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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
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"## Uczenie maszynowe –
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"# 6. Naiwny klasyfikator bayesowski"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"* Naiwny klasyfikator bayesowski jest algorytmem dla problemu klasyfikacji wieloklasowej.\n",
"* Naszym celem jest znalezienie funkcji uczącej $f \\colon x \\mapsto y$, gdzie $y$ oznacza jedną ze zdefiniowanych wcześniej klas.\n",
"* Klasyfikacja probabilistyczna polega na wskazaniu klasy o najwyższym prawdopodobieństwie:\n",
"$$ \\hat{y} = \\mathop{\\arg \\max}_y P( y \\,|\\, x ) $$\n",
"* Naiwny klasyfikator bayesowski należy do rodziny klasyfikatorów probabilistycznych"
]
},
{
"cell_type": "markdown",
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"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
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"source": [
"<img style=\"float: right;\" src=\"https://upload.wikimedia.org/wikipedia/commons/d/d4/Thomas_Bayes.gif\">\n",
"\n",
"**Thomas Bayes** (wymowa: /beɪ – –
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Twierdzenie Bayesa –
"\n",
"$$ P( Y \\,|\\, X ) = \\frac{ P( X \\,|\\, Y ) \\cdot P( Y ) }{ P ( X ) } $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"source": [
"Twierdzenie Bayesa opisuje związek między prawdopodobieństwami warunkowymi dwóch zdarzeń warunkujących się nawzajem."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Twierdzenie Bayesa\n",
"(po zastosowaniu wzoru na prawdopodobieństwo całkowite)\n",
"\n",
"$$ \\underbrace{P( y_k \\,|\\, x )}_\\textrm{ prawd. a posteriori } = \\frac{ \\overbrace{ P( x \\,|\\, y_k )}^\\textrm{ model klasy } \\cdot \\overbrace{P( y_k )}^\\textrm{ prawd. a priori } }{ \\underbrace{\\sum_{i} P( x \\,|\\, y_i ) \\, P( y_i )}_\\textrm{wyrażenie normalizacyjne} } $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"source": [
" * W tym przypadku „zdarzenie $x$” oznacza, że cechy wejściowe danej obserwacji przyjmują wartości opisane wektorem $x$.\n",
" * „Zdarzenie $y_k$” oznacza, że dana obserwacja należy do klasy $y_k$.\n",
" * **Model klasy** $y_k$ opisuje rozkład prawdopodobieństwa cech obserwacji należących do tej klasy.\n",
" * **Prawdopodobieństwo *a priori*** to prawdopodobienstwo, że losowa obserwacja należy do klasy $y_k$.\n",
" * **Prawdopodobieństwo *a posteriori*** to prawdopodobieństwo, którego szukamy: że obserwacja opisana wektorem cech $x$ należy do klasy $y_k$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Rola wyrażenia normalizacyjnego w twierdzeniu Bayesa\n",
"\n",
" * Wartość wyrażenia normalizacyjnego nie wpływa na wynik klasyfikacji.\n",
"\n",
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"*Przykład*: obserwacja nietypowa ma małe prawdopodobieństwo względem dowolnej klasy, wyrażenie normalizacyjne sprawia, że to prawdopodobieństwo staje się porównywalne z prawdopodobieństwami typowych obserwacji, ale nie wpływa na klasyfikację!"
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]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Klasyfikatory dyskryminatywne a generatywne\n",
"\n",
"* Klasyfikatory generatywne tworzą model rozkładu prawdopodobieństwa dla każdej z klas.\n",
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"* Klasyfikatory dyskryminatywne wyznaczają granicę klas (*decision boundary*) bezpośrednio.\n",
"* Naiwny klasyfikator bayesowski jest klasyfikatorem generatywnym (ponieważ wyznacza $P( x \\,|\\, y )$).\n",
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"* Wszystkie klasyfikatory generatywne są probabilistyczne, ale nie na odwrót.\n",
"* Regresja logistyczna jest przykładem klasyfikatora dyskryminatywnego."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Założenie niezależności dla naiwnego klasyfikatora bayesowskiego\n",
"\n",
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"* Naiwny klasyfikator bayesowski jest *naiwny*, ponieważ zakłada, że poszczególne cechy są niezależne od siebie:\n",
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"$$ P( x_1, \\ldots, x_n \\,|\\, y ) \\,=\\, \\prod_{i=1}^n P( x_i \\,|\\, x_1, \\ldots, x_{i-1}, y ) \\,=\\, \\prod_{i=1}^n P( x_i \\,|\\, y ) $$\n",
"* To założenie jest bardzo przydatne ze względów obliczeniowych, ponieważ bardzo często mamy do czynienia z ogromną liczbą cech (bitmapy, słowniki itp.)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Naiwny klasyfikator bayesowski –
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"# Przydtne 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": "subslide"
}
},
"outputs": [],
"source": [
"# Wczytanie danych (gatunki kosaćców)\n",
"\n",
"data_iris = pandas.read_csv('iris.csv')\n",
"data_iris_setosa = pandas.DataFrame()\n",
"data_iris_setosa['dł. płatka'] = data_iris['pl'] # \"pl\" oznacza \"petal length\"\n",
"data_iris_setosa['szer. płatka'] = data_iris['pw'] # \"pw\" oznacza \"petal width\"\n",
"data_iris_setosa['Iris setosa?'] = data_iris['Gatunek'].apply(lambda x: 1 if x=='Iris-setosa' else 0)\n",
"\n",
"m, n_plus_1 = data_iris_setosa.values.shape\n",
"n = n_plus_1 - 1\n",
"Xn = data_iris_setosa.values[:, 0:n].reshape(m, n)\n",
"\n",
"X = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n",
"Y = np.matrix(data_iris_setosa.values[:, 2]).reshape(m, 1)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"liczba przykładów: {0: 100, 1: 50}\n",
"prior probability: {0: 0.6666666666666666, 1: 0.3333333333333333}\n"
]
}
],
"source": [
"classes = [0, 1]\n",
"count = [sum(1 if y == c else 0 for y in Y.T.tolist()[0]) for c in classes]\n",
"prior_prob = [float(count[c]) / float(Y.shape[0]) for c in classes]\n",
"\n",
"print('liczba przykładów: ', {c: count[c] for c in classes})\n",
"print('prior probability:', {c: prior_prob[c] for c in classes})"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"# Wykres danych (wersja macierzowa)\n",
"def plot_data_for_classification(X, Y, xlabel, ylabel): \n",
" fig = plt.figure(figsize=(16*.6, 9*.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(.05, .05)\n",
" return fig"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
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"text/plain": [
"<Figure size 691.2x388.8 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plot_data_for_classification(X, Y, xlabel=u'dł. płatka', ylabel=u'szer. płatka')"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"średnia: [matrix([[1. , 4.906, 1.676]]), matrix([[1. , 1.464, 0.244]])]\n",
"odchylenie standardowe: [matrix([[0. , 0.8214402 , 0.42263933]]), matrix([[0. , 0.17176728, 0.10613199]])]\n",
"(1, 3)\n"
]
}
],
"source": [
"XY = np.column_stack((X, Y))\n",
"XY_split = [XY[np.where(XY[:,3] == c)[0]] for c in classes]\n",
"X_split = [XY_split[c][:,0:3] for c in classes]\n",
"Y_split = [XY_split[c][:,3] for c in classes]\n",
"\n",
"X_mean = [np.mean(X_split[c], axis=0) for c in classes]\n",
"X_std = [np.std(X_split[c], axis=0) for c in classes]\n",
"print('średnia: ', X_mean) \n",
"print('odchylenie standardowe: ', X_std)\n",
"\n",
"print(X_std[0].shape)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"# Rysowanie średnich\n",
"def draw_means(fig, means, xmin=0.0, xmax=7.0, ymin=0.0, ymax=7.0):\n",
" class_color = {0: 'r', 1: 'g'}\n",
" classes = range(len(means))\n",
" ax = fig.axes[0]\n",
" mean_x1 = [means[c].item(0, 1) for c in classes]\n",
" mean_x2 = [means[c].item(0, 2) for c in classes]\n",
" for c in classes:\n",
" ax.plot([mean_x1[c], mean_x1[c]], [xmin, xmax],\n",
" color=class_color.get(c, 'c'), linestyle='dashed')\n",
" ax.plot([ymin, ymax], [mean_x2[c], mean_x2[c]],\n",
" color=class_color.get(c, 'c'), linestyle='dashed') "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"from scipy.stats import norm\n",
"\n",
"# Prawdopodobieństwo klasy dla pojedynczej cechy\n",
"# Uwaga: jeżeli odchylenie standardowe dla danej cechy jest równe 0, \n",
"# to nie można określić prawdopodbieństwa klasy!\n",
"def prob(x, c, feature, mean, std):\n",
" sd = std[c].item(0, feature)\n",
" if sd == 0:\n",
" print('Nie można określić prawdopodobieństwa klasy dla cechy {}.!'.format(feature))\n",
" return norm(mean[c].item(0, feature), sd).pdf(x)\n",
"\n",
"# Prawdopodobieństwo klasy\n",
"# Uwaga: tu bierzemy iloczyn dwóch cech (1. i 2.), w ogólności może być ich więcej\n",
"def class_prob(x, c, mean, std, features=[1, 2]):\n",
" result = 1\n",
" for feature in features:\n",
" result *= prob(x[feature], c, feature, mean, std)\n",
" return result"
]
},
{
"cell_type": "code",
"execution_count": 9,
2022-04-08 09:24:18 +02:00
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(1, 3)\n",
"[matrix([[0. , 0.8214402 , 0.42263933]]), matrix([[0. , 0.17176728, 0.10613199]])]\n",
"[matrix([[1. , 4.906, 1.676]]), matrix([[1. , 1.464, 0.244]])]\n",
"[[1.57003335e-06 1.61965173e-23 3.09005273e-08]]\n"
]
}
],
"source": [
"print(X_std[0].shape)\n",
"print(X_std)\n",
"print(X_mean)\n",
"\n",
"X_prob_0=class_prob(X, 0, X_mean, X_std)\n",
"print(X_prob_0)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"# Wykres prawdopodobieństw klas\n",
"def plot_prob(fig, X_mean, X_std, classes, xmin=0.0, xmax=7.0, ymin=0.0, ymax=7.0):\n",
" class_color = {0: 'r', 1: 'g'}\n",
" ax = fig.axes[0]\n",
" x1, x2 = np.meshgrid(np.arange(xmin, xmax, 0.02),\n",
" np.arange(xmin, xmax, 0.02))\n",
" for c in classes:\n",
" fun1 = lambda x: prob(x, c, 1, X_mean, X_std)\n",
" fun2 = lambda x: prob(x, c, 2, X_mean, X_std)\n",
" p = fun1(x1) * fun2(x2)\n",
" plt.contour(x1, x2, p, levels=np.arange(0.0, 1.0, 0.1),\n",
" colors=class_color.get(c, 'c'), lw=3)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/pawel/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:12: UserWarning: The following kwargs were not used by contour: 'lw'\n",
" if sys.path[0] == '':\n"
]
},
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 691.2x388.8 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plot_data_for_classification(X, Y, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n",
"draw_means(fig, X_mean)\n",
"plot_prob(fig, X_mean, X_std, classes)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"# Prawdopodobieństwo a posteriori\n",
"def posterior_prob(x, c):\n",
" normalizer = sum(class_prob(x, c, X_mean, X_std)\n",
" * prior_prob[c]\n",
" for c in classes)\n",
" return (class_prob(x, c, X_mean, X_std) \n",
" * prior_prob[c]\n",
" / normalizer)"
]
},
{
"cell_type": "markdown",
2022-04-08 09:24:18 +02:00
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
2021-03-02 08:32:40 +01:00
"source": [
"Aby teraz przewidzieć klasę $y$ dla dowolnego zestawu cech $x$, wystarczy sprawdzić, dla której klasy prawdopodobieństwo *a posteriori* jest większe:"
]
},
{
"cell_type": "code",
"execution_count": 13,
2022-04-08 09:24:18 +02:00
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
2021-03-02 08:32:40 +01:00
"outputs": [],
"source": [
"# Funkcja klasyfikująca (funkcja predykcji)\n",
"def predict_class(x):\n",
" p = [posterior_prob(x, c) for c in classes]\n",
" if p[1] > p[0]:\n",
" return 1\n",
" else:\n",
" return 0"
]
},
{
"cell_type": "code",
"execution_count": 14,
2022-04-08 09:24:18 +02:00
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
2021-03-02 08:32:40 +01:00
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1\n",
"0\n"
]
}
],
"source": [
"x = [1, 2.0, 0.5] # długość płatka: 2.0, szerokość płatka: 0.5\n",
"y = predict_class(x)\n",
"print(y) # 1 –
"\n",
"x = [1, 2.5, 1.0] # długość płatka: 2.5, szerokość płatka: 1.0\n",
"y = predict_class(x)\n",
"print(y) # 0 –
]
},
{
"cell_type": "markdown",
2022-04-08 09:24:18 +02:00
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
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"source": [
"Zobaczmy, jak to wygląda na wykresie. Narysujemy w tym celu granicę między klasą 1 a 0:"
]
},
{
"cell_type": "code",
"execution_count": 15,
2022-04-08 09:24:18 +02:00
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
2021-03-02 08:32:40 +01:00
"outputs": [],
"source": [
"# Wykres granicy klas dla naiwnego Bayesa\n",
"def plot_decision_boundary_bayes(fig, X_mean, X_std, xmin=0.0, xmax=7.0, ymin=0.0, ymax=7.0):\n",
" ax = fig.axes[0]\n",
" x1, x2 = np.meshgrid(np.arange(xmin, xmax, 0.02),\n",
" np.arange(ymin, ymax, 0.02))\n",
" p = [posterior_prob([1, x1, x2], c) for c in classes]\n",
" p_diff = p[1] - p[0]\n",
" plt.contour(x1, x2, p_diff, levels=[0.0], colors='c', lw=3);"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/pawel/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:8: UserWarning: The following kwargs were not used by contour: 'lw'\n",
" \n"
]
},
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 691.2x388.8 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plot_data_for_classification(X, Y, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n",
"plot_decision_boundary_bayes(fig, X_mean, X_std)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Dla porównania: regresja logistyczna na tych samych danych"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"def powerme(x1,x2,n):\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",
"\n",
"# Funkcja logistyczna\n",
"def safeSigmoid(x, eps=0):\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",
"# Funkcja hipotezy dla regresji logistycznej\n",
"def h(theta, X, eps=0.0):\n",
" return safeSigmoid(X*theta, eps)\n",
"\n",
"# Funkcja kosztu dla regresji logistycznej\n",
"def J(h,theta,X,y, lamb=0):\n",
" m = len(y)\n",
" f = h(theta, X, eps=10**-7)\n",
" j = -np.sum(np.multiply(y, np.log(f)) + \n",
" np.multiply(1 - y, np.log(1 - f)), axis=0)/m\n",
" if lamb > 0:\n",
" j += lamb/(2*m) * np.sum(np.power(theta[1:],2))\n",
" return j\n",
"\n",
"# Gradient funkcji kosztu\n",
"def dJ(h,theta,X,y,lamb=0):\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",
"# Funkcja klasyfikująca\n",
"def classifyBi(theta, X):\n",
" prob = h(theta, X)\n",
" return prob"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"# Przygotowanie danych dla wielomianowej regresji logistycznej\n",
"\n",
"data = np.matrix(data_iris_setosa)\n",
"\n",
"Xpl = powerme(data[:, 1], data[:, 0], n)\n",
"Ypl = np.matrix(data[:, 2]).reshape(m, 1)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"# Metoda gradientu prostego dla regresji logistycznej\n",
"def GD(h, fJ, fdJ, theta, X, y, alpha=0.01, eps=10**-3, maxSteps=10000):\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"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"theta = [[ 4.01960795]\n",
" [ 3.89499137]\n",
" [ 0.18747599]\n",
" [-1.3524039 ]\n",
" [-2.00123783]\n",
" [-0.87625505]]\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(h, J, dJ, theta_start, Xpl, Ypl, \n",
" alpha=0.1, eps=10**-7, maxSteps=100000)\n",
"print(r'theta = {}'.format(theta))"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"# Wykres granicy klas\n",
"def plot_decision_boundary(fig, theta, Xpl, xmin=0.0, xmax=7.0):\n",
" ax = fig.axes[0]\n",
" xx, yy = np.meshgrid(np.arange(xmin, xmax, 0.02),\n",
" np.arange(xmin, xmax, 0.02))\n",
" l = len(xx.ravel())\n",
" C = powerme(yy.reshape(l, 1), xx.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], colors='m', lw=3);"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/pawel/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:10: UserWarning: The following kwargs were not used by contour: 'lw'\n",
" # Remove the CWD from sys.path while we load stuff.\n"
]
},
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 691.2x388.8 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plot_data_for_classification(Xpl, Ypl, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n",
"plot_decision_boundary(fig, theta, Xpl)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/pawel/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:10: UserWarning: The following kwargs were not used by contour: 'lw'\n",
" # Remove the CWD from sys.path while we load stuff.\n",
"/home/pawel/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:8: UserWarning: The following kwargs were not used by contour: 'lw'\n",
" \n"
]
},
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 691.2x388.8 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plot_data_for_classification(Xpl, Ypl, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n",
"plot_decision_boundary(fig, theta, Xpl)\n",
"plot_decision_boundary_bayes(fig, X_mean, X_std)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Inny przykład"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"# Wczytanie danych (gatunki kosaćców)\n",
"\n",
"data_iris = pandas.read_csv('iris.csv')\n",
"data_iris_versicolor = pandas.DataFrame()\n",
"data_iris_versicolor['dł. płatka'] = data_iris['pl'] # \"pl\" oznacza \"petal length\"\n",
"data_iris_versicolor['szer. płatka'] = data_iris['pw'] # \"pw\" oznacza \"petal width\"\n",
"data_iris_versicolor['Iris versicolor?'] = data_iris['Gatunek'].apply(lambda x: 1 if x=='Iris-versicolor' else 0)\n",
"\n",
"m, n_plus_1 = data_iris_versicolor.values.shape\n",
"n = n_plus_1 - 1\n",
"Xn = data_iris_versicolor.values[:, 0:n].reshape(m, n)\n",
"\n",
"X = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n",
"Y = np.matrix(data_iris_setosa.values[:, 2]).reshape(m, 1)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"liczba przykładów: {0: 100, 1: 50}\n",
"prior probability: {0: 0.6666666666666666, 1: 0.3333333333333333}\n"
]
}
],
"source": [
"classes = [0, 1]\n",
"count = [sum(1 if y == c else 0 for y in Y.T.tolist()[0]) for c in classes]\n",
"prior_prob = [float(count[c]) / float(Y.shape[0]) for c in classes]\n",
"\n",
"print('liczba przykładów: ', {c: count[c] for c in classes})\n",
"print('prior probability:', {c: prior_prob[c] for c in classes})"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 691.2x388.8 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plot_data_for_classification(X, Y, xlabel=u'dł. płatka', ylabel=u'szer. płatka')"
]
},
{
"cell_type": "code",
"execution_count": 27,
2022-04-08 09:24:18 +02:00
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
2021-03-02 08:32:40 +01:00
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"średnia: [matrix([[1. , 4.906, 1.676]]), matrix([[1. , 1.464, 0.244]])]\n",
"odchylenie standardowe: [matrix([[0. , 0.8214402 , 0.42263933]]), matrix([[0. , 0.17176728, 0.10613199]])]\n"
]
}
],
"source": [
"XY = np.column_stack((X, Y))\n",
"XY_split = [XY[np.where(XY[:,3] == c)[0]] for c in classes]\n",
"X_split = [XY_split[c][:,0:3] for c in classes]\n",
"Y_split = [XY_split[c][:,3] for c in classes]\n",
"\n",
"X_mean = [np.mean(X_split[c], axis=0) for c in classes]\n",
"X_std = [np.std(X_split[c], axis=0) for c in classes]\n",
"print('średnia: ', X_mean) \n",
"print('odchylenie standardowe: ', X_std)"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/pawel/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:12: UserWarning: The following kwargs were not used by contour: 'lw'\n",
" if sys.path[0] == '':\n"
]
},
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 691.2x388.8 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plot_data_for_classification(X, Y, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n",
"draw_means(fig, X_mean)\n",
"plot_prob(fig, X_mean, X_std, classes)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/pawel/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:8: UserWarning: The following kwargs were not used by contour: 'lw'\n",
" \n"
]
},
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 691.2x388.8 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plot_data_for_classification(X, Y, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n",
"plot_decision_boundary_bayes(fig, X_mean, X_std)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"# Przygotowanie danych dla wielomianowej regresji logistycznej\n",
"\n",
"data = np.matrix(data_iris_versicolor)\n",
"\n",
"Xpl = powerme(data[:, 1], data[:, 0], n)\n",
"Ypl = np.matrix(data[:, 2]).reshape(m, 1)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"theta = [[-10.68923095]\n",
" [ 5.52649967]\n",
" [ 5.83316957]\n",
" [ -0.60707243]\n",
" [ -0.46353729]\n",
" [ -2.82974456]]\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(h, J, dJ, theta_start, Xpl, Ypl, \n",
" alpha=0.05, eps=10**-7, maxSteps=100000)\n",
"print(r'theta = {}'.format(theta))"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/pawel/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:10: UserWarning: The following kwargs were not used by contour: 'lw'\n",
" # Remove the CWD from sys.path while we load stuff.\n"
]
},
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 691.2x388.8 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plot_data_for_classification(Xpl, Ypl, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n",
"plot_decision_boundary(fig, theta, Xpl)"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/pawel/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:10: UserWarning: The following kwargs were not used by contour: 'lw'\n",
" # Remove the CWD from sys.path while we load stuff.\n",
"/home/pawel/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:8: UserWarning: The following kwargs were not used by contour: 'lw'\n",
" \n"
]
},
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 691.2x388.8 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plot_data_for_classification(Xpl, Ypl, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n",
"plot_decision_boundary(fig, theta, Xpl)\n",
"plot_decision_boundary_bayes(fig, X_mean, X_std)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Kiedy naiwny Bayes nie działa?"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"# Wczytanie danych\n",
"import pandas\n",
"import numpy as np\n",
"\n",
"alldata = pandas.read_csv('bayes_nasty.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",
"Xbn = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n",
"Xbnp = powerme(data[:, 1], data[:, 2], n)\n",
"Ybn = np.matrix(data[:, 0]).reshape(m, 1)"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
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"text/plain": [
"<Figure size 691.2x388.8 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plot_data_for_classification(Xbn, Ybn, xlabel=r'$x_1$', ylabel=r'$x_2$')"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"liczba przykładów: {0: 69, 1: 30}\n",
"prior probability: {0: 0.696969696969697, 1: 0.30303030303030304}\n"
]
}
],
"source": [
"classes = [0, 1]\n",
"count = [sum(1 if y == c else 0 for y in Ybn.T.tolist()[0]) for c in classes]\n",
"prior_prob = [float(count[c]) / float(Ybn.shape[0]) for c in classes]\n",
"\n",
"print('liczba przykładów: ', {c: count[c] for c in classes})\n",
"print('prior probability:', {c: prior_prob[c] for c in classes})"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"średnia: [matrix([[1. , 0.03949835, 0.02825019]]), matrix([[1. , 0.09929617, 0.06206227]])]\n",
"odchylenie standardowe: [matrix([[0. , 0.52318432, 0.60106092]]), matrix([[0. , 0.61370281, 0.6081128 ]])]\n"
]
}
],
"source": [
"XY = np.column_stack((Xbn, Ybn))\n",
"XY_split = [XY[np.where(XY[:,3] == c)[0]] for c in classes]\n",
"X_split = [XY_split[c][:,0:3] for c in classes]\n",
"Y_split = [XY_split[c][:,3] for c in classes]\n",
"\n",
"X_mean = [np.mean(X_split[c], axis=0) for c in classes]\n",
"X_std = [np.std(X_split[c], axis=0) for c in classes]\n",
"print('średnia: ', X_mean) \n",
"print('odchylenie standardowe: ', X_std)"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/pawel/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:12: UserWarning: The following kwargs were not used by contour: 'lw'\n",
" if sys.path[0] == '':\n"
]
},
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 691.2x388.8 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plot_data_for_classification(Xbn, Ybn, xlabel=r'$x_1$', ylabel=r'$x_2$')\n",
"draw_means(fig, X_mean, xmin=-1.0, xmax=1.0, ymin=-1.0, ymax=1.0)\n",
"plot_prob(fig, X_mean, X_std, classes, xmin=-1.0, xmax=1.0, ymin=-1.0, ymax=1.0)"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/pawel/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:8: UserWarning: The following kwargs were not used by contour: 'lw'\n",
" \n"
]
},
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 691.2x388.8 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plot_data_for_classification(Xbn, Ybn, xlabel=r'$x_1$', ylabel=r'$x_2$')\n",
"plot_decision_boundary_bayes(fig, X_mean, X_std, xmin=-4.0, xmax=4.0, ymin=-4.0, ymax=4.0)"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"theta = [[-0.31582268]\n",
" [ 0.43496774]\n",
" [-0.21840373]\n",
" [-7.88802319]\n",
" [22.73897346]\n",
" [-4.43682364]]\n"
]
}
],
"source": [
"# Uruchomienie metody gradientu prostego dla regresji logistycznej\n",
"theta_start = np.matrix(np.zeros(Xbnp.shape[1])).reshape(Xbnp.shape[1], 1)\n",
"theta, errors = GD(h, J, dJ, theta_start, Xbnp, Ybn, \n",
" alpha=0.05, eps=10**-7, maxSteps=100000)\n",
"print(r'theta = {}'.format(theta))"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/pawel/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:10: UserWarning: The following kwargs were not used by contour: 'lw'\n",
" # Remove the CWD from sys.path while we load stuff.\n"
]
},
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 691.2x388.8 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plot_data_for_classification(Xbnp, Ybn, xlabel=r'$x_1$', ylabel=r'$x_2$')\n",
"plot_decision_boundary(fig, theta, Xbnp, xmin=-4.0, xmax=4.0)"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/pawel/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:8: UserWarning: The following kwargs were not used by contour: 'lw'\n",
" \n",
"/home/pawel/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:10: UserWarning: The following kwargs were not used by contour: 'lw'\n",
" # Remove the CWD from sys.path while we load stuff.\n"
]
},
{
"data": {
"image/png": "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
"text/plain": [
"<Figure size 691.2x388.8 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plot_data_for_classification(Xbn, Ybn, xlabel=r'$x_1$', ylabel=r'$x_2$')\n",
"plot_decision_boundary_bayes(fig, X_mean, X_std, xmin=-4.0, xmax=4.0, ymin=-4.0, ymax=4.0)\n",
"plot_decision_boundary(fig, theta, Xbnp, xmin=-4.0, xmax=4.0)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"* Naiwny klasyfikator Bayesa nie działa, jeżeli dane nie różnią się ani średnią, ani odchyleniem standardowym."
]
}
],
"metadata": {
"celltoolbar": "Slideshow",
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.3"
},
"livereveal": {
"start_slideshow_at": "selected",
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"theme": "white"
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}
},
"nbformat": 4,
"nbformat_minor": 4
}
