247 lines
126 KiB
Text
247 lines
126 KiB
Text
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "7ececd15",
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"metadata": {},
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"source": [
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"# Estimateur par intervalle"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "e925282e",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ba74960c",
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"metadata": {},
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"source": [
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"Densité $f: \\mathbb{R} \\to [0, \\infty)$ inconnue, échantillon $x_1, \\ldots, x_N$ i.i.d. de $f$. On veut estimer $f$ à partir de cet échantillon.\n",
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"\n",
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"$$\n",
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"f: x \\rightarrow \\frac{1}{\\sigma \\sqrt{2\\pi}} e^{-\\frac{1}{2} \\left( \\frac{x-\\mu}{\\sigma} \\right)^2}\n",
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"$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "c336ac3f",
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"metadata": {},
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"outputs": [],
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"source": [
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"mu = 1\n",
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"sigma = 1\n",
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"\n",
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"def unknown_density(x):\n",
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" return 1 / (sigma * np.sqrt(2 * np.pi)) * np.exp(-0.5 * ((x - mu) / sigma) ** 2)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "44e372eb",
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"metadata": {},
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"outputs": [],
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"source": [
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"def generate_samples(density, n_samples):\n",
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" samples = []\n",
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" x_min, x_max = -5, 5\n",
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" y_max = 0.45 \n",
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"\n",
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" while len(samples) < n_samples:\n",
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" # 1. Tirer un x candidat uniformément dans l'intervalle\n",
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" x_cand = np.random.uniform(x_min, x_max)\n",
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" # 2. Tirer une hauteur uniforme u\n",
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" u = np.random.uniform(0, y_max)\n",
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" \n",
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" # 3. Accepter si u est sous la courbe de votre densité\n",
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" if u < density(x_cand):\n",
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" samples.append(x_cand)\n",
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" \n",
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" return np.array(samples)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"id": "02cedfd4",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 1000x600 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"samples = generate_samples(unknown_density, 2000)\n",
|
|
"\n",
|
|
"x_plot = np.linspace(-5, 5, 1000)\n",
|
|
"y_plot = unknown_density(x_plot)\n",
|
|
"\n",
|
|
"plt.figure(figsize=(10, 6))\n",
|
|
"\n",
|
|
"plt.hist(samples, bins=50, density=True, alpha=0.6, color='skyblue', label='Échantillons iid générés')\n",
|
|
"\n",
|
|
"plt.plot(x_plot, y_plot, 'r-', lw=2, label='Densité théorique (unknown_density)')\n",
|
|
"\n",
|
|
"plt.title('Vérification de la génération des $x_i$ iid')\n",
|
|
"plt.xlabel('$x$')\n",
|
|
"plt.ylabel('Densité')\n",
|
|
"plt.legend()\n",
|
|
"plt.grid(axis='y', alpha=0.3)\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"id": "e086397e",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"Text(0.5, 1.0, 'Noyau uniforme')"
|
|
]
|
|
},
|
|
"execution_count": 5,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 1000x400 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"kernel = lambda u: 0.5 * (np.abs(u) <= 1) \n",
|
|
"\n",
|
|
"# plot kernel\n",
|
|
"u_plot = np.linspace(-2, 2, 1000)\n",
|
|
"plt.figure(figsize=(10, 4))\n",
|
|
"plt.plot(u_plot, kernel(u_plot), 'b-', lw=2, label='Noyau uniforme')\n",
|
|
"plt.title('Noyau uniforme') "
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "52f92c9f",
|
|
"metadata": {},
|
|
"source": [
|
|
"$$\n",
|
|
"\\hat{f}(x) = \\frac{1}{N h} \\sum_{i=1}^N K\\left( \\frac{x - x_i}{h} \\right)\n",
|
|
"$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 6,
|
|
"id": "db70a5dc",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def estimator(kernel, samples, bandwidth = 0.5):\n",
|
|
" N = len(samples)\n",
|
|
" def estimate(x):\n",
|
|
" S = 0\n",
|
|
" for x_i in samples:\n",
|
|
" S += kernel((x - x_i) / bandwidth)\n",
|
|
" return S / (N * bandwidth)\n",
|
|
" return estimate"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "3081f332",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"(1000,) (1000,)\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"<matplotlib.legend.Legend at 0x7b8f2c6d3470>"
|
|
]
|
|
},
|
|
"execution_count": 7,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
},
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"estimate = estimator(unknown_density, samples, 0.2)\n",
|
|
"\n",
|
|
"x_plot = np.linspace(-5, 5, 1000)\n",
|
|
"y_density = unknown_density(x_plot)\n",
|
|
"y_testimate = np.array([estimate(x) for x in x_plot])\n",
|
|
"\n",
|
|
"print(x_plot.shape, y_testimate.shape)\n",
|
|
"\n",
|
|
"plt.plot(x_plot, y_density, 'r-', lw=2, label='Densité théorique (unknown_density)')\n",
|
|
"plt.plot(x_plot, y_testimate, 'g-', lw=2, label='Estimation par noyau (estimator)')\n",
|
|
"plt.title('Comparaison entre l\\'estimation par noyau et la densité théorique')\n",
|
|
"plt.xlabel('$x$')\n",
|
|
"plt.ylabel('Densité')\n",
|
|
"plt.legend()"
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": ".venv",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.12.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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