{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Uczenie maszynowe\n", "# 6. Problem nadmiernego dopasowania" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 6.1. Regresja wielomianowa" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Wprowadzenie: wybór cech" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Niech naszym zadaniem będzie przewidzieć cenę działki o kształcie prostokąta.\n", "\n", "Jakie cechy wybrać?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" } }, "source": [ "Możemy wybrać dwie cechy:" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ " * $x_1$ – szerokość działki, $x_2$ – długość działki:\n", "$$ h_{\\theta}(\\vec{x}) = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" } }, "source": [ "...albo jedną:" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ " * $x_1$ – powierzchnia działki:\n", "$$ h_{\\theta}(\\vec{x}) = \\theta_0 + \\theta_1 x_1 $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" } }, "source": [ "Można też zauważyć, że cecha „powierzchnia działki” powstaje przez pomnożenie dwóch innych cech: długości działki i jej szerokości." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" } }, "source": [ "**Wniosek:** możemy tworzyć nowe cechy na podstawie innych poprzez wykonywanie na nich różnych operacji matematycznych." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Regresja wielomianowa" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" } }, "source": [ "W regresji wielomianowej będziemy korzystać z cech, które utworzymy jako potęgi cech wyjściowych." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "# Przydatne importy\n", "\n", "import ipywidgets as widgets\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas\n", "\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "# Przydatne funkcje\n", "\n", "\n", "def cost(theta, X, y):\n", " \"\"\"Wersja macierzowa funkcji kosztu\"\"\"\n", " m = len(y)\n", " J = 1.0 / (2.0 * m) * ((X * theta - y).T * (X * theta - y))\n", " return J.item()\n", "\n", "\n", "def gradient(theta, X, y):\n", " \"\"\"Wersja macierzowa gradientu funkcji kosztu\"\"\"\n", " return 1.0 / len(y) * (X.T * (X * theta - y))\n", "\n", "\n", "def gradient_descent(fJ, fdJ, theta, X, y, alpha=0.1, eps=10**-5):\n", " \"\"\"Algorytm gradientu prostego (wersja macierzowa)\"\"\"\n", " current_cost = fJ(theta, X, y)\n", " logs = [[current_cost, theta]]\n", " while True:\n", " theta = theta - alpha * fdJ(theta, X, y)\n", " current_cost, prev_cost = fJ(theta, X, y), current_cost\n", " if abs(prev_cost - current_cost) > 10**15:\n", " print(\"Algorithm does not converge!\")\n", " break\n", " if abs(prev_cost - current_cost) <= eps:\n", " break\n", " logs.append([current_cost, theta])\n", " return theta, logs\n", "\n", "\n", "def plot_data(X, y, xlabel, ylabel):\n", " \"\"\"Wykres danych (wersja macierzowa)\"\"\"\n", " fig = plt.figure(figsize=(16 * 0.6, 9 * 0.6))\n", " ax = fig.add_subplot(111)\n", " fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n", " ax.scatter([X[:, 1]], [y], c=\"r\", s=50, label=\"Dane\")\n", "\n", " ax.set_xlabel(xlabel)\n", " ax.set_ylabel(ylabel)\n", " ax.margins(0.05, 0.05)\n", " plt.ylim(y.min() - 1, y.max() + 1)\n", " plt.xlim(np.min(X[:, 1]) - 1, np.max(X[:, 1]) + 1)\n", " return fig\n", "\n", "\n", "def plot_fun(fig, fun, X):\n", " \"\"\"Wykres funkcji `fun`\"\"\"\n", " ax = fig.axes[0]\n", " x0 = np.min(X[:, 1]) - 1.0\n", " x1 = np.max(X[:, 1]) + 1.0\n", " Arg = np.arange(x0, x1, 0.1)\n", " Val = fun(Arg)\n", " return ax.plot(Arg, Val, linewidth=\"2\")\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "# Wczytanie danych (mieszkania) przy pomocy biblioteki pandas\n", "\n", "alldata = pandas.read_csv(\n", " \"data_flats.tsv\", header=0, sep=\"\\t\", usecols=[\"price\", \"rooms\", \"sqrMetres\"]\n", ")\n", "data = np.matrix(alldata[[\"sqrMetres\", \"price\"]])\n", "\n", "m, n_plus_1 = data.shape\n", "n = n_plus_1 - 1\n", "Xn = data[:, 0:n]\n", "Xn /= np.amax(Xn, axis=0)\n", "Xn2 = np.power(Xn, 2)\n", "Xn2 /= np.amax(Xn2, axis=0)\n", "Xn3 = np.power(Xn, 3)\n", "Xn3 /= np.amax(Xn3, axis=0)\n", "\n", "X = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n + 1)\n", "X2 = np.matrix(np.concatenate((np.ones((m, 1)), Xn, Xn2), axis=1)).reshape(m, 2 * n + 1)\n", "X3 = np.matrix(np.concatenate((np.ones((m, 1)), Xn, Xn2, Xn3), axis=1)).reshape(\n", " m, 3 * n + 1\n", ")\n", "y = np.matrix(data[:, -1]).reshape(m, 1)\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Postać ogólna regresji wielomianowej:\n", "\n", "$$ h_{\\theta}(x) = \\sum_{i=0}^{n} \\theta_i x^i $$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "# Funkcja regresji wielomianowej\n", "\n", "\n", "def h_poly(Theta, x):\n", " \"\"\"Funkcja wielomianowa\"\"\"\n", " return sum(theta * np.power(x, i) for i, theta in enumerate(Theta.tolist()))\n", "\n", "\n", "def polynomial_regression(theta):\n", " \"\"\"Funkcja regresji wielomianowej\"\"\"\n", " return lambda x: h_poly(theta, x)\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" } }, "source": [ "Najprostszym przypadkiem regresji wielomianowej jest funkcja kwadratowa:" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Funkcja kwadratowa:\n", "\n", "$$ h_{\\theta}(x) = \\theta_0 + \\theta_1 x + \\theta_2 x^2 $$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plot_data(X2, y, xlabel=\"x\", ylabel=\"y\")\n", "theta_start = np.matrix([0, 0, 0]).reshape(3, 1)\n", "theta, logs = gradient_descent(cost, gradient, theta_start, X2, y)\n", "plot_fun(fig, polynomial_regression(theta), X)\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" } }, "source": [ "Innym szczególnym przypadkiem regresji wielomianowej jest funkjca sześcienna:" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Funkcja sześcienna:\n", "\n", "$$ h_{\\theta}(x) = \\theta_0 + \\theta_1 x + \\theta_2 x^2 + \\theta_3 x^3 $$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": true, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 397519.38046962]\n", " [-841341.14146733]\n", " [2253713.97125102]\n", " [-244009.07081946]]\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plot_data(X3, y, xlabel=\"x\", ylabel=\"y\")\n", "theta_start = np.matrix([0, 0, 0, 0]).reshape(4, 1)\n", "theta, _ = gradient_descent(cost, gradient, theta_start, X3, y)\n", "plot_fun(fig, polynomial_regression(theta), X)\n", "\n", "print(theta)\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Regresję wielomianową można potraktować jako szczególny przypadek regresji liniowej wielu zmiennych:\n", "\n", "$$ h_{\\theta}(x) = \\theta_0 + \\theta_1 x + \\theta_2 x^2 + \\theta_3 x^3 $$\n", "$$ x_1 = x, \\quad x_2 = x^2, \\quad x_3 = x^3, \\quad \\vec{x} = \\left[ \\begin{array}{ccc} x_0 \\\\ x_1 \\\\ x_2 \\end{array} \\right] $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" } }, "source": [ "(W tym przypadku za kolejne cechy przyjmujemy kolejne potęgi zmiennej $x$)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Uwaga praktyczna: przyda się normalizacja cech, szczególnie skalowanie!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Do tworzenia cech „pochodnych” możemy używać nie tylko potęgowania, ale też innych operacji matematycznych, np.:\n", "\n", "$$ h_{\\theta}(x) = \\theta_0 + \\theta_1 x + \\theta_2 \\sqrt{x} $$\n", "$$ x_1 = x, \\quad x_2 = \\sqrt{x}, \\quad \\vec{x} = \\left[ \\begin{array}{ccc} x_0 \\\\ x_1 \\end{array} \\right] $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" } }, "source": [ "Jakie zatem cechy wybrać? Najlepiej dopasować je do konkretnego problemu." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Wielomianowa regresja logistyczna\n", "\n", "Podobne modyfikacje cech możemy również stosować dla regresji logistycznej." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "def powerme(x1, x2, n):\n", " \"\"\"Funkcja, która generuje n potęg dla zmiennych x1 i x2 oraz ich iloczynów\"\"\"\n", " X = []\n", " for m in range(n + 1):\n", " for i in range(m + 1):\n", " X.append(np.multiply(np.power(x1, i), np.power(x2, (m - i))))\n", " return np.hstack(X)\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [ { "data": { "text/plain": [ "matrix([[ 1. , 0.36596696, -0.11214686],\n", " [ 0. , 0.4945305 , 0.47110656],\n", " [ 0. , 0.70290604, -0.92257983],\n", " [ 0. , 0.46658862, -0.62269739],\n", " [ 0. , 0.87939462, -0.11408015],\n", " [ 0. , -0.331185 , 0.84447667],\n", " [ 0. , -0.54351701, 0.8851383 ],\n", " [ 0. , 0.91979241, 0.41607012],\n", " [ 0. , 0.28011742, 0.61431157],\n", " [ 0. , 0.94754363, -0.78307311]])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Wczytanie danych\n", "import pandas\n", "import numpy as np\n", "\n", "alldata = pandas.read_csv(\"polynomial_logistic.tsv\", sep=\"\\t\")\n", "data = np.matrix(alldata)\n", "\n", "m, n_plus_1 = data.shape\n", "n = n_plus_1 - 1\n", "Xn = data[:, 1:]\n", "\n", "Xpl = powerme(data[:, 1], data[:, 2], n)\n", "Ypl = np.matrix(data[:, 0]).reshape(m, 1)\n", "\n", "data[:10]\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "def plot_data_for_classification(X, Y, xlabel, ylabel):\n", " \"\"\"Wykres danych (wersja macierzowa)\"\"\"\n", " fig = plt.figure(figsize=(16 * 0.6, 9 * 0.6))\n", " ax = fig.add_subplot(111)\n", " fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n", " X = X.tolist()\n", " Y = Y.tolist()\n", " X1n = [x[1] for x, y in zip(X, Y) if y[0] == 0]\n", " X1p = [x[1] for x, y in zip(X, Y) if y[0] == 1]\n", " X2n = [x[2] for x, y in zip(X, Y) if y[0] == 0]\n", " X2p = [x[2] for x, y in zip(X, Y) if y[0] == 1]\n", " ax.scatter(X1n, X2n, c=\"r\", marker=\"x\", s=50, label=\"Dane\")\n", " ax.scatter(X1p, X2p, c=\"g\", marker=\"o\", s=50, label=\"Dane\")\n", "\n", " ax.set_xlabel(xlabel)\n", " ax.set_ylabel(ylabel)\n", " ax.margins(0.05, 0.05)\n", " return fig\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" } }, "source": [ "Przyjmijmy, że mamy następujące dane i chcemy przeprowadzić klasyfikację dwuklasową dla następujących klas:\n", " * czerwone krzyżyki\n", " * zielone kółka" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plot_data_for_classification(Xpl, Ypl, xlabel=r\"$x_1$\", ylabel=r\"$x_2$\")\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Propozycja hipotezy:\n", "\n", "$$ h_\\theta(x) = g(\\theta^T x) = g(\\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\theta_3 x_3 + \\theta_4 x_4 + \\theta_5 x_5) \\; , $$\n", "\n", "gdzie $g$ – funkcja logistyczna, $x_3 = x_1^2$, $x_4 = x_2^2$, $x_5 = x_1 x_2$." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "def safeSigmoid(x, eps=0):\n", " \"\"\"Funkcja sigmoidalna zmodyfikowana w taki sposób,\n", " żeby wartości zawsz były odległe od asymptot o co najmniej eps\n", " \"\"\"\n", " y = 1.0 / (1.0 + np.exp(-x))\n", " if eps > 0:\n", " y[y < eps] = eps\n", " y[y > 1 - eps] = 1 - eps\n", " return y\n", "\n", "\n", "def h(theta, X, eps=0.0):\n", " \"\"\"Funkcja hipotezy\"\"\"\n", " return safeSigmoid(X * theta, eps)\n", "\n", "\n", "def J(h, theta, X, y, lamb=0):\n", " \"\"\"Funkcja kosztu\"\"\"\n", " m = len(y)\n", " f = h(theta, X, eps=10**-7)\n", " j = (\n", " -np.sum(np.multiply(y, np.log(f)) + np.multiply(1 - y, np.log(1 - f)), axis=0)\n", " / m\n", " )\n", " if lamb > 0:\n", " j += lamb / (2 * m) * np.sum(np.power(theta[1:], 2))\n", " return j\n", "\n", "\n", "def dJ(h, theta, X, y, lamb=0):\n", " \"\"\"Pochodna funkcji kosztu\"\"\"\n", " g = 1.0 / y.shape[0] * (X.T * (h(theta, X) - y))\n", " if lamb > 0:\n", " g[1:] += lamb / float(y.shape[0]) * theta[1:]\n", " return g\n", "\n", "\n", "def classifyBi(theta, X):\n", " \"\"\"Funkcja decyzji\"\"\"\n", " prob = h(theta, X)\n", " return prob\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "def GD(h, fJ, fdJ, theta, X, y, alpha=0.01, eps=10**-3, maxSteps=10000):\n", " \"\"\"Metoda gradientu prostego dla regresji logistycznej\"\"\"\n", " errorCurr = fJ(h, theta, X, y)\n", " errors = [[errorCurr, theta]]\n", " while True:\n", " # oblicz nowe theta\n", " theta = theta - alpha * fdJ(h, theta, X, y)\n", " # raportuj poziom błędu\n", " errorCurr, errorPrev = fJ(h, theta, X, y), errorCurr\n", " # kryteria stopu\n", " if abs(errorPrev - errorCurr) <= eps:\n", " break\n", " if len(errors) > maxSteps:\n", " break\n", " errors.append([errorCurr, theta])\n", " return theta, errors\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "theta = [[ 1.59558981]\n", " [ 0.12602307]\n", " [ 0.65718518]\n", " [-5.26367581]\n", " [ 1.96832544]\n", " [-6.97946065]]\n" ] } ], "source": [ "# Uruchomienie metody gradientu prostego dla regresji logistycznej\n", "theta_start = np.matrix(np.zeros(Xpl.shape[1])).reshape(Xpl.shape[1], 1)\n", "theta, errors = GD(\n", " h, J, dJ, theta_start, Xpl, Ypl, alpha=0.1, eps=10**-7, maxSteps=10000\n", ")\n", "print(r\"theta = {}\".format(theta))\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "def plot_decision_boundary(fig, theta, X):\n", " \"\"\"Wykres granicy klas\"\"\"\n", " ax = fig.axes[0]\n", " xx, yy = np.meshgrid(np.arange(-1.0, 1.0, 0.02), np.arange(-1.0, 1.0, 0.02))\n", " l = len(xx.ravel())\n", " C = powerme(xx.reshape(l, 1), yy.reshape(l, 1), n)\n", " z = classifyBi(theta, C).reshape(int(np.sqrt(l)), int(np.sqrt(l)))\n", "\n", " plt.contour(xx, yy, z, levels=[0.5], lw=3)\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_868/1169766636.py:9: UserWarning: The following kwargs were not used by contour: 'lw'\n", " plt.contour(xx, yy, z, levels=[0.5], lw=3)\n" ] }, { 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plot_data_for_classification(Xpl, Ypl, xlabel=r\"$x_1$\", ylabel=r\"$x_2$\")\n", "plot_decision_boundary(fig, theta, Xpl)\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "# Wczytanie danych\n", "\n", "alldata = pandas.read_csv(\"polynomial_logistic.tsv\", sep=\"\\t\")\n", "data = np.matrix(alldata)\n", "\n", "m, n_plus_1 = data.shape\n", "Xn = data[:, 1:]\n", "\n", "n = 10\n", "Xpl = powerme(data[:, 1], data[:, 2], n)\n", "Ypl = np.matrix(data[:, 0]).reshape(m, 1)\n", "\n", "theta_start = np.matrix(np.zeros(Xpl.shape[1])).reshape(Xpl.shape[1], 1)\n", "theta, errors = GD(\n", " h, J, dJ, theta_start, Xpl, Ypl, alpha=0.1, eps=10**-7, maxSteps=10000\n", ")\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_868/1169766636.py:9: UserWarning: The following kwargs were not used by contour: 'lw'\n", " plt.contour(xx, yy, z, levels=[0.5], lw=3)\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Przykład dla większej liczby cech\n", "fig = plot_data_for_classification(Xpl, Ypl, xlabel=r\"$x_1$\", ylabel=r\"$x_2$\")\n", "plot_decision_boundary(fig, theta, Xpl)\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 6.2. Problem nadmiernego dopasowania" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Obciążenie a wariancja" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "# Dane do prostego przykładu\n", "\n", "data = np.matrix(\n", " [\n", " [0.0, 0.0],\n", " [0.5, 1.8],\n", " [1.0, 4.8],\n", " [1.6, 7.2],\n", " [2.6, 8.8],\n", " [3.0, 9.0],\n", " ]\n", ")\n", "\n", "m, n_plus_1 = data.shape\n", "n = n_plus_1 - 1\n", "Xn1 = data[:, 0:n]\n", "Xn1 /= np.amax(Xn1, axis=0)\n", "Xn2 = np.power(Xn1, 2)\n", "Xn2 /= np.amax(Xn2, axis=0)\n", "Xn3 = np.power(Xn1, 3)\n", "Xn3 /= np.amax(Xn3, axis=0)\n", "Xn4 = np.power(Xn1, 4)\n", "Xn4 /= np.amax(Xn4, axis=0)\n", "Xn5 = np.power(Xn1, 5)\n", "Xn5 /= np.amax(Xn5, axis=0)\n", "\n", "X1 = np.matrix(np.concatenate((np.ones((m, 1)), Xn1), axis=1)).reshape(m, n + 1)\n", "X2 = np.matrix(np.concatenate((np.ones((m, 1)), Xn1, Xn2), axis=1)).reshape(\n", " m, 2 * n + 1\n", ")\n", "X5 = np.matrix(\n", " np.concatenate((np.ones((m, 1)), Xn1, Xn2, Xn3, Xn4, Xn5), axis=1)\n", ").reshape(m, 5 * n + 1)\n", "y = np.matrix(data[:, -1]).reshape(m, 1)\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plot_data(X1, y, xlabel=\"x\", ylabel=\"y\")\n" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "scrolled": true, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Koszt: 0.41863137063802436\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plot_data(X1, y, xlabel=\"x\", ylabel=\"y\")\n", "theta_start = np.matrix([0, 0]).reshape(2, 1)\n", "theta, history = gradient_descent(cost, gradient, theta_start, X1, y, eps=10**-8)\n", "plot_fun(fig, polynomial_regression(theta), X1)\n", "print(f\"Koszt: {history[-1][0]}\")" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Ten model ma duże **obciążenie** (**błąd systematyczny**, *bias*) – zachodzi **niedostateczne dopasowanie** (*underfitting*)." ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Koszt: 0.05470339875188901\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plot_data(X2, y, xlabel=\"x\", ylabel=\"y\")\n", "theta_start = np.matrix([0, 0, 0]).reshape(3, 1)\n", "theta, history = gradient_descent(cost, gradient, theta_start, X2, y, eps=10**-8)\n", "plot_fun(fig, polynomial_regression(theta), X1)\n", "print(f\"Koszt: {history[-1][0]}\")" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Ten model jest odpowiednio dopasowany." ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Koszt: 0.007232337911078077\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plot_data(X5, y, xlabel=\"x\", ylabel=\"y\")\n", "theta_start = np.matrix([0, 0, 0, 0, 0, 0]).reshape(6, 1)\n", "theta, history = gradient_descent(cost, gradient, theta_start, X5, y, alpha=0.5, eps=10**-8)\n", "plot_fun(fig, polynomial_regression(theta), X1)\n", "print(f\"Koszt: {history[-1][0]}\")" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Ten model ma dużą **wariancję** (*variance*) – zachodzi **nadmierne dopasowanie** (*overfitting*)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" } }, "source": [ "(Zwróć uwagę na dziwny kształt krzywej w lewej części wykresu – to m.in. efekt nadmiernego dopasowania)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" } }, "source": [ "Nadmierne dopasowanie występuje, gdy model ma zbyt dużo stopni swobody w stosunku do ilości danych wejściowych.\n", "\n", "Jest to zjawisko niepożądane.\n", "\n", "Możemy obrazowo powiedzieć, że nadmierne dopasowanie występuje, gdy model zaczyna modelować szum/zakłócenia w danych zamiast ich „głównego nurtu”. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" } }, "source": [ "Zobacz też: https://pl.wikipedia.org/wiki/Nadmierne_dopasowanie" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Obciążenie (błąd systematyczny, *bias*)\n", "\n", "* Wynika z błędnych założeń co do algorytmu uczącego się.\n", "* Duże obciążenie powoduje niedostateczne dopasowanie." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Wariancja (*variance*)\n", "\n", "* Wynika z nadwrażliwości na niewielkie fluktuacje w zbiorze uczącym.\n", "* Wysoka wariancja może spowodować nadmierne dopasowanie (modelując szum zamiast sygnału)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 6.3. Regularyzacja" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "def SGD(\n", " h,\n", " fJ,\n", " fdJ,\n", " theta,\n", " X,\n", " Y,\n", " alpha=0.001,\n", " maxEpochs=1.0,\n", " batchSize=100,\n", " adaGrad=False,\n", " logError=False,\n", " validate=0.0,\n", " valStep=100,\n", " lamb=0,\n", " trainsetsize=1.0,\n", "):\n", " \"\"\"Stochastic Gradient Descent - stochastyczna wersja metody gradientu prostego\n", " (więcej na ten temat na następnym wykładzie)\n", " \"\"\"\n", " errorsX, errorsY = [], []\n", " errorsVX, errorsVY = [], []\n", "\n", " XT, YT = X, Y\n", "\n", " m_end = int(trainsetsize * len(X))\n", "\n", " if validate > 0:\n", " mv = int(X.shape[0] * validate)\n", " XV, YV = X[:mv], Y[:mv]\n", " XT, YT = X[mv:m_end], Y[mv:m_end]\n", " m, n = XT.shape\n", "\n", " start, end = 0, batchSize\n", " maxSteps = (m * float(maxEpochs)) / batchSize\n", "\n", " if adaGrad:\n", " hgrad = np.matrix(np.zeros(n)).reshape(n, 1)\n", "\n", " for i in range(int(maxSteps)):\n", " XBatch, YBatch = XT[start:end, :], YT[start:end, :]\n", "\n", " grad = fdJ(h, theta, XBatch, YBatch, lamb=lamb)\n", " if adaGrad:\n", " hgrad += np.multiply(grad, grad)\n", " Gt = 1.0 / (10**-7 + np.sqrt(hgrad))\n", " theta = theta - np.multiply(alpha * Gt, grad)\n", " else:\n", " theta = theta - alpha * grad\n", "\n", " if logError:\n", " errorsX.append(float(i * batchSize) / m)\n", " errorsY.append(fJ(h, theta, XBatch, YBatch).item())\n", " if validate > 0 and i % valStep == 0:\n", " errorsVX.append(float(i * batchSize) / m)\n", " errorsVY.append(fJ(h, theta, XV, YV).item())\n", "\n", " if start + batchSize < m:\n", " start += batchSize\n", " else:\n", " start = 0\n", " end = min(start + batchSize, m)\n", " return theta, (errorsX, errorsY, errorsVX, errorsVY)\n" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "# Przygotowanie danych do przykładu regularyzacji\n", "\n", "n = 6\n", "\n", "data = np.matrix(np.loadtxt(\"ex2data2.txt\", delimiter=\",\"))\n", "np.random.shuffle(data)\n", "\n", "X = powerme(data[:, 0], data[:, 1], n)\n", "Y = data[:, 2]\n" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "def draw_regularization_example(\n", " X, Y, lamb=0, alpha=1, adaGrad=True, maxEpochs=2500, validate=0.25\n", "):\n", " \"\"\"Rusuje przykład regularyzacji\"\"\"\n", " plt.figure(figsize=(16, 8))\n", " plt.subplot(121)\n", " plt.scatter(\n", " X[:, 2].tolist(),\n", " X[:, 1].tolist(),\n", " c=Y.tolist(),\n", " s=100,\n", " cmap=plt.cm.get_cmap(\"prism\"),\n", " )\n", "\n", " theta = np.matrix(np.zeros(X.shape[1])).reshape(X.shape[1], 1)\n", " thetaBest, err = SGD(\n", " h,\n", " J,\n", " dJ,\n", " theta,\n", " X,\n", " Y,\n", " alpha=alpha,\n", " adaGrad=adaGrad,\n", " maxEpochs=maxEpochs,\n", " batchSize=100,\n", " logError=True,\n", " validate=validate,\n", " valStep=1,\n", " lamb=lamb,\n", " )\n", "\n", " xx, yy = np.meshgrid(np.arange(-1.5, 1.5, 0.02), np.arange(-1.5, 1.5, 0.02))\n", " l = len(xx.ravel())\n", " C = powerme(xx.reshape(l, 1), yy.reshape(l, 1), n)\n", " z = classifyBi(thetaBest, C).reshape(int(np.sqrt(l)), int(np.sqrt(l)))\n", "\n", " plt.contour(xx, yy, z, levels=[0.5], lw=3)\n", " plt.ylim(-1, 1.2)\n", " plt.xlim(-1, 1.2)\n", " plt.legend()\n", " plt.subplot(122)\n", " plt.plot(err[0], err[1], lw=3, label=\"Training error\")\n", " if validate > 0:\n", " plt.plot(err[2], err[3], lw=3, label=\"Validation error\")\n", " plt.legend()\n", " plt.ylim(0.2, 0.8)\n" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "scrolled": true, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_868/2651435526.py:12: MatplotlibDeprecationWarning: The get_cmap function was deprecated in Matplotlib 3.7 and will be removed two minor releases later. Use ``matplotlib.colormaps[name]`` or ``matplotlib.colormaps.get_cmap(obj)`` instead.\n", " cmap=plt.cm.get_cmap(\"prism\"),\n", "/tmp/ipykernel_868/2678993393.py:5: RuntimeWarning: overflow encountered in exp\n", " y = 1.0 / (1.0 + np.exp(-x))\n", "/tmp/ipykernel_868/2651435526.py:38: UserWarning: The following kwargs were not used by contour: 'lw'\n", " plt.contour(xx, yy, z, levels=[0.5], lw=3)\n", "No artists with labels found to put in legend. Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_regularization_example(X, Y)\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Regularyzacja\n", "\n", "Regularyzacja jest metodą zapobiegania zjawisku nadmiernego dopasowania (*overfitting*) poprzez odpowiednie zmodyfikowanie funkcji kosztu.\n", "\n", "Do funkcji kosztu dodawane jest specjalne wyrażenie (**wyrażenie regularyzacyjne** – zaznaczone na czerwono w poniższych wzorach), będące „karą” za ekstremalne wartości parametrów $\\theta$.\n", "\n", "W ten sposób preferowane są wektory $\\theta$ z mniejszymi wartosciami parametrów – mają automatycznie niższy koszt.\n", "\n", "Jak silną regularyzację chcemy zastosować? Możemy o tym zadecydować, dobierajac odpowiednio **parametr regularyzacji** $\\lambda$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "notes" } }, "source": [ "Przedstawiona tu metoda regularyzacji to tzw. metoda L2 (*ridge*). Istnieją również inne metody regularyzacji, które charakteryzują się trochę innymi własnościami, np. L2 (*lasso*) lub *elastic net*. Więcej na ten temat można przeczytać np. tu:\n", "* [L1 and L2 Regularization Methods](https://towardsdatascience.com/l1-and-l2-regularization-methods-ce25e7fc831c)\n", "* [Ridge and Lasso Regression: L1 and L2 Regularization](https://towardsdatascience.com/ridge-and-lasso-regression-a-complete-guide-with-python-scikit-learn-e20e34bcbf0b)\n", "* [Elastic Net Regression](https://towardsdatascience.com/elastic-net-regression-from-sklearn-to-tensorflow-3b48eee45e91)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Regularyzacja dla regresji liniowej – funkcja kosztu\n", "\n", "$$\n", "J(\\theta) \\, = \\, \\dfrac{1}{2m} \\left( \\displaystyle\\sum_{i=1}^{m} \\left( h_\\theta(x^{(i)}) - y^{(i)} \\right)^2 \\color{red}{ + \\lambda \\displaystyle\\sum_{j=1}^{n} \\theta^2_j } \\right)\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "* $\\lambda$ – parametr regularyzacji\n", "* jeżeli $\\lambda$ jest zbyt mały, skutkuje to nadmiernym dopasowaniem\n", "* jeżeli $\\lambda$ jest zbyt duży, skutkuje to niedostatecznym dopasowaniem" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Regularyzacja dla regresji liniowej – gradient\n", "\n", "$$\\small\n", "\\begin{array}{llll}\n", "\\dfrac{\\partial J(\\theta)}{\\partial \\theta_0} &=& \\dfrac{1}{m}\\displaystyle\\sum_{i=1}^m \\left( h_{\\theta}(x^{(i)})-y^{(i)} \\right) x^{(i)}_0 & \\textrm{dla $j = 0$ }\\\\\n", "\\dfrac{\\partial J(\\theta)}{\\partial \\theta_j} &=& \\dfrac{1}{m}\\displaystyle\\sum_{i=1}^m \\left( h_{\\theta}(x^{(i)})-y^{(i)} \\right) x^{(i)}_j \\color{red}{+ \\dfrac{\\lambda}{m}\\theta_j} & \\textrm{dla $j = 1, 2, \\ldots, n $} \\\\\n", "\\end{array} \n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Regularyzacja dla regresji logistycznej – funkcja kosztu\n", "\n", "$$\n", "\\begin{array}{rtl}\n", "J(\\theta) & = & -\\dfrac{1}{m} \\left( \\displaystyle\\sum_{i=1}^{m} y^{(i)} \\log h_\\theta(x^{(i)}) + \\left( 1-y^{(i)} \\right) \\log \\left( 1-h_\\theta(x^{(i)}) \\right) \\right) \\\\\n", "& & \\color{red}{ + \\dfrac{\\lambda}{2m} \\displaystyle\\sum_{j=1}^{n} \\theta^2_j } \\\\\n", "\\end{array}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Regularyzacja dla regresji logistycznej – gradient\n", "\n", "$$\\small\n", "\\begin{array}{llll}\n", "\\dfrac{\\partial J(\\theta)}{\\partial \\theta_0} &=& \\dfrac{1}{m}\\displaystyle\\sum_{i=1}^m \\left( h_{\\theta}(x^{(i)})-y^{(i)} \\right) x^{(i)}_0 & \\textrm{dla $j = 0$ }\\\\\n", "\\dfrac{\\partial J(\\theta)}{\\partial \\theta_j} &=& \\dfrac{1}{m}\\displaystyle\\sum_{i=1}^m \\left( h_{\\theta}(x^{(i)})-y^{(i)} \\right) x^{(i)}_j \\color{red}{+ \\dfrac{\\lambda}{m}\\theta_j} & \\textrm{dla $j = 1, 2, \\ldots, n $} \\\\\n", "\\end{array} \n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Implementacja metody regularyzacji" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "def J_(h, theta, X, y, lamb=0):\n", " \"\"\"Funkcja kosztu z regularyzacją\"\"\"\n", " m = float(len(y))\n", " f = h(theta, X, eps=10**-7)\n", " j = 1.0 / m * -np.sum(\n", " np.multiply(y, np.log(f)) + np.multiply(1 - y, np.log(1 - f)), axis=0\n", " ) + lamb / (2 * m) * np.sum(np.power(theta[1:], 2))\n", " return j\n", "\n", "\n", "def dJ_(h, theta, X, y, lamb=0):\n", " \"\"\"Gradient funkcji kosztu z regularyzacją\"\"\"\n", " m = float(y.shape[0])\n", " g = 1.0 / y.shape[0] * (X.T * (h(theta, X) - y))\n", " g[1:] += lamb / m * theta[1:]\n", " return g\n" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "slider_lambda = widgets.FloatSlider(\n", " min=0.0, max=0.5, step=0.005, value=0.01, description=r\"$\\lambda$\", width=300\n", ")\n", "\n", "\n", "def slide_regularization_example_2(lamb):\n", " draw_regularization_example(X, Y, lamb=lamb)\n" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "2485672f2aee49bbba398c5847212626", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=0.01, description='$\\\\lambda$', max=0.5, step=0.005), Button(descripti…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "widgets.interact_manual(slide_regularization_example_2, lamb=slider_lambda)\n" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "def cost_lambda_fun(lamb):\n", " \"\"\"Koszt w zależności od parametru regularyzacji lambda\"\"\"\n", " theta = np.matrix(np.zeros(X.shape[1])).reshape(X.shape[1], 1)\n", " thetaBest, err = SGD(\n", " h,\n", " J,\n", " dJ,\n", " theta,\n", " X,\n", " Y,\n", " alpha=1,\n", " adaGrad=True,\n", " maxEpochs=2500,\n", " batchSize=100,\n", " logError=True,\n", " validate=0.25,\n", " valStep=1,\n", " lamb=lamb,\n", " )\n", " return err[1][-1], err[3][-1]\n", "\n", "\n", "def plot_cost_lambda():\n", " \"\"\"Wykres kosztu w zależności od parametru regularyzacji lambda\"\"\"\n", " plt.figure(figsize=(16, 8))\n", " ax = plt.subplot(111)\n", " Lambda = np.arange(0.0, 1.0, 0.01)\n", " Costs = [cost_lambda_fun(lamb) for lamb in Lambda]\n", " CostTrain = [cost[0] for cost in Costs]\n", " CostCV = [cost[1] for cost in Costs]\n", " plt.plot(Lambda, CostTrain, lw=3, label=\"training error\")\n", " plt.plot(Lambda, CostCV, lw=3, label=\"validation error\")\n", " ax.set_xlabel(r\"$\\lambda$\")\n", " ax.set_ylabel(\"cost\")\n", " plt.legend()\n", " plt.ylim(0.2, 0.8)\n" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_cost_lambda()\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 5.4. Krzywa uczenia się" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "* Krzywa uczenia pozwala sprawdzić, czy uczenie przebiega poprawnie.\n", "* Krzywa uczenia to wykres zależności między wielkością zbioru treningowego a wartością funkcji kosztu.\n", "* Wraz ze wzrostem wielkości zbioru treningowego wartość funkcji kosztu na zbiorze treningowym rośnie.\n", "* Wraz ze wzrostem wielkości zbioru treningowego wartość funkcji kosztu na zbiorze walidacyjnym maleje." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "def cost_trainsetsize_fun(m):\n", " \"\"\"Koszt w zależności od wielkości zbioru uczącego\"\"\"\n", " theta = np.matrix(np.zeros(X.shape[1])).reshape(X.shape[1], 1)\n", " thetaBest, err = SGD(\n", " h,\n", " J,\n", " dJ,\n", " theta,\n", " X,\n", " Y,\n", " alpha=1,\n", " adaGrad=True,\n", " maxEpochs=2500,\n", " batchSize=100,\n", " logError=True,\n", " validate=0.25,\n", " valStep=1,\n", " lamb=0.01,\n", " trainsetsize=m,\n", " )\n", " return err[1][-1], err[3][-1]\n", "\n", "\n", "def plot_learning_curve():\n", " \"\"\"Wykres krzywej uczenia się\"\"\"\n", " plt.figure(figsize=(16, 8))\n", " ax = plt.subplot(111)\n", " M = np.arange(0.3, 1.0, 0.05)\n", " Costs = [cost_trainsetsize_fun(m) for m in M]\n", " CostTrain = [cost[0] for cost in Costs]\n", " CostCV = [cost[1] for cost in Costs]\n", " plt.plot(M, CostTrain, lw=3, label=\"training error\")\n", " plt.plot(M, CostCV, lw=3, label=\"validation error\")\n", " ax.set_xlabel(\"trainset size\")\n", " ax.set_ylabel(\"cost\")\n", " plt.legend()\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Krzywa uczenia a obciążenie i wariancja\n", "\n", "Wykreślenie krzywej uczenia pomaga diagnozować nadmierne i niedostateczne dopasowanie:\n", "\n", "\n", "\n", "Źródło: http://www.ritchieng.com/machinelearning-learning-curve" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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