{ "cells": [ { "attachments": {}, "cell_type": "markdown", "metadata": { "pycharm": { "name": "#%% md\n" } }, "source": [ "# Preprocessing: Resize\n", "\n", "This section demonstrates the resize transformation used to convert unbounded-DP queries into bounded-DP queries.\n", "\n", "There are situations where knowing 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 example dataset" ] }, { "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", "\n", "# Load data\n", "import opendp.prelude as dp\n", "import numpy as np\n", "age = np.genfromtxt(dp.examples.get_california_pums_path(), delimiter=',', names=var_names)[:]['age'].tolist() # type: ignore" ] }, { "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ "## When dataset size is known\n", "\n", "To set a baseline for comparison, we'll first assume that we _do_ know the dataset size.\n", "We'll provide `size` in the domain.\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: 43.84811402354421\n" ] } ], "source": [ "import opendp.prelude as dp\n", "\n", "dp.enable_features(\"contrib\")\n", "\n", "input_domain = dp.vector_domain(dp.atom_domain(T=float), size=1000)\n", "input_metric = dp.symmetric_distance()\n", "\n", "dp_mean = (\n", " (input_domain, input_metric) >>\n", " # Impute NaN values\n", " dp.t.then_impute_constant(0.0) >>\n", " # Clamp age values\n", " dp.t.then_clamp(bounds=age_bounds) >>\n", " # Aggregate\n", " dp.t.then_mean() >>\n", " # Noise\n", " dp.m.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 unknown\n", "We now assume that size is not known.\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: 1001\n" ] } ], "source": [ "# First, estimate the number of records in the dataset.\n", "dp_count = (input_domain, input_metric) >> dp.t.then_count() >> dp.m.then_laplace(scale=1.)\n", "dp_count_release = dp_count(age)\n", "print(\"DP count:\", 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: 44.60152231817973\n" ] } ], "source": [ "def make_mean_measurement(target_size):\n", " \"\"\"a convenience constructor for building a mean measurement that resizes to `target_size`\"\"\"\n", " return ((dp.vector_domain(dp.atom_domain(T=float)), dp.symmetric_distance()) >>\n", " dp.t.then_impute_constant(age_prior) >>\n", " dp.t.then_resize(size=target_size, constant=age_prior) >>\n", " dp.t.then_clamp(age_bounds) >>\n", " dp.t.then_mean() >>\n", " dp.m.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:\", 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): 43.09883682992345\n", "DP mean (n=1000): 44.671207844903705\n", "DP mean (n=2000): 41.396972829360706\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): \", lower_n)\n", "print(\"DP mean (n=1000):\", real_n)\n", "print(\"DP mean (n=2000):\", 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", "\n", "input_space = dp.vector_domain(dp.atom_domain(T=float)), input_metric\n", "\n", "@lru_cache(maxsize=None)\n", "def make_count_with(*, epsilon):\n", " counter = input_space >> dp.t.then_count()\n", " return dp.binary_search_chain(\n", " lambda s: counter >> dp.m.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", " # Impute NaN values\n", " dp.t.then_impute_constant(age_prior) >>\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", " dp.t.then_resize(size=target_size, constant=age_prior) >>\n", " # Clamp age values\n", " dp.t.then_clamp(bounds=age_bounds) >>\n", " # Compute the mean\n", " dp.t.then_mean()\n", " )\n", " return dp.binary_search_chain(\n", " lambda s: mean_chain >> dp.m.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", " dp.t.then_impute_constant(0.0) >>\n", " dp.t.then_clamp(bounds=age_bounds) >>\n", " dp.t.then_sum()\n", " )\n", " return dp.binary_search_chain(\n", " lambda s: bounded_age_sum >> dp.m.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=1.0)\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", "size = 1000\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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" ] }, "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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", 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" ] }, "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": { "kernelspec": { "display_name": ".venv", "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": "3.13.2" } }, "nbformat": 4, "nbformat_minor": 2 }