{ "cells": [ { "cell_type": "markdown", "source": [ "# Stochastically Testing Privacy Mechanisms #\n", "\n", "How do you validate that a differential privacy implementation actually works?\n", "\n", "One approach that can build confidence that the differential privacy property holds for an implementation is stochastic testing: run many iterations of the algorithm against neighboring databases and check that for any output, the expected probability is bounded by $\\epsilon$.\n" ], "metadata": { "nteract": { "transient": { "deleting": false } } } }, { "cell_type": "code", "source": [ "# Preamble: imports and figure settings\n", "\n", "from eeprivacy import PrivateClampedMean\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib as mpl\n", "from scipy import stats\n", "\n", "np.random.seed(1234) # Fix seed for deterministic documentation\n", "\n", "mpl.style.use(\"seaborn-white\")\n", "\n", "MD = 20\n", "LG = 24\n", "plt.rcParams.update({\n", " \"figure.figsize\": [25, 7],\n", " \"legend.fontsize\": MD,\n", " \"axes.labelsize\": LG,\n", " \"axes.titlesize\": LG,\n", " \"xtick.labelsize\": LG,\n", " \"ytick.labelsize\": LG,\n", "})\n" ], "outputs": [], "execution_count": 1, "metadata": { "collapsed": true, "jupyter": { "source_hidden": false, "outputs_hidden": false }, "nteract": { "transient": { "deleting": false } }, "execution": { "iopub.status.busy": "2020-09-28T23:12:28.291Z", "iopub.execute_input": "2020-09-28T23:12:28.298Z", "iopub.status.idle": "2020-09-28T23:12:28.998Z", "shell.execute_reply": "2020-09-28T23:12:29.022Z" } } }, { "cell_type": "markdown", "source": [ "In the test below, we run a `PrivateClampedMean` for a large number of trials for two different databases: one with a single element `0` and one with a single element `1`.\n", "\n", "Then, we bin the results and compute the \"realized $\\epsilon$\" for each bin. By chance, sometimes this will slightly exceed the $\\epsilon$ value. The test fails if the realized $\\epsilon$ greatly exceeds the desired $\\epsilon$ for any of the bins." ], "metadata": { "nteract": { "transient": { "deleting": false } } } }, { "cell_type": "code", "source": [ "private_mean = PrivateClampedMean(lower_bound=0, upper_bound=1)\n", "\n", "T = 1000000\n", "A = [private_mean.execute(values=[], epsilon=0.1) for t in range(T)]\n", "B = [private_mean.execute(values=[1], epsilon=0.1) for t in range(T)]\n", "\n", "L = 0\n", "U = 1\n", "\n", "A = np.clip(A, L, U)\n", "B = np.clip(B, L, U)\n", "\n", "bins = np.linspace(L, U, num=50)\n", "\n", "fig, ax = plt.subplots()\n", "ax.set_yscale(\"log\")\n", "\n", "plt.hist(A, color='b', alpha=0.5, bins=bins)\n", "plt.hist(B, color='r', alpha=0.5, bins=bins)\n", "plt.title(\"Compare output likelihood for neighboring databases\")\n", "plt.xlabel(\"Output\")\n", "plt.ylabel(\"Count (log scale)\")\n", "plt.show()\n", "\n", "A, bin_edges = np.histogram(A, bins=bins)\n", "B, bin_edges = np.histogram(B, bins=bins)\n", "\n", "realized_epsilon = np.abs(np.log(A / B))\n", "\n", "plt.hist(realized_epsilon, color=\"k\", bins=20)\n", "plt.title(\"Realized ε\")\n", "plt.xlabel(\"ε\")\n", "plt.ylabel(\"Count\")\n", "plt.show()" ], "outputs": [ { "output_type": "display_data", "data": { "text/plain": "
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\n" 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