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@shawntan
Last active April 4, 2024 07:26
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "e0bd173a",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from matplotlib import pyplot as plt\n",
"import random"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "4eaae171",
"metadata": {},
"outputs": [],
"source": [
"def consecutive_average(x):\n",
" return np.mean(abs(x[1:] - x[:-1]))\n",
"\n",
"def plot_distribution(genfun, n=10000):\n",
" x = genfun(n)\n",
" plt.hist(x, bins=100)\n",
" print(\"Distribution\")\n",
" plt.show()\n",
" # x = genfun(4000)\n",
" factor = 2.66\n",
" plt.scatter(np.arange(x.shape[0]), x)\n",
" mean = np.mean(x)\n",
" plt.plot([0, x.shape[0]], [mean, mean], color='black')\n",
" \n",
" wheeler_bound = consecutive_average(x) * factor # wheeler\n",
" threesig_bound = 3 * np.std(x, ddof=1) \n",
" \n",
" def plot_bounds(mean, bound, color, label):\n",
" plt.plot([0, x.shape[0]], [mean + bound, mean + bound], linestyle='--', color=color, label=label)\n",
" plt.plot([0, x.shape[0]], [mean - bound, mean - bound], linestyle='--', color=color, label=label)\n",
"\n",
" plot_bounds(mean, wheeler_bound, color='red', label='wheeler')\n",
" plot_bounds(mean, threesig_bound, color='orange', label='3$\\sigma$') \n",
" plt.legend(loc='lower right')\n",
" print(\"Wheeler bound outliers:\", np.mean(abs(x - mean) > wheeler_bound))\n",
" print(\"3 sigma bound outliers:\", np.mean(abs(x - mean) > threesig_bound))"
]
},
{
"cell_type": "markdown",
"id": "3e2191cf",
"metadata": {},
"source": [
"## Chebyshev Inequality\n",
"\n",
"**ANY** distribution with standard deviation $\\sigma$ and mean $\\mu$ will satisfy the following,\n",
"$$ \\Pr(|X-\\mu |\\geq k\\sigma )\\leq{\\frac {1}{k^{2}}}.$$\n",
"\n",
"For $k= 3$, $p \\leq \\frac{1}{k^2} = \\frac{1}{9} = 0.111...$\n",
"\n",
"Meaning outliers **less** than $12\\%$ of the time."
]
},
{
"cell_type": "markdown",
"id": "272d834f",
"metadata": {},
"source": [
"## Random walk"
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "90e3fea1",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Distribution\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Wheeler bound outliers: 0.735\n",
"3 sigma bound outliers: 0.0\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def generate_random_walk(n):\n",
" x = np.zeros(n)\n",
" for i in range(1, n):\n",
" x[i] = x[i - 1] + np.random.choice([-1, 0, 0, 1], size=1) + 0.05 * np.random.randn(1)\n",
" return x\n",
"plot_distribution(generate_random_walk, n=200)"
]
},
{
"cell_type": "markdown",
"id": "8d929f19",
"metadata": {},
"source": [
"## Gumbel distribution"
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "e55866ca",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Distribution\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Wheeler bound outliers: 0.0139\n",
"3 sigma bound outliers: 0.0119\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def generate_extreme_values(n):\n",
" eps = 1e-6\n",
" x = (1 - eps) * np.random.rand(n) + 0.5 * eps\n",
" x = -np.log(-np.log(x))\n",
" return x\n",
"plot_distribution(generate_extreme_values)"
]
},
{
"cell_type": "markdown",
"id": "04cc3fda",
"metadata": {},
"source": [
"## Exponential distribution"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "6901f737",
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Distribution\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Wheeler bound outliers: 0.0336\n",
"3 sigma bound outliers: 0.0187\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_distribution(generate_exp_values)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.8"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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