{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "bdc1e7d8-503b-4f40-a90b-05590d68bed8", "metadata": { "tags": [ "remove-cell" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "---------------------------------\n", "Working on the host: Joachims-MacBook-Pro.local\n", "\n", "---------------------------------\n", "Python version: 3.10.2 | packaged by conda-forge | (main, Feb 1 2022, 19:30:18) [Clang 11.1.0 ]\n", "\n", "---------------------------------\n", "Python interpreter: /opt/miniconda3/envs/srh/bin/python\n" ] } ], "source": [ "%matplotlib inline\n", "# Load the \"autoreload\" extension\n", "%load_ext autoreload\n", "# always reload modules\n", "%autoreload 2\n", "# black formatter for jupyter notebooks\n", "#%load_ext nb_black\n", "# black formatter for jupyter lab\n", "%load_ext lab_black\n", "\n", "%run ../../src/notebook_env.py" ] }, { "cell_type": "markdown", "id": "cb9f6c7b-87ad-4641-96f6-843b463201cc", "metadata": {}, "source": [ "# Polynomiale Regression" ] }, { "cell_type": "code", "execution_count": 2, "id": "0aa8b22b-6c3a-4a5d-b3b6-e2ae3aae7175", "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "from sklearn.linear_model import LinearRegression\n", "from sklearn.model_selection import train_test_split\n", "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.metrics import mean_squared_error\n", "import statsmodels.api as sm" ] }, { "cell_type": "markdown", "id": "a594c395-2905-41f3-9a6a-932c64567467", "metadata": { "tags": [] }, "source": [ "Die polynomiale Regression ist eine spezielle Art der linearen Regression, bei der die Beziehung zwischen der unabhängigen Variablen $x$ und der abhängigen Variablen $y$ durch ein Polynom $n$-ten Grades in $x$ modelliert wird. Mit anderen Worten, wir nehmen neben dem ursprünglichen linearen Term auch Potenzen zweiter Ordnung und höherer Potenzen einer Variablen in das Modell auf. Die Einbeziehung von Polynomen $n$-ten Grades führt zu einer nichtlinearen Beziehung zwischen $y$ und $x$, aber das Modell ist immer noch ein lineares Modell, da die Beziehung zwischen den Koeffizienten ($\\beta_i$) und den erwarteten Beobachtungen linear ist. Somit kann die Modellgleichung wie folgt geschrieben werden" ] }, { "cell_type": "markdown", "id": "a8de333c-6b0e-4997-ba37-597804a4633b", "metadata": {}, "source": [ "$$\\hat y = \\beta_0+\\beta_1x+\\beta_2x^2+...+\\beta_kx^k+\\epsilon\\text{.}$$" ] }, { "cell_type": "markdown", "id": "f77b0617-df86-4bf3-ad7d-d969f32a1429", "metadata": {}, "source": [ "Die Werte der Koeffizienten werden durch Anpassung des Polynoms an die Beobachtungsdaten ($y$) bestimmt. Wie bei der einfachen linearen Regression, die im vorigen Abschnitt behandelt wurde, geschieht dies durch Minimierung der **Summe der quadrierten Fehler ($SSE$)**, die durch folgende Gleichung gegeben ist" ] }, { "cell_type": "markdown", "id": "cc4d61bf-05c2-4876-97b2-9add5d96b348", "metadata": {}, "source": [ "$$SSE = \\sum e^2 = \\sum (\\hat y - y)^2\\text{.}$$" ] }, { "cell_type": "markdown", "id": "8f1ae4d7-4b35-40da-bbfe-2144b2456b07", "metadata": {}, "source": [ "Bei der Anpassung eines Polynoms an Beobachtungen stellt sich das Problem der Wahl der Ordnung $k$ des Polynoms. Wie man die richtige Zahl für das Polynom wählt, ist eine Frage eines wichtigen Konzepts, das **Modellauswahl** oder **Informationskriterium** genannt wird. Der Einfachheit halber verwenden wir die Wurzel des mittleren quadratischen Fehlers (root-mean-square error, RMSE), definiert durch" ] }, { "cell_type": "markdown", "id": "af57342b-904c-4a38-afce-790e913a756c", "metadata": {}, "source": [ "$$RMSE = \\sqrt{\\frac{\\sum_{i=1}^n (\\hat y - y)^2}{n}}$$" ] }, { "cell_type": "markdown", "id": "70ae8de5-20d9-4366-a39d-c033bf9fee97", "metadata": {}, "source": [ "um die Eignung des Modells zu bewerten." ] }, { "cell_type": "markdown", "id": "0b48b978-1f10-4421-ad5e-54a72ce9b33c", "metadata": {}, "source": [ "## Polynomiale Regression\n", "----------------------------------------" ] }, { "cell_type": "markdown", "id": "ab34d38b-7e6c-4bf4-92c4-cc31a0997eda", "metadata": {}, "source": [ "Wir beginnen mit unserer Übung, indem wir Daten sammeln. Die Daten werden von einer Funktion generiert, die Sie nicht kennen. Diese Vorbedingung macht das Beispiel realistischer, da wir in realen Anwendungen die genauen Spezifikationen des zugrunde liegenden Datenerzeugungsprozesses nicht kennen. Am Ende dieses Abschnitts lüften wir das Geheimnis des Datengenerierungsprozesses.\n", "\n", "Dies sind die Daten, unsere Beobachtungen, in tabellarischer Form. Wir haben $25$ Datenpunkte, jeder Datenpunkt ist ein ($x,y$) Paar." ] }, { "cell_type": "code", "execution_count": 3, "id": "38f1c8b4-a553-42ae-b1c3-3e3031b2a22a", "metadata": {}, "outputs": [], "source": [ "n = 25\n", "np.random.seed(4)\n", "x = np.random.uniform(0, 1, n)\n", "y = np.sin(2 * np.pi * x) + np.random.normal(0, 0.35, n)\n", "poly_data = pd.DataFrame({\"x\": x, \"y\": y})" ] }, { "cell_type": "markdown", "id": "4f177885-a074-4025-881f-d2165e1e8cc7", "metadata": {}, "source": [ "Hier sind die Daten in Form eines Streudiagramms dargestellt:" ] }, { "cell_type": "code", "execution_count": 4, "id": "1f83c90b-4e72-4499-90e2-0da206ed7def", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "X = poly_data[\"x\"]\n", "y = poly_data[\"y\"]\n", "ax.scatter(X, y, edgecolor=\"k\", color=\"white\")\n", "ax.set_xlabel(\"x\")\n", "ax.set_ylabel(\"y\")" ] }, { "cell_type": "markdown", "id": "2237a4db-c443-46bf-9566-38cd269f9583", "metadata": {}, "source": [ "### Anpassen einer Kurve in Python: Die Notation in Python" ] }, { "cell_type": "markdown", "id": "e59d4813-60c4-414a-a309-a2872c3368dd", "metadata": { "tags": [] }, "source": [ "Python bietet leistungsstarke Funktionen zur Anpassung eines Polynoms an Daten. Um ein $k$-dimensionales Polynom anzupassen, verwenden wir `linear_model` aus dem `sklearn` Paket und fügen dem Funktionsaufruf `LinearRegression()` zusätzliche `PolynomialFeatures` hinzu. Darüber hinaus gibt es zwei verschiedene Möglichkeiten, eine polynomiale Regression zu kodieren.\n", "\n", "Für ein Polynom $2$. Ordnung besteht die erste Möglichkeit darin, `model.predict(X-werte)` einzugeben und zu plotten, und die zweite Möglichkeit ist die Koeffizienten mit `model.coef_` aus dem Model auszulesen und daraus äquivalent zu $\\hat y = \\beta_0+\\beta_1x+\\beta_2x^2+...+\\beta_kx^k+\\epsilon$ , `model.coef_[0][0] + model.coef_[0][1] * X-werte + model.coef_[0][2] * (X-werte)**2 + ...` zu konstruieren.\n", "\n", "Um die Verwirrung zu lindern, zeigen wir ein Beispiel in Python. Wir konstruieren zwei Polynome der Ordnung $2$ für `poly_data`." ] }, { "cell_type": "code", "execution_count": 5, "id": "9229c076-f64a-4e95-b10b-29dfa7b13442", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "LinearRegression()" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X = poly_data[\"x\"].values.reshape(-1, 1)\n", "y = poly_data[\"y\"].values.reshape(-1, 1)\n", "\n", "# Polynomialer Fit\n", "poly = PolynomialFeatures(degree=2)\n", "X_poly = poly.fit_transform(X)\n", "\n", "model = LinearRegression()\n", "model.fit(X_poly, y)" ] }, { "cell_type": "markdown", "id": "28f17a60-c9b9-41de-adaa-7a1558ac68e7", "metadata": {}, "source": [ "Zum Auslesen der Koeffizienten und des Achsenabschnitts des Modells verwenden wir das Attribut `coef_` und `intercept_`." ] }, { "cell_type": "markdown", "id": "8291b22e-4656-4f74-a3fc-04051dde047d", "metadata": {}, "source": [ "Wir überprüfen die Ergebnisse des Modells." ] }, { "cell_type": "code", "execution_count": 6, "id": "c23d4958-734b-4653-9050-65e779678ce8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Achsenabschnitt: [1.07678298]\n", "Koeffizienten: [[ 0. -2.45381544 0.82240915]]\n" ] } ], "source": [ "print(f\"Achsenabschnitt: {model.intercept_}\")\n", "print(f\"Koeffizienten: {model.coef_}\")" ] }, { "cell_type": "markdown", "id": "bc4c256c-64ef-4e76-a319-a17abf6d6208", "metadata": {}, "source": [ "Bei der Ausgabe der Koeffizienten dient der nullte Koeffizient als Platzhalter für den Achsenabschnitt und kann daher ignoriert werden. Setzen wir nun die Parameter in die Gleichung ein, erhalten wir die Regressionslinie." ] }, { "cell_type": "code", "execution_count": 7, "id": "b868bf8c-292b-4c01-9adf-f3dc5a9ee89a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Definiere x- Achse zur Vorhersage von Datenpunkten\n", "x_axis = np.linspace(0, 1, 50)\n", "# Konstruiere Regressionslinie\n", "regline = (\n", " model.intercept_ + model.coef_[0][1] * x_axis + model.coef_[0][2] * x_axis**2\n", ")\n", "\n", "fig, ax = plt.subplots()\n", "ax.scatter(poly_data[\"x\"], poly_data[\"y\"], label=\"Beobachtungen\")\n", "ax.plot(x_axis, regline, label=\"Regressionlinie\")\n", "ax.legend()" ] }, { "cell_type": "markdown", "id": "be62f4e8-dc97-4a90-8461-47a73ac9a1cb", "metadata": {}, "source": [ "Andererseits können wir die Regressionslinie auch mit der Methode `predict()` für beliebige $x$-Werte erzeugen." ] }, { "cell_type": "code", "execution_count": 8, "id": "2e218397-a02a-40a1-8fcb-af045e2d194e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X_poly = poly.transform(x_axis.reshape(-1, 1))\n", "regline = model.predict(X_poly)\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(x_axis, regline, label=\"Regressionlinie\")\n", "ax.scatter(x=X, y=y, label=\"Beobachtungen\")\n", "ax.legend()" ] }, { "cell_type": "markdown", "id": "494cbb47-8437-4604-a2fc-08785e9d48f9", "metadata": { "tags": [] }, "source": [ "### Anpassen einer Kurve in Python (Fortsetzung)" ] }, { "cell_type": "markdown", "id": "f7872c85-87e8-48e8-a5dd-28fedd2fc1c3", "metadata": {}, "source": [ "Da wir nun die Notation in Python kennen, beginnen wir mit der Erstellung von $6$ verschiedenen Modellen, mit $k=1,2,3,5,9,12$. Für jedes Modell berechnen wir den $RMSE$. Schließlich stellen wir die Daten zusammen mit der Regressionslinie dar, die durch jedes einzelne Modell gegeben ist. Der Einfachheit halber konstruieren wir eine Schleife, um den Kodierungsaufwand zu verringern." ] }, { "cell_type": "code", "execution_count": 9, "id": "b6a7a620-af33-406c-ba04-89204ebda159", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "RMSE = []\n", "X = poly_data[\"x\"].values.reshape(-1, 1)\n", "y = poly_data[\"y\"].values.reshape(-1, 1)\n", "x_axis = np.linspace(0, 1, 25)\n", "\n", "orders = [1, 2, 3, 5, 9, 12]\n", "\n", "fig, ax = plt.subplots(figsize=(16, 18), ncols=2, nrows=3)\n", "ax = np.ravel(ax)\n", "for e, order in enumerate(orders):\n", " poly = PolynomialFeatures(degree=order)\n", " X_poly = poly.fit_transform(X)\n", " model = LinearRegression()\n", " model.fit(X_poly, y)\n", " y_hat = model.predict(X_poly)\n", " mse = mean_squared_error(y, y_hat)\n", " rmse = np.sqrt(mse)\n", " RMSE.append(rmse)\n", "\n", " X_poly = poly.transform(x_axis.reshape(-1, 1))\n", " regline = model.predict(X_poly)\n", " ax[e].plot(x_axis, regline, label=f\"Regressionslinie der {order}. Ordnung\")\n", " ax[e].scatter(x=X, y=y, label=\"Beobachtungen\")\n", " ax[e].text(s=f\"RMSE (k={order}): {np.round(rmse, 4)}\", y=0.8, x=0.5, size=18)\n", " ax[e].legend()" ] }, { "cell_type": "markdown", "id": "aae4e9b4-3f5f-49e3-b8f8-94b65dbfe255", "metadata": {}, "source": [ "Fantastische Diagramme! Die Abbildung zeigt, dass wenn wir $k$, die Ordnung des Polynoms, erhöht, wird die Kurve flexibler und passt immer besser zu den Daten. Je besser die Daten angepasst werden, desto geringer wird der Fehler, $RMSE$.\n", "\n", "Der Einfachheit halber plotten wir den $RMSE$ gegen $k$." ] }, { "cell_type": "code", "execution_count": 10, "id": "3343ae40-6a75-4c24-95d9-688cff887e03", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 0, 'k-te Ordnung')" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.plot(orders, RMSE)\n", "ax.set_ylabel(\"RMSE\")\n", "ax.set_xlabel(\"k-te Ordnung\")" ] }, { "cell_type": "markdown", "id": "83671afe-7877-4f22-b910-57b11a2fb568", "metadata": {}, "source": [ "Daher stellt sich wieder einmal die Frage, welches Polynom am besten zu den Daten passt. Glauben wir, dass das Polynom der Ordnung $9$ am besten zu dem zugrunde liegenden Datenerzeugungsprozess passt? Obwohl wir eine hervorragende Anpassung an die Beobachtungsdaten erhalten, indem wir die Ordnung des Polynoms erhöhen, bleibt es fraglich, ob das Polynom hoher Ordnung gut verallgemeinert werden kann. Stellen Sie sich vor, wir führen eine neue Messreihe durch und erhalten neue Daten. Glauben Sie, dass die wild schwingende Kurve eines Polynoms hoher Ordnung immer noch gut zu den Daten passt? Nein, wahrscheinlich nicht!\n", "\n", "Dieses Verhalten wird als Überanpassung bezeichnet. Erinnern Sie sich daran, dass das Ziel darin besteht, die Parameter aus den Daten zu lernen. Wir sind also daran interessiert, eine gute Verallgemeinerung des Modells zu erreichen und nicht unbedingt perfekt angepasste Beobachtungsdaten." ] }, { "cell_type": "markdown", "id": "d839a8bf-3da1-48ec-849f-23f99d6dbe82", "metadata": {}, "source": [ "### Aus den Daten lernen" ] }, { "cell_type": "markdown", "id": "a0c88d1d-1481-412e-8bb5-b72dae29e192", "metadata": {}, "source": [ "Wie können wir das Problem lösen? Wie bestimmen wir das beste Polynom $n$-ter Ordnung für unseren Datensatz? Nun, es gibt viele Methoden und Strategien, um einer Überanpassung entgegenzuwirken. In diesem Abschnitt verfolgen wir einen einfachen Ansatz. Zunächst teilen wir den Datensatz in zwei Teile auf. Einen Teil nennen wir **Trainingsmenge**, den anderen Teil nennen wir **Validierungsmenge**. Dann verwenden wir alle Daten des Trainingssatzes, um die Modellparameter $\\beta_i$ zu lernen, und zwar auf die gleiche Weise wie oben. Danach wenden wir das gelernte Modell an, um die Daten des Validierungssatzes vorherzusagen, und bewerten die Leistung des Modells, indem wir den $RMSE$ berechnen. Wir verwenden also die Validierungsmenge, um die, durch $k$ gegebene, Komplexität des Modells zu optimieren.\n", "\n", "Leider brauchen wir, wenn wir aus Daten lernen wollen, letztendlich auch Daten, aus denen wir lernen können. Bislang haben wir mit $25$ Beobachtungen gearbeitet. Das ist nicht viel. In realen Anwendungen müssten wir wahrscheinlich neue Beobachtungen durch eine neue Messreihen gewinnen. In unserer Übung können wir jedoch relativ leicht mehr Daten erzeugen. Daher setzen wir dieses Beispiel mit einem neuen Datensatz von $150$ Beobachtungen fort.\n", "\n", "Lassen Sie uns die Daten plotten!" ] }, { "cell_type": "code", "execution_count": 11, "id": "88703357-aace-4874-b042-7af41c8144be", "metadata": {}, "outputs": [], "source": [ "n = 150\n", "np.random.seed(415)\n", "x = np.random.uniform(0, 1, n)\n", "y = np.sin(2 * np.pi * x) + np.random.normal(0, 0.3, n)\n", "new_poly_data = pd.DataFrame({\"x\": x, \"y\": y})" ] }, { "cell_type": "code", "execution_count": 12, "id": "ea3e649d-4690-4ebb-b0dc-987e8832f249", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "new_poly_data.plot.scatter(x=\"x\", y=\"y\")" ] }, { "cell_type": "markdown", "id": "83d0c05d-7cc2-44d0-922d-9fc6fc77af43", "metadata": {}, "source": [ "### Trainings- und Validierungsmenge" ] }, { "cell_type": "markdown", "id": "efa03b8d-35dd-4052-9798-fe28c1da2f28", "metadata": {}, "source": [ "Nun sind wir bereit, unsere Trainings- und Validierungsmenge zu erstellen. Dazu verwenden wir die Funktion `train_test_split()` aus dem `sklearn`-Paket. Wir teilen die Daten so auf, dass $65 \\%$ der Daten dem Trainingsset und der Rest, $35 \\%$ der Daten, dem Validationsset zugewiesen werden." ] }, { "cell_type": "code", "execution_count": 13, "id": "0c7425c9-dabc-43f3-b2c2-59fe2df04fba", "metadata": {}, "outputs": [], "source": [ "X = new_poly_data.x.values.reshape(-1, 1)\n", "y = new_poly_data.y.values.reshape(-1, 1)\n", "X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.35, random_state=42)" ] }, { "cell_type": "code", "execution_count": 14, "id": "9e4416de-aa43-486a-88c1-8763c02f3842", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Trainingset\n", "X_train: (97, 1)\n", "y_train: (97, 1)\n", "\n", "Validierungsset\n", "X_val: (53, 1)\n", "y_val: (53, 1)\n" ] } ], "source": [ "# Überprüfen der Dimension von Training und Validierungsdatensatz\n", "print(\"Trainingset\")\n", "print(f\"X_train: {np.shape(X_train)}\")\n", "print(f\"y_train: {np.shape(y_train)}\")\n", "\n", "print(\"\\nValidierungsset\")\n", "print(f\"X_val: {np.shape(X_val)}\")\n", "print(f\"y_val: {np.shape(y_val)}\")" ] }, { "cell_type": "code", "execution_count": 15, "id": "6a651aad-94b5-45cf-bc8c-d0143f03430d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot\n", "plt.scatter(X_train, y_train, label=\"Trainingsdaten\", color=\"blue\")\n", "plt.scatter(X_val, y_val, label=\"Validierungsdaten\", color=\"red\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "id": "cf805597-9666-47ac-a16a-2ff3da7eac0a", "metadata": {}, "source": [ "### Modellbildung und Modellbewertung" ] }, { "cell_type": "markdown", "id": "c688717d-8b6d-49f5-934c-b7b1bfdf66d7", "metadata": {}, "source": [ "In dieser Übung werden wir $10$ Modelle mit $k=1,2,...,10$ erstellen. Wir bewerten jedes der $10$ polynomialen Regressionsmodelle, indem wir den $RMSE$ auf dem Trainingssatz berechnen. Nach der Erstellung des Modells und der Ermittlung der Modellparameter $\\beta_i$ verwenden wir das Modell, um die Antwortvariable in der Validierungsmenge vorherzusagen. Auch hier stützen wir uns auf den $RMSE$, um die Vorhersagen für den Validierungssatz zu bewerten. Schließlich stellen wir den $RMSE$ jedes Modells sowohl für die Trainingsmenge als auch für die Validierungsmenge dar. Anhand des $RMSE$ bewerten wir die Generalisierung des Modells." ] }, { "cell_type": "code", "execution_count": 16, "id": "ff9296cc-f47a-4a57-8ae4-3cb613da0455", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "RMSE train (k=1): 0.554\n", "RMSE val (k=1): 0.539\n", "------------------------\n", "RMSE train (k=2): 0.553\n", "RMSE val (k=2): 0.538\n", "------------------------\n", "RMSE train (k=3): 0.312\n", "RMSE val (k=3): 0.324\n", "------------------------\n", "RMSE train (k=4): 0.306\n", "RMSE val (k=4): 0.329\n", "------------------------\n", "RMSE train (k=5): 0.284\n", "RMSE val (k=5): 0.344\n", "------------------------\n", "RMSE train (k=6): 0.282\n", "RMSE val (k=6): 0.346\n", "------------------------\n", "RMSE train (k=7): 0.282\n", "RMSE val (k=7): 0.345\n", "------------------------\n", "RMSE train (k=8): 0.282\n", "RMSE val (k=8): 0.345\n", "------------------------\n", "RMSE train (k=9): 0.282\n", "RMSE val (k=9): 0.345\n", "------------------------\n", "RMSE train (k=10): 0.282\n", "RMSE val (k=10): 0.345\n", "------------------------\n" ] } ], "source": [ "rmse_train = []\n", "rmse_val = []\n", "\n", "for order in range(1, 11):\n", " # Polynomial Fit\n", " poly = PolynomialFeatures(degree=order)\n", " X_train_poly = poly.fit_transform(X_train) # .reshape(-1, 1)\n", " X_val_poly = poly.fit_transform(X_val) # .reshape(-1, 1)\n", " model = LinearRegression()\n", " model.fit(X=X_train_poly, y=y_train)\n", "\n", " # Berechne RMSE - Trainingsset\n", " mse = mean_squared_error(y_train, model.predict(X_train_poly))\n", " rmse = np.sqrt(mse)\n", " print(f\"RMSE train (k={order}): {np.round(rmse,3)}\")\n", " rmse_train.append(rmse)\n", "\n", " # Berechne RMSE - Validierungsset\n", " mse = mean_squared_error(y_val, model.predict(X_val_poly))\n", " rmse = np.sqrt(mse)\n", " print(f\"RMSE val (k={order}): {np.round(rmse,3)}\")\n", " rmse_val.append(rmse)\n", " print(\"------------------------\")" ] }, { "cell_type": "code", "execution_count": 17, "id": "93cf36ed-19a2-461e-8572-6e87d49cca6f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "k = range(1, 11)\n", "fig, ax = plt.subplots()\n", "ax.plot(k, rmse_train, label=\"Trainingsset\", color=\"blue\")\n", "ax.plot(k, rmse_val, label=\"Validierungsset\", color=\"red\")\n", "ax.set_ylabel(\"RMSE\")\n", "ax.set_xlabel(\"k-te Ordnung\")\n", "ax.legend()" ] }, { "cell_type": "markdown", "id": "dd9f5b48-bc87-45a4-b6c7-f2e68b737fc8", "metadata": {}, "source": [ "Die Abbildung zeigt, dass der Fehler bei den Trainingsdaten (blaue Linie) stetig abnimmt. Das macht durchaus Sinn, denn je komplexer das Modell wird, indem $k$ erhöht wird, desto besser passt das Modell zu den Trainingsdaten. Das gleiche Verhalten haben wir im obigen Abschnitt beobachtet, als wir unser Modell mit nur $25$ Beobachtungen trainiert haben. Wenn wir uns den $RMSE$ für den Validierungssatz (rote Linie) ansehen, sehen wir, dass mit zunehmendem $k$ und damit zunehmender Modellkomplexität der Fehler abnimmt. Es gibt jedoch einen \"Sweet Spot\", der durch den niedrigsten $RMSE$ angezeigt wird, an dem das Modell gerade komplex genug ist, um auf den bisher ungesehenen Validierungsdaten gut zu generalisieren. Wenn die Modellkomplexität weiter zunimmt, beginnt auch der $RMSE$ zu steigen. Dies deutet auf eine Überanpassung des Modells hin. Das Modell merkt sich also die Daten in der Trainingsmenge gut, aber die Vorhersagekraft des Modells für bisher ungesehene Daten, wie die Daten der Validierungsmenge, wird schlechter. Ein Blick auf die obige Abbildung zeigt, dass der niedrigste Fehler im Validierungssatz, der so genannte Sweet Spot, für ein Regressionsmodell $3$-ter Ordnung erreicht wird." ] }, { "cell_type": "markdown", "id": "7340a352-7422-43b3-bb43-1909056b7e7d", "metadata": {}, "source": [ "### Vorstellung des Modells" ] }, { "cell_type": "markdown", "id": "c6c973fb-191a-45fd-85c9-51f846e515c5", "metadata": {}, "source": [ "Im vorangegangenen Abschnitt haben wir festgestellt, dass ein polynomiales Regressionsmodell der Ordnung $3$ in der Validierungsgruppe am besten funktioniert. Nun stellen wir dieses Modell auf dem gesamten Datensatz dar, um seine Qualität visuell zu bewerten. Außerdem stellen wir die Funktion dar, die dem Prozess der Datengenerierung zugrunde liegt.\n", "\n", "> __Datenerzeugung:__ Die Eingabewerte $x_n$ für die zugrundeliegende Funktion werden gleichmäßig im Bereich $U(0,1)$ erzeugt, und die entsprechenden Zielwerte $y$ erhält man, indem man zunächst die entsprechenden Werte der Funktion $\\sin( \\pi x )$ berechnet und dann zufälliges Rauschen mit einer Gaußschen Verteilung mit einer Standardabweichung von $0,35$ hinzufügt." ] }, { "cell_type": "code", "execution_count": 18, "id": "76463a18-ec40-488f-9e59-d8c2556a0791", "metadata": {}, "outputs": [], "source": [ "# Erzeuge Daten\n", "n = 100\n", "np.random.seed(4)\n", "x = np.random.uniform(0, 1, n)\n", "y = np.sin(2 * np.pi * x) + np.random.normal(0, 0.35, n)\n", "raw_data = pd.DataFrame({\"x\": x, \"y\": y})" ] }, { "cell_type": "code", "execution_count": 19, "id": "2bd5972a-2160-483e-a49a-5a1cb7aa07f3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X = raw_data[\"x\"].values.reshape(-1, 1)\n", "y = raw_data[\"y\"].values.reshape(-1, 1)\n", "\n", "# Polynomial Fit\n", "poly = PolynomialFeatures(degree=3)\n", "X_poly = poly.fit_transform(X)\n", "model = LinearRegression()\n", "model.fit(X_poly, y)\n", "\n", "x_axis = np.linspace(0, 1, 150)\n", "x_axis_poly = poly.fit_transform(x_axis.reshape(-1, 1))\n", "y_reg_line = model.predict(x_axis_poly)\n", "\n", "\n", "fig, ax = plt.subplots()\n", "ax.scatter(X, y, label=\"Stichprobe\")\n", "ax.plot(x_axis, y_reg_line, label=\"Regressionslinie\")\n", "ax.plot(x_axis, np.sin(2 * np.pi * x_axis), label=\"Datenerzeugungsfunktion\")\n", "ax.legend()" ] }, { "cell_type": "markdown", "id": "a85fd729-4b62-477a-ae3e-c40d555c4a6c", "metadata": {}, "source": [ "Die Abbildung zeigt, dass unser Modell die Daten gut abbildet und wir daher recht zufrieden damit sein können." ] }, { "cell_type": "code", "execution_count": null, "id": "5745125c-5739-4a16-875e-ccc854e8ae9b", "metadata": {}, "outputs": [], "source": [] } ], "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": "3.10.2" }, "vscode": { "interpreter": { "hash": "31f2aee4e71d21fbe5cf8b01ff0e069b9275f58929596ceb00d14d90e3e16cd6" } } }, "nbformat": 4, "nbformat_minor": 5 }