{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Probabilistic Programming Concepts" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import os\n", "import glob\n", "from pathlib import Path\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib as mpl\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "sns.set_context('notebook', font_scale=1.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bayes theorem and parameter estimation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In general, the problem is set up like this:\n", " \n", "- We have some observed outcomes $y$ that we want to model\n", "- The model is formulated as a probability distribution with some parameters $\\theta$ to be estimated \n", "- We want to estimate the posterior distribution of the model parameters given the data\n", "$$\n", "P(\\theta \\mid y) = \\frac{P(y \\mid \\theta) \\, P(\\theta)}{\\int P(y \\mid \\theta^*) \\, P(\\theta^*) \\, d\\theta^*}\n", "$$\n", "- For formulating a specification using probabilistic programming, it is often useful to think of how we would simulated a draw from the model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Probabilistic Programming\n", "\n", "Statistical objects of interest have the same form as the expectation\n", "$$E[f(\\theta)] = {\\int f(\\theta)p(\\theta) d\\theta}$$\n", "For example, in addition to the marginal in the denominator of Bayes' theorem, the posterior predictive distribution is\n", "$$p(\\hat{y} \\mid y) = {\\int p(\\hat{y} \\mid \\theta) p(\\theta \\mid y) d\\theta}$$\n", "Probabilistic programming is a way to encode such concepts so they can be automatically calculated\n", "\n", "- DSL for model construction, inference and evaluation\n", "- Inference Engines\n", "- PyMC3, PyStan and TFP" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimating integrals" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Integration problems are common in statistics whenever we are dealing with continuous distributions. For example the expectation of a function is an integration problem\n", "\n", "$$\n", "E[f(x)] = \\int{f(x) \\, p(x) \\, dx}\n", "$$\n", "\n", "In Bayesian statistics, we need to solve the integration problem for the marginal likelihood or evidence\n", "\n", "$$\n", "p(X \\mid \\alpha) = \\int{p(X \\mid \\theta) \\, p(\\theta \\mid \\alpha) d\\theta}\n", "$$\n", "\n", "where $\\alpha$ is a hyperparameter and $p(X \\mid \\alpha)$ appears in the denominator of Bayes theorem\n", "\n", "$$\n", "p(\\theta | X) = \\frac{p(X \\mid \\theta) \\, p(\\theta \\mid \\alpha)}{p(X \\mid \\alpha)}\n", "$$\n", "\n", "In general, there is no closed form solution to these integrals, and we have to approximate them numerically. The first step is to check if there is some **reparameterization** that will simplify the problem. Then, the general approaches to solving integration problems are\n", "\n", "1. Numerical quadrature\n", "2. Importance sampling, adaptive importance sampling and variance reduction techniques (Monte Carlo swindles)\n", "3. Markov Chain Monte Carlo\n", "4. Asymptotic approximations (Laplace method and its modern version in variational inference)\n", "\n", "This lecture will review the concepts for quadrature and Monte Carlo integration." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Numerical integration (Quadrature)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You may recall from Calculus that integrals can be numerically evaluated using quadrature methods such as Trapezoid and Simpson's's rules. This is easy to do in Python, but has the drawback of the complexity growing as $O(n^d)$ where $d$ is the dimensionality of the data, and hence infeasible once $d$ grows beyond a modest number." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Integrating functions" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from scipy.integrate import quad" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def f(x):\n", " return x * np.cos(71*x) + np.sin(13*x)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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mkR63BUO+YEW/yyQKEnn8wAii8WTOgrJKclOfB75AFAeH5yq9lFVPMskx4AsUDDKLbGy2IRBNpEds5mNwRlmNgohYwKakVuGMdwHt9WaYDcuL5ijYLA/RUshGj9uCaCK5rNPBSkKiIAExwLyz05kODlYT169rhIYBv6e4QsXxLkQQjiULBplFxISFY2P5ffKJJMfITEhx5hEgxBQAZVXNZ72Ly4LMIlvaHBiaCSqeJLfa8M6Hc4pCdxU0xiNRkMDzp6fQPxWoijTUbDjq9FjXZCNLoQoQv8xSLYX1zVboNKyg+2UyVfvQWYQoOMx6GHQa2e6jeCKJ/ukA1uWYF5KubB4ja6EQ4VgC8+E4mnK4j8ThSeNzlRuIRKIggWL6HK0UOzqdODg8R+20K0y6O6rEmIJRp8U6j62gpSCmo3Y1SNtvNhhjQgGbTFEYng0hGk9iTQ5R6ElZRSMSXGCrHTHIn8tScKdGt04tVm5eColCAUrR52gl2N7hhD8Uq4ohHauZAV8Qei1DiyN/OmomW1rtODrqzyvoQzPK5igspVlBAduZSSE7KpelkL6Q0eCngogV5bkCzWaDFjajrqK/y+q9ylUJpepzVG52dNYDALmQKsyQTxiVuXRWdz42t9rhC0TzBoAHfUHoNAytTulik41mhwnjMkXhbGruRy5LwaTXwmHWkyhIIG0p2LNbCgDgthnJUqhWfIsR/OzNUdxzaXvJ+hyVi7VNVlgMWrw5RKJQScb8IdkXbrHn1bE8PvnBmSDa6s2yxCYb7fVmjPtDslIez04uotlugt2kz/maRpvyaunVhDdlKSztkJpJo9WIabIUqpMfvzqEaDyJD1/dU+mlFESrYdjW7iRLocJM+MNotsvrcNnXYgdj+auCh4tMRxVpqzcjluDpi5MUzngXsc6T3UoQabIZyVKQwOR8BHotQ31dboF12wxkKVQj4VgCP3h5EDdsaFxWxVmt7Oh04sT4PMIx+W0MiOKJJ5LwLkRkWwoWow49bkve7J1BhXMUltJeL+xjZFZaHnwyyXFuanFZ0dpSyFKQhjCG05S3AJEshSrloVeHML0YwR9d11vppUhme4cT8SSn6tIKMbUYQSLJ06Mv5bCl1YFjOf5u/mAM/lCsqBoFkTanYMWMShSFMX8IwWiioKXQaBUsBcp+y8/UQgSNOTKPRBptRsyH4xW7uSNRyEIwGse/7z2Lt6xx4S1r1DM8ZHun0JyMXEiVQQzgysk8EtnSZseYP4yZwPJuo4dGhL/nek/24jE5iHnwUtNHz3iFIHOuwjWRJrsRoViCuvUWQGhxkV8UxGyu6Qq5kEgUsvDgiwOYXoziz2/ZUOmlyKLJZkKb00zB5gohpnrKjSkAmZXNy62FvaemYNRp0hPPisGk18JtNWBUYhuFcylRWNOYvz5CvPuluEJ+hBYX+W8axN/l9GJl2pGTKCzBH4rhP54/h7dubMKlXfWVXo5stndSsLlSiJaCkrTRza1C+5RswebnT3txZa8LJv3yvkNKaKuvkxxTODcVgLNOD5c1/92teKEjUchNJJ7AXDBW0FKotMCSKCzhOy/0Yz4cx5/fsr7SS1HEjg4nRudC6ZF/xMoxPheCSa+Bw5w7syQXzjoD2uvNyyyF4Zkgzk0FcP16+XOZc9HuNEuOKfRPLaJXQh8n8UJGwebcXKhmzn/TUOliQBKFDHyLEXxn33ncsbWlaiaryWVHKq7wJlkLK874vDBwXWlr682t9mXtLn5/RmhyWFJRqDdjZC4kqV33ualAwcwjQAg0A2Qp5EMUzMYCloLLKtREUUyhCvjaM2cQjifxpzer00oABN+0XssorlABhBoF5RXHW1odOD8dwEL4QrfR509Noc1pLujTl0NbvRnReBLTgfwXnflwDNOLEfRKEAVnnR56LSNLIQ9TC9nHcC7FqNPCWVe5CnEShRRnvYv48atDeN8VnaqpS8iGSa9FX4sdB4dnK72UVceEP4yWItpQiK1KHt8/AkCYi/zi2WncsKFRsfWRjQsZSPldSP1TQr+lXgmCxBhLp6US2ZlKBY7dtsLdEdxWI1kKleafnjoJs16LT+1eV+mlFM32DieOjPhpEtsKkkhyTMyHFaWjily91oVr17nxladPYXgmiP2DswhEEyV1HQFAm1NaAVu/2PNIgqUAAI12U0Urcasdf1AQBSkxp0oKLIkCgJfP+bDnxCT++MY16SCPmtne4UQgmsAZr7TZv0TxTKcL1+Sno4owxvBP92yDhjF87rHD2HvKC52G4S1rS1sr01YvrYDt3NQitBomuZK60WqkBIc8+EMxmPVaGHWFs8gaK9gUb9WLQjLJ8Q+/Po42p1kVPY6ksL0jVcRGcYUVI124VkRMARAqjv/37X14ud+HB18awGXd9bAaSzsT3GrUwVmnL1jA1j8lzISW2jK+0VY5l4ca8IdikjPT3BVsdbHqReFXR8ZxdHQen3nb+pLlgVeaHrcFDrOegs0ryIRfuOsuJqYgct8VHbhmrRvReBLXr28qen/ZaK83Fyxg658KyApwN9mM8AWiiCeSxS6vJpkLxuDM0wgvk0abEYFoAsHoyleIr2pRSCQ5HthzGus9VrzzkrZKL6dkMMawvYOK2FaSsTmxxYVy95GI4Ebait19TXjH9vJM+2t35i9gSyQ5zvsCkjKPRBptRnAO+LK06iAES8Eu2VJIpaUurPzvclWLwpOHx3BuKoBP714PjaZ02R3VwPYOJ057F6gXzQoxMR+GQafJ2xJZDu31dfj2By9PN7ArNW31QgFbrgZ2o6kRnFIK10SaqNVFXuS4j9JVzYsrH6NZtaIQTyTxtT1nsLHZhls3N1d6OSVne6cTnAOHR8haWAnG/ULmUSlTR8tJe70ZoVgiawM+ADg3LWQeybUUAMia1bCa8IdicMoVhQoI7KoVhV8cHEP/dG1aCQCwvZ06pq4k43OhogrXVpp0C+0ccQWxRkFWTMFO/Y/yIctSECvEK9AUb1WKQjyRxNefPYNNLXa8bbOn0sspC/UWA3rcFspAWiHG/WG0lsnVUw4KDds5N7UIh1kvawyt6Af35pk1vVqJxpMIRhOSRaHBYgBjZCmsGE8eHsegL4hP716nGnNfCds7nHhzeI4Gn5SZZJJjcj6saLhOpWgrMFehf2oRvY0WWd8Po04Lh1lPBWxZ8IeE1iVSs490Wg1cFkNFUnxXpSg8+NIAehst2N1Xm1aCyPYOJ6YWIhjzk4+3nEwHIogneVHVzCuNw6yHzaTLWcDWL7ER3lJoVnN2RFGQmn0ECLUKZCmsAG8OzeLQ8Bw+uKu7JmMJmVAR28owPicO11GPKABCXCGb+2ghHIN3ISKp59FSaFZzdkRRkNNWvbFCArvqROH7Lw3AatThnkvbK72UstPXYodBp8GbQ9Qcr5xcGK6jnpgCIMQVsolCuhGemyyFUuEPSe97JNJYoaZ4q0oUvAth/OrIOO69rL3krQOqEYNOg8u76/H86alKL6WmEauZ1RRTAIS50Ke9C8suPP2pdNS1TUothTDFsZZwIaYgI3CfEtiV/l2uKlF46NUhxBIc9+/qrvRSVoy3bvTgjHcRQz5pg9oJ+YzPh2HQatAg4wtfDdyyqRmcA3uOT160/fWBWZj0GnQ2KBOFcCxJRZNL8AcVuI+sRkTiSSys8O9y1YhCNJ7Ej14Zwo0bGtEjo0pT7ezuE3rnPHNyssArCaWMz4XhcRhVF6Pqa7Gho8GMp49NpLdF4gk8eWgMt25ultwILxNx1CTFFS5mTgw0m6R7KMS5CyvdGG/ViMJTR8cxvRjBH9ZIJ1SpdLksWNtkxTMnvJVeSs0y7g+VpOfRSsMYw9s2NePFs770tLdnT3gxH47j7p3KYm6VHjpfrfhDMdiMOui00i+5jdbKFAOuGlH46RvD6Ggw49oS96ZXAzdtbMKr530XjXkkSsfwTAgd9dJmDlQbb9vSjGgiib2nhLjT4wdG0WQz4mqF3xPqf5QdOc3wRESBnV7hquZVIQrDM0G8eNaHey/tUJ2JXwpu6vMgluB44cx0pZdSc4RjCUzMh9HRoD5LAQB2dtbDbTXg6WMT8C1GsPeUF3ftaINW4fdEHFJFonAx8zJaXIikK8RXuJdUWUWBMWZljH2dMTbOGAsxxt5gjL2jnMfMxmP7R8AYVkUaajZ2djrhrNNjzwmKK5QasXeQ1Olk1YZWw3DzJg/2nprC4wdGEE9y3LVTeRt5h1kPrYblbLS3WpEzS0GkwWLAG1/YveKJMeW2FJ4A8AcAvgDgDgDHATzBGLu9zMdNk0xyPLZ/BNesdZetDXG1o9NqcMP6Ruw9NUVzm0vM0IyQ1dWhUlEAgFs2N2MxEscDe4R+YBub7Yr3pdEw1NfpaabCEuQ0wxNhjMFtNSq22pRSNlFIXfh3A/go5/w7nPNnAXwQwMsA/rVcx13KS+d8GJ0L4d7LOlbqkFXJTX0ezASiODhMhWylZCQlCmq1FADgLWtcsBp1CEYTuLsIK0HEZTFiJkDuo0yUiEKlKKelcBcAP4BfiBu4UIXxfQAbGWObynjsND99Yxh2kw63bKrtPkeFuG59I3Qaht8eIxdSKRmeDcGg06RbHasRo06Lt25sglbDSjLprcFiIPfREuZCMThKNICp3JRTFLYAOM45Xzqw9XDG82XFH4zhN8cm8K4dbTUzf1kpDrMeu/s8ePClARwfm8/6Gs45fvrGMP7+yeM4M7mwwitUJ0O+INrrzapPYPir2zfiex+6PF1nUAwNVgN8FZgDUEreHJrF5HxpArzhWALReJIsBQAuADNZts9kPH8RjDEnY6w78wFAcXT4vw+NIhpP4j2r3HUk8qW7tsBp1uOTDx1AYEmV5Gwgik/8aD8+99hhPPjiedz81d/jw997HQeob1JehmeDqnYdibQ4zLh2XWNJ9uWyGFQdU5hejOC9//kK/vnpUyXZn5JmeJWk3IHmfFHNbM99GsD5JY8XlB58a7sTn7h+DTa3Kg+c1RJuqxFfv28HBnwBfOHnR8E5x2Ikjl8cHMVtX3sBz5704gt39OH1z+/Gn+5ej0PDc7jvP1/BXFC9X/ByMzQTVG2NQrlosBjgD8UQSyx1Eijnu/vO488eOViy/eXjoVeHEI0ncXTUX5L9zaVaXDjN6miDUs6ucD5ksQYANKT+zWZFPADge0u2tUOhMGzvcKbbRxMCV/W68Kmb1uOre05jaCaII6N+YUB7owXf/uDV2NLmAAB8avc67N7UhDu+vg+/PDyOD1zVVeGVlxbOOX59ZAI7Op2Ku5v6gzEshOM1YSmUElcqvjIbjJbEHfWbo+P4P08eByBYu3WG8l22IvEEfvDyIABh+lw0nlTU7iMTtVkK5RSFYwDuYYxplsQVtqb+Pbr0DZzzOQAXNf+v5cloleKTb12LwyNzODW5gPdf2YW3bfbgsu6GZalvQnqiDY/vH6k5UXjxrA9/8tAB6DQMd2xrwceu7U0LolSGZ8V01NWZ6pwLV2qEp2+xeFE4OurHnz5yCHaTDvPhOM56F7GtvXw3ek8eEtrh3HtpOx7dP4JzU4voaynO06A2USin++gJAE4Ady7Zfj+AU5zz42U8NpEHrYbhO394Ofb9xVvxN3duwpW9rqy50Iwx3LOzHQeH53BuarECKy0fz53ywqDT4P5d3XjmhBdv/8Y+/DajMZwUaqFGoRyIc52LzUDyLoTxsR+8AWedHv95/2UAgNOT5fsccs7xnX3nsa7Jio9d1wsAODGePSlDDqL7lUQB+DWA5wB8hzH2YcbYjYyx7wG4BsBny3hcooS8c3srNAz42YGRSi+lpOw95cWVPQ34mzs34aW/eis8diOeeHNU1j6GSRSykrYUihSFf3n6FGaDUfzX/Zfhsq56GLSasmbFvXp+BsfH5/Hha3rQ67bAoNOURBTSlsJqT0lN1SS8C8DDAL4M4CkA2wDczTn/ZbmOS5SWJrsJ161vxBMHRpGskWro4Zkgzk0FcP16IdvGbtLjpj4Pfn96CpF4Qvp+ZoNwmPWwm9TxZV8pxJjCTJFTw46Pz+OKHhe2tDmg02rQ22jB6TKKwnf3nUd9nR537WiDTqvBBo8NJ8aLP958KAbGAJtKBnuVNfuIcz7POf8k57yZc27bLcerAAAgAElEQVTinO/knP+8nMckSs89O9sx5g/jlX5fpZdSEsRJdDdsaEpvu7nPg0A0gVf6s+U/ZGdoJkRB5iw4zXpoWHHuI845BqaD6M2YfbLeYyub+yiWSOKZk17cs7M9XdO0sdmGE+PzRU8+mwvFYDfpVVPLsiq6pBLFcfMmD2wmHR6rERfS3lNTaK83Y03GYPpda1ww67XLppDlY2QmSEHmLAj9jwyYLkIUphYjWIzE0e26ILrrPVaMzoXKMtXNuxBBIsmxtunCXOq+Fjt8gWjRHV/9IfnN8CoJiQJREJNei7dva8Fvjk4gHJPuXqlGIvEEXjo3jRs2NF6U2WbSa3Hdejf2nJiUdGeYTHKMzIYonpCDBosBM0VUNQ9MC/Ga7iWWAoCyxBUm/EL1sidjzraYdXS8yLiCmvoeASQKhESuX9+EYDSBkxPqbn+xf2AWwWgC169vWvbc7j4Pxv1hHMvRBiSTyYUwookkFa7loNj+R+enBTdRr/vCnfsFUSi9C0kUhZYMUdiUEoVi4wpzQRIFogbZ1i7k8B8ZmSvwyupm7+kpGLQavGXN8rrKt25sAmOQNHdieEaYo0CWQnbcViN8RXRKPT8dhF7L0Oq8cJHuaKiDUacpS7B53C/8PZvtF47nqNOj1WEqOgNJyYCdSkKiQEiixWGC22rAoZHSlP5Xir2nvLi8px6WLJkgLqsRl3bWSxKFoRpomV1OGorsfzQwHUBnQ91FM421Goa1TVac9pbeUpicD8Ok1yy7ePe12IsWBXIfETUJYwxb2xw4omJRGJsL4fTkYjoVNRu7N3lwdHQ+feeYi+GZIBjDRXeyxAUaLAbMBWOIK+x/dH46gJ6MeILIeo8Np8vgwhz3h9HiMC/roNDXYkf/dEBxLI1zLrTNJlEgapGt7U6c8S4gGC199sdKcHBYcH1d1ZutJZfA7j5h7saeE968+xqeCaLFboJRt7pbsufClZovPJtqBieHZJJjwJddFNZ5rJiYD6cLwkrF5HwYHvvymRh9LXYkkhxnFVongWgCiSSn7COiNtnW5kCSI+c8hmqnP9WqY02jNedr1jRa0OWqw3Mn84vC0EwQ7eQ6ykkxrS7G58OIxJMXZR6JbEgFm896S2stiJbCUvpahOMpzUBSW98jgESBkMHWVLD5sEpdSP1TATTbTVnjCSKMMdy4oQkvnZvO6TKIxBM4OuZHX7OtXEtVPS6LcNetJNg8MB0AgJzuI6C0PZCSSZ6yFJa7ArtcFpj1WsVxBbX1PQJIFAgZeOwmeOxGHClRn/mV5tx0AL2Nyy80S7lxYxPCsSRezlHBfWBwDuFYEteUaChNLSK6j5RMYOvPIwptTjPMem1JM5BmglHEEvyidFQRrYahx21JC5VcREvBTqJA1Cpb25w4pMK0VM45zk8tShKFK3saYNJrsDeHC2nf2SloNQxX9jZkfZ4ozn00MB2ASa+BJ0vbbY2GYZ3HWtJaBbFGoTmLKACAx26EV2FV83xIXQN2ABIFQiaXtDvQPxXAQri0gb5y4wtEMR+OX1QMlQuTXour17jx3KmprNXN+876sL3DSY3w8lBfZwBjyjqlnp8OoNtlydkraF2TDadKaCmMi6KQxX0ECBby5LwyURCnrqmlQypAokDIRIwrHB1VV7C5f0ow/6VYCoDgQhpKdVPNxB+M4cjIHK5e6y75GmsJbar/0YzCmEI215FIb6MFUwuRkrVcmZhfXs2cSZPdBF8goii9lgLNRM2zNTWd7MioulxIUjKPMrlxo9AGY++pi11IL/dPI8mBa0gUCtJgMciOKcQTSQzNBPOKgjsVryi2UZ3IhD8ErYalW34vxWM3gnNgWkF8ZDYYg17LYDGoJ3WZRIGQhctqRJvTrLoMpP7pAAw6jeR5zG1OMzZ4bHhuiSjsOzsNi0GLHZ00+7sQSqqaR2ZDiCd51nRUkUabcPGeLnJeg8i4PwyPzZh1+iCA9EjRyZRFIYe5YBTOOoOqxgqTKBCy2dbuUF0GUv/UInpclpxf/GzcsLERr52fuahV84tnfbiy1wW9lr46hXApaIp3PpXl05vXUhBFobjJbiKT8+GLuqMuRSxqUyIKs8Eo6lUUTwBIFAgFbG13YNAXTOdgq4H+KWnpqJncuKEJsQTHC6mhPCOzQZyfDpDrSCJKOqWKoiDFUiiV+0goXMsnCilLQcHxZoMx1NepJ/MIIFEgFCC2FD6lkjbasZSfWq4oXNpVjyabEZ977DAefWMY+85MAwCuWUeiIAWX1YjZYBQJGWNcz08HYDPp0nOes+7XUjr3EeccE/4wmu253YouiwEaBkwpsRQCURIFovbZ0CxWlapDFIZmgognuaR01Ez0Wg0e/59vQV+rHZ997DC+9KsTaLIZsa5J3n5WKy6LAZwLLhSpDPiEdNR8PniDTgNnnb4klsJCJI5gNIFmR/YgMwDotBq4rEZFaamzwRjqLeQ+ImqcZrsJNpOupLni5URuOmomHQ11ePhjV+ELd/Qhmkjipj6PqoKGlURJAdvorLS5126rsSSWwoXCtfwJCB67EZML8iwFznk60KwmcjeBIYgcMMbKOkS91IjpqHItBRGNhuGj1/bi7p3tqFNRamGlEV1AvsUo4Cn8+mSSY2QuhN2bCr/YbTWUxFKYKFC4JuKxmdJFblJZjMQRT3IKNBOrA0EUFiTNM640/VMBuCyGoqtKGywGmPQkClJpsMqzFKYDEUTjSbTXF04bbrSZSmop5As0A0IBm1empSBWM1NMgVgVbPBYMReMlSwDpJz0T0vreUSUFrmdUkdmhcFGbRJqSUplKYh3/01ZZilk0mQzYnoxipiMqmZRDEkUiFXB+lSwWQ1xhf6pgGLXEaGc+jq9kLUj8eI9mhKF9vrCMYVGmxGBaKLogU8T82G4LIaCw5LEtFQ5QiQG2CnQTKwKNpShr3058Adj8AWiZClUAJ1WA4/dhLE5aW6XtKUgwX2ULmBbKK5WZsIfytkdNROxgE1Ot1TRfaS2QDOJAqEIl9UIl8VQlnm5peTcdCrILLHnEVFamh2mgvOuRUbngnDW6WHNMwRJJF3AVmRcYdwfLhhkBjIK2GTUKqQtBRIFYrWw3lPaFsblIN8UL6L8tDrMkrN2RmZDkuIJANBoLU0B2+R8WJKl0JQSIa8sUYiBMXV1SAVIFIgi2NBsw5kqz0Aa8AWhYUBHg7SLDVFaWhwmjM2FJH1GRmdDkjKPgNK0ugjHEpgNxiRZCi6rERoGWQVss4EoHGa9rH5b1QCJAqGY9R4bAtEERuekuQcqwaAvgFanuWAgkSgPLU4zIvEkZoP5hzJxzlOWQuEgM3ChMK4YS0F8rygw+dBqGBptRllpqUIzPHW5jgASBaII1nsEP30p2l0kkhyffvhNfPO5s0XvK5NBXxBdLmkXGqL0tKZcM2MFbhxmgzGEYgnJloJeq0F9ka0uxJTRXHMUliJ3AttcMAanygrXABIFogjWpTKQTk0Un4H04Ivn8fODY/jnp0/hlX5f0fsTGfQF0OWieEKlaEnFCArFFUZmgwCkZR6JNNqKa3UhDgBqyNN8L5Mmm1F2oJksBWJV4TDr0eIwFW0pnPUu4CtPn8KNGxrR5arDZx87hECkuPxzQEhHnQ3G0E2WQsUQLYVCGUgXahSki4LbaizKUhAHAOXryJqJUNUsz1IgUSBWHWK7C6XEE0n82U8PwWLQ4ivvvgT/cu8lGJkN4R+fOlH02gZnhMwjshQqh9tqhF7LCtYqiDUK7RJjCoBoKSivUxDnR7us0i7cHpsJM4EoonFpVc0zAfUN2AFIFIgi2dBswxnvoqye+Zl8a+85HB7x4x/u2opGmxGXdzfgI1f34EevDKXnFyhl0Ce4JCimUDk0GgaPvXCtwuhcCDajDnaz9B6dRVsKi1EYtBpJdRHAhQI2KbUR4VgCoVgC9RKtkGqCRIEoinVNVkTjSQz4ArLfG4om8M29Z3H71mbcvrUlvf0zb9uALlcdHthzuqi1DabWJKUVM1E+Wh1mjBe0FIJoqzfLakveaDMiFEsodjX6AlG4rNLnJzfJGMt5oZqZLAVilbGpVZjCdmxsXvZ7Xzw7jXAsifuu6Lxou0mvxe1bW3BweK6o2MKALwiP3Yg6A3WIryQtThPGClgKIzJqFETEVhdKrQXfYkRykBkAmmxCfMQrIQNJrdXMAIkCUSTrPTYYdRocHp6T/d5nTk7CatThyh7Xsud29boQT3K8MTireG1DviC6GiieUGlaHGZMzoeRzONiHJVRzSzithZXqzATiMoSBbHVhZRaBVEUyFIgVh16rQabWu04POqX9b5kkuOZE15ct94Ng275x/Cy7nrotQwvn1OenjrgC1A8oQpodZoQS3BM52ih7Q/FsBCJS+qOmolYdKZUFHyBaNrakILLYoBWwyS5j2YDgvtIjuhUCyQKRNFsa3Pg2KhfVrD56Jgf3oUIbtqYfcpWnUGHS9qdeFlhzUIwGod3IYJu6nlUcVpSoy5zxRWU1CgAF/ofKXcfybMUNBqGRomzmsl9RKxqtrU7EYgm0mMvpbDnhBcaBty4sSnna3atceHoqB8L4fwtErIxNCNcaCjIXHlaCtQqKKlRAIS7cMaAKQVpqaGokB0k907eY5dWwDZH7iNiNbOt3QEAODwi3YX0zIlJ7Oysz/ul3NXrQiLJ8frAjOw1DUwLotBNNQoVpzUVK8hVqyBn4lomOq0GDXXKJrCJ0+DcEmsURJodpvQIz3zMBmOoM2hV2XOLRIEomt5GKywGLQ6PSAs2j/tDODY2j5v68g9o39lVD4NWoyiukE5HpZhCxamv08Oo0+S2FOZCMOu1ivzvSltdXGhxIT2mAAiuMCldX9Xa4gIgUSBKgFbDsLnNITnY/MwJLwBgd19u1xEgpKbu7HLiJSWiMBNEfZ1edb3saxHGGFqdZozluMNWUqMgorSATWyGJ1eIWp0mBKIJzIfzp0rPBqKqG8MpQqJAlIRtbQ4cH5uXNNj8mROT6Gyow9qmwtPQdvW6cXx8Pu2jlQo1wqsumu0mjOfolDroC8qOJ4i4rQZllkJKFOS6j9JB8wJ1F7Mq7XsEkCgQJWJbhxOReLJgH6RAJI4Xz/lwU1+TpDvDXWtc4Bx49by8uMLAdJAa4VURLU5T1k6pgUgcpycXsLXNoWi/jTbBUpA76MmXEhL5lkL+TCqRuWBUdbOZRcomCoyxzYyxbzHGXmOMhRljnDHWXa7jEZVlW+pLfaRAsHnvqSlE40m8bXOzpP1e0uGASS8vrhCJJzDmD6GTLIWqoTVVwBZfYkkeGplDkgM7O+sV7ddtNSIST2JRZuX7TEBe3yORVmdqPoQkS4HcR0u5DMCdACYAvFjG4xBVQJerDnaTDocKiMJTR8fhshhweXeDpP0adVpc1tUga8bCyGwInIMshSqixWlCkmNZ6+k3h4TkhB2dTkX7dadnNctzL8rteyTSZDNBq2F5LYV4Ion5cIwshSz8kHPezjl/B4BflvE4RBXAGMO2dieOjObOQArHEnjupBe3bPbImlt7aVc9Tk8uSK5XEDOPKKZQPbTm8MUfGJxFb6NF8QXUrbCqWW7fIxGthsFjM+a1FPyhGDgHGshSuBjOubSm40TNsLXdgZPjCwjHElmf33dmGoFoArduacn6fC4u7apHkgOHhqVlN53zCqJAlkL10CK6XTLusDnneHN4TrHrCFBe1Sy371EmLU5z3vGi4jxqNbbNBijQTJSQS9odiCc5jo1lv3g/dXQCdpMOu3qXN8DLx/ZOJxgDDgxJa453dMyPZrtJ8uxdovxky9oZ8AUxE4gWJQpum7KmeHL7HmXS4sgeNBe5UM1MolA0jDEnY6w78wGgvcLLIiSyq9cNs16Lh18bXvZcLJHEnhOT2N3nydoALx92kx7rm2zYL7Fj6tFRP7YozGYhyoPdpEODxYADgxfciwdSf8+dXcriCQDQUCe0upiWaSnI7XuUSZvTjHF/OGfGU9pSqGX3EWPshlT2kJSHu4j1fBrA+SWPF4rYH7GCOOr0ePel7fjFwbFl5vwr/T74QzHcukVa1tFSdnbV48DQbN72ywCwGImjfzqgOMWRKA+MMdx7WTt+e3wCw6m+VAeGZmE16rCuyaZ4v+lWFzICzUr7Hom0OEyIxpPpWoelqLkZHiDdUjgJ4EMSH8VMcX8AQM+Sx7VF7I9YYT50dTeiiSR++MrgRdufOjqBOoMW161vVLTfS7vqsRCO41yBpnsnxufBObClza7oOET5+OCubjDG8IOXBwAA+wdnsaPTKSvpIBtuq7xWF0r7Hom0FKhVmE2JhVpjCpKSdDnnEwC+V96lAJzzOQAXpa8oKX0nKkdvoxU3bWzCj18ZxB/fsAYmvRaBSBy/PTaJGzc0waRX1iBsZyplcf/gLNZ5ct9ZinUSZClUH61OM27b0oyHXxvGR6/txenJBdwisV4lH26bvKpmpX2PRMRMqjF/CFvbl3/OZoJR6LUMFoP6muEBVRZTIGqDj1zTA18gil8cHIV3IYz3/ufLmA1Gl43dlEOP24L6On3BuMLRUT+abEY0paZkEdXFR67pwUIkji/8/GiqaE15PEFErqWgtO+RiJhJlbNtx3QQHQ11qr2hLdvwWsZYHYDbUz9ekvr3NsbYFIApzvnz5To2UVl2rXFhY7MN39p7Dt949ix8i1F8+/7LcM065eEmxhguTcUV8nF0jILM1cyOznrs6HTid8cnhZ87lGceibitRkwvSI8piAKi1H3kshhg0GlyNvjrn15Er7twX69qpZyWQhOAR1OPP0xt+/fUz18s43GJCsMYw0ev7cWAL4hwLIFHPn5V3mE6UtnRWY9zU4G0z3YpwWgcZ72LJApVzkeu6QEArG2ywlGCDB231YhQLIGAxFYXxVoKjDG0OExZaxUSSY6B6SDWNKq3cLJslgLnfACAOu0nomjeub0Vs4Eobt3SjI4STT+7tEu4q3xzeBZvzTLG88T4ApKc4gnVzq2bm9HrtuC6dcqSDpaSOavZIqGXkdK+R5m0OsxZaxVGZoOIJpJY06heS6FsokCsbvRaDT52XW9J93lJu5CpcmBwLqsoHE3Nc6DMo+pGp9Xg15+6FnptaRwVohtoejEiqbXJ9KKyvkeZtDhNeCVLk8b+KaGavlfFlgIFmgnVYDZosanFjjcGs7fRPjLqh9tqQDMFmasek15bdCqqiDvd6kJaXGEmoKzvUSatDjMmFyJILKmbEVOme1VsKZAoEKri6rVuvDEwC+/CctP96Kgfm1sdqs36IJQhuo+mJGYgzQSiRbdAaXGakEjyZZ/Dc1MB1NfpixadSkKiQKiK917egXiS49E3Ri7aHo4lcMa7SPGEVYh4AZba6mJ6MQpXCSwFAMuCzeemFlVtJQAkCoTK6HFbcPVaFx56degi0/3kxAISSU6ZR6sQvVaD+jq95FqFYjqkimTr+goIMYVet3rjCQCJAqFC3ndFF0bnQvj9man0ttfOC0E/CjKvTqQWsAWjcYRiCbgU1iiIpMdyZnR99YdimF6MYI2E2ePVDIkCoTpu3uSB22rAj18ZAiDEEv7td6dxRU8D2pzKBsAT6kYQhcKBZrHFRbHuI7tJD6tRd5Gl0C8GmclSIIiVxaDT4D2XdeDZk5M4OurHx3+4H/V1BnzzfTspyLxKcdukWQqT88JFvBRtUIS5ChcshQvpqGQpEMSKc98VneAA3vMfL2N6MYL/+MCl6SwUYvXRaDVKCjSLBWdioLgYWp1mnJsKpOcq9E8vQqdh6FL5xD8SBUKVdDTU4dp1jQhGE/ine7ZiW3vxjdUI9eK2GRCIJhCKZh8FKzKREoVmR/GWwi2bPTjrXcQbqSaN57wBdDbUlawor1Koe/XEquYf796K/7r/Mty1g4bzrXbEArZCLqRxfxh1Bi3spuKbOdy9ox0Osx7f3XceQKoRnoormUVIFAjV0uY04+ZNy9tdEKuPRqu0AraJ+RCaHaaSxJ7MBi3ed2Unnj42gUFfINUIT93xBIBEgSCIGiBtKRSIK4zNhUsSTxC5f1cXNIzhS786gWgiSZYCQRBENeC2CSmmBS0Ff7gk8QSRFocZt29tSc+HUHvmEUCiQBBEDeCyiJZC7lqFeCIJ70IYLSUUBQD4cGo+BAByHxEEQVQDBp0GDnP+VhdTixEkuXB3X0q2dzixs9OJBotB1Y3wRGieAkEQNYHbasgrCmL1caktBQB44L07MJmlc68aIVEgCKImaCxQ1VzKGoWldLrq0KnyojURch8RBFETFOp/JLakKIelUEuQKBAEURO4C7S6mPCHYdZr4TDrV3BV6oNEgSCImqDRZsRCJI5wLHuri/F5IfOImibmh0SBIIiawJ2akTCVw1oYnwuVJZ5Qa5AoEARRE3S5hGri89OBrM+XunCtViFRIAiiJliXmnh2xru47LlEkmNyIVLSFhe1CokCQRA1gctqRIPFgLPehWXPTS9GkEhyshQkQKJAEETNsLbJitOTyy2FsTlKR5UKiQJBEDXDuiYrzkwupKehiZSzcK3WIFEgCKJmWO+xYT4cX5aBVMoxnLUOiQJBEDVDrmDzxHwYRp0GzjoqXCsEiQJBEDXDWk9KFCYvDjaP+6lwTSokCgRB1AyNViMcZv0yS2F8LlTyltm1CokCQRA1A2MsFWxeIgr+0g/XqVVIFAiCqCnWeaw47b2QgZRMckzOUzWzVEgUCIKoKdY12TAXjMEXENpoTwciiCc5WQoSIVEgCKKmWJcONgsupGOj8wCAtnqKKUiBRIEgiJpiXZMNAHA25UJ6YM9ptDnNuHqtu8IrUwckCgRB1BQeuxE2ow5nvIt4+tgEDo348and62DUaSu9NFVAM5oJgqgpGGNY67Hi5PgCXjrnw5pGC+7e0VbpZakGshQIgqg51jVZ8drADM56F/GZWzZAp6VLnVToN0UQRM2x3iPEFba1O3DrluYKr0ZdkCgQBFFzbO9wQsOAv7h1I7W2kAnFFAiCqDku627Agb++Gc46Q6WXojrIUiAIoiYhQVAGiQJBEASRhkSBIAiCSFM2UWCM3cMYe4Qx1s8YCzHGzjPGvs8Y6y7XMQmCIIjiKKel8DkAJgD/B8CtAP4OwFsAHGCM9ZTxuARBEIRCypl9dCfn3Jvx8/OMsd8DOAfgkwD+vIzHJgiCIBRQNkthiSCI284DmAbQXq7jEgRBEMpZ0ToFxtgWAI0Ajsp4mxYARkZGyrImgiCIWiTjmimrEyATpxOVG8aYEcDvAawB0Mc5n8ryGicA55LNlwF4tPwrJAiCqEmu5Zzvk/piSZYCY+wGAM9J3Gcj53x6yfu1AH4AYDuAt2cThBSfBvC3WbY/COAfACQkrkGkHcALAK4FsFpMDTrn1QGd8+qgmHPWAmgB8LqcN0l1H50E8CGJr13I/IExpoFwUb8bwHs557/L894HAHwvy/Y5zvmcxONnHlv87wjnfEDu+9UInTOdc61C56zonM/JfYMkUeCcTyD7xTovKUH4LoD3AXg/5/xnBY4zB0D2xZ8gCIIoDWULNDNB4v4LwAcAfIhz/nC5jkUQBEGUhnJmH30dwIchCMNpxthVGc/Nc86Pl/HYBEEQhALKWryW+vdjqUcmzwO4oYzHFpkD8EWsLpcUnfPqgM55dbDi57xiKakEQRBE9UNdUgmCIIg0JAoEQRBEGlWKAmPMyhj7OmNsPNWW+w3G2DskvncNY+znjDE/Y2yBMfZrxtimcq+5WJSeM2Pso4yx/2aMDabedya1n8aVWHcxFPN3ztgHY4w9yxjjjLEHyrXWUlHkZ5sxxv6IMbafMRZkjM0xxl5hjL2l3OsuhiLP+R7G2EuMsdnU42XG2HvKveZiYIy1M8a+xhjbxxhbTH02b5Dx/ksZY88wxgKpc36YMdZWqvWpUhQAPAHgDwB8AcAdAI4DeIIxdnu+NzHGmiBUB3YD+CCA+wA0QOjgWu1N+hSdM4Qg1TyAv4LQwvzfALwHwOuptiLVjNJzzuRjADaWYW3lophz/jaArwB4HMDtqf38GoClPEstGUq/zx8E8BiAMQi1UO8DMArgEcbYh8u64uJYC+HaswjgGTlvZIz1AdgLgAF4N4TP9w4Aexlj1pKsjnOuqgeEDzsHcFfGNgZgH4ATBd77FQAhAK0Z21wQLprfqvS5lemcm7Jsuz61v/9V6XMrxzlnvL4NQtbGPal9PVDp8yrj3/keCG1gdlX6PFbwnPcCGACgydimSW3bW+lzy7PuzPW+K3X+N0h8708hiKAlY9vG1N/+L0qxPjVaCncB8AP4hbiBC7+Z7wPYWMAVdBeA33HOxzLe6wPwSwhtOKoVxefMs7Qwx4VeKNVsHRXzdxb5FoDfc84fL88SS04x5/y/IJzry+VdYskp5pxjABY558mM9yYh3IFHyrPc4slcrxwYY3oAbwfwGOc8kLG/kwBegXBjUDRqFIUtAI5n+cUeznh+GYwxM4QOrdnadh8G0JRyL1Ujis45D29N/SunhflKU9Q5M8buA3AjgD8pw9rKhdLPth7AVQCOMMa+zBibZIzFGWPHUi6WaqaYv/P/BdDHGPs8Y8zNGGtkjH0ewAYAXy3DWitNLwAzcl/D5F4HsqJGUXABmMmyfSbj+WzUQzBLlby30ig952UwxhogVJufgWCKViuKz5kx5gbwNQCf55wPl2Ft5ULpObsAGCHEyd4JYbLhbQCOAPgeY2xp8Wg1ofjvzDn/BYB3APgMgCkAXgixs3s5578p8TqrAfF3kev3ZU7d/BbFig7ZKSH5Ku4KVeMV895KUvS6GWN1AH4OIbh+Hee8ak3sFErP+esAzkO4k1QbSs5ZvLkzAbidcz4IAIyxPRDuLv8GQruZakXR35kxdjOAhwD8BEJwXQshYP0Txti7Oee/Kukqq4eyXsPUKAo+ZL97aEj9m01FAWAWwi9MyXsrjdJzTpO6g/hvCJkKb+OcH5fti/UAAALBSURBVC7wlkqj6JxTF4r3QnCR2TNaDwOAMZVxtcg5j5dwraWi2M/2SVEQAME3zxj7DYC/Zow15YgvVRqlf2cGIe7wLOf8ExlP/SaVSfgNALUmCr7Uv7l+XyHOebjYg6jRfXQMgh9x6dq3pv7N6ifnnIcA9CO7320rgKkq/dIACs9ZhDFmghDI2wVhyNFLpV9iyVF6zpshfK73QrhYig8A+ETq/7tLutLSUcxn+2yOfYqqqCi4uQIo/Tt7IAyQeSPLc28A6El97muJfgjZk7muYSWJEapRFJ6AMLLzziXb7wdwiufvvvoEgJsZY83ihpSP/U4AeWc9VBjF58yEMag/hzC56Z2c8+fLtsrSovScH4MQYF76AAQXw40AXiv5aktDMZ/tn0G4uHaLG1J307cB6OdLpiFWEUrPeRZAGMAVWZ67CoCvFHfN1QTnPAbB+rkn5QoGADDG1kO44SvNNazSObsKcnwZgGcBTENozX0jhAFASQB3ZrxuL1LZbRnbPAAmAByAEJC7A8DLEMyyzkqfW5nO+ZcQXAtfhPBlyXysqfS5leOcc+xPDXUKxfydXQCGIUxJvA+CGDyWOu/3VvrcynTOX02d37chFGbeAeCR1LbPV/rcCpz3u1OP/y+13r9N/XxbxmsGAAwsed8mCCm3e1LnfE/qb34OgK0ka6v0L0fhL9QOIYg4AeFu4QCAdy15TdaLBYB1EFwp86lf7lMANlf6nMp1zqkPXK7H9yp9XuX6O2fZV9WLQrHnDKFS/1FcuIt+fel7q/FRxGdbC+DjAPZDKFKcgZCv/36kOkBX6yPPd3Ig4zXLRCG1/XIIQhpInfdPAXSUam3UOpsgCIJIo8aYAkEQBFEmSBQIgiCINCQKBEEQRBoSBYIgCCINiQJBEASRhkSBIAiCSEOiQBAEQaQhUSAIgiDSkCgQBEEQaf4fPvxjtU1phFwAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 1, 100)\n", "plt.plot(x, f(x))\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Exact solution" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0202549" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy import sin, cos, symbols, integrate\n", "\n", "x = symbols('x')\n", "integrate(x * cos(71*x) + sin(13*x), (x, 0,1)).evalf(6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Using quadrature" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.02025493910239419" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y, err = quad(f, 0, 1.0)\n", "y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Multiple integration\n", "\n", "Following the `scipy.integrate` [documentation](http://docs.scipy.org/doc/scipy/reference/tutorial/integrate.html), we integrate\n", "\n", "$$\n", "I=\\int_{y=0}^{1/2}\\int_{x=0}^{1-2y} x y \\, dx\\, dy\n", "$$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0104166666666667" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x, y = symbols('x y')\n", "integrate(x*y, (x, 0, 1-2*y), (y, 0, 0.5))" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.010416666666666668" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.integrate import nquad\n", "\n", "def f(x, y):\n", " return x*y\n", "\n", "def bounds_y():\n", " return [0, 0.5]\n", "\n", "def bounds_x(y):\n", " return [0, 1-2*y]\n", "\n", "y, err = nquad(f, [bounds_x, bounds_y])\n", "y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Curse of dimensionality and concentration of measure" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot([0,1,1,0,0], [0,0,1,1,0])\n", "θ = np.linspace(0, 2*np.pi, 100)\n", "plt.scatter(np.random.rand(1000), np.random.rand(1000))\n", "plt.plot(0.5+0.5*np.cos(θ), 0.5+0.5*np.sin(θ))\n", "plt.axis('square')\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose we inscribe an $d$-dimensional sphere in a $d$-dimensional cube. What happens as $n$ grows large?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The volume of a $d$-dimensional unit sphere is\n", "\n", "$$V = \\frac{\\pi^{\\frac{d}{2}}}{\\frac{d}{2} \\Gamma(\\frac{d}{2})}$$\n", "\n", "The Gamma function has a factorial growth rate, and hence as $d \\to \\infty$, $V(d) \\to 0$.\n", "\n", "In fact, for a sphere of radius $r$, as $d \\to infty$, almost all the volume is contained in an annulus of width $r/d$ near the boundary of the sphere. And since the volume of the unit sphere goes to 0 while the volume of unit sphere is constant at 1 while $d$ goes to infinity, essentially all the volume is contained in the corners outside the sphere. \n", "\n", "For more explanation of why this matters, see this [doc](https://www.math.ucdavis.edu/~strohmer/courses/180BigData/180lecture1.pdf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Drawing pictures" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### DBDA diagrams\n", "\n", "- [Using LaTeX](https://github.com/tinu-schneider/DBDA_hierach_diagram)\n", "- [Using R and LibreOffice](https://github.com/rasmusab/distribution_diagrams)\n", "\n", "Example\n", "\n", "![img](https://camo.githubusercontent.com/461d1c11baae73b680b14f10709551fa2f28be1b/68747470733a2f2f7261772e6769746875622e636f6d2f74696e752d7363686e65696465722f444244415f686965726163685f6469616772616d2f6d61737465722f4578616d706c652e706e67)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plate diagrams\n", "\n", "- [Using `daft`](http://daft-pgm.org)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "import daft" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Coin toss model" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "pgm = daft.PGM(shape=[2.5, 3.0], origin=[0, -0.5])\n", "\n", "pgm.add_node(daft.Node(\"alpha\", r\"$\\alpha$\", 0.5, 2, fixed=True))\n", "pgm.add_node(daft.Node(\"beta\", r\"$\\beta$\", 1.5, 2, fixed=True))\n", "pgm.add_node(daft.Node(\"p\", r\"$p$\", 1, 1))\n", "pgm.add_node(daft.Node(\"n\", r\"$n$\", 2, 0, fixed=True))\n", "pgm.add_node(daft.Node(\"y\", r\"$y$\", 1, 0, observed=True))\n", "\n", "pgm.add_edge(\"alpha\", \"p\")\n", "pgm.add_edge(\"beta\", \"p\")\n", "pgm.add_edge(\"n\", \"y\")\n", "pgm.add_edge(\"p\", \"y\")\n", "\n", "pgm.render()\n", "plt.close()\n", "pgm.figure.savefig(\"bias.png\", dpi=300)\n", "pass" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "from IPython.display import Image" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "execution_count": 13, "metadata": { "image/png": { "width": 400 } }, "output_type": "execute_result" } ], "source": [ "Image(\"bias.png\", width=400)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Linear regression model" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "# Instantiate the PGM.\n", "pgm = daft.PGM(shape=[4.0, 3.0], origin=[-0.3, -0.7])\n", "\n", "# Hierarchical parameters.\n", "pgm.add_node(daft.Node(\"alpha\", r\"$\\alpha$\", 0.5, 2))\n", "pgm.add_node(daft.Node(\"beta\", r\"$\\beta$\", 1.5, 2))\n", "pgm.add_node(daft.Node(\"sigma\", r\"$\\sigma$\", 0, 0))\n", "\n", "# Deterministic variable.\n", "pgm.add_node(daft.Node(\"mu\", r\"$\\mu_n$\", 1, 1))\n", "\n", "# Data.\n", "pgm.add_node(daft.Node(\"x\", r\"$x_n$\", 2, 1, observed=True))\n", "pgm.add_node(daft.Node(\"y\", r\"$y_n$\", 1, 0, observed=True))\n", "\n", "# Add in the edges.\n", "pgm.add_edge(\"alpha\", \"mu\")\n", "pgm.add_edge(\"beta\", \"mu\")\n", "pgm.add_edge(\"x\", \"mu\")\n", "pgm.add_edge(\"mu\", \"y\")\n", "pgm.add_edge(\"sigma\", \"y\")\n", "\n", "# And a plate.\n", "pgm.add_plate(daft.Plate([0.5, -0.5, 2, 2], label=r\"$n = 1, \\cdots, N$\",\n", " shift=-0.1, rect_params={'color': 'white'}))\n", "\n", "# Render and save.\n", "pgm.render()\n", "plt.close()\n", "pgm.figure.savefig(\"lm.png\", dpi=300)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "execution_count": 15, "metadata": { "image/png": { "width": 400 } }, "output_type": "execute_result" } ], "source": [ "Image(filename=\"lm.png\", width=400)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Evaluation\n", "\n", "Ref: [Understanding predictive information criteria for Bayesian model](http://www.stat.columbia.edu/~gelman/research/published/waic_understand3.pdf)" ] }, { "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": "3.7.7" } }, "nbformat": 4, "nbformat_minor": 2 }