Skip to content

Instantly share code, notes, and snippets.

@mcwitt
Last active January 24, 2024 22:42
Show Gist options
  • Save mcwitt/9a251f6c75d0263e7851341f2adf2ddd to your computer and use it in GitHub Desktop.
Save mcwitt/9a251f6c75d0263e7851341f2adf2ddd to your computer and use it in GitHub Desktop.
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "e41bccde-100f-40b1-b748-eafb91231422",
"metadata": {},
"outputs": [],
"source": [
"%config InlineBackend.figure_format = \"retina\""
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "f1cc9c93-07ef-4329-b669-89081a7e884f",
"metadata": {},
"outputs": [],
"source": [
"from functools import partial\n",
"\n",
"import jax\n",
"import jax.numpy as jnp\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np"
]
},
{
"cell_type": "markdown",
"id": "0f006340-602b-4bb8-a713-aa4db3c434a9",
"metadata": {},
"source": [
"Define a piecewise continuous function of $x$ with a discontinuity in the first derivative whose location is controlled by a parameter $p$:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "01a4688e-993d-46aa-8897-810cfac92d64",
"metadata": {},
"outputs": [],
"source": [
"def f(x, p):\n",
" return jnp.where(x < p, 1 - x / p, 0.0)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "a480630e-d858-4bc6-9f69-b40b39a03bf0",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f0bfebf8ad0>"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {
"image/png": {
"height": 413,
"width": 547
}
},
"output_type": "display_data"
}
],
"source": [
"for p in [0.2, 0.4, 0.6, 0.8]:\n",
" x = np.array([0, p, 1])\n",
" plt.plot(x, f(x, p), label=str(p))\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"id": "5b9c9470-7325-44d4-831c-3cfd529df7f6",
"metadata": {},
"source": [
"Approximate the integral between 0 and 1 with Monte Carlo integration (the exact result is $p/2$):"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "d3ff239d-3701-4f28-8304-3f0b8fd906b6",
"metadata": {},
"outputs": [],
"source": [
"def mc_integral(x, p):\n",
" return np.mean(f(x, p))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "46fd2ee4-118b-44ba-b55d-24e4683cc76f",
"metadata": {},
"outputs": [],
"source": [
"x = np.random.uniform(0, 1, 1_000)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "9fde80b1-b6ee-4c41-8202-c8d5d6973210",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Array(0.2401973, dtype=float32)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mc_integral(x, 0.5)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "501615e2-8172-40d2-ae7b-05e7052264ed",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Array(0.49294382, dtype=float32)"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mc_integral(x, 1.0)"
]
},
{
"cell_type": "markdown",
"id": "482b21aa-10f9-4da5-8fe1-106cc042e4b8",
"metadata": {},
"source": [
"Fix the randomness and differentiate by the parameter $p$. The exact answer is $1/2$."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "353157a3",
"metadata": {},
"outputs": [],
"source": [
"mc_integral_with_fixed_randomness = partial(mc_integral, x)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "0f913680-a476-4712-951b-6130703d9062",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Array(0.2401973, dtype=float32)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mc_integral_with_fixed_randomness(0.5)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "7de48e13-50e2-47e3-afd0-585b9d3b762b",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Array(0.2401973, dtype=float32)"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mc_integral_with_fixed_randomness(0.5)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "3d370b6e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"nan\n",
"0.4468972\n",
"0.49760544\n",
"0.51474005\n",
"0.50705624\n"
]
}
],
"source": [
"for p in np.linspace(0., 1.0, 5):\n",
" print(jax.grad(mc_integral_with_fixed_randomness)(p))"
]
},
{
"cell_type": "markdown",
"id": "cfed8499-d5fa-4503-9c9c-72a50e19e698",
"metadata": {},
"source": [
"Note that we get `nan` at $p=0$, because there are no samples $x$ with $x < 0$."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "c315866a-6656-4a4a-81d0-61e13179e5da",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.52856994\n",
"0.45231035\n",
"0.5032847\n",
"0.517582\n",
"0.50705624\n"
]
}
],
"source": [
"for p in np.linspace(0.1, 1.0, 5):\n",
" print(jax.grad(mc_integral_with_fixed_randomness)(p))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "94082131-36a9-42a9-9335-3a75a068874b",
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.11.6"
},
"widgets": {
"application/vnd.jupyter.widget-state+json": {
"state": {},
"version_major": 2,
"version_minor": 0
}
}
},
"nbformat": 4,
"nbformat_minor": 5
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment