.4 = 4600$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Variance - $\\sigma^2$\n",
    "---\n",
    "The variance is a measure of the \"spread\" of the distribution (can also be considered as confidence).\n",
    "\n",
    "* $var[X] = \\mathbb{E}[(X - \\mu)^2] = \\sum (x-\\mu)^2 p(x) = \\sum x^2 p(x) + \\mu^2 \\sum p(x) -2 \\mu \\sum x p(x) =  \\mathbb{E}[X^2] - \\mu^2$\n",
    "* **The Standard Deviation** - $std[X] = \\sqrt{var[X]}$\n",
    "* Example: the variance of a fair six-sided dice: $$var[X] = \\sum_{i=1}^6 \\frac{1}{6} (i-3.5)^2$$ $$ E[X^2] = 1^2 *\\frac{1}{6} + 2^2 *\\frac{1}{6} + 3^2 *\\frac{1}{6} + 4^2*\\frac{1}{6} + 5^2*\\frac{1}{6} + 6^2*\\frac{1}{6} = \\frac{91}{6} $$ $$ var[X] = E[X^2] -\\mu ^2 = \\frac{91}{6} - 3.5^2 \\approx 2.92 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## <img src=\"https://img.icons8.com/ultraviolet/80/000000/heat-map.png\" style=\"height:50px;display:inline\"> Vectors of Random Variables\n",
    "---\n",
    "* Let $\\overline{X}$ be a $d$-dimensional **random** vector\n",
    "    * $\\overline{X} = [x_1, x_2, ..., x_d]$\n",
    "* The $d$-dimensional **mean vector $\\overline{\\mu}$** is:\n",
    "    * $\\overline{\\mu} = \\mathbb{E}[\\overline{X}] = [\\mathbb{E}[x_1], \\mathbb{E}[x_2], ..., \\mathbb{E}[x_d]] = [\\mu_1, \\mu_2, ..., \\mu_d]$\n",
    "* The **covariance matrix $\\Sigma$** is defined as the (**square**) matrix, where each component $\\sigma_{ij}$ is the covariance of $x_i, x_j$:\n",
    "    * $\\sigma_{ij} = \\mathbb{E}[(x_i - \\mu_i)(x_j - \\mu_j)]$\n",
    "    * $$\\Sigma = \n",
    " \\begin{pmatrix}\n",
    "  \\sigma_1 ^2 & \\sigma_{1,2} & \\cdots & \\sigma_{1,d} \\\\\n",
    "  \\sigma_{2,1} & \\sigma_2^2 & \\cdots & \\sigma_{2,d} \\\\\n",
    "  \\vdots  & \\vdots  & \\ddots & \\vdots  \\\\\n",
    "  \\sigma_{d,1} & \\sigma_{d,2} & \\cdots & \\sigma_d^2 \n",
    " \\end{pmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## <img src=\"https://img.icons8.com/office/80/000000/normal-distribution-histogram.png\" style=\"height:50px;display:inline\"> Multivariate Normal Distribution\n",
    "---\n",
    "* $ x \\sim N_d (\\mu, \\Sigma)$\n",
    "* $$f(x) = \\frac{1}{(2\\pi)^{\\frac{d}{2}} |\\Sigma|^{\\frac{1}{2}}} e^{- \\frac{1}{2}(x - \\mu)^{T} \\Sigma^{-1} (x - \\mu)}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support. ' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option);\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width / mpl.ratio, fig.canvas.height / mpl.ratio);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>');\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"800\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Our 2-dimensional distribution will be over variables X and Y\n",
    "%matplotlib notebook\n",
    "N = 60\n",
    "X = np.linspace(-3, 3, N)\n",
    "Y = np.linspace(-3, 4, N)\n",
    "X, Y = np.meshgrid(X, Y)\n",
    "\n",
    "# Mean vector and covariance matrix\n",
    "mu = np.array([0., 1.])\n",
    "Sigma = np.array([[ 1. , -0.5], [-0.5,  1.5]])\n",
    "\n",
    "# Pack X and Y into a single 3-dimensional array\n",
    "pos = np.empty(X.shape + (2,))\n",
    "pos[:, :, 0] = X\n",
    "pos[:, :, 1] = Y\n",
    "\n",
    "F = multivariate_normal(mu, Sigma)\n",
    "Z = F.pdf(pos)\n",
    "\n",
    "# Create a surface plot and projected filled contour plot under it.\n",
    "fig = plt.figure(figsize=(8,5))\n",
    "ax = fig.gca(projection='3d')\n",
    "ax.plot_surface(X, Y, Z, rstride=3, cstride=3, linewidth=1, antialiased=True,\n",
    "                cmap=cm.viridis)\n",
    "\n",
    "# cset = ax.contourf(X, Y, Z, zdir='z', offset=-0.15, cmap=cm.viridis)\n",
    "\n",
    "# Adjust the limits, ticks and view angle\n",
    "ax.set_zlim(-0.15,0.2)\n",
    "ax.set_zticks(np.linspace(0,0.2,5))\n",
    "ax.view_init(27, -21)\n",
    "plt.tight_layout()\n",
    "\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### <img src=\"https://img.icons8.com/dusk/64/000000/lambda.png\" style=\"height:30px;display:inline\"> Lagrange Multipliers\n",
    "---\n",
    "* A method for optimization with **equality constraints** (can also be inequalities)\n",
    "* The general case: $$ \\min f(x,y) $$ $$ \\textit{s.t. (subject to)}: g(x,y)=0 $$\n",
    "    * Alternatively, can be defined as a maximization problem ($\\max$)\n",
    "* The *Lagrange* function (*Lagrangian*) is defined by: $$ \\mathcal{L}(x,y,\\lambda) = f(x,y) -\\lambda \\cdot g(x,y) $$\n",
    "* Geometric Intuition: let's look at the following figure (here we **maximize** instead of minimize) - <br>\n",
    "    * <img src=\"./assets/tut_01_lagrange.jpg\" style=\"height:400px\"> <br>\n",
    "    * To maximize $f(x,y)$ subject to $g(x,y)=0$ is to find the largest value $c \\in \\{7,8,9,10,11\\}$ such that the level curve (contour) $f(x,y) = c$ intersects with $g(x,y)=0$\n",
    "    * It happens when the curves just touch each other\n",
    "        * When they have a common tangent line\n",
    "    * Otherwise, the value of $c$ should be increased\n",
    "    * Since the gradient of a function is **perperndicular** to the contour lines:\n",
    "        * The *contour lines* of $f$ and $g$ are **parallel** iff the *gradients* of $f$ and $g$ are **parallel**\n",
    "        * Thus, we want points $(x,y)$ where $g(x,y) = 0$ and $$\\nabla_{x,y}f(x,y)=\\lambda \\nabla_{x,y} g(x,y) $$\n",
    "            * $\\lambda$ - *The Lagrange Multiplier* is required to adjust the **magnitudes** of the (parallel) gradient vectors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "###  <img src=\"https://img.icons8.com/dusk/64/000000/lambda.png\" style=\"height:30px;display:inline\"><img src=\"https://img.icons8.com/dusk/64/000000/lambda.png\" style=\"height:30px;display:inline\"> Multiple Constraints\n",
    "---\n",
    "* Extenstion of the above for problems with **multiple constraints** using a similar argument\n",
    "* The general case: minimize $f(x)$ s.t. $g_i(x)=0$, $i = 1,2,..., m$ \n",
    "* The **Lagrangian** is a weighted sum of objective and constraint functions: $$ \\mathcal{L}(x, \\lambda_1, ..., \\lambda_m) = f(x) - \\sum_{i=1}^m \\lambda_i g_i(x)$$\n",
    "    * $\\lambda_i$ is the Lagrange multipler associated with $g_i(x) = 0$\n",
    "* The **solution** is obtained by solving the (unconstrained) optimization problem: $$\\nabla_{x, \\lambda_1, ..., \\lambda_m}\\mathcal{L}(x, \\lambda_1, ..., \\lambda_m) = 0 \\iff \\begin{cases}\n",
    "    \\nabla_x \\big[f(x) - \\sum_{i=1}^m \\lambda_ig_i(x) = 0 \\big]\\\\\n",
    "    g_1(x) = ... = g_m(x) = 0\n",
    "  \\end{cases}$$\n",
    "  * Amounts to solving $d + m$ equations in $d+m$ unkowns\n",
    "      * $d = |x|$ is the dimension of $x$"
   ]
  },
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   "source": [
    "#### <img src=\"https://img.icons8.com/dusk/64/000000/task.png\" style=\"height:30px;display:inline\"> Exercise - Max Entropy Distribution\n",
    "---\n",
    "Maximize $H(P) = -\\sum_{i=1}^d p_i \\log p_i$ subject to $\\sum_{i=1}^d p_i = 1$"
   ]
  },
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    "#### <img src=\"https://img.icons8.com/dusk/64/000000/idea.png\" style=\"height:30px;display:inline\"> Solution\n",
    "---\n",
    "* The Lagrangian is: $$L(P,\\lambda) = -\\sum_{i=1}^d p_i \\log p_i -\\lambda \\big(\\sum_{i=1}^dp_i -1 \\big) $$\n",
    "* Find stationary point for $L$:\n",
    "    * $\\forall i$, $\\frac{\\partial L(P,\\lambda)}{\\partial p_i} = -\\log p_i -1 -\\lambda =0 \\rightarrow p_i = e^{-\\lambda - 1}$\n",
    "    * $\\frac{\\partial L(P,\\lambda)}{\\partial \\lambda} = -\\sum_{i=1}^d p_i + 1 = 0 \\rightarrow \\sum_{i=1}^d e^{-\\lambda - 1} = 1 \\rightarrow e^{-\\lambda - 1} = \\frac{1}{d} = p_i$\n",
    "    * The Max Entropy distribution is the **uniform distribution**."
   ]
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   "source": [
    "## <img src=\"https://img.icons8.com/bubbles/50/000000/thumb-up.png\" style=\"height:50px;display:inline\"> Useful Inequalities\n",
    "---\n",
    "* **Markov Inequality** - for a non-negative R.V (Random Variable) $X \\geq 0$ and for *any*  positive number $\\lambda > 0$: $$ Pr(X \\geq \\lambda) \\leq \\frac{\\mathbb{E}[X]}{\\lambda} $$\n",
    "    * Proof: Assume $X$ can take values $x_1 < x_2 < ... <x_j = \\lambda < ... <x_n$, then:\n",
    "    $$ \\mathbb{E}[X] = \\sum_{i=1}^n x_i \\cdot Pr(X=x_i) \\geq \\sum_{i=j}^n x_i \\cdot Pr(X=x_i) \\geq \\sum_{i=j}^n \\lambda \\cdot Pr(X=x_i) = \\lambda \\cdot \\sum_{i=j}^n Pr(X=x_i) =  \\lambda \\cdot Pr(X \\geq \\lambda)$$\n",
    "    \n",
    "* **Chebyshev Inequality** - for any R.V (Random Variable)  $X$ and for *any*  positive number $\\lambda > 0$: $$ Pr(|X-\\mathbb{E}[X]| \\geq \\lambda) \\leq \\frac{Var(X)}{\\lambda^2} $$\n",
    "    * Proof using the Markov Inequality.\n",
    "* **Hoeffding Inequality** -  Let $X_1, ..., X_n$ be i.i.d. random variables, bounded by the intervals $a_i \\leq X_i \\leq b_i$. Let the empirical mean be defined according to $\\overline{X} = \\frac{1}{n} \\sum_{i=1}^n X_i$. It holds that: $$ P(|\\overline{X} - \\mathbb{E}[\\overline{X}]| \\geq \\epsilon) \\leq 2e^{-\\frac{2n^2\\epsilon^2}{\\sum_{i=1}^n(a_i - b_i)^2}} $$"
   ]
  },
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   "source": [
    "### <img src=\"https://img.icons8.com/bubbles/50/000000/video-playlist.png\" style=\"height:50px;display:inline\"> Recommended Videos\n",
    "---\n",
    "#### <img src=\"https://img.icons8.com/cute-clipart/64/000000/warning-shield.png\" style=\"height:30px;display:inline\"> Warning!\n",
    "* These videos do not replace the lectures and tutorials.\n",
    "* Please use these to get a better understanding of the material, and not as an alternative to the written material.\n",
    "\n",
    "#### Video By Subject\n",
    "\n",
    "* Basic Probability - <a href=\"https://www.youtube.com/watch?v=KzfWUEJjG18\">Math Antics - Basic Probability</a>\n",
    "* Probability for ML - <a href=\"https://www.youtube.com/watch?v=wG_gQpXJNGU\">Machine Learning 1/5: Probability</a>\n",
    "* Lagrange Multipliers - <a href=\"https://www.youtube.com/watch?v=8mjcnxGMwFo\">Lagrange Multipliers | Geometric Meaning & Full Example</a>\n",
    "* Hoefdding's Inequality - <a href=\"https://www.youtube.com/watch?v=zz4C-xECIp4\">Chernoff, Hoeffding, etc. bounds || @ CMU || Lecture 5c of CS Theory Toolkit</a>\n",
    "* Markov and Chebyshev Inequalities - <a href=\"https://www.youtube.com/watch?v=s8geHBRvSos\">MIT 6.041SC - Probability Bounds</a>"
   ]
  },
  {
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   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "## <img src=\"https://img.icons8.com/dusk/64/000000/prize.png\" style=\"height:50px;display:inline\"> Credits\n",
    "---\n",
    "* Icons from <a href=\"https://icons8.com/\">Icon8.com</a> - https://icons8.com\n",
    "* Datasets from <a href=\"https://www.kaggle.com/\">Kaggle</a> - https://www.kaggle.com/"
   ]
  }
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