{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "# Working with Unknown Dataset Sizes\n", "\n", "This notebook demonstrates the features built into OpenDP to handle unknown or private dataset sizes.\n", "\n", "There are situations where simply the number of observations itself can leak private information.\n", "For example, if a dataset contained all the individuals with a rare disease in a community,\n", "then knowing the size of the dataset would reveal how many people in the community had that condition.\n", "In general, any given dataset may be some well-defined subset of a population.\n", "The given dataset's size is equivalent to a count query on that subset,\n", "so we should protect the dataset size just as we would protect any other query we want to provide privacy guarantees for." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Load exemplar dataset" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "%[ -e data.csv ] || wget https://raw.githubusercontent.com/opendp/opendp/main/docs/source/data/PUMS_california_demographics_1000/data.csv" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2021-04-15T16:41:40.471981Z", "iopub.status.busy": "2021-04-15T16:41:40.458021Z", "iopub.status.idle": "2021-04-15T16:41:40.634785Z", "shell.execute_reply": "2021-04-15T16:41:40.635247Z" } }, "outputs": [], "source": [ "# Define parameters up-front\n", "# Each parameter is either a guess, a DP release, or public information\n", "var_names = [\"age\", \"sex\", \"educ\", \"race\", \"income\", \"married\"] # public information\n", "age_bounds = (0., 120.) # an educated guess\n", "age_prior = 38. # average age for entire US population (public information)\n", "size = 1000 # records in dataset, public information\n", "\n", "# Load data\n", "import numpy as np\n", "age = np.genfromtxt('data.csv', delimiter=',', names=var_names)[:]['age'].tolist() # type: ignore" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## When dataset size is known\n", "\n", "For contrast, we briefly start with the assumption that the dataset size is not protected.\n", "If you know the dataset size (or any other parameter) is publicly available,\n", "then you may make use of such information while building your measurement.\n", "\n", "OpenDP treats any descriptors in the input domain as public information.\n", "We incorporate the `size` descriptor into the input domain in the analysis below." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2021-04-15T16:41:40.645482Z", "iopub.status.busy": "2021-04-15T16:41:40.644181Z", "iopub.status.idle": "2021-04-15T16:41:40.686094Z", "shell.execute_reply": "2021-04-15T16:41:40.685529Z" }, "pycharm": { "name": "#%%\n" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "DP mean: 48.41546783313125\n" ] } ], "source": [ "from opendp.transformations import *\n", "from opendp.measurements import then_laplace\n", "from opendp.mod import enable_features\n", "from opendp.domains import vector_domain, atom_domain\n", "from opendp.metrics import symmetric_distance\n", "\n", "enable_features(\"contrib\", \"floating-point\")\n", "\n", "input_domain = vector_domain(atom_domain(T=float), size=1000)\n", "input_metric = symmetric_distance()\n", "\n", "dp_mean = (\n", " (input_domain, input_metric) >>\n", " # Clamp age values\n", " then_clamp(bounds=age_bounds) >>\n", " # Aggregate\n", " then_mean() >>\n", " # Noise\n", " then_laplace(scale=1.)\n", ")\n", "\n", "print(\"DP mean:\", dp_mean(age))" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "In this case, OpenDP assumes that you truthfully and correctly know the size of the dataset.\n" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "### When dataset size is unkown\n", "If you don't have a prior, ballpark estimate for `size`, you can first spend some of your privacy budget\n", "to estimate the dataset size.\n", "Here is an example:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "DP count: 999\n" ] } ], "source": [ "# First, estimate the number of records in the dataset.\n", "dp_count = (input_domain, input_metric) >> then_count() >> then_laplace(scale=1.)\n", "dp_count_release = dp_count(age)\n", "print(\"DP count: {0}\".format(dp_count_release))" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "If we want to conduct a bounded-DP analysis, we can establish the size descriptor via the \"resize\" transformation. \n", "The resize is a 2-stable dataset transformation, where you pass a fixed target size into the constructor.\n", "If the true dataset has more records than the underlying dataset, it is sampled down,\n", "and if the true dataset has fewer records than the underlying dataset, additional constant rows are imputed." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2021-04-15T16:41:40.731918Z", "iopub.status.busy": "2021-04-15T16:41:40.731318Z", "iopub.status.idle": "2021-04-15T16:41:40.740106Z", "shell.execute_reply": "2021-04-15T16:41:40.739600Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "DP mean: 45.518070978540095\n" ] } ], "source": [ "def make_mean_measurement(target_size):\n", " \"\"\"a convenience constructor for building a mean measurement that resizes to `target_size`\"\"\"\n", " return ((vector_domain(atom_domain(T=float)), symmetric_distance()) >>\n", " then_resize(size=target_size, constant=age_prior) >>\n", " then_clamp(age_bounds) >>\n", " then_mean() >>\n", " then_laplace(scale=1.0))\n", "\n", "\n", "dp_mean = make_mean_measurement(dp_count_release)\n", "dp_mean_release = dp_mean(age)\n", "print(\"DP mean: {0}\".format(dp_mean_release))" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "### Providing incorrect dataset size values\n", "\n", "The resize transformation does not assume you truthfully or correctly know the size of the dataset.\n", "Moreover, it cannot respond with an error message if you get the size incorrect;\n", "doing so would permit an attack whereby an analyst could repeatedly guess different dataset sizes until the error message went away,\n", "thereby leaking the exact dataset size.\n", "\n", "In this example, we intentionally provide under-estimates and over-estimates of `size` and still receive an answer." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2021-04-15T16:41:40.694235Z", "iopub.status.busy": "2021-04-15T16:41:40.693539Z", "iopub.status.idle": "2021-04-15T16:41:40.711013Z", "shell.execute_reply": "2021-04-15T16:41:40.711551Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "DP mean (n=200): 42.81880656946988\n", "DP mean (n=1000): 43.49853735856283\n", "DP mean (n=2000): 40.50278188564646\n" ] } ], "source": [ "lower_n = make_mean_measurement(target_size=200)(age)\n", "real_n = make_mean_measurement(target_size=1000)(age)\n", "higher_n = make_mean_measurement(target_size=2000)(age)\n", "\n", "print(\"DP mean (n=200): {0}\".format(lower_n))\n", "print(\"DP mean (n=1000): {0}\".format(real_n))\n", "print(\"DP mean (n=2000): {0}\".format(higher_n))" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "There is an interesting trade-off to this approach, that can be demonstrated visually via simulations.\n", "Before we move on to the visualizations, let's make a few helper functions for building measurements that consume a specified privacy budget." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [], "source": [ "from functools import lru_cache\n", "from opendp.mod import binary_search_chain\n", "\n", "input_space = vector_domain(atom_domain(T=float)), input_metric\n", "\n", "@lru_cache(maxsize=None)\n", "def make_count_with(*, epsilon):\n", " counter = input_space >> then_count()\n", " return binary_search_chain(\n", " lambda s: counter >> then_laplace(scale=s),\n", " d_in=1, d_out=epsilon, \n", " bounds=(0., 10000.))\n", "\n", "@lru_cache(maxsize=None)\n", "def make_mean_with(*, target_size, epsilon):\n", " mean_chain = (\n", " input_space >>\n", " # Resize the dataset to length `target_size`.\n", " # If there are fewer than `target_size` rows in the data, fill with a constant.\n", " # If there are more than `target_size` rows in the data, only keep `data_size` rows\n", " then_resize(size=target_size, constant=age_prior) >>\n", " # Clamp age values\n", " then_clamp(bounds=age_bounds) >>\n", " # Compute the mean\n", " then_mean()\n", " )\n", " return binary_search_chain(\n", " lambda s: mean_chain >> then_laplace(scale=s),\n", " d_in=1, d_out=epsilon, \n", " bounds=(0., 10.))\n", "\n", "@lru_cache(maxsize=None)\n", "def make_sum_with(*, epsilon):\n", " bounded_age_sum = (\n", " input_space >>\n", " # Clamp income values\n", " then_clamp(bounds=age_bounds) >>\n", " then_sum()\n", " )\n", " return binary_search_chain(\n", " lambda s: bounded_age_sum >> then_laplace(scale=s),\n", " d_in=1, d_out=epsilon,\n", " bounds=(0., 1000.))" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "\n", "In this simulation, we are running the same procedure `n_simulations` times. In each iteration, we collect the estimated count and mean." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Status:\n", "0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%\n" ] } ], "source": [ "n_simulations = 1000\n", "\n", "history_count = []\n", "history_mean = []\n", "\n", "print(\"Status:\")\n", "for i in range(n_simulations):\n", " if i % 100 == 0:\n", " print(f\"{i / n_simulations:.0%} \", end=\"\")\n", " \n", " count_chain = make_count_with(epsilon=0.05)\n", " history_count.append(count_chain(age))\n", " \n", " mean_chain = make_mean_with(target_size=history_count[-1], epsilon=1.)\n", " history_mean.append(mean_chain(age))\n", "\n", "print(\"100%\")" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Now we plot our simulation data, with counts on the X axis and means on the Y axis." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import statistics\n", "\n", "true_mean_age = statistics.mean(age)\n", "\n", "# The light blue circles are DP means\n", "plt.plot(history_count, history_mean, 'o', fillstyle='none', color = 'cornflowerblue')\n", "\n", "def compute_expected_mean(count):\n", " count = max(count, size)\n", " return ((true_mean_age * size) + (count - size) * age_prior) / count\n", "\n", "expected_count = list(range(min(history_count), max(history_count)))\n", "expected_mean = list(map(compute_expected_mean, expected_count))\n", "\n", "# The dark blue dots are the average DP mean per dataset size\n", "for count in expected_count:\n", " sims = [m for c, m in zip(history_count, history_mean) if c == count]\n", " if len(sims) > 6:\n", " plt.plot(count, statistics.mean(sims), 'o', color = 'indigo')\n", "\n", "# The red line is the expected value by dp release of dataset size\n", "plt.plot(expected_count, expected_mean, linestyle='--', color = 'tomato')\n", "plt.ylabel('DP Release of Age')\n", "plt.xlabel('DP estimate of row count')\n", "plt.show()" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "In this plot, the red dashed line is the expected outcome,\n", "and each of the points represents a `(count, mean)` tuple from one iteration of the simulation.\n", "Due to the behavior of the resize preprocess transformation,\n", "underestimated counts lead to higher variance means,\n", "and overestimated counts bias the mean closer to the imputation constant.\n", "On the other hand, underestimated counts are unbiased, and overestimated counts have reduced variance.\n", "\n", "Keep in mind that it is valid to postprocess the count to be smaller,\n", "reducing the likelihood of introducing bias by imputing.\n", "If the count is overestimated, the amount of bias introduced to the statistic\n", "by imputation when resizing depends on how much the count estimate differs from the true dataset count,\n", "and how much the imputation constant differs from the true dataset mean.\n", "Since both of these quantities are private (and unknowable), they are not accounted for in accuracy estimates." ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "In the next plot, we see the range of DP means calculated as a function of the resized row count.\n", "Note that the range of possible DP mean values decreases as the resized count increases, and that the DP mean gets\n", "closer to the prior for the true value: 38." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import pandas as pd\n", "import seaborn as sns\n", "\n", "releases = []\n", "# X axis ticks\n", "n_range = range(100, 2001, 200)\n", "# Number of samples per boxplot\n", "n_simulations = 50\n", "\n", "for n in n_range:\n", " mean_chain = make_mean_with(target_size=n, epsilon=1.)\n", " for index in range(n_simulations):\n", " \n", " # get mean of age at the given n\n", " releases.append((n, mean_chain(age)))\n", "\n", "# get released values\n", "df = pd.DataFrame.from_records(releases, columns=['resize to row count', 'DP mean'])\n", "\n", "# The boxplots show the distribution of releases per n\n", "plot = sns.boxplot(x = 'resize to row count', y = 'DP mean', data = df)\n", "# The blue line is the true mean\n", "plot.axhline(true_mean_age)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "The results from this approach have a similar interpretation as in the prior plot.\n", "Underestimated counts lead to higher variance means,\n", "and overestimated counts lead to greater bias in means.\n", "Thankfully, the count is a low-sensitivity query, so count estimates are usually very close to the true count." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### OpenDP `resize` vs. other approaches\n", "The standard formula for the mean of a variable is:\n", "$\\bar{x} = \\frac{\\sum{x}}{n}$\n", "\n", "The conventional, and simpler, approach in the differential privacy literature, is to: \n", "\n", "1. compute a DP sum of the variable for the numerator\n", "2. compute a DP count of the dataset rows for the denominator\n", "3. take their ratio\n", "\n", "This is sometimes called a 'plug-in' approach, as we are plugging-in differentially private answers for each of the\n", "terms in the original formula, without any additional modifications, and using the resulting answer as our\n", "estimate while ignoring the noise processes of differential privacy. While this 'plug-in' approach does result in a\n", "differentially private value, the utility here is generally lower than the solution in OpenDP. Because the number of\n", "terms summed in the numerator does not agree with the value in the denominator, the variance is increased and the\n", "resulting distribution becomes both biased and asymmetrical, which is visually noticeable in smaller samples." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Status:\n", "0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%\n" ] } ], "source": [ "n_simulations = 1_000\n", "history_plugin = []\n", "history_resize = []\n", "\n", "# sized estimators are more robust to noisy counts, so epsilon is small\n", "# the less epsilon provided to this count, the more the result will be biased towards the prior\n", "resize_count = make_count_with(epsilon=0.2)\n", "\n", "# plugin estimators want a much more accurate count\n", "plugin_count = make_count_with(epsilon=0.5)\n", "plugin_sum = make_sum_with(epsilon=0.5)\n", "\n", "print(\"Status:\")\n", "for i in range(n_simulations):\n", " if i % 100 == 0:\n", " print(f\"{i / n_simulations:.0%} \", end=\"\")\n", "\n", " history_plugin.append(plugin_sum(age) / plugin_count(age))\n", "\n", " resize_mean = make_mean_with(target_size=resize_count(age), epsilon=.8)\n", " history_resize.append(resize_mean(age))\n", " \n", "print('100%')" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "sns.kdeplot(history_resize, fill=True, linewidth=3,\n", " label = 'Resize Mean')\n", "sns.kdeplot(history_plugin, fill=True, linewidth=3,\n", " label = 'Plug-in Mean')\n", "\n", "ax.plot([true_mean_age,true_mean_age], [0,2], linestyle='--', color = 'forestgreen')\n", "plt.xlabel('DP Release of Age')\n", "leg = ax.legend()" ] }, { "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "We have noticed that for the same privacy loss,\n", "the distribution of answers from OpenDP's resizing approach to the mean is tighter around the true dataset value (thus lower in error) than the conventional plug-in approach.\n", "\n", "*Note, in these simulations, we've shown equal division of the epsilon for all constituent releases,\n", "but higher utility (lower error) can be generally gained by moving more of the epsilon into the sum,\n", "and using less in the count of the dataset rows, as in earlier examples.*" ] } ], "metadata": { "interpreter": { "hash": "3220da548452ac41acb293d0d6efded0f046fab635503eb911c05f743e930f34" }, "kernelspec": { "display_name": "Python 3.8.13 ('psi')", "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": "3.9.13" } }, "nbformat": 4, "nbformat_minor": 2 }