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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import numpy.random as r\n",
"from numpy.random import laplace, random, binomial\n",
"\n",
"%matplotlib inline\n",
"\n",
"r.seed(42)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"p = 0.7\n",
"samples = [binomial(1, p, n) for n in [np.power(4, i)*1000 for i in range(4)]]"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"@np.vectorize\n",
"def randomized_response_mechanism(d, alpha, beta):\n",
" if random() < alpha:\n",
" return d\n",
" elif random() < beta:\n",
" return 1\n",
" else:\n",
" return 0\n",
" \n",
"def randomized_response_count(data, alpha, beta):\n",
" randomized_data = randomized_response_mechanism(data, alpha, beta)\n",
" return len(data) * (randomized_data.mean() - (1 - alpha)*beta)/alpha\n",
"\n",
"def randomized_response_accuracy_simulation(data, alpha, beta, n_samples=1000):\n",
" return [randomized_response_count(data, alpha, beta) - data.sum()\n",
" for _ in range(n_samples)]"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x106837c50>"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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88grXX389ubm5ZGVllbnWN998w5gxY1iwYAEnTpxgy5YttG3btty6vv76a6Kjozl27Bhx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\nFBWxOnAbZ1n0Sk6uEPD7pqTQLSmJuKpeWzPai4g0WQryIiLS9OzaZdb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i1h13mMbiP/0p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\nZmZmZk3k/53o+ZX8rb4rAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1068378d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"facets = {len(sample): pd.Series(randomized_response_accuracy_simulation(sample, 0.5, 0.5)) \n",
" for sample in samples}\n",
"\n",
"axes = pd.DataFrame(facets).plot(kind=\"density\", figsize=(17, 7))\n",
"axes.set_xlabel(\"Error\")\n",
"axes.set_xlim((-750, 750))\n",
"axes.legend([\"{} participants\".format(line.get_label()) for line in axes.get_lines()])"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def laplace_mechanism(data, f, eps):\n",
" return f(data) + laplace(0, 1.0/eps)\n",
"\n",
"def laplace_count(data, eps):\n",
" return laplace_mechanism(data, np.sum, eps)\n",
"\n",
"def laplace_accuracy_simulation(data, eps, n_samples=1000):\n",
" return [laplace_count(data, eps) - data.sum()\n",
" for _ in range(n_samples)]"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x118358ac8>"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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7OJ6dzaAaNRhasybJeXm03rmT144cIa+UVsi9t8G9/BircnYRkeuVn5/PhQsX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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11867c940>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"laplace_facets = {len(sample): pd.Series(laplace_accuracy_simulation(sample, np.log(3))) \n",
" for sample in samples}\n",
"\n",
"axes = pd.DataFrame(laplace_facets).plot(kind=\"density\", figsize=(17, 7))\n",
"axes.set_xlabel(\"Error\")\n",
"axes.set_xlim((-7.5, 7.5))\n",
"axes.legend([\"{} participants\".format(line.get_label()) for line in axes.get_lines()])"
]
}
],
"metadata": {
"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": "3.5.1"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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