uczenie-maszynowe/wyk/06_Problem_nadmiernego_dopasowania.ipynb
2023-11-22 14:27:10 +01:00

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{
"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": [
"[<matplotlib.lines.Line2D at 0x7f5e984f62c0>]"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 960x540 with 1 Axes>"
]
},
"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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\n",
"text/plain": [
"<Figure size 960x540 with 1 Axes>"
]
},
"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": {
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\n",
"text/plain": [
"<Figure size 960x540 with 1 Axes>"
]
},
"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_531/1169766636.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": {
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\n",
"text/plain": [
"<Figure size 960x540 with 1 Axes>"
]
},
"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_531/1169766636.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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\n",
"text/plain": [
"<Figure size 960x540 with 1 Axes>"
]
},
"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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\n",
"text/plain": [
"<Figure size 960x540 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plot_data(X1, y, xlabel=\"x\", ylabel=\"y\")\n"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f5e97eb62f0>]"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 960x540 with 1 Axes>"
]
},
"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, _ = gradient_descent(cost, gradient, theta_start, X1, y, eps=0.00001)\n",
"plot_fun(fig, polynomial_regression(theta), X1)\n"
]
},
{
"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": 21,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f5e29f90310>]"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 960x540 with 1 Axes>"
]
},
"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, _ = gradient_descent(cost, gradient, theta_start, X2, y, eps=0.000001)\n",
"plot_fun(fig, polynomial_regression(theta), X1)\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Ten model jest odpowiednio dopasowany."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f5e29807520>]"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 960x540 with 1 Axes>"
]
},
"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, _ = gradient_descent(cost, gradient, theta_start, X5, y, alpha=0.5, eps=10**-7)\n",
"plot_fun(fig, polynomial_regression(theta), X1)\n"
]
},
{
"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": [
"<img style=\"margin:auto\" width=\"90%\" src=\"fit.png\"/>"
]
},
{
"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": [
"<img style=\"margin:auto\" width=\"40%\" src=\"bias2.png\"/>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"<img style=\"margin:auto\" width=\"60%\" src=\"curves.jpg\"/>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## 6.3. Regularyzacja"
]
},
{
"cell_type": "code",
"execution_count": 23,
"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": 24,
"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": 25,
"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": 26,
"metadata": {
"scrolled": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/tmp/ipykernel_531/2678993393.py:5: RuntimeWarning: overflow encountered in exp\n",
" y = 1.0 / (1.0 + np.exp(-x))\n",
"/tmp/ipykernel_531/2651435526.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": {
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\n",
"text/plain": [
"<Figure size 1600x800 with 2 Axes>"
]
},
"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": 27,
"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": 28,
"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": 30,
"metadata": {
"scrolled": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "1c4820beb85e4c129e0adc0b7516de95",
"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": [
"<function __main__.slide_regularization_example_2(lamb)>"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"widgets.interact_manual(slide_regularization_example_2, lamb=slider_lambda)\n"
]
},
{
"cell_type": "code",
"execution_count": 31,
"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": 32,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
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"text/plain": [
"<Figure size 1600x800 with 1 Axes>"
]
},
"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": 33,
"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",
"<img width=\"100%\" src=\"learning-curves.png\"/>\n",
"\n",
"Źródło: http://www.ritchieng.com/machinelearning-learning-curve"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1600x800 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_learning_curve()\n"
]
}
],
"metadata": {
"celltoolbar": "Slideshow",
"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": "3.10.12"
},
"livereveal": {
"start_slideshow_at": "selected",
"theme": "white"
}
},
"nbformat": 4,
"nbformat_minor": 4
}