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@Gilles86
Created August 30, 2023 10:39
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{
"cells": [
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from scipy.optimize import minimize\n",
"import scipy.stats as ss\n",
"import seaborn as sns\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 95,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x2935be170>]"
]
},
"execution_count": 95,
"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": [
"dist = ss.gamma(1, 0, 2)\n",
"samples = dist.rvs(1000)\n",
"\n",
"x = np.linspace(1e-6, 10)\n",
"p = dist.pdf(x)\n",
"\n",
"plt.plot(x, p, c='k', lw=2)"
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.0, 250.0)"
]
},
"execution_count": 97,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dist = ss.gamma(1, 0, 2)\n",
"samples = dist.rvs(1000)\n",
"\n",
"x = np.linspace(1e-6, 5)\n",
"p = dist.pdf(x)\n",
"\n",
"plt.plot(x, p, c='k', lw=2)\n",
"ax = plt.gca()\n",
"\n",
"# sns.histplot(.rvs(1000))\n",
"\n",
"dist.mean()\n",
"\n",
"ax2=ax.twinx()\n",
" \n",
"\n",
"cost_function = lambda xhat, x, pdf, p: np.sum(pdf*(np.abs(x - xhat))**p, -1)\n",
"\n",
"# plt.plot(x, cost_function(x, x, p, 2))\n",
"\n",
"ax2.plot(x, cost_function(x[:, np.newaxis], x[np.newaxis, :], p[np.newaxis, :], 1))\n",
"ax2.plot(x, cost_function(x[:, np.newaxis], x[np.newaxis, :], p[np.newaxis, :], 2))\n",
"ax2.plot(x, cost_function(x[:, np.newaxis], x[np.newaxis, :], p[np.newaxis, :], 3))\n",
"ax2.plot(x, cost_function(x[:, np.newaxis], x[np.newaxis, :], p[np.newaxis, :], 4))\n",
"\n",
"plt.ylim(0, 250)"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {},
"outputs": [],
"source": [
"def get_cost_gradient_function(x, pdf, p):\n",
" cost_function = lambda xhat: np.sum(pdf*(np.abs(x - xhat))**p, -1)\n",
" gradient = lambda xhat: -np.sum(pdf*(p * (x-xhat) * np.abs(x - xhat)**(p-2.)), -1)\n",
"\n",
" return cost_function, gradient\n",
"\n",
"\n",
"def get_lp_estimate(x, pdf, p, use_gradient=True):\n",
"\n",
" cost_function, gradient = get_cost_gradient_function(x, pdf, p)\n",
"\n",
" mean = np.trapz(x*pdf, x)\n",
" # return cost_function, gradient\n",
" if use_gradient:\n",
" return minimize(cost_function, mean, jac=gradient, method='BFGS').x\n",
" else:\n",
" return minimize(cost_function, mean).x\n"
]
},
{
"cell_type": "code",
"execution_count": 106,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x291e50a00>]"
]
},
"execution_count": 106,
"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": [
"cost, gradient = get_cost_gradient_function(x, p, 5.)\n",
"plt.plot(x, [gradient(e) for e in x])\n",
"plt.plot(x, [cost(e) for e in x])\n",
"# plt.plot(x, np.gradient([cost(e) for e in x], x))\n"
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {},
"outputs": [],
"source": [
"pdf = p\n",
"gradient = lambda xhat: np.sum(pdf*(p * (x-xhat) * np.abs(x - xhat)**(p-2.)), -1)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"gradient()"
]
},
{
"cell_type": "code",
"execution_count": 109,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"30.4 ms ± 782 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%%timeit\n",
"ps = np.linspace(3, 10)\n",
"\n",
"x = np.linspace(1e-6, 10, 500)\n",
"p = dist.pdf(x)\n",
"\n",
"ests = [get_lp_estimate(x, p, exp)[0] for exp in ps]\n",
"plt.plot(ps, ests)"
]
},
{
"cell_type": "code",
"execution_count": 93,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"27.5 ms ± 180 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
]
}
],
"source": [
"%%timeit\n",
"ps = np.linspace(3, 10)\n",
"ests = [get_lp_estimate(x, p, exp, use_gradient=False)[0] for exp in ps]"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x29295ff10>]"
]
},
"execution_count": 90,
"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": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "base",
"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": "3.10.6"
},
"orig_nbformat": 4
},
"nbformat": 4,
"nbformat_minor": 2
}
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