{ "cells": [ { "cell_type": "markdown", "id": "17bf9cc9", "metadata": {}, "source": [ "# Expectation Maximization\n", "\n", "## Motivation\n", "\n", "Im supervised Learning haben wir gesehen, dass Lineare Regression (eventuell mit einem Kernel) uns helfen könnte, Daten zu klassifizieren. Beim unsupervised Learning haben wir zur Klassifikation k-Means und Kernel-k-Means eingesetzt, jeweils ergänzt durch Datenskalierung und Hauptachsentransformation. Dabei haben wir gute Ergebnisse gesehen, wenn die Cluster im Feature-Raum konvex und gut approximierbar mit einer Normalverteilung ohne Kovarianz (also gut approximierbar durch Vollkugeln) waren. Wenn die Cluster aber zwar normalverteilt aber mit unterschiedlicher Kovarianz waren, und nicht linear voneinander getrennt werden konnten, haben wir keine guten Ergebnisse mit k-Means gesehen." ] }, { "cell_type": "markdown", "id": "7c410d5c", "metadata": {}, "source": [ "```{admonition} Beispiel\n", "Formuliert als Expectation-Maximization-Verfahren ist das k-Means-Verfahren:\n", " \n", "1. Initialisierung (Clustermittelpunkte festlegen) \n", "2. Iterativ bis zur Konvergenz der Clustermittelpunkte: \n", " a. (E-Schritt): Punkte dem jeweils nächsten Clustermittelpunkt zuteilen und so zu einer Klasseneinteilung kommen \n", " b. (M-Schritt): Neue Clustermittelpunkte als Mittelwert aller Elemente einer Klasse festlegen \n", " \n", "Der E-Schritt (Expectation) heißt so, weil wir unsere Erwartung über den Wert der latenten Variable updaten.\n", "\n", "Der M-Schritt (Maximization) heißt so, weil wir eine Fitness-Funktion maximieren - konkret minimieren wir die Summe aller Entferungen der Punkte zu den ihnen zugeteilten Clustermittelpunkten.\n", "```\n", "\n", "Es liegt nahe, ein Verfahren zu verwenden, welches die Form der Cluster berücksichtigt." ] }, { "cell_type": "markdown", "id": "6bd6fd49", "metadata": {}, "source": [ "### Gemischte Gausssche Modelle, supervised\n", "\n", "Wenn wir von Daten in $\\mathbb{R}^d$ Einteilungen in $k$ Klassen (Label) gegeben haben, können wir für jeden Teildatensatz aller Punkte einer Klasse die Sample-Kovarianz und den Sample-Erwartungswert ausrechnen und damit eine $n$-variate Normalverteilung aufstellen, die diesen Teildatensatz modelliert.\n", "\n", "Daraus resultiert ein Modell für die gesamten Daten, wenn wir mit $p_i$ die Anzahl der Punkte in Klasse $i$ geteilt durch die Anzahl an Punkten im Sample insgesamt bezeichnen und mit $f_i(x)$ die geschätzte Dichte der Normalverteilung von Klasse $i$, nämlich die Dichte\n", "\n", "$$\n", "f(x) = \\sum_{i=1}^k p_i f_i(x).\n", "$$\n", "\n", "Dieses Modell können wir natürlich auch wieder benutzen, um einzuschätzen, zu welcher Klasse ein Punkt gehört. Dazu berechnen wir für einen Punkt $x$ die Dichten\n", "\n", "$$\n", "P_i(x) = p_i f_i(x)\n", "$$\n", "\n", "und wählen das $i$ aus, für das dieser Ausdruck maximal wird." ] }, { "cell_type": "markdown", "id": "910b0ddc-28b9-4939-af06-b6923be33f6f", "metadata": {}, "source": [ "Als Entstehungsprozess kann man sich das so vorstellen: ein (fiktives) gemischtes Gausssches Modell wurde verwendet um die Datenpunkte zu sampeln, indem zunächst nach der diskreten Verteilung der $p_i$ eine Klasse $j$ ausgewählt wurde und dann mit der Dichte $f_j(x)$ ein Sample daraus gezogen wurde, und das so oft, wie es Datenpunkte gibt.\n", "\n", "Nun kann es leicht passieren, wenn sich die Cluster überschneiden, dass manche Punkte $x$ durch das Modell anders klassifiziert werden, als dies ursprünglich der Fall war -- dagegen gibt es kein grundsätzliches Gegenmittel. Dennoch können wir so das am besten an die Daten angepasste gemischte Gausssche Modell bestimmen und damit Daten sampeln, die den vorliegenden sehr ähnlich sehen werden (vorausgesetzt die Normalverteilungsannahme war korrekt).\n", "\n", "Wir wollen noch eine weitere Beobachtung machen: das gemischte Gausssche Modell gibt uns mehr als nur eine neue Klasseneinteilung, sondern zu jedem Punkt zu jeder Klasse eine Wahrscheinlichkeit dafür, dass der Punkt zu dieser Klasse gehört. Das ist wesentlich mehr Information und kann deutlich nützlicher sein. Vor allem bei den nicht korrekt klassifizierten Punkten erhalten wir damit eine Möglichkeit, unsere Gewissheit bei der Klasseneinteilung zu quantifizieren." ] }, { "cell_type": "code", "execution_count": 1, "id": "2fc62322-b991-4b28-8fec-061419c28b58", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x720 with 2 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from sklearn.datasets import load_iris\n", "from sklearn.decomposition import PCA\n", "from scipy.stats import multivariate_normal as mvn\n", "\n", "x, y = load_iris(return_X_y=True)\n", "# work in principal components, to plot later in the first two:\n", "xpc = PCA().fit_transform(x)\n", "\n", "k = 3\n", "assert k == np.max(y) + 1\n", "\n", "mvns = list(range(k))\n", "for i in range(k):\n", " # for simplicty, take only first 2 PCs here:\n", " mu = np.mean(xpc[y == i][:,:2], axis=0)\n", " sigma = np.cov(xpc[y == i][:,:2], rowvar=False)\n", " mvns[i] = mvn(mean=mu, cov=sigma, allow_singular=True)\n", "\n", "round_mvns = list(range(k))\n", "for i in range(k):\n", " mu = np.mean(xpc[y == i][:,:2], axis=0)\n", " sigma = np.eye(2)\n", " round_mvns[i] = mvn(mean=mu, cov=sigma, allow_singular=True)\n", " \n", "fig = plt.gcf()\n", "fig.set_size_inches(10, 10)\n", "ax1 = plt.subplot(221)\n", "ax2 = plt.subplot(222, sharex=ax1, sharey=ax1)\n", "plt.figtext(0.35, 0.95, \"First 2 principal components of Iris data\")\n", "ax1.set_title(\"kMeans fit\")\n", "ax2.set_title(\"Gaussian Mixture Model (GMM)\")\n", "xs, ys = np.mgrid[-4:4.1:.2, -4:4.1:.1]\n", "for i in range(k):\n", " zs = round_mvns[i].pdf(np.dstack((xs, ys)))\n", " ax1.contour(xs, ys, zs,\n", " cmap=plt.cm.Oranges, alpha=.7)\n", " ax1.scatter(xpc[y == i][:,0], xpc[y == i][:,1],\n", " c=np.ones_like(y[y == i])*i, vmin=0, vmax=k-1,\n", " label=str(i))\n", " zs = mvns[i].pdf(np.dstack((xs, ys)))\n", " ax2.contour(xs, ys, zs,\n", " cmap=plt.cm.Oranges, alpha=.7)\n", " ax2.scatter(xpc[y == i][:,0], xpc[y == i][:,1],\n", " c=np.ones_like(y[y == i])*i, vmin=0, vmax=k-1,\n", " label=str(i))\n", "ax1.legend()\n", "ax2.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "4edbd04f-d789-4890-ae84-e1cf84ca0cb8", "metadata": {}, "source": [ "### Gemischte Gausssche Modelle, unsupervised\n", "\n", "Das eben beschriebene Vorgehen ist nicht möglich, wenn wir keine Klasseneinteilung vorgegeben haben.\n", "In diesem Fall ist die Klasse eine **latente Variable**, die wir nicht kennen, die aber in der Modellbeschreibung wesentlich ist.\n", "Was wir gut modellieren können, sind bedingte Wahrscheinlichkeiten, wenn wir auf den Wert der latenten Variable bedingen - also die Verteilung einer einzelnen Klasse. Die Verteilung der latenten Variable ist schwieriger zu beschreiben, wenn wir nur ungelabelte Daten zur Verfügung haben.\n", "\n", "Es bietet sich ein zweistufiges Verfahren an: zunächst ließe sich mit k-Means eine Klasseneinteilung finden (die oftmals nicht besonders gut ist, wenn die Homoskedastizitätsvoraussetzung nicht erfüllt ist) und dann auf Grundlage dieser Klasseneinteilung ein gemischtes Gausssches Modell aufstellen, d.h. eine Schätzung der latenten Variable gewinnen.\n", "\n", "Nun lässt sich wiederum feststellen, dass die Klasseneinteilung, die uns das gemischte Modell berechnen lässt, im Allgemeinen von der Klasseneinteilung abweicht, die wir zuvor mit k-Means berechnet haben. Diesmal aber ist naheliegend, dass das gemischte Modell eine bessere Klasseneinteilung leistet, denn nun werden ja zusätzlich die Formen der Cluster berücksichtigt (approximiert durch Ellipsoide aufgrund der Normalverteilungsannahme).\n", "\n", "Mit dieser verbesserten Klasseneinteilung, also der verbesserten Schätzung der latenten Variable, kann man nun erneut ein gemischtes Gaussches Modell aufsetzen, d.h. die Kovarianzmatrizen und Mittelpunkte neu schätzen, ganz ähnlich zum Iterationsschritt im k-Means-Verfahren." ] }, { "cell_type": "markdown", "id": "4e2c1ddd-47f5-4fda-8730-2fbf720cbdbf", "metadata": {}, "source": [ "Wir wollen nun noch eine Beobachtung machen: Wenn im Aufstellen der Kovarianzmatrizen jeweils nur die Güte des Modells für eine einzelne Klasse betrachtet wird (also der beste Fit), dann berücksichtigen wir nicht die Auswirkung dieser Modelländerung auf die anderen Klassen - die wird es aber meist geben.\n", "Es wäre also besser, im Iterationsschritt simultan alle Parameter zu optimieren auf die Zielgröße - das gemischte Modell mit dem besten Fit.\n", "\n", "Um für eine beliebige Verteilung einen guten Schätzer zu konstruieren, haben wir das Maximum-Likelihood-Verfahren genutzt, und das wollen wir auch im Fall einer Mischung von Normalverteilungen versuchen." ] }, { "cell_type": "markdown", "id": "62807228", "metadata": {}, "source": [ "## Maximum Likelihood in Modellen mit latenten Variablen\n", "\n", "Die Wahrscheinlichkeitsdichte im gemischten Gausschen Modell, wo $\\theta_j$ die Parameter $\\mu_j,\\Sigma_j$ bezeichnet einer einzelnen Mischkomponente, und $p_j$ die Verteilung der Komponenten, ist\n", "\n", "$$\n", "f(x) = \\sum_{j=1}^k p_j f_j(x, \\theta_j) = P(X=x|M=\\theta) = L(\\theta),\n", "$$\n", "\n", "das ist die Likelihood (also die Wahrscheinlichkeit der Daten, berechnet in unserem Modell), wenn wir mit $M$ unser Modell bezeichnen und mit $X$ die Daten. Die Modellannahme ist jetzt also: $X$ ist mit $f$ verteilt. Dabei ist $\\theta$ die Menge an Parametern $p_j$ zusammen mit den Parametern $\\mu_j,\\Sigma_j$, die in $f_j$ versteckt sind. Wenn wir diese Größe als Likelihood auffassen, dann als Funktion in diesen Parametern.\n", "\n", "Tipp: wenn Sie sich gern in der Notation $\\theta$ als Liste über $\\theta_j$ vorstellen wollen, setzten Sie einfach $\\theta_0 := (p_1,\\dots,p_k)$.\n", "\n", "Wenn wir die Modellierung, dass die Einteilung der Datenpunkte in Klassen, durch Wahrscheinlichkeiten ausgedrückt werden, ernst nehmen, können wir auch gleich die Einteilung als Zufallsvariable $Y$ modellieren. Es ist also $Y_i = j$ wenn der $i$-te Datenpunkt von Klasse $j$ ist, aber wir kennen die Variable $Y$ nicht." ] }, { "cell_type": "markdown", "id": "b74204e1-ef8f-4417-b364-77300cdf1ad4", "metadata": {}, "source": [ "Unser Modell, formuliert mit der latenten Variable $Y$, ist\n", "\n", "$$\n", "P(Y = j\\ |\\ \\theta) =& p_j \\\\\n", "P(X=x\\ |\\ Y=j, \\theta) =& f_j(x,\\ \\mu_j,\\Sigma_j) \\\\\n", "P(X=x\\ |\\ \\theta) =& \\sum_{j=1}^k P(X=x,\\ Y=j\\ |\\ \\theta) \\\\\n", " =& \\sum_{j=1}^k P(Y = j, \\theta) P(X=x\\ |\\ Y=j, \\theta)\n", "$$" ] }, { "cell_type": "markdown", "id": "af409d6d-1e49-4868-b81e-d2b6a24a71c2", "metadata": {}, "source": [ "### Nullstellen der Ableitung bestimmen?\n", "\n", "Direkt die Nullstellen der Ableitung von $L(\\theta)$ zu bestimmen ist nicht leicht, aber auch der beliebte Trick, $\\ell(\\theta) = \\log L(\\theta)$ zu maximieren, bringt hier nicht viel, denn\n", "\n", "$$\n", "\\ell(\\theta) =& \\log P(X=x\\ |\\ \\theta) \\\\\n", " =& \\log \\left( \\sum_{j=1}^k P(X=x, Y=j\\ |\\ \\theta) \\right) \\\\\n", " =& \\log \\left( \\sum_{j=1}^k p_j f_j(x\\ |\\ \\theta_i) \\right)\n", "$$\n", "\n", "und aus der Summen-Nummer kommen wir mit dem Logarithmus nicht so leicht raus.\n", "\n", "### Jensen to the rescue!\n", "\n", "Wir können unsere Ziele etwas abschwächen und mit der Jensenschen Ungleichung arbeiten (denn der Logarithmus ist konkav und $\\sum_{j=1}^k p_j = 1$):\n", "\n", "$$\n", "\\ell(\\theta) \\geq \\sum_{j=1}^k p_j \\log f_j(x\\ |\\ \\theta_i)\n", "$$\n", "\n", "Das charmante an dem Ausdruck auf der rechten Seite ist, dass ein $\\theta$, welches die rechte Seite maximiert, keine kleinere linke Seite haben kann. In Formeln: wenn wir ein $\\theta^{(i)}$ gegeben haben, dann ein $\\theta^{(i+1)}$ bestimmen, für dass die rechte Seite größer wird, dann ist auch $\\ell(\\theta^{(i+1)}) \\geq \\ell(\\theta^{(i)})$.\n", "\n", "Wir wollen feststellen, dass sich im Ausdruck für den Beitrag einer Klasse $p_j f_j$ auch eine fette $1 = \\frac{q(j)}{q(j)}$ hinein multiplizieren lässt, hier\n", "\n", "$$\n", "\\ell(\\theta) =& \\log \\left( \\sum_{j=1}^k P(X=x, Y=j\\ |\\ \\theta) \\right) \\\\\n", " =& \\log \\left( \\sum_{j=1}^k q(j) \\frac{P(X=x, Y=j\\ |\\ \\theta)}{q(j)} \\right)\n", "$$\n", "\n", "Die Nützlichkeit sieht man nach Anwenden der Jensenschen Ungleichung, diesmal auf die Konvexkombination $\\sum_{j=1}^k q(j) = 1$, wobei wir ab jetzt also annehmen, dass $q$ eine Wahrscheinlichkeitsdichte ist: \n", "\n", "$$\n", "\\ell(\\theta) \\geq & \\sum_{j=1}^k q(j) \\log \\left( \\frac{P(X=x, Y=j\\ |\\ \\theta)}{q(j)} \\right) =: L(\\theta,q) \\\\\n", " = & \\sum_{j=1}^k q(j) \\left( \\log \\left( P(X=x, Y=j\\ |\\ \\theta \\right) - \\log q(j) \\right) \\\\\n", " = & \\sum_{j=1}^k q(j) \\log P\\left(X=x, Y=j\\ |\\ \\theta\\right) \\qquad - \\sum_{j=1}^k q(j) \\log q(j) \\\\\n", " = & \\sum_{j=1}^k q(j) \\log P\\left(X=x, Y=j\\ |\\ \\theta\\right) \\qquad + H(q)\n", "$$\n", "\n", "Wir haben also eine untere Schranke an $\\ell(\\theta)$ gefunden, die wir schreiben können als Summe eines Ausdrucks, der leichter zu berechnen ist, und der Entropie der Verteilung mit Dichte $q$. Da die Entropie nicht von $\\theta$ abhängt, lässt sich $L(\\theta,q)$ durch maximieren des anderen Summanden maximieren.\n", "\n", "Diese Beobachtung wollen wir wieder aufgreifen (daher haben wir dem Kind auch einen Namen $L(\\theta,q)$ gegeben), aber jetzt erstmal einen allgemeinen Lösungsansatz diskutieren." ] }, { "cell_type": "markdown", "id": "d7362fe4-3f80-4786-9c4f-34e64000f04f", "metadata": {}, "source": [ "## Auxiliary Functions\n", "\n", "Wenn wir eine Funktion $\\ell(\\theta)$ nicht maximieren können,\n", "können wir versuchen, behelfsmäßig so zu tun als sei $\\theta$ in einigen Teilausdrücken von $\\ell(\\theta)$ konstant, dann maximieren, und dann die anderen Teilausdrücke konstant halten bzw. darüber maximieren. Um das zu formalisieren, führen wir eine Hilfsfunktion $Q(\\theta,\\vartheta)$ ein, die leichter in $\\theta$ zu maximieren ist als $\\ell$, aber dennoch $Q(\\theta, \\theta) = \\ell(\\theta)$ erfüllt und außerdem $Q(\\theta,\\vartheta) \\leq \\ell(\\theta)$ für alle $\\vartheta$ erfüllt.\n", "\n", "Mit diesen Voraussetzungen kann man bereits zeigen, dass ein iterativer Prozess zu immer besseren Approximationen $\\theta^{(i)}$ an das $\\theta$, welches $\\ell(\\theta)$ maximiert, führt. Dabei bezeichnen wir mit $\\theta^{(i+1)}$ das $\\theta$ sodass $Q(\\theta, \\theta^{(i)})$ maximal wird (nach Annahme finden wir das leicht).\n", "\n", "$$\n", "\\ell(\\theta^{(i)}) =& Q(\\theta^{(i)}, \\theta^{(i)}) \\\\\n", " \\leq & Q(\\theta^{(i+1)}, \\theta^{(i)}) \\text{ (M-Schritt)} \\\\\n", " \\leq & Q(\\theta^{(i+1)}, \\theta^{(i+1)}) \\text{ (E-Schritt)} \\\\\n", " & = \\ell(\\theta^{(i+1)}) \n", "$$\n", "\n", "Insgesamt haben wir also $\\ell(\\theta^{(i)}) \\leq \\ell(\\theta^{(i+1)})$, d.h. zumindest verschlechtern wir uns dabei nicht mit unserer Schätzung!\n", "\n", "Es bleibt für uns, wenn wir diesen Ansatz wählen wollen, noch die Wahl einer geschickten Hilfsfunktion $Q(\\theta,\\vartheta)$.\n" ] }, { "cell_type": "markdown", "id": "ebc6d2ec-0e46-422e-987a-a74855a92d8d", "metadata": {}, "source": [ "## Vollständige-Daten log-Likelihood\n", "\n", "Die letzte Zutat zur Entwicklung des E-M-Algorithmus für das gemischte Gausssche Modell ist die vollständige-Daten-log-Likelihood. Das ist die log-Likelihood in der fiktiven Welt, in der wir tatsächlich die vollständigen Daten, d.h. nicht nur die Werte von $X$ sondern auch die der latenten Variable $Y$, also die tatsächlichen Klassen der Datenpunkte kennen.\n", "\n", "Die vollständigen Daten sind also $(x_i,y_i)$, was mir mit $(X,Y)$ modellieren.\n", "\n", "Es ist nun nützlich, die Variable $Y_i$ auch one-hot-encoded anzusehen: $Y_{ij} = 1$ wenn $Y_i = j$ und $Y_{ij} = 0$, wenn $Y_i \\neq j$. Manche schreiben dafür auch $[Y_i=j]$ (Iversen-Bracket).\n", "\n", "Die log-Likelihood der Daten unter dem gemischten Gaussschen Modell ist\n", "\n", "$$\n", "\\ell_c(\\theta) = \\log P((X,Y)|\\theta) =& \\sum_{i=1}^n \\log P(X=x_i, Y=y_i\\ |\\ \\theta) \\\\\n", " & \\sum_{i=1}^n \\log \\prod_{j=1}^k {P(X=x_i, Y=y_i\\ |\\ \\theta)}^{Y_{ij}} \\\\\n", " & \\sum_{i=1}^n \\sum_{j=1}^k Y_{ij} \\log P(X=x_i, Y=y_i\\ |\\ \\theta)\n", "$$\n", "\n", "dabei haben wir in der ersten Umformung eine fette $1$ hinzugefügt, da $Y_{ij}$ nur für einen Faktor in dem Produkt $\\prod_{j=1}^k (...)^{Y_{ij}}$ überhaupt $1$ ist, ansonsten $0$, und damit der entsprechende Faktor $1$.\n", "Die zweite Umformung ist nur $\\log \\prod (...)^t = \\sum t \\log (...)$.\n", "\n", "Man beachte auch, dass das $\\theta$ jetzt wirklich nur noch $\\theta_1,\\dots,\\theta_k$ ist, denn die $p_i$ sind in der Verteilung von $Y$ kodiert.\n", "\n", "Wir können noch weiter vereinfachen:\n", "\n", "$$\n", "\\log P(X=x_i, Y=y_i) = \\log \\left( p_{y_i} f_{y_i}(x_i) \\right) = \\log p_{y_i} + \\log f_{y_i}(x_i)\n", "$$\n", "\n", "### Erwartungswert über die latente Variable\n", "\n", "Wenn wir eine Verteilung $q(y)$ für die latente Variable $Y$ annehmen, dann können wir den Erwartungswert über diese bilden:\n", "\n", "$$\n", "\\mathbb{E}_{Y \\sim q} \\ell_c(\\theta) =& \\mathbb{E}_{Y \\sim q} \\left( \\sum_{i=1}^n \\sum_{j=1}^k Y_{ij} \\left( \\log p_{y_i} + \\log f_{y_i}(x_i\\ |\\ \\theta_i) \\right) \\right) \\\\\n", " =& \\sum_{i=1}^n \\sum_{j=1}^k \\mathbb{E}_{Y \\sim q} Y_{ij} \\left( \\log p_{j} + \\log f_{j}(x_i\\ |\\ \\theta_i) \\right) \\\\\n", " =& \\sum_{i=1}^n \\sum_{j=1}^k \\tau_{ij} \\left( \\log p_{j} + \\log f_{j}(x_i\\ |\\ \\theta_i) \\right)\n", "$$\n", "\n", "Hierbei nennen wir die mit $\\tau_{ij}$ bezeichneten Terme **responsibilites** oder **Verantwortlichkeiten**, denn sie sind in unserem Modell verantwortlich für die Einteilung der Punkte $x_i$ in Klassen:\n", "\n", "$$\n", "\\tau_{ij} := \\mathbb{E}_{Y \\sim q} Y_{ij} = P(Y_i = j\\ |\\ X=x_i,\\theta) = \\frac{P(Y_i = j, X=x_i)\\ |\\ \\theta)}{P(X=x_i\\ |\\ \\theta}\n", "$$\n", "\n", "Wenn wir die $\\tau_{ij}$ festhalten, haben wir mit $\\mathbb{E}_{Y \\sim q} \\ell_c(\\theta)$ eine Größe, die wir maximieren können (auch wenn die $\\tau_{ij}$ natürlich eigentlich von $\\theta$ abhängen). Wir wollen die $\\tau_{ij}$ als Funktion von $\\theta$ betrachten, aber nennen dieses nun $\\vartheta$.\n", "\n", "Wir definieren also\n", "\n", "$$\n", "Q(\\theta,\\vartheta) := \\sum_{i=1}^n \\sum_{j=1}^k \\tau_{ij}(\\vartheta) \\left( \\log p_{j} + \\log f_{j}(x_i\\ |\\ \\theta_j) \\right)\n", "$$\n", "\n", "Das ist für $\\theta=\\vartheta$ die erwartete vollständige-Daten log-Likelihood unter unserer Annahme $q$ an die Verteilung der latenten Variable $Y$.\n", "Wir bemerken noch, dass der andere Term $\\log P(X=x_i, Y=j) = \\left( \\log p_{j} + \\log f_{j}(x_i\\ |\\ \\theta_i) \\right)$ von $\\theta$ abhängt, nicht von $\\vartheta$.\n", "\n", "### Der Unterschied zwischen $L(\\theta, q)$ und $Q(\\theta, \\theta)$\n", "\n", "Wir erinnern uns nochmal an die Beobachtung zuvor, die wir mit Hilfe der Jensenschen Ungleichung gefunden haben:\n", "\n", "$$\n", "\\ell(\\theta) \\geq L(\\theta, q) = \\sum_{j=1}^k q(j) \\log P\\left(X=x, Y=j\\ |\\ \\theta\\right) \\qquad + H(q)\n", "$$\n", "\n", "und stellen fest, dass der Summand, der nicht $H(q)$ ist, genau die erwartete vollständige-Daten log-Likelihood ist, also\n", "\n", "$$\n", "\\ell(\\theta) \\geq L(\\theta, q) = \\mathbb{E}_{Y \\sim q} \\ell_c(\\theta) + H(q) = Q(\\theta,\\theta) + H(q)\n", "$$\n", "\n", "Da $H(q)$ nicht von $\\theta$ abhängt, können wir also $Q(\\theta,\\vartheta)$ in $\\theta$ maximieren und haben damit $L(\\theta, q)$ in $\\theta$ maximiert.\n", "\n", "### Der Unterschied zwischen $\\ell(\\theta)$ und $L(\\theta, q)$\n", "\n", "Wir stellen die Formel für $L(\\theta, q)$ noch einmal anders um. Dabei wollen wir die gemeinsame Verteilung $P(X=x, Y=j)$ durch bedingte Verteilungen ausdrücken, $P(Y=j, X=x) = P(Y=j|X=x)P(X=x)$ und erhalten damit:\n", "\n", "$$\n", "\\ell(\\theta) \\geq& L(\\theta, q) = \\sum_{j=1}^k q(j) \\log \\left( \\frac{P(X=x, Y=j\\ |\\ \\theta)}{q(j)} \\right) \\\\\n", " & = \\sum_{j=1}^k q(j) \\log \\left( \\frac{ P(Y=j\\ |\\ X=x, \\theta) P(X=x\\ |\\ \\theta) }{q(j)} \\right) \\\\\n", " & = \\sum_{j=1}^k q(j) \\log \\left( \\frac{P(Y=j\\ |\\ X=x, \\theta)}{q(j)} \\right) \\qquad + \\sum_{j=1}^k q(j) \\log\\left( P(X=x\\ |\\ \\theta) \\right) \\\\\n", " & = -H(q\\ |\\ Y_{|X=x}, \\theta) + \\ell(\\theta)\n", "$$\n", "\n", "Die Differenz zwischen $\\ell(\\theta)$ und $L(\\theta,q)$ ist also genau die relative Entropie der geschätzten Verteilung $q$ zur tatsächlichen Verteilung $Y_{|X=x}$:\n", "\n", "$$\n", "\\ell(\\theta) - L(\\theta, q) = H(q\\ |\\ Y_{|X=x}, \\theta)\n", "$$\n", "\n", "Damit ist auch $\\ell(\\theta) - Q(\\theta,\\theta) = H(q\\ |\\ Y_{|X=x}, \\theta) + H(q)$, wir verstehen also ganz genau, inwiefern sich $\\ell(\\theta)$ mit $Q(\\theta,\\theta)$ maximieren lässt." ] }, { "cell_type": "markdown", "id": "e1518734-5a5e-4223-b9e7-b8cdfda07385", "metadata": {}, "source": [ "## E-M-Algorithmus zum fitten eines gemischten Gaussschen Modells\n", "\n", "Der Algorithmus wird mit einer Wahl von $\\theta^{(0)}$ initialisiert (und das Ergebnis hängt im Allgemeinen sehr von dieser Initialisierung ab, wie wir bereits bei k-Means gesehen haben). Eine mögliche Wahl ist, bei den $\\mu_j$ (den Clusterzentren) das k-Means-Verfahren (mit k-Means++-Initialisierung) auf die Daten anzuwenden und dann die konvergierten Zentroide als $\\mu_j$ zu nehmen. Für die Kovarianzmatrizen kann man mit Einheitsmatrizen starten (das entspricht einer translierten Standardnormalverteilung). Das Mischverhältnis, also die $p_i$ kann man auf $p_i = \\frac{1}{k}$ initialisieren.\n", "\n", "Dann führt man iterativ abwechselnd den E-Schritt und den M-Schritt durch:\n", "\n", "* **E-Schritt**: Update den Parameter $\\vartheta$: setze $\\vartheta = \\theta$ und berechne die Responsibilities $\\tau_{ij} := \\tau_{ij}(\\theta)$ um wieder eine korrekte Formel für $Q(\\theta,\\theta)$ bzw. eine neue Schätzung für $q$ und damit $L(\\theta, q)$ aufzustellen. In diesem Schritt schätzen wir die latente Variable mit dem Ziel, die relative Entropie zur tatsächlichen Verteilung der latenten Variable zu minimieren (also möglichst gut zu approximieren). Je besser die Schätzung, desto näher liegt $L(\\theta, q)$ an $\\ell(\\theta)$.\n", "* **M-Schritt**: Update den Parameter $\\theta$: maximiere die erwartete vollständige log-Likelihood $Q(\\theta,\\vartheta)$ in $\\theta$ (während $\\vartheta$ fest gehalten wird, also die Verantwortlichkeiten $\\tau_{ij}$ konstant sind). Damit wird $L(\\theta, q)$ maximiert, eine untere Schranke an $\\ell(\\theta)$.\n", "\n", "Das Verfahren konvergiert, da die Approximationen an ein Maximum von $\\ell(\\theta)$ nie schlechter werden (man könnte sagen, wegen der Jensenschen Ungleichung).\n", "\n", "Bisher haben wir nicht benötigt, welche Form die Dichtefunktionen $f_j$ haben - tatsächlich funktioniert alles, was wir diskutiert haben, bis jetzt auch für beliebige Verteilungen! Wenn man sorgfältig arbeitet, darf auch die latente Variable eine stetige Variable sein, wenn man geeignet Summen von $j=1$ bis $k$ durch entsprechende Integrale ersetzt. So gesehen ist der E-M-Algorithmus eigentlich nicht ein Algorithmus sondern eine Schablone, um viele konkrete E-M-Algorithmen zu entwickeln.\n", "\n", "Noch allgemeiner, wenn es nicht zwangsläufig um die Maximierung einer Likelihood unter latenten Variablen geht, spricht man von M-M-Algorithmen. Das steht für Majorisieren-Maximieren und man spricht auch von Optimierungstransfer. Mit diesen Stichworten können Sie Literatur auftreiben, wenn Sie eine Verallgemeinerung des E-M-Algorithmus benötigen.\n", "\n", "Wir wollen uns jetzt aber doch erstmal auf den Fall einer diskreten endlichen latenten Variable $Y$ beschränken und uns in Richtung einer Implementierung in Python bewegen." ] }, { "cell_type": "markdown", "id": "dacc2085-13b9-437d-bed3-a10084dec3b9", "metadata": {}, "source": [ "### Konkrete Formeln für das gemischte Gaussche Modell\n", "\n", "Um den Algorithmus konkret implementieren zu können, müssen wir natürlich auch konkrete Dichtefunktionen verwenden, und das wollen wir nun tun, also uns daran erinnern, dass die multivariate Normalverteilung diese Dichte hat:\n", "\n", "$$\n", "f_j(x) = f_j(x, \\mu_j, \\Sigma_j) = \\dfrac{1}{\\sqrt{(2\\pi)^n \\det\\Sigma_j}} e^{-\\frac{(x-\\mu_j)^T \\Sigma_j^{-1} (x - \\mu_j)}{2}}.\n", "$$\n", "\n", "Weil wir uns das Leben leicht machen wollen, betrachten wir erstmal den univariaten Fall, also ist\n", "\n", "$$\n", "f_j(x) = f_j(x, \\mu_j, \\sigma_j) = \\dfrac{1}{\\sqrt{2\\pi \\sigma_j}} e^{-\\frac{(x-\\mu_j)^2}{2\\sigma_j^2}}.\n", "$$\n", "\n", "Im Iterationsverfahren haben wir nun $\\theta^{(i)}$ gegeben, d.h. $\\mu_j^{(i)}$ und $\\Sigma_j^{(i)}$ sowie Mischungsparameter $p_j^{(i)}$. Achtung: das ist ein anderes $i$ als der Stichprobenindex $i$ wie im Ausdruck $x_i$ und dieser Unterschied ergibt sich nur aus dem Kontext.\n", "\n", "Im E-Schritt berechnen wir die Verantwortlichkeiten\n", "\n", "$$\n", "\\tau_{ij}(\\theta^{(i)}) =& \\frac{P(Y_i = j, X=x_i\\ |\\ \\theta)}{P(X=x_i\\ |\\ \\theta)} \\\\\n", " =& \\frac{P(Y_i = j, X=x_i\\ |\\ \\theta)}{\\sum_{m=1}^k P(Y_i = m, X=x_i\\ |\\ \\theta)} \\\\\n", " =& \\frac{p_j^{(i)} f_j\\left(x_i,\\mu_j^{(i)},\\sigma_j^{(i)}\\right)}{\\sum_{m=1}^k p_m^{(i)} f_m\\left(x_i,\\mu_m^{(i)},\\sigma_m^{(i)}\\right)}\n", "$$\n", "\n", "Im M-Schritt maximieren wir $Q(\\theta,\\vartheta)$ in $\\theta$, indem wir Nullstellen der Ableitung nach $\\theta$ bestimmen, also lösen wir das Gleichungssystem\n", "\n", "$$\n", "0 =& \\frac{d}{d\\theta} Q(\\theta, \\vartheta) \\\\\n", " =& \\frac{d}{d\\theta} \\sum_{i=1}^n \\sum_{j=1}^k \\tau_{ij}(\\vartheta) \\left( \\log p_{j} + \\log f_{j}(x_i\\ |\\ \\theta_j) \\right) \\\\\n", " =& \\sum_{i=1}^n \\sum_{j=1}^k \\tau_{ij}(\\vartheta)\\frac{d}{d\\theta} \\left( \\log p_{j} + \\log f_{j}(x_i\\ |\\ \\theta_j) \\right)\n", "$$\n", "\n", "Als ersten Schritt betrachten wir die Ableitungen nach den $\\mu_j$:\n", "\n", "$$\n", "\\frac{d}{d\\mu_j} \\log f_j(x_i) =& - \\frac{\\frac{d}{d\\mu_j}(x-\\mu_j)^2}{2\\sigma_j} = \\frac{2(x-\\mu_j)}{2\\sigma_j} \\\\\n", "\\frac{d}{d\\mu_j} Q(\\theta, \\theta^{(i)}) =& \\sum_{i=1}^n \\sum_{j=1}^k \\tau_{ij}(\\vartheta) \\frac{d}{d\\mu_j} \\log f_{j}(x_i\\ |\\ \\theta_j) \\\\\n", " =& \\sum_{i=1}^n \\sum_{j=1}^k \\tau_{ij}(\\vartheta) \\frac{2(x-\\mu_j)}{2\\sigma_j}\n", "$$\n", "\n", "Wir können mit $2\\sigma_j$ durchmultiplizieren und nach $\\mu_j$ umstellen, dann erhalten wir die geschlossene Formel\n", "\n", "$$\n", "\\mu_j^{(i+1)} = \\frac{\\sum_{i=1}^n \\tau_{ij} x_i }{ \\sum_{i=1}^n \\tau_{ij}}.\n", "$$\n", "\n", "Als nächsten Schritt betrachten wir die Ableitungen nach den $\\sigma_j$:\n", "\n", "$$\n", "\\frac{d}{d\\sigma_j} \\log f_j(x_i) =& -\\frac{1}{\\sigma_j} + \\frac{(x_i-\\mu_j)^2}{\\sigma_j^3} \\\\\n", "\\frac{d}{d\\sigma_j} Q(\\theta, \\theta^{(i)}) =& \\sum_{i=1}^N \\tau_{ij} \\left( \\frac{(x_i-\\mu_j)^2}{\\sigma_j^3} -\\frac{1}{\\sigma_j} \\right)\n", "$$\n", "\n", "Stellt man die Gleichung $0 = \\frac{d}{d\\sigma_j} Q(\\theta, \\theta^{(i)})$ nach $\\sigma_j$ um (durchmultiplizieren mit $\\sigma_j^3$), so ergibt sich\n", "\n", "$${\\left(\\sigma_j^{(i+1)}\\right)}^2 = \\frac{\\sum_{i=1}^N \\tau_{ij}(x_i-\\mu_j)^2}{\\sum_{i=1}^N \\tau_{ij}}$$\n", "\n", "Schließlich können wir analog über die Nullstellen der Ableitung nach $p_j$ die Formel aufstellen, die $p_j$ als über die $x_i$ gemittelte Verantwortlichkeit von $x_i$ für Klasse $j$ darstellt:\n", "\n", "$$\n", "p_j^{(i+1)} = \\frac{\\sum_{i=1}^n \\tau_{ij}}{n}\n", "$$\n", "\n", "Damit sind nun neue Parameter $\\theta^{(i+1)}$ gefunden." ] }, { "cell_type": "markdown", "id": "e715cdac-c429-453a-a083-3d9173dab0de", "metadata": {}, "source": [ "#### Spezialfall k-Means\n", "\n", "Wenn wir $p_j = \\frac{1}{k}$ und $\\Sigma_j = E_d$ festhalten, erhalten wir die Formeln\n", "\n", "$$\n", "\\tau_{ij}(\\theta^{(i)}) = \\frac{f_j\\left(x_i,\\mu_j^{(i)},E_d\\right)}{\\sum_{m=1}^k f_m\\left(x_i,\\mu_m^{(i)},E_d\\right)}\n", "$$\n", "\n", "Ein echter Unterschied zum klassischen k-Means-Verfahren ist, dass wir heute hier mit **soft assignments** (weichen Zuweisungen) gearbeitet haben, d.h. wir haben für jede Mögliche Klasseneinteilung eines Punktes $x_i$ eine Wahrscheinlichkeit $\\tau_{ij}$ bestimmt. Im klassischen k-Means legt man sich aber fest, man macht ein **hard assignment** (feste Zuweisung). Wir können auch einfach $\\widetilde{\\tau_{ij}} := 1$ zuweisen, wenn $\\tau_{ij}$ unter allen $\\tau_{im}$ das größte ist, ansonsten $\\widetilde{\\tau_{ij}} := 0$ setzen. Damit bekommen wir\n", "\n", "$$\n", "\\mu_j^{(i+1)} =& \\frac{\\sum_{i=1}^n \\widetilde{\\tau_{ij}} x_i }{ \\sum_{i=1}^n \\widetilde{\\tau_{ij}}} \\\\\n", " =& \\frac{\\sum_{i=1}^n \\widetilde{\\tau_{ij}} x_i }{n} \\\\\n", " =& \\sum_{i=1, y_i=j}^n \\frac{x_i}{n}\n", "$$\n", "\n", "Das ist genau das arithmetische Mittel der $x_i$, die in Klasse $j$ liegen. Verwendet man stattdessen das soft assignment, ist es ein gewichtetes Mittel der $x_i$, das denjenigen Punkten mit ungewisserer Zuteilung weniger Gewicht gibt- auch eine offensichtliche Optimierung gegenüber klassischem k-Means." ] }, { "cell_type": "markdown", "id": "e3e6e97c-d9b6-4b35-984a-2227bcface8c", "metadata": {}, "source": [ "#### Allgemeinere Modelle implementieren\n", "\n", "Wenn Sie allgemeinere Modelle implementieren wollen als das, was wir hier besprechen, müssen Sie den Teil, in dem explizite geschlossene Formeln für $p_j$, $\\mu_j$, $\\sigma_j$ berechnet werden, entsprechend anpassen. Wir konnten geschlossene Formeln finden, weil $\\log$ von einer Dichte, die mit $e^{(...)}$ geschrieben werden kann, eben besonders einfach ist. Als Faustregel sind also alle Verteilungen ähnlich zu behandeln und können anstelle der Normalverteilung verwendet werden, die auch von dieser Bauart sind. Eine präzise Formulierung wäre, dass alle Verteilungen aus einer sogenannten exponentiellen Familie geeignet sind." ] }, { "cell_type": "markdown", "id": "1f38f6a1-2c08-4ebf-a196-3e8710b20378", "metadata": {}, "source": [ "### Implementierung in Python\n", "\n", "#### Univariate Daten" ] }, { "cell_type": "code", "execution_count": 2, "id": "8bba2c3d-46f3-44bf-9960-d15f3adf65fa", "metadata": {}, "outputs": [], "source": [ "# Variante für univariate Gausssche Mischungen,\n", "# nicht-vektorisiert (für das bessere Verständnis)\n", "\n", "from scipy.stats import norm\n", "\n", "def EM(xs, pis, mus, sigmas):\n", " K = len(pis)\n", " N = xs.shape[0]\n", " \n", " #(E)-Schritt\n", " taus = np.zeros((N,K))\n", " for i in range(N):\n", " reg = 0\n", " for j in range(K):\n", " taus[i,j] = pis[j] * norm.pdf(xs[i],\n", " loc=mus[j],\n", " scale=sigmas[j])\n", " reg += taus[i,j]\n", " for j in range(K):\n", " taus[i,j] /= reg\n", " \n", " #(M)-Schritt\n", " Npis = np.zeros(K)\n", " for j in range(K):\n", " Npis[j] = taus[:,j].sum()\n", " pis = Npis / N\n", "\n", " mus = np.zeros(K)\n", " for j in range(K):\n", " for i in range(N):\n", " mus[j] += taus[i, j] * xs[i]\n", " mus[j] /= Npis[j]\n", "\n", " sigmas = np.zeros(K)\n", " for j in range(K):\n", " for i in range(N):\n", " sigmas[j] += taus[i, j] * ((xs[i]- mus[j])**2)\n", " sigmas[j] /= Npis[j]\n", " sigmas[j] = np.sqrt(sigmas[j])\n", " \n", " ll_new = 0.0\n", " for i in range(N):\n", " s = 0\n", " for j in range(K):\n", " s += pis[j] * norm.pdf(xs[i],\n", " loc=mus[j],\n", " scale=sigmas[j])\n", " # compute new log-likelihood:\n", " ll_new += np.log(s)\n", " \n", " return pis, mus, sigmas, taus, ll_new" ] }, { "cell_type": "markdown", "id": "7c16f899-221f-4e5c-9d16-d930109684bf", "metadata": {}, "source": [ "Wie auch beim k-Means-Verfahren wollen wir nun zugucken, wie sich im Laufe der Iteration der Fit verbessert. Dazu basteln wir erstmal Versuchsdaten:" ] }, { "cell_type": "code", "execution_count": 3, "id": "27a5fd4d-337a-4c69-91ac-a2083b5f56cb", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "np.random.seed(12345)\n", "pi = 1.0/3\n", "real_mu_1, real_sigma_1 = 0, 1.5\n", "real_mu_2, real_sigma_2 = 6, 3.5\n", "component1_sample = norm.rvs(real_mu_1,\n", " real_sigma_1,\n", " int(pi*1500))\n", "component2_sample = norm.rvs(real_mu_2,\n", " real_sigma_2,\n", " int((1-pi)*1500))\n", "mixture_samples = np.concatenate((component1_sample,\n", " component2_sample))\n", "\n", "fig, ax = plt.subplots()\n", "hist = ax.hist(mixture_samples, bins=51,\n", " color='grey', alpha=.5,\n", " label=\"gewichtete Summe\")\n", "bins = hist[1]\n", "ax.hist(component1_sample, alpha=.75, bins=bins,\n", " color='navy', label=\"Komponente 1\")\n", "ax.hist(component2_sample, alpha=.75, bins=bins,\n", " color='gold', label=\"Komponente 2\")\n", "ax.set_xlabel(\"$x$\")\n", "ax.set_ylabel(\"Dichte\")\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 4, "id": "9144677a-6b29-49b9-84a5-8f3f499922c4", "metadata": {}, "outputs": [], "source": [ "# Initiale theta aufstellen:\n", "pis = np.ones(2) + np.random.random(2)\n", "pis /= pis.sum()\n", "mus = np.random.random(2) * 2*np.std(mixture_samples)\\\n", " + np.mean(mixture_samples)\n", "sigmas = np.sqrt(np.random.random(2) + 1)" ] }, { "cell_type": "code", "execution_count": 5, "id": "5da2c828-1efc-434e-9cf6-ce564ccb8bc6", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x720 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Darstellung der echten Parameter vs. die initialen:\n", "fig, ax = plt.subplots(figsize=(10,10))\n", "hist = ax.hist(mixture_samples, bins=51,\n", " density=True,\n", " label=\"Daten\")\n", "xmin, xmax = ax.get_xlim()\n", "norm_pdf_domain = np.linspace(xmin, xmax, 100)\n", "ax.plot(norm_pdf_domain,\n", " pis[0]*norm.pdf(norm_pdf_domain,\n", " mus[0], sigmas[0]) +\n", " pis[1]*norm.pdf(norm_pdf_domain,\n", " mus[1], sigmas[1]),\n", " color='blue',\n", " label=\"Schätzung Mischung\")\n", "ax.vlines(real_mu_1, 0, .2,\n", " color='purple', label=\"wahres $\\mu_1$\")\n", "ax.vlines(real_mu_2, 0, .2,\n", " color='tomato', label=\"wahres $\\mu_2$\")\n", "ax.vlines(mus[0], 0, .2,\n", " color='fuchsia', label=\"$\\mu_1^{(0)}$\")\n", "ax.vlines(mus[1], 0, .2,\n", " color='orange', label=\"$\\mu_2^{(0)}$\")\n", "ax.set_xlabel(\"$x$\")\n", "ax.set_ylabel(\"Dichte\")\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "id": "6538d8da-3ff3-4bbb-898e-49eb3d4b6511", "metadata": {}, "outputs": [ { "data": { "text/html": [ "<video width=\"720\" height=\"720\" controls autoplay loop>\n", " <source type=\"video/mp4\" src=\"data:video/mp4;base64,AAAAHGZ0eXBNNFYgAAACAGlzb21pc28yYXZjMQAAAAhmcmVlAANO221kYXQAAAKuBgX//6rcRem9\n", "5tlIt5Ys2CDZI+7veDI2NCAtIGNvcmUgMTU1IHIyOTE3IDBhODRkOTggLSBILjI2NC9NUEVHLTQg\n", "QVZDIGNvZGVjIC0gQ29weWxlZnQgMjAwMy0yMDE4IC0gaHR0cDovL3d3dy52aWRlb2xhbi5vcmcv\n", "eDI2NC5odG1sIC0gb3B0aW9uczogY2FiYWM9MSByZWY9MyBkZWJsb2NrPTE6MDowIGFuYWx5c2U9\n", "MHgzOjB4MTEzIG1lPWhleCBzdWJtZT03IHBzeT0xIHBzeV9yZD0xLjAwOjAuMDAgbWl4ZWRfcmVm\n", "PTEgbWVfcmFuZ2U9MTYgY2hyb21hX21lPTEgdHJlbGxpcz0xIDh4OGRjdD0xIGNxbT0wIGRlYWR6\n", "b25lPTIxLDExIGZhc3RfcHNraXA9MSBjaHJvbWFfcXBfb2Zmc2V0PS0yIHRocmVhZHM9MjIgbG9v\n", "a2FoZWFkX3RocmVhZHM9MyBzbGljZWRfdGhyZWFkcz0wIG5yPTAgZGVjaW1hdGU9MSBpbnRlcmxh\n", 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matplotlib.animation as animation\n", "from IPython import display as ipydisplay\n", "from sklearn.cluster import KMeans\n", "\n", "def init_theta(samples):\n", " pis = np.ones(2) / 2\n", " mus = np.random.random(2) * 2*np.std(samples)\\\n", " + np.mean(samples)\n", " # a better way would be:\n", " #mus = KMeans(2).fit(samples.reshape(-1,1)).cluster_centers_\n", " sigmas = np.ones(2)\n", " return pis, mus, sigmas\n", "\n", "def em_iteration_draw(run_nr, ax, samples, history):\n", " pis, mus, sigmas, taus = history[run_nr][0:4]\n", " ys = np.zeros_like(samples, dtype=bool)\n", " if(len(taus) == len(samples)):\n", " for i in range(len(samples)):\n", " if(taus[i,1] > 0.5):\n", " ys[i] = 1\n", " ax.clear()\n", " ax.set_ylim(0, 0.2)\n", " ax.hist(samples, bins=51,\n", " density=True, alpha=0.5,\n", " label=\"Daten\")\n", " if(len(taus) == len(samples)):\n", " ax.scatter(samples[ys], np.zeros_like(samples[ys]),\n", " alpha=0.4, c=taus[ys][:,0],\n", " label=\"Als 0 klassifiziert\")\n", " xmin, xmax = ax.get_xlim()\n", " norm_pdf_domain = np.linspace(xmin, xmax, 100)\n", " ax.plot(norm_pdf_domain,\n", " pis[0]*norm.pdf(norm_pdf_domain,\n", " mus[0], sigmas[0]) +\n", " pis[1]*norm.pdf(norm_pdf_domain,\n", " mus[1], sigmas[1]),\n", " color='blue',\n", " label=\"Schätzung Nr. %d\" % (run_nr))\n", " ax.plot(norm_pdf_domain,\n", " pi *norm.pdf(norm_pdf_domain,\n", " real_mu_1, real_sigma_1) +\n", " (1-pi)*norm.pdf(norm_pdf_domain,\n", " real_mu_2, real_sigma_2),\n", " color='red',\n", " label=\"Echte Verteilung\")\n", " ax.set_xlabel(\"$x$\")\n", " ax.set_ylabel(\"Dichte\")\n", " ax.legend()\n", " \n", "def plot_ani(samples, history):\n", " fig, ax = plt.subplots(figsize=(10, 10))\n", " ani = animation.FuncAnimation(fig, em_iteration_draw,\n", " fargs=(ax, samples, history),\n", " interval=1000,\n", " frames=len(history))\n", " video = ani.to_html5_video()\n", " html = ipydisplay.HTML(video)\n", " ipydisplay.display(html)\n", " plt.close()\n", "\n", "\n", "max_iter = 210\n", "tol = 0.01\n", "pis, mus, sigmas = init_theta(mixture_samples)\n", "taus = np.zeros((len(xs), len(pis)))\n", "# record all values in each iteration step for plotting:\n", "history = [(pis, mus, sigmas, taus, 0)]\n", "\n", "for i in range(max_iter):\n", " pis, mus, sigmas = history[-1][0:3]\n", " history += [EM(mixture_samples,\n", " pis,\n", " mus,\n", " sigmas)]\n", " if np.abs(history[-1][-1] - history[-2][-1]) < tol:\n", " break\n", " \n", "plot_ani(mixture_samples, history)" ] }, { "cell_type": "markdown", "id": "32f0608d-777f-400f-84bf-e63603e3b9e3", "metadata": {}, "source": [ "#### Multivariate Daten\n", "\n", "Für den allgemeineren multivariaten Fall mühen wir uns nicht mehr mit der Herleitung ab, sondern lesen direkt den entsprechenden Code:" ] }, { "cell_type": "code", "execution_count": 7, "id": "537343eb-8f22-43f4-ad84-1ee0e32d7289", "metadata": {}, "outputs": [], "source": [ "from scipy.stats import multivariate_normal as mvn\n", "\n", "def EMmulti(xs, pis, mus, sigmas, tol=0.01, max_iter=100):\n", " \"\"\"vectorized E-M for multivariate Gaussian mixtures\"\"\"\n", "\n", " n, d = xs.shape\n", " k = len(pis)\n", "\n", " ll_old = 0.0\n", " for i in range(max_iter):\n", "\n", " # (E)-Schritt\n", " taus = np.zeros((k, n))\n", " for j in range(k):\n", " taus[j, :] = pis[j] * mvn(mus[j], sigmas[j]).pdf(xs)\n", " taus /= taus.sum(axis=0)\n", "\n", " # (M)-Schritt\n", " pis = taus.sum(axis=1)\n", " pis /= n\n", "\n", " mus = np.dot(taus, xs)\n", " mus /= taus.sum(axis=1)[:, None]\n", "\n", " sigmas = np.zeros((k, d, d))\n", " for j in range(k):\n", " xcs = xs - mus[j, :]\n", " sigmas[j] = (taus[j,:,None,None]\\\n", " * np.matmul(xcs[:,:,None],\n", " xcs[:,None,:])).sum(axis=0)\n", " sigmas /= taus.sum(axis=1)[:,None,None]\n", "\n", " ll_new = 0.0\n", " for pi, mu, sigma in zip(pis, mus, sigmas):\n", " ll_new += pi * mvn(mu, sigma).pdf(xs)\n", " ll_new = np.log(ll_new).sum()\n", "\n", " if np.abs(ll_new - ll_old) < tol:\n", " break\n", " ll_old = ll_new\n", "\n", " return ll_new, pis, mus, sigmas" ] }, { "cell_type": "markdown", "id": "df33041f-34b3-4756-a01e-ca6a580df1ee", "metadata": {}, "source": [ "# Anwendungsbeispiele\n", "\n", "## Aufenthaltsorte\n", "\n", "In `data.csv` sind Aufenthaltsorte aufgezeichnet. Die Daten kommen mit der MIT-Lizenz aus [einem Blogpost](https://towardsdatascience.com/simple-gps-data-visualization-using-python-and-open-street-maps-50f992e9b676),\n", "in dem OpenStreetMaps-Einbindung erklärt wird - das ist hier aber nicht erforderlich." ] }, { "cell_type": "code", "execution_count": 8, "id": "928a9666-38bc-4ec6-a296-317e0e04204d", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "data = np.genfromtxt(\"data.csv\", delimiter=',')\n", "fig, ax = plt.subplots()\n", "ax.scatter(data[:,0], data[:,1], alpha=0.01)\n", "ax.set_title(\"Zu clusternde Daten\")\n", "ax.set_xlabel(\"latitude\")\n", "ax.set_ylabel(\"longitude\")\n", "ax.plot(np.mean(data[:,0]), np.mean(data[:,1]), marker=\"+\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "b0c983dc-3bb1-438d-a668-7ed541ded978", "metadata": {}, "source": [ "Die Transformation auf Hauptkomponenten ist wenig nützlich bei diesen Daten:" ] }, { "cell_type": "code", "execution_count": 9, "id": "13f1453d-af47-47e2-be96-825a96efeb6f", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.decomposition import PCA\n", "\n", "pc = PCA().fit_transform(data)\n", "fig, ax = plt.subplots()\n", "ax.scatter(pc[:,0], pc[:,1], alpha=0.01)\n", "ax.set_title(\"Zu clusternde Daten in Hauptkomponenten\")\n", "ax.plot(np.mean(pc[:,0]), np.mean(pc[:,1]), marker=\"+\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "id": "b1918b28-be78-445b-8028-585358fbe204", "metadata": {}, "outputs": [], "source": [ "np.random.seed(1234321)\n", "pis = np.array([0.2,0.2,0.2,0.2,0.2])\n", "mus = np.random.random((5,2)) + np.mean(data)\n", "sigmas = np.array([np.eye(2)] * 5)\n", "ll_new, pis, mus, sigmas = EMmulti(data, pis, mus, sigmas)" ] }, { "cell_type": "code", "execution_count": 11, "id": "7713d7fb-b66c-4641-b206-71f5814d90d3", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ys = np.concatenate([mvn(m, s).rvs(int(p*2000))\n", " for p, m, s in zip(pis, mus, sigmas)])\n", "\n", "fig, ax = plt.subplots()\n", "ax.scatter(data[:,0],data[:,1],alpha=0.01)\n", "ax.scatter(ys[:,0],ys[:,1],alpha=0.01)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "ef7a3638-b851-4c59-ad9e-d0a4d6f93c2a", "metadata": {}, "source": [ "Eine Interpretation wäre nun, dass wir die längeren Aufenthaltsorte damit identifiziert haben." ] }, { "cell_type": "markdown", "id": "2bd0f4fc-48fb-40c1-9370-e40025a8f23b", "metadata": {}, "source": [ "## Iris-Klassifikation\n", "\n", "Wir werden jetzt die GMM (Gaussian Mixture Model)-Implementierung von Scikit-learn benutzen, um den Iris-Datensatz zu modellieren.\n" ] }, { "cell_type": "code", "execution_count": 12, "id": "4339ab3d-bf7b-47bd-8a94-4872c34c6781", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Initialization 0\n", " Iteration 10\n", "Initialization converged: True\n", "converged after 17 steps\n" ] } ], "source": [ "from sklearn.mixture import GaussianMixture\n", "from sklearn.metrics import accuracy_score\n", "from sklearn.datasets import load_iris\n", "x, y = load_iris(return_X_y=True)\n", "k=3\n", "\n", "# Zum Darstellen in Hauptkomponenten transformieren:\n", "xpc = PCA().fit_transform(x)\n", "\n", "# Fit mit E-M-Algorithmus:\n", "gm = GaussianMixture(n_components=k,\n", " random_state=42,\n", " max_iter=100,\n", " init_params='k-means++',\n", " verbose=1).fit(xpc)\n", "if(gm.converged_):\n", " print(\"converged after %d steps\" % gm.n_iter_)\n", "else:\n", " print(\"could not reach convergence\")" ] }, { "cell_type": "markdown", "id": "31e13c11-adb7-458c-9291-84308d388f96", "metadata": {}, "source": [ "Aus dem Gausschen Mischungsmodell können wir auch die individuellen Wahrscheinlichkeiten gewinnen:" ] }, { "cell_type": "code", "execution_count": 13, "id": "d24214e4-8f17-4f86-8198-c2633a3ea968", "metadata": {}, "outputs": [], "source": [ "y_pred = gm.predict(xpc)\n", "y_pred_proba = gm.predict_proba(xpc)\n", "y_pred_maxproba = np.max(y_pred_proba,\n", " axis = 1)" ] }, { "cell_type": "markdown", "id": "d49a3a82-c10a-47a2-8dc5-100a2ca57acf", "metadata": {}, "source": [ "Hier wollen wir einmal die Permutation finden, die die höchste Übereinstimmung mit den tatsächlichen Klassen liefert:" ] }, { "cell_type": "code", "execution_count": 14, "id": "35596a33-7f64-4044-853b-b80e66d4521b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Genauigkeit: 97%\n" ] } ], "source": [ "from itertools import permutations\n", "best_accuracy = 0.0\n", "for permutation in permutations(range(k)):\n", " y_pred_permuted = np.array([permutation[value]\n", " for value in y_pred])\n", " this_accuracy = accuracy_score(y_pred_permuted, y)\n", " if(this_accuracy > best_accuracy):\n", " best_accuracy = this_accuracy\n", " y_pred_bestperm = y_pred_permuted\n", "\n", "print(\"Genauigkeit: %2.f%%\" % (100*best_accuracy))" ] }, { "cell_type": "markdown", "id": "7938a27c-cf7e-4ace-b882-49476c29e74e", "metadata": {}, "source": [ "Und schließlich plotten, wie das Ergebnis aussieht:" ] }, { "cell_type": "code", "execution_count": 15, "id": "ac35d6e6-5523-42c8-b20c-bd361a126861", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ " \n", "# Wir betrachten direkt die Marginalverteilungen\n", "# in den ersten 2 Hauptkomponenten:\n", "mvns = [mvn(mean=mu[:2],\n", " cov=sigma[:2,:2],\n", " allow_singular=True)\n", " for mu, sigma in zip(gm.means_,\n", " gm.covariances_)]\n", "\n", "x_wrongs = xpc[y_pred_bestperm != y]\n", "\n", "fig, ax = plt.subplots(figsize=(8,8))\n", "ax.set_title(\"mixed Gaussian model, sklearn EM-fit\")\n", "xs, ys = np.mgrid[-4:4.1:.2, -2:2.1:.1]\n", "for i in range(k):\n", " zs = mvns[i].pdf(np.dstack((xs, ys)))\n", " ax.contour(xs, ys, zs,\n", " cmap=plt.cm.Oranges, alpha=.7)\n", "ax.scatter(xpc[:,0], xpc[:,1],\n", " c=y_pred_bestperm, vmin=0, vmax=k-1,\n", " label='Daten')\n", "ax.scatter(x_wrongs[:,0], x_wrongs[:,1],\n", " c='red', marker='x',\n", " label='Fehlklassifiziert')\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "313a0545-927b-460a-9194-d9575daf6a28", "metadata": {}, "source": [ "## MNIST\n", "\n", "Auf dem MNIST-Datensatz schauen wir uns an, wie gut GMM funktioniert und wie man damit auch generativ neue Samples einer Klasse generiert." ] }, { "cell_type": "code", "execution_count": 16, "id": "b1461ff7-2482-40d3-b82a-314943d1be0e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "kept 29 of 64 dimensions for 95% of variance \n" ] } ], "source": [ "from sklearn.datasets import load_digits\n", "x,y = load_digits(return_X_y=True)\n", "vargoal = .95 # keep so much of variance\n", "pca = PCA(vargoal)\n", "pca.fit(x)\n", "print(\"kept %d of %d dimensions for %2.f%% of variance \"\n", " % (len(pca.components_), x.shape[1], 100*vargoal))\n", "data = pca.transform(x)" ] }, { "cell_type": "code", "execution_count": 17, "id": "dfde9366-bd91-4e71-82cc-c2123051913c", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 100 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_digits(x):\n", " so_many_rows = min(100, len(x)) // 10\n", " fig, ax = plt.subplots(so_many_rows, 10, figsize=(8, 8),\n", " subplot_kw=dict(xticks=[], yticks=[]))\n", " fig.subplots_adjust(hspace=0.05, wspace=0.05)\n", " for i, axi in enumerate(ax.flat):\n", " im = axi.imshow(x[i].reshape(8, 8), cmap='binary')\n", " im.set_clim(0, 16)\n", " plt.show()\n", "\n", "plot_digits(x)" ] }, { "cell_type": "code", "execution_count": 18, "id": "715c78f9-0cb6-4d80-8102-fed54dfd4b8d", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[ 1 11 12 15 24 49 50 62 65 98]\n" ] } ], "source": [ "gm = GaussianMixture(100, random_state=23)\n", "gm.fit(data)\n", "\n", "new_data, new_labels = gm.sample(10)\n", "new_data_in_old_coordinates = pca.inverse_transform(new_data)\n", "plot_digits(new_data_in_old_coordinates)\n", "print(new_labels)" ] }, { "cell_type": "markdown", "id": "a4c47178-d237-4934-a0e8-878c1cfcf0f0", "metadata": {}, "source": [ "Diese neuen Ziffern hat das GMM für uns generiert. Warum aber sind die zugehörigen Label nicht die Ziffern 0--9?\n", "\n", "Weil wir im Training gar nicht versucht haben, pro Ziffer genau eine Normalverteilung in der Mischung zu haben. Mit den hier verwendeten 100 einzelnen Normalverteilungen klappt es aber, neue Ziffern zu generieren. Wenn wir die Klassifikation noch separat laufen lassen (etwa mit SVMs oder auch direkt als latente Variable im E-M-Algorithmus), haben wir ein Modell, mit dem wir auch gezielt neue Ziffern einer bestimmten Klasse generieren können (z.B. gezielt eine $7$).\n", "\n", "Um etwas Einsicht in unser Modell zu gewinnen, schauen wir uns einzelne Mischungskomponenten an:" ] }, { "cell_type": "code", "execution_count": 19, "id": "74e47f30-54f8-43fd-94f5-b280a76f9d07", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i in range(10):\n", " mu = gm.means_[i]\n", " sigma = gm.covariances_[i]\n", " new_data = mvn(mu, sigma).rvs(10)\n", " new_data_in_old_coordinates = pca.inverse_transform(new_data)\n", " plot_digits(new_data_in_old_coordinates)" ] }, { "cell_type": "markdown", "id": "5c54b0b3-c7b7-44da-b20f-d2651e001960", "metadata": {}, "source": [ "Wir sehen also durchaus, dass die Mischungskomponenten innerhalb einer Klasse bleiben, es aber eben verschiedene \"Nullen\" gibt. Wenn wir nur 10 Mischungskomponenten verwenden, sieht das Modell schlechter aus:" ] }, { "cell_type": "code", "execution_count": 20, "id": "c0193b85-cba9-469a-9f5d-9b439fb41ff0", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[0 1 1 1 2 5 6 7 8 9]\n" ] } ], "source": [ "gm = GaussianMixture(10, random_state=23)\n", "gm.fit(data)\n", "\n", "new_data, new_labels = gm.sample(10)\n", "new_data_in_old_coordinates = pca.inverse_transform(new_data)\n", "plot_digits(new_data_in_old_coordinates)\n", "print(new_labels)" ] }, { "cell_type": "markdown", "id": "87c93ec8-9633-4287-9ec3-f7ab23523531", "metadata": {}, "source": [ "Um in unserem Paradigma ohne zusätzliche Algorithmen z.B. eine $7$ zu generieren, können wir direkt auf dem Teildatensatz der $7$er trainieren:" ] }, { "cell_type": "code", "execution_count": 21, "id": "e6e441f7-6d6b-40da-9fbd-f68e3297f459", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gm7 = GaussianMixture(10, random_state=23)\n", "gm7.fit(data[y == 7])\n", "\n", "new_data, new_labels = gm7.sample(10)\n", "new_data_in_old_coordinates = pca.inverse_transform(new_data)\n", "plot_digits(new_data_in_old_coordinates)" ] }, { "cell_type": "markdown", "id": "29437463-22e5-4251-ba8c-2c16fbb623d6", "metadata": {}, "source": [ "## Fashion-MNIST\n", "\n", "Einfach nur weil es geht, gucken wir uns genau das gleiche auf dem Fashion-MNIST-Datensatz an:" ] }, { "cell_type": "code", "execution_count": 22, "id": "3d6e3226-797d-4faa-8db8-0823b48eb61f", "metadata": { "tags": [ "hide-input" ] }, "outputs": [], "source": [ "from itertools import product\n", "from urllib.request import urlretrieve\n", "import gzip\n", "import numpy as np\n", "\n", "filepattern = \"%s-%s-ubyte.gz\"\n", "baseurl = \"http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/\"\n", "\n", "def load_mnist_labels(filename):\n", " with gzip.open(filename, 'rb') as file:\n", " return np.frombuffer(file.read(),\n", " dtype=np.uint8,\n", " offset=8)\n", " \n", "def load_mnist_images(filename):\n", " with gzip.open(filename, 'rb') as file:\n", " return np.frombuffer(file.read(),\n", " dtype=np.uint8,\n", " offset=16).reshape(-1, 784)\n", "\n", "def load_mnist(kind='train'):\n", " labelfilename = filepattern % (kind, \"labels-idx1\")\n", " imagefilename = filepattern % (kind, \"images-idx3\")\n", " urlretrieve(baseurl + labelfilename, \"./\" + labelfilename)\n", " urlretrieve(baseurl + imagefilename, \"./\" + imagefilename)\n", " labels = load_mnist_labels(labelfilename)\n", " images = load_mnist_images(imagefilename)\n", " return images, labels" ] }, { "cell_type": "code", "execution_count": 23, "id": "ab39812c-f04a-4493-8354-7b2858706915", "metadata": {}, "outputs": [], "source": [ "x_train, y_train = load_mnist(kind='train')\n", "#x_test, y_test = load_mnist(kind='t10k')" ] }, { "cell_type": "code", "execution_count": 24, "id": "ee64b034-8898-4581-82bd-450641d9a315", "metadata": {}, "outputs": [], "source": [ "def show_fashion_image(raw_data, ax):\n", " im = ax.imshow(raw_data.reshape(28, 28), cmap='binary')\n", " im.set_clim(0, 16)" ] }, { "cell_type": "markdown", "id": "4df6bba1-62f4-4064-9e66-8d9d154eebb2", "metadata": {}, "source": [ "Wir schauen uns an, wie lange PCA.fit und EM (der gm.fit) auf diesem etwas größeren Datensatz brauchen:" ] }, { "cell_type": "code", "execution_count": 31, "id": "cb13e55c-8cb3-49b5-9aea-dc3415fd424e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.56 s ± 290 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n" ] }, { "data": { "text/html": [ "<style>#sk-container-id-3 {color: black;background-color: white;}#sk-container-id-3 pre{padding: 0;}#sk-container-id-3 div.sk-toggleable {background-color: white;}#sk-container-id-3 label.sk-toggleable__label {cursor: pointer;display: 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input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-3 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-3 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-3 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-3 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-3 div.sk-item {position: relative;z-index: 1;}#sk-container-id-3 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-3 div.sk-item::before, #sk-container-id-3 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-3 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-3 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-3 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-3 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-3 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-3 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-3 div.sk-label-container {text-align: center;}#sk-container-id-3 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-3 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>PCA(n_components=0.9)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" checked><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">PCA</label><div class=\"sk-toggleable__content\"><pre>PCA(n_components=0.9)</pre></div></div></div></div></div>" ], "text/plain": [ "PCA(n_components=0.9)" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vargoal = .90\n", "pca = PCA(vargoal)\n", "%timeit pca.fit(x_train)\n", "pca.fit(x_train)" ] }, { "cell_type": "code", "execution_count": 32, "id": "8028a575-a1f0-4751-a7f8-990e2ad3a6ad", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "kept 84 of 784 dimensions for 90% of variance \n" ] } ], "source": [ "print(\"kept %d of %d dimensions for %2.f%% of variance \"\n", " % (len(pca.components_), x_train.shape[1], 100*vargoal))\n", "fashion_data = pca.transform(x_train)" ] }, { "cell_type": "code", "execution_count": 33, "id": "f89f9871-7fdc-4853-bad0-7e438062af76", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 17.8 s, sys: 23.6 s, total: 41.5 s\n", "Wall time: 2.7 s\n" ] }, { "data": { "text/html": [ "<style>#sk-container-id-4 {color: black;background-color: white;}#sk-container-id-4 pre{padding: 0;}#sk-container-id-4 div.sk-toggleable {background-color: white;}#sk-container-id-4 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-4 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-4 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-4 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-4 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-4 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-4 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-4 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-4 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-4 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-4 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-4 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-4 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-4 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-4 div.sk-item {position: relative;z-index: 1;}#sk-container-id-4 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-4 div.sk-item::before, #sk-container-id-4 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-4 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-4 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-4 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-4 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-4 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-4 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-4 div.sk-label-container {text-align: center;}#sk-container-id-4 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-4 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-4\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>GaussianMixture(n_components=100, random_state=23)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-4\" type=\"checkbox\" checked><label for=\"sk-estimator-id-4\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">GaussianMixture</label><div class=\"sk-toggleable__content\"><pre>GaussianMixture(n_components=100, random_state=23)</pre></div></div></div></div></div>" ], "text/plain": [ "GaussianMixture(n_components=100, random_state=23)" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%%time\n", "gm = GaussianMixture(50, random_state=23)\n", "gm.fit(fashion_data[y_train == 1])" ] }, { "cell_type": "code", "execution_count": 34, "id": "7a5855eb-e2ea-481a-8f3f-4c618d155b38", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def draw_gm_sample(gm, pca, n=10):\n", " new_data, new_labels = gm.sample(n)\n", " new_data_in_old_coordinates = pca.inverse_transform(new_data)\n", "\n", " fig, axs = plt.subplots(1, len(new_data),\n", " figsize=(8, 8),\n", " subplot_kw=dict(xticks=[],\n", " yticks=[]))\n", " fig.subplots_adjust(hspace=0.05, wspace=0.05)\n", " for datapoint, ax in zip(new_data, axs):\n", " show_fashion_image(pca.inverse_transform(datapoint), ax)\n", " plt.show()\n", "\n", "draw_gm_sample(gm, pca, n=10)" ] }, { "cell_type": "code", "execution_count": 35, "id": "3ab8baba", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 28.8 s, sys: 16.6 s, total: 45.4 s\n", "Wall time: 3.42 s\n", "CPU times: user 3min 33s, sys: 2min 48s, total: 6min 21s\n", "Wall time: 25.2 s\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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j0UClUkGpVAouFj0ez4jDxobj1VdfxUMPPYQrrrgCS5Yswd69e9HZ2Rm32cTtdqOtrQ0NDQ34+OOPsXLlSt77/f39uOGGGzBjxgyIRCLcdNNN+Mtf/oK8vLyoizK/348pU6awZ2HJkiWYO3cu75zDhw+jrq4OwJDDC+0Lp0+fRl9f37Djh0gkwkUXXZRwiNjZcPXVV8Pr9bJnbdy4cZg4cWLMa/r6+mAymeB0OvH++++z44888siojxUAf/zJyMjABRdcgFOnTsFms8FsNie2qYq2NRX6R7fd4W7cZ86cSYp6IPyfXq8X3HIPp9ogZEjtVF9fT956662kyrxv3z5isVjIqVOnyLFjxyJk5srrdDpJY2Mj2b59O3n22WdT0sZCKudw1casWbNYiAshQyEZBoOBGAwG0tzczNQ5/7pmzP5x8fv9MWUW6hf9/f3k2muvTUk7U/ndbndEGBRXZr/fT5xOJ+ns7CRNTU28PrRz586kyvvKK68ItrHP5+PJ7PV6id1uJ3q9nrhcLnaey+UiJpMp6X2DMjg4SBwOB3E6ncTtdkftGx6PhxiNRlJXV5dQWNC4cePII488clZyFxUVkT179jBZQqEQaW5uJlarNa5xjhBCZDJZ0vtyc3Mz77elUPPa7NmzicvlIkajkXz++efkq6++IkeOHCFvvvkmufnmm5MmZzT6+vrYGILRVOFi6FN5r0czmD8RhjXwxkClUkGn08VUMY4FKpWKF34QaxVsNBohEolQU1OTsp3R119/Hdd5XDd86jafn5+PoqIi1NTUjKWIggwMDCQciB8IBHDo0KExkig+FApFVPUVIQR+vx+EEGRkZECtVjOnGKPRyHM6SQbffPMNWltbececTqdgIgGRSIRAIMAc0A4dOgSv15twwpHRghACq9XKnA6j7XJCoRCkUiny8/ORn5+fkLNfe3t7xNiYny8cjx8NvV7Pc0gKBoPQ6XRRw4aEGM4MMBa43W6YzWaeDHa7PcJ7nybHkclk0Gq1KC0txcaNG5Mmp06nO6v2GVEYC1ftGQwGk/7gUvLy8mAwGNDQ0ICjR48m3BBFRUX47rvvxkg6YaqqqqBWq1FeXo6amhpeJwvHZDKhvLwc1dXVKRvYP/vsM/Z3NHUiHXy4Klx6XKVSobS0lHdeMjh16hT6+vpgsVjiWuB5vV6m1k8VAwMD8Hg8PJsRd8Cm3qwKhQIFBQUoLi5GSUkJNm/ejNWrV+Ohhx5Kqrzvv/8+1q9fzxah1BYars6Vy+XIysqCUqlEKBTCwMAATpw4wVTsAPDGG28kTe49e/bgiy++wJkzZ6DVapGVlRXVDOV2u9lCvbS0FOeddx7v/Z/+9KcxP+tvf/sb7/VIQs8+/fRT9ncgEOCZImJhMBjQ1dWV8OeNBtOmTUNubi573dTUhPb2dt4YrVQqIZfLUVpaivPPPx+VlZW45pprkiqnxWJh4SonT55EW1sb9Ho98vPzBf1pwhnRBEobwel0oqOjY9RcohPltddeQ15eHmprazF79uyY9ky6a6b2DAD4+OOPsWHDhqTISgnfXdhsNt6qjPzLnujz+VBeXi4YMJ1M+vv7cfToURw6dIi5fQORq1qbzYa+vj7eJOnxeNike7bJKRJl6tSpqKqqglarhcPhGNZelIpVejiXX3456urqkJOTg2AwyEI+KCKRCBqNJkLzMnPmTFRWVibdF4EQgmeeeQZyuRxNTU3QaDRsYhdCp9MhPz8fBQUFLDkD5ec///mYyvqTn/yEOTqVl5fjiiuuwMKFC4e9TiwWs77j8/lw5MgR3vsHDx4UvO6pp57C0qVLI2IJt2zZggULFiQk+5YtW3D69GkWYiZEKBSC0+nkLWILCgoSTis4WnzzzTdMu2C1WlFbW4uSkpKIRbROp0NtbW1SbPex2LlzJ6ZMmYLx48ejqKgobu3mWalwaVKFeGbqseDkyZMRzizh6mUALAYN+H5Qt1gsMBgMSZOVEv5AZWVl8QZ37gIl3pXmWBIIBFiGDrVazQb2cPUot40pdrudTQCjlZwiXri7G5lMFpeDSiJZgMaCuro6nDlzBsDQwsXlcvEGnGg7+KqqKtx9991YsWJFUuQEwBvICSHo6emBRCJBVlZWXF6X3CxPl19++ZjIyGXTpk3MDBIebwsgYvFNd8pKpRJisRh+v5/Fb3PhLiopFRUVWLRoESZPniy4mLj77rt5r+fMmTOs/F1dXWycFUroEAqFWJY1ikgkStkCnLtrplq2rKwswUxJ5wIj8XIGEkwmD3wfEgKApaP7wQ9+MKIPP1sUCgW6u7uZt5tSqYwYKOkkLxaL4fP5oFQqUVlZiczMTJSVlaVEbq/XC4fDAbFYHKESoonyuSugs0kGfrZkZGRg0aJF7HVbW1uEHSgYDIIQAqVSCafTiVAoBJ/PB41Gk9RdkUgkYsnN/X4/Ojs74fV6MXny5Ihzw/uJUqkcM9f5RNi3bx+WL1+Ozs5OlJeX89RgXJmbm5tZ/1EqldDpdFi7du2op9CMBnfCsVqtPNtetN+8q6sLCoUCeXl5vIH0bMOZCCFYs2YNHn300Zjnvf/++7j77ruhUChw5swZfPfdd9Dr9aisrIwIb+jv70dfXx9bxIrFYrjdbjQ1NUW9f3d3N9uNX3LJJQAQ4YXL/d7XXnstbr/9dtxyyy2YNGlSzHtzEwmYTCb2jFFoyFi4ire6ujpWk4wZTz31FJ588kkYDAbeLjjazq61tRVffvklTpw4kSwReVx33XUAhpKF9PT0QCqVxrWwGVEcKLdTZGRkJN0Rh7J27VpWpYXqsoVWNNxqBAqFApmZmbBardi9e3cKpB5qs6ysLJ7akO5CQ6EQT6U7MDCQMjsGANTW1vJi/MaNG4fx48ejoqKCHROLxVCpVMjOzobFYsHAwACsVutZOXmNFGrDpAsl7gDCfZC5bex2u2Oqx5LJm2++idOnT2POnDkROyXu4NvX14euri62Y0027777LoChDFMqlQrTpk1j+USFNDuBQADFxcXIzs6OmhLvbBhu8gT4O72qqipcddVVeOCBBzB//vyInK0SiYQ3znm9XowfP57Z84UoKSmBwWDgLQjCd7ZXXnkl+/uTTz7B8uXLYTKZ8JOf/GRY+b1eLwwGA8rKypCXl8dbUHE1V3QsIYQI7pCTxYEDB1BYWIjzzz8fwNC4F01bWVlZiWXLlmHt2rXJFDGC8vJyXHjhhaitrWU5nGMxov1zuBoyPIA4mWRkZEAikfAmI27HIv9KPxjeEEajMar9YiyhDxdNgUYT3HPhyu/3+1MyEVHa29shkUgwODgIh8PBylZx+wBdVGVnZ7NAZOq9mGzCByzurtJut7O/uW1M1TdctW8qiWXLp6WopFJpRPsmc0G4atUqAMCuXbtYW1qtVtjtdsEJksosl8tHPfY6Xuc0WiSAQpOBKJXKCBscjR2n0AXXcMnRd+7cGRGXzOXf/u3fIo59+OGH+O1vfxvzvp2dnWhubmYq5HB1KPUklsvlsFgssNlscDqd2LlzZ8z7jiU00YYQQiaVVJusuDt6pVIJn88X8zsAI1DhCpFs+1Y4WVlZyMrKgt1ujxhUqNcwV63k8Xhw+PDhlHSuyy+/HAaDAQUFBcjOzo5wo5fJZExWl8uFwsJClr8yFWzZsoUlJu/v70cwGOTZr4ChNqY7f7oy5u7mkpXtCfjeptLR0QGNRgOlUom9e/ciNzeX94DSkBCZTAaPx5OycAohotVcFIlEGBwchMViicgpvHXrVtxwww1JkG4Imiy8uroajY2NOP/881lVFiEtEH0uvV4vent7UzJY0qpC69atw5w5czB16lQ2SXIzIwGARqOBTCbjLRqpo040uBPa+PHjmQfvz3/+c+ZEx/2cCRMmwGAw4L777htW9oqKCtTX1/N20dyxTiQSIT8/H7m5uWhqamJVRYSq6ySLZcuWweVyobOzE319fbjwwgvZeyNJMD+W/O53v8Njjz2GwcFBeL1eyGSyiAIUQozYgkt3Gan2Xjx+/Dhb0SqVyogJVCwWIzc3l7e7yMjIwA9/+MNkihkhE12ByeVyZGRk8KrM0Kw+Vqs1oaonY01eXl7E5AnwV5M0VSLdoR48eJCVoEsGVLWoUqmg1WqhUCgwffp0TJgwgad2JoSwnX8yw2vipbu7Gw6Hg3eMysl95uiAnsxUbZQbbrgBTz31FJ5++mns37+fhSUIaR7orjQjI4NVBkk2NMH5nXfeiQsuuABKpRJHjhxh8dZCuFwu5l9x9OhRfPvtt1HvTwhh1Xz6+vqg1+vR09PDK/pw1VVX4f777wcwlFEoES/Zv/71rwCGHJfMZjNvoSKRSKBWq1mxc7obTTWZmZnIzc3FwoULeYvqUCgUEfaWSt555x2YzWZ4vV5IJBLodDqUlJRE9SinjHgCdblcMJvNKbPBUBoaGthqWCqVRqg7xWJxxAMtEoki1DnJRCwWM1uhED6fD1arFYSQhAK3U0UsD9cDBw7gwIEDSZPlk08+AcBX3RYUFAi6ydOSfDKZjNnvzhVoGr/wQYY7aLpcLhaDPVbVTGJBy1rt2LGD5ciNBle+8N1esqDmE25f6OvrExzIqUc/dUAEgBMnTvDKdAlBJ0euGjs82cRINXa7du2C2+2GXq+P2LhIJBKmuaK5nVMdGkIRSh4RCoXgcDhYzmeAb2JJNi0tLaweLzfP93A5vxOeQKk7t9vtht1uH1ZHPNZcd911zJOVqhKjuf7T0IBUQ22G0dz9nU4n7HY7zjvvvJTlGQ6nra0NO3fuxI4dO3Dw4EFedpRoE2hzczP27NmTLBEBfB+Xd+TIkZjOV/QBtlgsKCgogNfrxUcffZQkKYdn0qRJKCwsjJgY8/LyMGHCBABDD/ekSZNSIR6PRYsW4fbbb2fqLyHOhYUgd/fo9/vhcDhw/fXXC3rj050cV+MSHgMqxNNPPw0AuOuuu9ixX/ziF7xzsrOz8cEHH6CoqCjmvcJ3kKWlpVAqlViwYEHEtdyFVU1NDUpKSkaUxH00EVo407EiGAyira0N3377LQYGBmA2m1l8fqooLS1Ffn5+XIUyKAnbQGnKJZrIPVoVhmTBHbxdLlfUL0/tEeeCWsPn8yErKwsSiQQej4fX+UUiEQoLC3k2OW5dvFQxfvx4iMViiMViBAIBng1DIpHA6/XyNACBQAB5eXkpS7Lh9/sxODjIVLlUJopUKoVWq2U2MJfLNWwNx2TR09PD1JxCycjPhT7MhdroBwcHozqPSSSSmCnzksWHH36IpUuXsvEr2iTj9XrhcrnYswp8r92IxqZNm9jfu3btYn9zd4J79uyBXq/HypUrh41DD188pVrblyg01l6n06G1tZWntpVIJMjLy0NGRgby8/Ph8XgiTBbJhmqtCCFobW1FQUHBsE5jI3IiokZ1WmEhldAC2V6vF16vV3DAoWnaaDHaVONyuaDT6SAWi2E0GqFWqyN2cdyJKNm7uGhQGyIhhOcYRGPk+vv7UV1dzYK6tVrtiIrpjgZisRhOpxNGoxEGgwFKpZJng5FKpTxHFq/Xm9JwIS779+9nYQ3D9ddUqG7D+dGPfgRgSO1Mywpy8fl8kMlkMJvNrJB1qrjxxhtZvmYhWzKFeu7bbDb09vYiPz+f9WWFQiHoacwNReHuprh+DPPnzx9x1Zmuri4YDAZBR75w2VPpuU8JhUKsUlBDQwNzmgSGxrfi4mKmYcvMzDwnbKJOpxPNzc1ob29HbW3t2EygXM4Fbyqv1wuPx8MLOucS7rhgMplSOpHu3r0bCxYsQGlpKQvgFlqZNzQ0QK/XRy2JlKoVvUgkYs4SlJycHLaYojtVs9kcs8zVWDJz5kym0h8cHERmZiZv4KbtRs8pKyvD448/ziunlCq4sYJcQqEQurq6oNfrmTqyrKwMV199dTLF41FUVMR2DoFAAB0dHWhubmbvU22FWq0edjBKBhdccAGAoT5aUlKCgwcPYmBgIML+Rj37qaqUG+t+1113Yd26dbzzMzIy2ARwyy23QCaTsTSh1IsdAEsvefjwYd7199xzD8/ZSIhrr72W1YiNpmmjE6xMJovqY5EsaHICACzZDrX/Ui9hikgkSplzGaWvrw/FxcWYOXMmZs6cGdc1CdtAvV4vT207nB5/rBGLxcjIyEjIVuh2u1PmyAAM7UAJITFXiRaLBT6fD6Wlpfjxj3+cROmiQwt7A8K5Y7mLEqlUGnVBkww2btyIzs5OKBQKVFVVMXVRONw43PHjxydbTEE0Gg3cbnfEToV6lOfm5qKqqgo5OTnDOrWMNYODgzAYDHC5XJg5cyamTp3K+9256eTcbjergJIqwpO+KJVK5Ofn8zy0heD+FkK7T258ZyAQwOnTp9lrbvq/lpYWwcxi8Zg6LrvsMpSVlaGsrEww6xoAlp1Kq9Wm1CkHQFx9k/rSEEJSPpcIbQaH0xYkNIEGg0GcOHECO3fuZPr78J1IshGLxSwHJzDUCOFfmjoMAEM/WKp3zR6PJ+bO0Wg0oqenB3K5HJMmTRJ0cgivXj+W7N27F5s3b8b777+PTZs24dChQ1ErnNCKIalUIf32t7/Fs88+i4aGBpbLNFp7u91uNsClUrUYzt69e9HS0hIx2WRmZqKyshKXXnopJkyYkPJdhsfj4RV71mg0vIUI177f1taG5ubmlDqL0CLglNLSUkyePJntTIGhCdBsNvMmW+7iUEirwtUCtLS08KonhU+4NOzu9ttvZ8eGs29ef/31uP766wF8HyvOVQ1Tpzi6M5VKpSPO7zpavPnmm6irqxOUIxgMoq6uDh9//DHa2tpY6s9UEj5m2e32YZPtJKTHlEgkmDVrFmbNmsXq+qWqFijFbrczW5bJZBJ0sJDJZJDJZMxGOm7cuCRLyWfbtm2oqamBRqOBQqGA2+1mOzq/34+CgoKIhcnLL7+MNWvWoKenBzKZDP/1X/81pjISQvDggw9i/fr1uPjii2Oe6/f7YbPZkJWVBY/HA7/fD7/fn3Dtw9HiN7/5DYCh3QZ34OM6EdFFVH5+Pnw+H1wuF0/1mGomT56MoqIinvy0FihdDDQ1NeHll1/Ggw8+mCoxAQxppfr7+9nvzXWaCQQCMJlMkEgkmDJlSsS1qXYqEtKSsGLJnMmfq36eNGkSiyml0CQWL730EpYuXYqtW7eybE0qlUrQQebmm2/GNddcg/feew/btm3D008/jdWrVwvKuW3bNuzbtw/XXHMNBgcHYbfbef2Z1tXk2kZTmSEOGEpYQbU+s2bN4r3HnUuoZivVi0GbzQaj0Yj+/n5IpVIUFhYyj/dojNgQ6PP5YDAYsG/fvpHeYlQYGBhg6heq+49VHPdcwOFwsM4fbsek3oHhNo5HHnkE9913H/R6PY4dOzbsDzsavP7667jtttuGPY874GRlZbH0iWOR8zQRwlPGcScjr9cLu90OtVrNBp3wShupJC8vL2JFHAqFYLfb2Urd6XSmzEmLi1QqjRpzKJFIIJPJzplnLx5kMlnMzFTRzEXPPvssli5dipKSEt7vEs271Gw280w51BkrGtTGmpOTg5ycHJ4cYrGY5yQXDAYjEuQnG4vFAolEgszMTGaSEOoHtD+nWuXsdruRnZ2NrKws5Ofnx7UjTmgC5XpJ2Ww2HDt2DH/6058Sl3QU6erqwoQJE5CVlRURBBuOSCRCb28vzGYzpk2blkQp+RBCWF5QuVwOmUzGBnfqKJKVlQWTycQSMQPfq+8qKytht9uTUgaKm37Lbrfj22+/xSWXXMKb9MViMeRyOS+bklQqjSgmnGyobVOv1yMvL483gXo8HvT29mLixIlQqVTwer3nVJiAQqFg3uOUUCgEq9XKiiKcCzHNwJCs5513Hurr61FVVcV7BsViMatvei6EsXChqRxjYbVamZmIEu07/PrXvwYwNGG++eabw37+7t27QQhhuXOHSycZLitXDq5TjtVqhVqt5lVwSQVisRjFxcUoKytDV1cXc/YEhjZg4QUcUh2e5XQ6MWPGjISuScgGSghBS0sLOjo6UF5ejvnz50f1GEwWX3/9NVvhCdljvV4vmpubcfr0afagp3LyBIYCsnfv3g29Xs+KZ1O7rUQiwcSJE1mV9mg88MADZ10GKlHUajV+9KMfRQwg3MTbPT09zHkg1Sok6vkn5NaflZWFiRMnstcmkymuQPlkIpVKIxJcl5WVsUGHxq0muyh8OM899xx27dqFv/71rxEmHbrrkEgk59TkuX//fqxbty6mo4vdbkdbW1tEaE60MlderxdvvPEGrrjiiri0L4FAAGq1mjnPPPTQQzHPp2FWQgn7adsGAgE0NjayCkmpRCQSQafTISsri4WN0UmSpiwNBoMsDDHVGiCumvnLL7/E/v378d1338W8JqEdqEgkgkwmYw8wVSWkkkAgENNhRSKRQKvVnjOFWynUOzSceGtShtcRTQYOhwMqlYrZDMOhzkP0O6SqzB2FLkq8Xi98Ph9P5cVd7RJC4HQ6z4mYSi5c5zgh6HuPPPJIskQSpL+/HwUFBaisrIwYD+gEei4+fzk5OVHVdLTEXUFBQYTKNlr2tR07duCjjz6KO3UlXWBSD9xwB6dw6PPU2trKdvXh0LKN5wKBQIAtrGlhB6oF4u7q6eIq1dmq6LxGM8GFq8WFSNiJKLwOZKptG1xdtdFohNPp5K3OpFIpU42cPHkSOp0u5e7SACKKkNMBRiwWw+Vy4dixYxEVN7i88MILePHFF8dUxnB27dqFxsZGZGZmRgzshBA0NzfzHEVSrWLs6OiAw+GA1WqFSqWK0FA4HA7s3bsXFRUVzB56LtDV1cU8r7lqPVpZSCqVwu12Y9asWZg5cyaOHTuWIkm/Z/r06Zg+fbrge3QhEwgEWMaqVKeopA4sQjgcDnR1daG0tFTQJCRktjIajXj88cd54SvDwf3dnn/++WEnEDrRdnZ2RvX1kMvlzD+C1sZNFQ6Hg40T4epp6i/BfX0uLLJoetof/ehHrCJPLBKaQLk2JIPBgJ6eHpjN5pFJOkr4fD6cPn0aJSUlCAaDTF1A4U7wU6ZMgcvlQm9vb0p2cFyeeeYZXHfddXA6nRGDSWZmZlxxqsm2KV1wwQW47rrrYLfbeQ8nIQRms5mtNgkhMStcJIuuri7YbDbMmDFD8OFUqVSYN28e1Go1tm3blnJ7PiVaRha/34/Ozk4Eg0FUV1dj+fLluOWWW86JgScaYrGYDUJSqRQDAwMwGo1JDcOKRSAQgNVq5S32xGIxioqKeJMnN/OWkGp0w4YNCU2e4ezcuXPYpCO0ODwNZ+H+7n6/H729vZBKpWyhmOoICQBRq0lxx4Y9e/agvLwcU6dOTZZYUVGr1Qnllx7xk9fW1ob29vaUZZqh0K2/3++HVqtFdnY2T6UbCARYHJLf74fb7R71gr4j4fjx4zAajWhraxPcqaVyl7xs2TLB41QmtVodEXienZ3NMon4fD6YTKaUl2KjzkyxJhiqoklVzl4honkjSiQSZjbh2pLONYQGbhqmpdPpEkrWPdbU1dWhs7OTV4lHyBmRqxYV0gzFq368+uqrMXnyZADglcpqamoa9tpYi2pqS+SqHFNtUwQwrA0RGOobSqXynEg/mCgjDmNpbm5GU1MTvv7669GUJ2EyMzNRWFjIU8+FDyr//Oc/cfDgQVRWVmLChAkR6tNU4PV6WVyfkB2GJuwfrlNR9djZDqSJ5ucMT4DPVXVkZGTA4XCkPIxl3LhxvH7BzaAVDAbZwDlt2jTs3bs3FSIK0tzcjMmTJ0fYX2hs2rnI888/j5tuugmDg4M827fL5cKpU6eg1WpZXCstbJ0q6urqYLPZ0Nrais8++wyXXHIJb0zIyMhgWiyz2Yzc3FxefOXzzz+PF154gb2eM2cObrvtNqxevRpSqRQqlQpz586FUqmEw+HAtm3b2Lnbt28HMFS1xe12o7e3F/X19THV8NSLNVwNyn1mpVJpRMKVf/7znwm0ytjws5/9DDabDTk5OZgwYQIv3p2Ob4sWLUqxlEM0NTVBJpPBbrejqqoKcrl82PE3oQmUEAKv1wuxWIw77rgDn3/+OV5//fWzEvps+ctf/oLc3FzMmTNH0AVZLpdj8eLFWLx4Me94R0dHskQU5MILL0RJSYlg/kefzwej0Qiv15uUuqVjUZJOo9GkfEW5ZcsWTJo0CYsWLUJfXx+vZqVIJEJubi4blFLtycqlsbFx2ALZ27ZtY6q8c4Ha2lpUVlaio6OD59mqVCrZjouSaqciavtcsGAB7r777oj3abF1mkyeEMJT24aXJ1Or1bwQDYfDAZvNxq4PJxAIYO/evaivrx+2Igsw5OfR1dUVkRObq+GhE77P54NcLofJZOIVS0gV99xzDx5++GH2mqvOHxwchNVqhdlsxvnnn5/yQh9KpRK5ubnQ6XTs9x7OsTAhiT0eDzo6OqDRaFBUVISampqUe3z19/fDbrcn7LCyYsWKMZIoPoQeLIrD4YDBYEhoAjobe2i89mD6UPr9fl7HIoTAZrPB7XajoKAAoVAIpaWlKc/4RFe4Lpcroji1SCQ6ZwoOhxNegFmIurq6c2oCpSFBCoWCtzPi9kmXywWr1YpQKJTyxOHxQDUrhBCe2ee1117jnVdSUhKh8t21axdycnIikihYLBZs3bo1oRA0utgIV+0LaY3sdjskEgksFkvMii3h14dCIej1et5Y0NjYiJMnT2Lp0qVwOp3Yvn07NmzYwGJjd+zYEbXQBSXa7ywSiZCZmQmn0wmJRJLyyRMYGi9EIhHrs9xi39FIWOq2tjaYzWbceuutGD9+PG6//Xa88sorI5M4AYqKigTtrb/4xS+wYsWKqIOh0+lER0cHz2a3f/9+fP7552MmazycOHEC8+fPx5QpU7BkyRJeZ9bpdFCr1XENpMmEEILvvvsOubm5PHuMSCRCMBiEwWDA4cOHsXDhQmg0Gvz+97/HSy+9lDJ5N2/ezOSsrq7mrcjPRdshZfv27YLJH4Ah23ldXd2wA1eyqampAQDmjxCO0+nEO++8A6VSialTp6KkpETwvHMBrg00nkXWbbfdxrNnAkMTklBquuF2hYcOHcIPf/hD3jGafH7btm2YPHkydDodPB6PYAREbm4uy6E8nKr8jjvuwIYNG0AIwZkzZ3DgwAFcf/310Gq1sFqtKCgoYNmMsrKyUFFRgdWrV8Nut6O3txf/8z//E/P+APDBBx9g9uzZyM3NRUFBAW/XrFQqUV5envKMSZTGxkZ0dXXBYrHAZDKhqqpqWNkS0qNIJBLodDpeJ0iWmiCas9L1118vGFLBpaurC7t372avL7roItx///2jL2QCbNiwAV9//TXWrVuHq666KmJAl8lkvEB/Lk8//fSYl91qamrCr3/9a94ESAiBxWIRzOCi1Woxffp0zJgxg/0eqc6Ect9997Ectw0NDVHrfZ5L9k9gaKf/+eefo7GxkZeIm2awysnJwZIlS1IooTA03lYoo05WVhZmzJgBn8+HjRs3Akhd5hmRSASVSoVrrrlGMIogEAjEtN+Hl7oajWQyc+fOxeHDhyP8M+6//378x3/8B4ChZ0yr1cbUTBFCUFhYiNraWl45MSEef/xxAEMOdE6nE1KplC1qsrOzQQjhqZirqqowa9YszJgxI67JBQAee+wxXHfddbjwwgtRVVXFk93j8aS8mhCXBQsW4Pzzz8e0adNw6aWXora2dlhnzhFNoNwk4bGcT8rLy3nv5+TkYPz48Zg+fTrPVTiWkISQmIWOw2P7wqux0LjK9vZ2NDY2suNvvPFGROaZZO2WGhsbeZUYEuHkyZNYvXo1br311lGWis9///d/o729nbcD0mq18Pl8LLOMEFwnl6+++mpMZRyOr776CocOHcL27dvR1NTEU/NzV+/DJZEfaQHks6G1tZWVtOOi0Wgwbty4qIurVOJyuSCVSqOqDisrKxEMBrFr166Uxyg6nU7s2LEDe/bsifAappVNhCZRsVg86uYfnU6H1atX8yrCAMD69evxzDPPYPny5ey83NxcZGZm8lJnUpkHBgag1+uHDf4Hhibs2tpatLa2YnBwEIQQFBQU8DQbMpmMt4CjifdzcnJYGbhYBSPmz58fNd1oIBDAt99+i61bt+Lw4cPnhDZCqVRCrVZj/PjxGD9+PPLz84fVQCScSIHr1GKxWFgeRyE6Ozvx9ddf8wYgvV6PDz/8EEeOHMHKlSvxwAMP8K7p7u5GaWkpAGDNmjV46623cO+990b9jFtvvRW33HILqqqqWAFcbsfKyMjAtGnTUFZWBpVKhZ6eHhBCUFpaCrfbjYsvvhiVlZWYNWsWHn74YbbaG03+93//F0uWLGGTywsvvIDLLrsMtbW1KCwshEKhYAN6KBSCwWCAx+MRrFE4ZcqUYQf0pUuX4ne/+x0cDkfEQylEU1NTxIC8du3aiPPkcjnGjRsHpVLJ6/DU6cLr9aKtrQ0VFRVx1QKtr69Hd3c39Ho97HY7du7ciW+++SbCqSk7Oxvvv/8+pkyZwmuT4dSwJ06cQEFBARYuXBjxHteJJVpqNi60zadMmYKioiLMnj0bv//97wVloeeePHkSq1atgtvtRnFxMS644ALMmzcPF1100bCy03CH8CLgpaWl7PmIh7P10o5mzxSC7pC4ISFcqNr22LFjKddOUMrLywVDVoR20QqFApmZmby+w20ft9stOHlRx554WbBgAY4dO8ZqjFJZaApSmuyee89QKMQ8oA0GA4qLi2NmiTt48CC+/fZbNDY2oqamBlVVVRGpQzUaDc+GSceo7777Dlu2bMGPf/xjlJSU8GJkuchkMpw5cyZCvQ2AeWNLpVIYDAasX78+5V7DGzduxLJlyxLyPTkry61Wq8WhQ4difmC4Hr6wsBDTp0+HTqfDLbfcwo53dXVh//79sNvtuOeeewAMZTeZOHFizGwrl1xyCSoqKqDT6aDVaqHRaCISnavVaojFYpYJxeVyIT8/H0VFRVi6dCn6+vpYRyGEoKKiYtRiqObPnw+lUgmXy4VVq1ahvb0dV155JcaNGwe1Wg2NRhMRq0hLr7W1tUUt8nz69OmoFVnWrVs3bJ3WLVu2YP369di6dWtCuxmxWAypVMprY5FIxFJzZWZmwmg0xhXErdFokJuby9L/jR8/HsuWLcOBAwfw8ccfo729HatWrcLy5csxZ84cDA4Owmg0QqFQQKPR4LHHHouajSkvLw92uz2uerWJBPW/8847mD17doRt8sknn8S7777L8+7OycnBihUrUFVVFXeFe2CoOHO4HSwWb775Jv793/9d8L3i4mL09fVh586dWL58Oc8UsnXrVpSUlMBms7FQAplMxhZH4V7tK1euxB/+8IeIz5g7dy7vdawcrDU1NVi0aBGuuOKKlOZKVqlUePLJJ6NmIxLiyiuvxOeff4777rtP8P3u7m6W7IBLoqrqXbt2ARia5KZPnw6Px4Of/vSnMRcdNPctdXiyWq3DptJsbm5GUVERK8AtBPe40WhEUVERpk2bhlAohNzcXMybNy/q2KxUKtHY2AipVIqqqqqIfqHVapGRkYHp06eDEIKFCxcy9X4quPnmmxO+5qx9yWO5o8+dOzciNkkkEqG6ujrioVu3bh3+9re/sTgpYMh9u6ysLKa976KLLkJFRQXy8vJQWFgo+PAqlUo2sdJkCrQDXHLJJVAoFLw0bh0dHaxE15133jlsG3DRaDR4+OGHsXHjRgQCATz44IPMe/muu+7CSy+9hAULFqC6uhq5ublQKpU8e6JIJGIVWhobG/HWW2/hN7/5Df785z+zIr1r1qwRrGpPB2nupCEUnqFQKHDDDTfgo48+imsAaWhowMGDB7F3796oyQmoJ11mZibMZnPcZe6oU4FGo8G8efNw66234t5778Vrr72Gt99+G2vWrGE7RIfDgePHj2PLli0AwIvFC0en0yVUX5AQgl/96lcxz9m+fTtycnIEPQbnzp2L9957j6eafPfdd9HX18frW3a7nZkZwr05gaGHeP369XHLDQx5lAvtsoEhjY9IJMKCBQvQ19fH+jUhBIsXL8bs2bOxcOFCdowWNiCE4NixY8wr8cMPP8TatWsjtB90wcMl1oK6oqIC1157LZYtW8ZqaHLJzs4WnKQpW7Zs4U1I48aNE8wck5OTE7UY8gcffAC9Xo9f/vKXUT9HiHnz5sW0jba3tw+bma2zs5N3js1mQ2NjI1pbWyPufeGFF+JnP/sZ/vGPf+DRRx+Nmf6QepXT9HMej4cX9xxObW0turu7UVhYGBFbHE3DRfu2VCrF7NmzkZOTE7PgRUZGBlpbW1FXVweTyRQRKSGXy1lZNoVCIbj44EI9vIX6zXBQZ6lPP/004WtjIUrEviMSiUwAUhtAGR8VhJB84P+fzP+P5AXSMieLtMzJ4f+bzOlxLjmwdg4noQk0TZo0adKkSTPEuZuFOk2aNGnSpDmHSU+gadKkSZMmzQhIT6Bp0qRJkybNCEhPoGnSpEmTJs0ISE+gadKkSZMmzQhIT6Bp0qRJkybNCEhPoGnSpEmTJs0ISE+gadKkSZMmzQhIT6Bp0qRJkybNCPg/Qo1Vgv7hbr0AAAAASUVORK5CYII=\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%time highres_pca = PCA(.99).fit(x_train)\n", "highres_data = highres_pca.transform(x_train)\n", "highres_gm = GaussianMixture(150, random_state=42)\n", "%time highres_gm.fit(highres_data[y_train == 1])\n", "draw_gm_sample(highres_gm, highres_pca, n=10)\n", "for i in range(10):\n", " highres_gm.fit(highres_data[y_train == i])\n", " draw_gm_sample(highres_gm, highres_pca, n=10)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }