{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Modely\n", "============\n", "\n", "smysl statistických modelů je \n", "\n", "- redukovat (komprimovat) data - popsat výsledek měření několika parametry\n", "- činit předpovědi - pokud závěry učiněné na daném vzorku extrapolujeme na zbytek populace\n", "- lze parametrizovat i simulovaná data (ušetření výpočetního času)\n", "\n", "paradigma: *získání spolehlivých údajů z nedokonalých dat*\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "mohou být \n", "\n", "- parametrické (tušíme funkční závislost) \n", "- neparametrické (vyhlazování / kubický spline)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$Y=r(X) + e$, $r(X)$ je nějaký model\n", "\n", "pro \"správný\" model platí $E(e)=0$, i když obecně rozdělení $e$ závisí na $X$\n", "\n", "z daného vzorku máme jen odhad $\\hat{r}(X)$, který se liší od skutečné $r(X)$ vlivem nejistot parametrů (a použití jen konečného vzorku pro jejich odhad, což dává možný **bias**)\n", "\n", "$$V(Y-\\hat{r}) = \\sigma^2 + E((\\hat{r}-r)^2)= \\sigma^2 + (E(\\hat{r})-r)^2 + V(\\hat{r})$$\n", "\n", "**bias - variance decomposition** – větší počet parametrů snižuje rezidua, ale zvyšuje nejistoty modelu (v důsledku korelací parametrů)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### lineární model:\n", "mnohorozměrná regrese je analogií vzorce pro proložení přímkou ($\\sigma^2_{xy}/\\sigma^2_{xx}$)\n", "\n", "$$\\beta= V^{-1} D(\\vec{X},Y)$$\n", "\n", "(platí po \"vycentrování\" komponent modelu $\\vec{X}$ a měření $Y$) \n", "\n", "transformace pomocí $V^{-1}$ odstraňuje vazby mezi komponentami modelu\n", "\n", "vektor reziduí $Y-\\beta X$ musí být dekorelován (ortogonální) s vektorem $\\vec{X}$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from matplotlib.pyplot import *\n", "import matplotlib\n", "from numpy import array,r_,sin\n", "matplotlib.rcParams['figure.figsize'] = [10, 5]\n", "from numpy import random\n", "freq=100\n", "func=lambda x:2+0.05*sin(freq*x)\n", "x=random.uniform(-1,1,size=100)\n", "rx=r_[-1:1:200j]\n", "y=func(x)+random.normal(0,1,x.size)\n", "plot(x,y,'+')\n", "plot(rx,func(rx),label=\"true model\")\n", "ok=legend()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "parametry,nejistoty,rezid. suma\n" ] }, { "data": { "text/plain": [ "(array([ 2.08966209, -0.05047858, 0.11152736]),\n", " array([ 0.10064753, 0.15847813, 0.1522184 ]),\n", " 112.51524941476872)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model=array([ones(x.size),x,sin(freq*x)]).T\n", "covr=inv(model.T.dot(model))\n", "errs=sqrt(covr.diagonal())\n", "pars=covr.dot(model.T.dot(y))\n", "dif=((y-model.dot(pars))**2).sum()\n", "print(\"parametry,nejistoty,rezid. suma\")\n", "pars,errs,dif" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 1. , -0.01238217, -0.00349425],\n", " [-0.01238217, 1. , 0.07150181],\n", " [-0.00349425, 0.07150181, 1. ]])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "covr/errs.reshape(1,3)/errs.reshape(3,1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "porovnání s konstantním modelem (ekvivalent aritmetického průměru)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([ 2.08065144]), array([ 0.1]), 113.23512939040886)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "modelc=array([ones(x.size)]).T\n", "covrc=inv(modelc.T.dot(modelc))\n", "errsc=sqrt(covrc.diagonal())\n", "parsc=covrc.dot(modelc.T.dot(y))\n", "difc=((y-modelc.dot(parsc))**2).sum()\n", "parsc,errsc,difc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "event. lineárním modelem (bez periodické funkce)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(array([ 2.08141319, -0.06710682]),\n", " array([ 0.10001585, 0.15684466]),\n", " 113.05206925264098)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "modell=array([ones(x.size),x]).T\n", "covrl=inv(modell.T.dot(modell))\n", "errsl=sqrt(covrl.diagonal())\n", "parsl=covrl.dot(modell.T.dot(y))\n", "difl=((y-modell.dot(parsl))**2).sum()\n", "parsl,errsl,difl" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "konstrukce modelu\n", "---------------------\n", "\n", "máme-li diskrétní hodnoty (kategorie) - může stačit *pruměrování* (očekávaná hodnota) a rozptyl v rámci kategorie \n", "\n", "v praxi spíš hledáme pro model spojitou funkci (interpolace mezi měřenými hodnotami)\n", "\n", "- hledáme funkce z nějaké množiny \"rozumných\"\n", "\n", "otázka \"jak přesně sledujeme data\" vede k vyvažování vztahu \"*bias-variance*\" ...\n", "\n", "lineární model $r = A H^{-1} A^T Y$ patří do skupiny lineárního vyhlazování (*linear smoother*) daného obecnější formulí\n", "\n", "$$ \\hat{r}(x) = \\sum_i {y_i\\ w(x_i,x)} $$ \n", "\n", "(uvedený maticový zápis dává hodnoty jen v bodech měřeni, první modelovou matici ale lze nahradit vektorem funkcí $a_i(x)$ a dostaneme funkci $r(x)$)\n", "\n", "pro polynom řádu 1 máme $w(x_i,x)=(x_i/n s^2_x) x$ (platí pro centrovanou nezávislou proměnnou $\\bar x=0$)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### další příklady \n", "#### k-nejbližších sousedů\n", "\n", "$w(x_i,x)=1/k$ pokud jde o jednoho z k sousedů bodu $x$, jinak 0\n", "\n", "#### vyhlazování s kernelem\n", "\n", "$w(x_i,x)=K(x-x_i)/\\sum_j K(x-x_j)$, kde nezáporný **kernel** splňuje podmínky\n", "$\\int x K(x) dx=0$, $\\int x^2 K(x) dx< \\infty$\n", "\n", "pro rovnoměrně rozdělená data vypadá jako konvoluce" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "parametrizace\n", "---------------\n", "\n", "náš odhad parametrů $\\theta$ minimalizuje \"loss function\" $L(\\bf{z}_n;\\theta)$ (může to být např. záporný logaritmus věrohodnosti) v prostoru parametrů\n", "\n", "tato funkce se pro každý vzorek (měření) $\\bf{z}_n$ liší od její \"střední hodnoty\" určované nad celou populací dat $\\bf{Z}$ (a která by minimalizací \n", "dala *skutečné* hodnoty parametrů)\n", "\n", "$$L(\\bf{z}_n;\\theta)=E(L(\\bf{Z};\\theta)) + \\eta_n(\\theta)$$\n", "\n", "druhý člen je náhodná odchylka pro daný konečný vzorek $\\bf{z}_n$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "\n", "### skryté a přebytečné proměnné\n", "\n", "rozdíl mezi věrohodností třídy $\\pi$ modelů obecnějších a $\\rho$ modelů s omezenými (fixovanými)\n", "parametry je úměrný $\\chi^2_{p-q}$ (p-q je počet fixovaných parametrů)\n", "\n", "\n", "rezidua jsou z definice nekorelována s modelem (nezávislými parametry), nicméně by měly splňovat také podmínky pro **bílý šum**\n", "\n", "- normální rozdělení\n", "- *stejné* rozdělení (zejména rozptyl) pro různá x\n", "- navzájem nekorelované\n", "\n", "testování dalších parametrů \n", "\n", "- t-test parametrů s nejistotami\n", "- F-test tříd modelů\n", "\n", "kovarianční matice klesá s 1/N (objemem měřených dat), stále více parametrů může být \n", "statisticky významných, ale skutečné fyzikální mechanismy na velikosti vzorku nezávisí\n", "\n", "- *přidání dalšího parametru do modelu musí mít fyzikální opodstatnění*\n", "- pouhá korelace neznamená příčinnou souvislost\n", "- pokud není splněna podmínka normálnosti rozdělení parametrů, standardní testy nepomůžou (lze aplikovat *bootstraping*)\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from numpy import polyfit,polyval,arange\n", "x=r_[-3:3:20j]\n", "#x=random.uniform(-3,3,20)\n", "tres=[7,0,-.5,-2,0]\n", "ytrue=polyval(tres,x)\n", "plot(x,ytrue,'k')\n", "y=ytrue+random.normal(size=x.shape)\n", "plot(x,y,'*')\n", "ords=arange(1,10)\n", "res=[polyfit(x,y,i,cov=True) for i in ords]\n", "#[[round(p,3) for p in r[0][::-1]] for r in res]" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "**validace** spočívá v aplikaci modelů na nový vzorek dat\n", "\n", "pokud nemáme nový vzorek, můžeme dělat podvýběry ze stávajícího \n", "\n", "- rozdělení na poloviny, obecněji *k*-dílů, jeden díl se použije na testování\n", "- jackknife ([viz](http://nymeria.physics.muni.cz/face/praxis/fdoc/id393/) redukce biasu)\n", "- [bootstrap](http://nymeria.physics.muni.cz/face/praxis/fdoc/id394/)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "slideshow": { "slide_type": "slide" } }, "outputs": [ { "data": { "text/plain": [ "Text(0.5,0,'stup. polynomu modelu')" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Lnse9YsUKDj/88E7p+80332xV33fddVenfH411NXVMXr06Ir76Yz7iDUAx7Q4Hgisb0sHETElIuY0NjZ2aGGSJEl50hlB7EnguIgYHBE9gIuA+9rSQUppYUppRl6ncyVJkjpCpbevuB14HBgaEQ0R8amU0nbgauAhYAUwP6X0Qhv7dUZMkiR1eZVeNTl9H+0PAA9U0O9CYOHQoUOvOOCbJUmSDlI+a1KSJOVe83al9evXM23atL2+Z/z48bs9s/JgkMsg5tKkJEnamwEDBrBgwYKsy+gwuXzot0uTkiTlx9qPn8eWlSt/r/2QYcMY8q/3tqvP6667jmOPPZarrroKgFmzZhERLFmyhN/97nds27aNG264galTp+523rp16zjnnHNYvnw5b7/9Npdddhm/+MUvGD58OG+//Xa7aslSLmfEJElSfhw6ahTU1u7eWFvLoRXcR+uiiy7izjvv3HU8f/58LrvsMu69916WLVvGo48+yrXXXrvfh4N/97vf5bDDDuO5557ji1/8IkuXLm13PVnJZRBzaVKSpPzoc9WVRM3ukSFqauh71ZXt7nP06NFs3LiR9evX8+yzz/Kud72L/v3784UvfIGRI0fykY98hN/85je88sor++xjyZIlXHLJJQCMHDmSkSNHtruerOQyiHkfMUmS8qO2Xz96n3feO7NitbX0Pv98uvftW1G/06ZNY8GCBdx5551cdNFFzJs3j1dffZWlS5fyzDPPcNRRR9HU1LTfPiL29kCfg0cug5gkScqXlrNilc6GNbvooou44447WLBgAdOmTeONN96gX79+1NbW8uijj/KrX/1qv+ePGzeOefPmAbB8+XKee+65imuqNoOYJEk6oF2zYhEdMhsGcPzxx/Pmm2/y7ne/m/79+3PxxRfz1FNPMXbsWObNm8ewYcP2e/6VV15JY2MjI0eO5Bvf+Aannnrqrt9dfvnlB8WtLHJ51WRETAGmDBgwIOtSJElSWZ+rrmTLmjUdMhvW7Pnnn3+n/z59ePzxx/f6vuZ944MGDWL58uUAHHroodxxxx17ff/3vve9DquxM+VyRsw9YpIk5U9tv34Muu1fOmQ2TCW5DGKSJElFYBCTJEnKiEFMkqSC2t/NUrVvHfnnlssg5g1dJUnqXHV1dWzatMkw1kYpJTZt2kRdXV2H9JfLqyZ91qQkSZ1r4MCBNDQ08Oqrr3Z4301NTR0WVPKorq6OgQMHdkhfuQxikiSpc9XW1jJ48OBO6bu+vp7RFTyHskhyuTQpSZJUBAYxSZKkjBjEJEmSMpLLIOZVk5IkqQhyGcR8xJEkSSqCXAYxSZKkIjCISZIkZcQgJkmSlBGDmCRJUkYMYpIkSRkxiEmSJGUkl0HM+4hJkqQiyGUQ8z5ikiSpCHIZxCRJkorAICZJkpQRg5gkSVJGDGKSJEkZMYhJkiRlxCAmSZKUEYOYJElSRgxikiRJGalaEIuIj0fE/4uIH0bE2dX6XEmSpLyqKIhFxM0RsTEilu/RPikiVkXEmoi4HiCl9K8ppSuATwIXVvK5kiRJXUGlM2JzgUktGyKiG3AT8DFgBDA9Ika0eMuXyr+XJEkqtIqCWEppCfDaHs2nAmtSSmtTSluBO4CpUfJ3wL+llJZV8rmSJEldQaSUKusgYhBwf0rphPLxNGBSSuny8vGlwAeA1cAngCeBZ1JK/7SP/mYAMwD69u178vz58yuq72DU2NhIER947riLxXEXi+MulqKOe8KECUtTSmPbck73Tqgj9tKWUkrfBr59oJNTSnOAOQBDhw5N48eP79jqDgL19fU47uJw3MXiuIvFcetAOuOqyQbgmBbHA4H1nfA5kiRJB7XOCGJPAsdFxOCI6AFcBNzXlg4iYkpEzGlsbOyE8iRJkvKh0ttX3A48DgyNiIaI+FRKaTtwNfAQsAKYn1J6oS39ppQWppRmFHF9WZIkFUdFe8RSStP30f4A8EB7+42IKcCUAQMGtLcLSZKk3MvlI46cEZMkSUWQyyAmSZJUBLkMYm7WlyRJRZDLIObSpCRJKoJcBjFJkqQiyGUQc2lSkiQVQS6DmEuTkiSpCHIZxCRJkorAICZJkpSRXAYx94hJkqQiyGUQc4+YJEkqglwGMUmSpCIwiEmSJGUkl0HMPWKSJKkIchnE3CMmSZKKIJdBTJIkqQgMYpIkSRkxiEmSJGXEICZJkpSRXAYxr5qUJElFkMsg5lWTkiSpCHIZxCRJkorAICZJkpQRg5gkSVJGDGKSJEkZMYhJkiRlxCAmSZKUEYOYJElSRnIZxLyhqyRJKoJcBjFv6CpJkoogl0FMkiSpCAxikiRJGTGISZIkZcQgJkmSlBGDmCRJUkYMYpIkSRkxiEmSJGXEICZJkpSRqgWxiBgSEd+PiAXV+kxJkqQ8qyiIRcTNEbExIpbv0T4pIlZFxJqIuB4gpbQ2pfSpSj5PkiSpK6l0RmwuMKllQ0R0A24CPgaMAKZHxIgKP0eSJKnLqSiIpZSWAK/t0XwqsKY8A7YVuAOYWsnnSJIkdUWRUqqsg4hBwP0ppRPKx9OASSmly8vHlwIfAL4MfA2YCHwvpXTjPvqbAcwA6Nu378nz58+vqL6DUWNjI0V84LnjLhbHXSyOu1iKOu4JEyYsTSmNbcs53TuhjthLW0opbQI+c6CTU0pzgDkAQ4cOTePHj+/Y6g4C9fX1OO7icNzF4riLxXHrQDrjqskG4JgWxwOB9W3pICKmRMScxsbGDi1MkiQpTzojiD0JHBcRgyOiB3ARcF9bOkgpLUwpzSjitKYkSSqOSm9fcTvwODA0Ihoi4lMppe3A1cBDwApgfkrphcpLlSRJ6loq2iOWUpq+j/YHgAfa229ETAGmDBgwoL1dSJIk5V4uH3Hk0qQkSSqCXAYxN+tLkqQiyGUQc0ZMkiQVQS6DmCRJUhEYxCRJkjKSyyDmHjFJklQEuQxi7hGTJElFkMsgJkmSVAS5DGIuTUqSpCLIZRBzaVKSJBVBLoOYJElSERjEJEmSMlLRQ78lSZIA1n78PLasXAnAUcCKcvshw4Yx5F/vzayuvMvljJib9SVJOrgcOmoU1Nbu3lhby6GjR2dT0EEil0HMzfqSJB1c+lx1JVGze6yImhr6XnVlRhUdHFyalCSpAxV1ia62Xz96n3cer999N2zbBrW19D7/fLr37Zt1abmWyxkxSZIOVkVeoms5K+ZsWOsYxCRJ6kBFXqJrnhVLEc6GtZJBTJKkDtQcRnbNihVsia7PVVey7X3vK0Tw7Ai53CMWEVOAKQMGDMi6FElSOxV1rxSUwsgb995LojizYc1q+/Xjd9d+vjDBs1K5nBHzqklJOvgVea+US3RqrVzOiElSV1LUmaGWs0LNijQ71OeqK9m4dGlhxqv2yeWMmCR1JUWdGSr6XimX6NQazohJqhpnht5RlJmhIu+VklrDICZloKiB5NBRo9jyy1+WbvbYrEAzQ0W80WXz2H93550cUZAxS23h0qSUgaIuVRX5/kpFvtGltzOQ9s0gJmWgqIGkyHuGinwVnXulpH3LZRCLiCkRMaexsTHrUqROUeRA4syQM0OS3pHLIOZ9xFQERQ0kzgw5MyTpHbkMYlIRFDmQODMkSSUGMSlDRQ0kzgxJUolBTMqQgUSSis0gJkmSlBGDmCRJUkYMYpIkSRkxiEmSJGXEICZJkpQRg5gkSVJGulfrgyKiJ/B/ga1AfUppXrU+W5IkKY8qmhGLiJsjYmNELN+jfVJErIqINRFxfbn5fGBBSukK4NxKPleSJKkrqHRpci4wqWVDRHQDbgI+BowApkfECGAg8FL5bTsq/FxJkqSDXkVBLKW0BHhtj+ZTgTUppbUppa3AHcBUoIFSGKv4cyVJkrqCSClV1kHEIOD+lNIJ5eNpwKSU0uXl40uBDwDXAd8BmoDH9rVHLCJmADMA+vbte/L8+fMrqu9g1NjYSK9evbIuo+ocd7E47mJx3MVS1HFPmDBhaUppbFvO6YzN+rGXtpRS2gxcdqCTU0pzgDkAQ4cOTePHj+/Y6g4C9fX1OO7iKOS4N65g89xr6PnJ+dBveNbVVJXft993ERR13O3RGUuEDcAxLY4HAuvb0kFETImIOY2NjR1amJQ7G1dwys+vgY0rsq6kerZuhnkXcNhbL8G8C0rHReH3XazvW2qFzghiTwLHRcTgiOgBXATc15YOUkoLU0ozijitqQIp6j9QP/wsbH6VIMHmV+GHV2ddUXX4fRfr+5ZaqdLbV9wOPA4MjYiGiPhUSmk7cDXwELACmJ9SeqGN/Tojpq6viP9ALbsNVj8E25tKx9ubYPWDpfauzu+7WN+31EqVXjU5PaXUP6VUm1IamFL6frn9gZTS+1NK700pfa0d/Tojpq6tqP9A/XgWbHtr97Ztb5XauzK/73cU4fuW2sDbSEhZKOo/UGfNgtrDdm+rPQw+8pVMyqkav+93FOH7ltogl0HMpUl1eUX9B2rMJfD+j0L3utJx9zp4/yQYfXG2dXU2v+/ScVG+72ZFvDhDbZbLIObSpLq8Iv8DNfUm6NmXREDPvjD1O1lX1Pn8vov1fUNxL84AA2gb5TKISV3d2BseZvjSKTRs68XOBA1bezF86TmMveHhrEvrVGNveJhBf1PPxI3XsHrnu5m48RoG/U19lx83UNxA0qMnXHwXbx12DFx8V+m4CIp4cQawaPXdnH3/BZzeL3H2/RewaPXdWZeUe7kMYi5Nqqv7beNW3qaOy7b+FS+mgVy27a94mzp+27g169I6VfP4XkwD+ejWb/BiGrhbe5dW1EAC0G84T576j8W5mWtBL85YtHYRsx7/Chu6BSmCDd2CWY//LYvWLsq6tFzLZRBzaVJFsWcgURdXtEBSVD+exaIecPbAAYwcdAxnDxzAoh50+YszZj/xdZrY/bGJTexk9hNfz6iig0NnPOJIktTC2Bse3n3W78HSDEGfXj146ksTM6pKnWXRmAuY9euFNNWUnvi3obY7s/ocCceey+SMa+tML299A+L3n3L48tY3Mqjm4GEQk6ROtq+l166+JFvUADr7d0t3hbBmTTXB7Nee6tJB7Ogevdmw7b/22q59y+XSpHvEJOngV9QA+vLml9vU3lXMPO0L1LF7AK2jhpmnfSGjig4OuQxi7hFTV9enV482tXcVRR23iuXonke3qb2rmDxkMrNO/zL9dyQiJfrvSMw6/W+YPKQrzwNWzqVJKQMtl2Xq6+sZP358dsVUUVHHrWKZOWYms346i6YdTbva6rrVMXPMzAyrqo7J7/9vTD5iBJvn/nd6fnK+F6a0gkFMktRpuv/B0xzS9yGi9nXStiPY8upH2f5fo7Muq1M1zwDNXjabDZs30L9nf2aOmVmcmaHy1cHjDWGtYhCTpE7Wp1ePve6L6upLst3/4Gnq+t9D1GwDIHq8Tl3/eyjNE3XtUDJ5yGQmD5nszK8OKJdBLCKmAFMGDBiQdSmSVLGnvjSRRWsX7WWGpOteOQhw6FGLoRzCmkXNtlI7X8qmKCln3KwvSZ1s0dpFzPrpLDZs3gDAhs0bmPXTWV3+juPR/fU2tUtFlMsZMUnqSmYvm73bxm2Aph1NzF42u0vvGzq659G7wuee7V1ZUe+fpvbJ5YyYJHUlhb2v1JiZ1HWr262tCFcPFvX+aWofZ8QkVdVue6UWFONqsqLODBX+6sGCcSawfZwRkzKyaO0izl5wNtf86hrOXnB2l98vBMXdK1XUmSEohbHF0xbzj8f+I4unLTaEdWHOBLZPLoOYjzhSV1fUQLK/vVJd2eQhk5n1wVn079kfgP49+zPrg7MMJZLyGcS8alJdXVEDSVH3SoEzQ5L2LpdBTOrqihpIivoMPhWLz1RVW7hZX8pAUTdvF/kZfCoOn6mqtnBGTMpAUTdvu1dK6rqcCWwfZ8SkDBT5sn6fwSd1Tc4Eto9BTMqIgUSS5NKkJElSRnIZxLyPmCRJKoJcBjHvIyZJkoogl0FMkiSpCAxikiRJGTGISZIkZcQgJkmSlBGDmCRJUkYMYpIkSRkxiEmSJGXEICZJkpSRqgWxiBgSEd+PiAXV+kxJkqQ8a1UQi4ibI2JjRCzfo31SRKyKiDURcf3++kgprU0pfaqSYiVJkrqS7q1831zgO8Ba02MjAAALXElEQVStzQ0R0Q24CZgINABPRsR9QDfgxj3O/7OU0saKq5UkSepCWhXEUkpLImLQHs2nAmtSSmsBIuIOYGpK6UbgnI4sUpIkqSuKlFLr3lgKYvenlE4oH08DJqWULi8fXwp8IKV09T7OPxL4GqUZtO+VA9ve3jcDmAHQt2/fk+fPn9+W8XQJjY2NFPGB5467WBx3sTjuYinquCdMmLA0pTS2Lee0dmlyb2IvbftMdSmlTcBnDtRpSmkOMAdg6NChafz48e2t76BVX1+P4y4Ox10sjrtYHLcOpJKrJhuAY1ocDwTWV1aOJElScVQSxJ4EjouIwRHRA7gIuK8jioqIKRExp7GxsSO6kyRJyqXW3r7iduBxYGhENETEp1JK24GrgYeAFcD8lNILHVFUSmlhSmlGEdeXJUlScbT2qsnp+2h/AHigQyuiNCMGTBkwYEBHdy1JkpQbuXzEkTNikiSpCHIZxCRJkoogl0HMzfqSJKkIchnEXJqUJElFkMsgJkmSVAS5DGIuTUqSpCLIZRBzaVKSJBVBLoOYJElSERjEJEmSMpLLIOYeMUmSVAS5DGLuEZMkSUWQyyAmSZJUBAYxSZKkjOQyiLlHTJIkFUEug5h7xCRJUhHkMohJkiQVgUFMkiQpIwYxSZKkjBjEJEmSMpLLIOZVk5IkqQhyGcS8alKSJBVBLoOYJElSERjEJEmSMmIQkyRJyohBTJIkKSMGMUmSpIwYxCRJkjJiEJMkScpI96wL2JuImAJMAZoi4oWs68lAH+C3WReRAcddLI67WBx3sRR13EPbekKklDqjkA4REU+llMZmXUe1Oe5icdzF4riLxXEXS3vG7dKkJElSRgxikiRJGcl7EJuTdQEZcdzF4riLxXEXi+MuljaPO9d7xCRJkrqyvM+ISZIkdVm5DGIRcXNEbIyI5VnXUi0RcUxEPBoRKyLihYiYmXVN1RARdRHx84h4tjzur2RdUzVFRLeIeDoi7s+6lmqJiHUR8XxEPBMRT2VdT7VExBERsSAiVpb///z0rGvqbBExtPw9N//vvyLiL7Kuqxoi4nPlv9OWR8TtEVGXdU3VEBEzy2N+oat/13vLKhHxhxHxcES8WP75rgP1k8sgBswFJmVdRJVtB65NKQ0HTgM+GxEjMq6pGrYAf5RSOgkYBUyKiNMyrqmaZgIrsi4iAxNSSqMKdnn7bODBlNIw4CQK8L2nlFaVv+dRwMnAW8C9GZfV6SLi3cCfA2NTSicA3YCLsq2q80XECcAVwKmU/m/8nIg4LtuqOtVcfj+rXA/8OKV0HPDj8vF+5TKIpZSWAK9lXUc1pZQ2pJSWlV+/Sekv6XdnW1XnSyWN5cPa8v8KsXExIgYCk4HvZV2LOldE/AEwDvg+QEppa0rp9WyrqrqzgF+mlH6VdSFV0h04NCK6A4cB6zOupxqGA0+klN5KKW0H/h04L+OaOs0+sspU4Jby61uAjx+on1wGsaKLiEHAaOBn2VZSHeXluWeAjcDDKaVCjBv4FvBXwM6sC6myBCyOiKURMSPrYqpkCPAq8M/lpejvRUTPrIuqsouA27MuohpSSr8Bvgn8GtgAvJFSWpxtVVWxHBgXEUdGxGHAHwPHZFxTtR2VUtoApQkWoN+BTjCI5UxE9ALuBv4ipfRfWddTDSmlHeWli4HAqeXp7S4tIs4BNqaUlmZdSwbOSCmNAT5GaQl+XNYFVUF3YAzw3ZTSaGAzrViy6CoiogdwLnBX1rVUQ3lf0FRgMDAA6BkRl2RbVedLKa0A/g54GHgQeJbSthvth0EsRyKillIIm5dSuifreqqtvFRTTzH2B54BnBsR64A7gD+KiNuyLak6Ukrryz83UtovdGq2FVVFA9DQYrZ3AaVgVhQfA5allF7JupAq+QjwnymlV1NK24B7gA9mXFNVpJS+n1Iak1IaR2nZ7sWsa6qyVyKiP0D558YDnWAQy4mICEr7R1aklP4h63qqJSL6RsQR5deHUvoLbGW2VXW+lNJfp5QGppQGUVqyeSSl1OX/izkiekbE4c2vgbMpLWd0aSmll4GXIqL5gcBnAb/IsKRqm05BliXLfg2cFhGHlf9uP4sCXJwBEBH9yj/fA5xPsb53gPuAT5RffwL44YFO6N6p5bRTRNwOjAf6REQD8OWU0vezrarTnQFcCjxf3i8F8IWU0gMZ1lQN/YFbIqIbpf8wmJ9SKsytHAroKODe0r9NdAd+kFJ6MNuSquYaYF55mW4tcFnG9VRFea/QRODTWddSLSmln0XEAmAZpaW5pynOnebvjogjgW3AZ1NKv8u6oM6yt6wC/C9gfkR8ilIgv+CA/XhnfUmSpGy4NClJkpQRg5gkSVJGDGKSJEkZMYhJkiRlxCAmSZKUEYOYpP2KiL8o34IgcxExNyKmZV1HNUTE+IjY761cWvMeSflmEJN0IH9B6aHFkqQOZhCTBOy66/2iiHg2IpZHxIUR8eeUnpX3aEQ8Wn5fY4tzpkXE3PLruRHxTxHxHxGxuvw8zQN9ZmNE/O+IWBYRP46IvuX2URHxREQ8FxH3lp/d1/K8syLi3hbHEyPinhZ9fq08jici4qhy+7Hlz3iu/PM9Ler+bkQ8GhFrI+LDEXFzRKxoHtv+xr1HXbMi4paIWBwR6yLi/Ij4RkQ8HxEPlh9j1lz/0+X2myPikHL7pIhYGRGPUborecvv5uaIeLJ83tR9fPZftjheHhGDDvQdSMqWQUxSs0nA+pTSSSmlE4AHU0rfBtYDE1JKE1rRxyDgw8Bk4J8iou4A7+9J6RmEY4B/p3RnaoBbgetSSiOB51u0N3sEGN4c3Cjdpf6fW/T5RErpJGAJcEW5/TvAreU+5wHfbtHfu4A/Aj4HLAT+D3A8cGJEjGrFuFt6L6XxTwVuAx5NKZ0IvA1MLv+ZzAUuLLd3B64st/8/YArwIeDoFn1+kdJjsE4BJgB/X35ElKSDnEFMUrPngY9ExN9FxIdSSm+0o4/5KaWdKaUXKT3GZ9gB3r8TuLP8+jbgzIjoDRyRUvr3cvstwLiWJ6XSI0H+Bbik/KzS04F/K/96K9C8b2oppXBI+T0/KL/+F+DMFl0uLPf5PPBKSun5lNJO4IUW57fWv5Uf9Pw80A1ofoTT8+W+hlJ6IPTqPcY3rNz+YrmWlg+BPxu4vvz4s3qgDnhPG+uSlEO5fNakpOpLKa2OiJOBPwZujIjFKaW/3dtbW7zec8Zrz2emtfUZam15/z9Tmr1qAu5KKW0vt29L7zy7bQf7/nuu5WdtKf/c2eJ183H3vbx/fzN9WwBSSjsjomUtzX3Ffs7d1/gD+G8ppVW7NZaXXcu2s/t/XB9oNlJSDjgjJgmAiBgAvJVSug34JjCm/Ks3gcNbvPWViBgeETXAeXt0c0FE1ETEe4EhwCr2rwZovgryT4DHyjNxv4uID5XbL6W0bLmblNJ6SsumX6K01HcgPwUuKr++GHisFee0tL9xt8VKYFBEvK983Dy+lcDg8p8dwPQW5zwEXBPlp6VHxOi99LuO8ncWEWOAwRXUKKlKnBGT1OxESnuPdgLbgCvL7XOAf4uIDeV9YtdTWvp7CVgO9GrRxypKoeIo4DMppaZywPteSumP9/KZm4HjI2Ip8AZwYbn9E5T2mB1GaYnzsn3UPA/om1L6RSvG9+fAzRHxP4BX99Pnvuxv3K1W/jO5DLgrIroDTwL/lFLaEhEzgEUR8VtKQfGE8mlfBb4FPFcOY+uAPS+GuBv40/Ly5ZPAaiTlXrwzay5J7Ve+ivD+lNKCNpzTmFJqV6Apn/8d4OmU0vfb24ckZckZMUkHpfIs2mbg2qxrkaT2ckZMkiQpI27WlyRJyohBTJIkKSMGMUmSpIwYxCRJkjJiEJMkScqIQUySJCkj/x9rqMMdIixysQAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "chi2=r_[[((y-polyval(res[i-1][0],x))**2).sum()/(len(x)) for i in ords]]\n", "semilogy(ords,chi2,'s')\n", "grid()\n", "semilogy(ords,chi2/(len(x)-ords-1)*len(x),'d')\n", "ynew=ytrue+random.normal(size=x.shape)\n", "gme=r_[[((ytrue-polyval(res[i-1][0],x))**2).sum()/(len(x)) for i in ords]]\n", "semilogy(ords,gme,'o')#,fillcolor=None)\n", "valme=r_[[((ynew-polyval(res[i-1][0],x))**2).sum()/(len(x)-i-1) for i in ords]]\n", "semilogy(ords,valme,'v')\n", "legend(['mse','red. chi2','gme','valid.'])\n", "ylim(0.02,10000)\n", "xlim(1,10)\n", "xlabel(\"stup. polynomu modelu\")\n", "#savefig(\"/tmp/general_err.png\",dpi=100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**legenda**\n", "\n", "- mse = průměrná hodnota čtverce rezidua\n", "- red. chi2 = suma čtverců reziduí dělená počtem stupňů volnosti\n", "- valid. = suma čtverců reziduí u nové (validační) sady dat\n", "- gme = generalizační chyba - suma čtverců reziduí modelu a skutečné střední hodnoty $y$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "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": "3.6.5" }, "toc": { "toc_cell": false, "toc_number_sections": true, "toc_threshold": 6, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }