03 - Differential Privacy with Gaussian Noise.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "16d187c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from math import e, exp, log, sqrt\n",
    "from scipy.stats import norm\n",
    "plt.style.use('ggplot')\n",
    "\n",
    "np.random.seed(42)\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcd09ee4",
   "metadata": {},
   "source": [
    "In this notebook, we'll explore using Gaussian noise to provide differential privacy guarantees. It has some nice properties, including the fact that we are used to reasoning about normally distributed error/noise!\n",
    "\n",
    "Let's use our same dataset to get an idea and compare between these different implementations of differential privacy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "25b0c1fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "mid_level_age = 45\n",
    "mid_level_salary = 50000\n",
    "\n",
    "age_scale = 10 #scale represents one standard deviation\n",
    "salary_scale = 10000\n",
    "\n",
    "salaries = [round(np.random.normal(mid_level_salary,salary_scale)) for _ in range(100)]\n",
    "ages = [round(np.random.normal(mid_level_age,age_scale)) for _ in range(100)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ee305c1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(ages, bins=20);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1e3ad74f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(salaries, bins=20);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "428eaf2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "loc = 0\n",
    "scale = 20\n",
    "\n",
    "x = np.arange(-50., 50., 0.1)\n",
    "pdf = norm.pdf(x, loc, scale)\n",
    "\n",
    "fig,ax= plt.subplots()\n",
    "ax.plot(x, pdf)\n",
    "ax.set_title('Gaussian Probability Density Function')\n",
    "ax.set_xlabel('actual number')\n",
    "ax.set_ylabel('probability density');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc1cb037",
   "metadata": {},
   "source": [
    "In order to scale our Gaussian distribution to meet differential privacy guarantees, we need to define our sensitivity, delta and epsilon. Let's keep it close to our prior notebook (with the exception that Laplace never needs Delta!). \n",
    "\n",
    "NOTE: This formula is only good for epsilon < 1 and is not as optimized (i.e. it adds more noise than necessary to meet the guarantees!). For real problems, please use a well-reviewed differential privacy library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9ec784bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23.94871751103854"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sensitivity=1\n",
    "delta = 10**-5\n",
    "epsilon=0.99\n",
    "sigma_squared = (2*sensitivity**2*log(1.25/delta))/epsilon**2 \n",
    "sigma_squared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "116768d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "loc = 0\n",
    "scale = sqrt(sigma_squared)\n",
    "\n",
    "x = np.arange(-50., 50., 0.1)\n",
    "pdf = norm.pdf(x, loc, scale)\n",
    "\n",
    "fig,ax= plt.subplots()\n",
    "ax.plot(x, pdf)\n",
    "ax.set_title('Gaussian Probability Density Function')\n",
    "ax.set_xlabel('actual number')\n",
    "ax.set_ylabel('probability density');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3785a3a0",
   "metadata": {},
   "source": [
    "This is a great time to remind ourselves that sensitivity for the Gaussian mechanism is different! (More on this in a minute!)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c00dff6",
   "metadata": {},
   "source": [
    "### Gaussian DP Mechanism\n",
    "\n",
    "Let's now implement a toy-example, please do not use this in real life! Instead, use a properly audited and well-known open-source library. :)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9a719602",
   "metadata": {},
   "outputs": [],
   "source": [
    "epsilon = 0.99 # Must be less than 1 to use this implementation!\n",
    "sensitivity = 1 \n",
    "delta=10**-5\n",
    "\n",
    "\n",
    "def gaussian_dp_mechanism(value, epsilon, sensitivity=sensitivity):\n",
    "    # Please do not use this function in real life - it is susceptible to well known attacks\n",
    "    # instead, use a well-known and audited open-source DP library \n",
    "    orig_value = value\n",
    "    gauss_scale = sqrt((2*sensitivity**2*log(1.25/delta))/epsilon**2)\n",
    "    value =  np.random.normal(value, gauss_scale)\n",
    "    print(\"Noise: {}\".format(value - orig_value))\n",
    "    return value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "efa31a2a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Noise: 1.75091927910006\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "101.75091927910006"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gaussian_dp_mechanism(len(ages), epsilon)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "65df093e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def filter_bounds(value, lower_bound, upper_bound):\n",
    "    if value < lower_bound:\n",
    "        return lower_bound\n",
    "    elif value > upper_bound:\n",
    "        return upper_bound\n",
    "    return value"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28157320",
   "metadata": {},
   "source": [
    "What about if we want to answer a more complicated query, like a sum? We need to know exactly how much one person can affect our outcome. Since we know this is a dataset of working persons, we might choose upper and lower bounds to artificially limit the amount that one person can affect the dataset. \n",
    "\n",
    "Let's take a look at how that might work with our ages!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5a24f83c",
   "metadata": {},
   "outputs": [],
   "source": [
    "bounded_ages = [filter_bounds(age, 20, 70) for age in ages]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "03943c9b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Noise: 137.21675881497413\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "4663.216758814974"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gaussian_dp_mechanism(np.sum(bounded_ages), epsilon, sensitivity=50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0f27f202",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4528"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(ages)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b3b74d2",
   "metadata": {},
   "source": [
    "And we can see how we want to spend our budget and adjust. Our count has lower sensitivity, so we will spend less on it. Of course, you may need to adjust your queries not only based on sensitivity, but also how accurate you want your query result to be!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "d780670c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Noise: 332.0995166206894\n",
      "Noise: 25.527328637215277\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "38.7015287377063"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count_epsilon = 0.20\n",
    "sum_epsilon = 0.79\n",
    "summed_ages = gaussian_dp_mechanism(np.sum(bounded_ages), sum_epsilon, sensitivity=50)\n",
    "count_ages = gaussian_dp_mechanism(len(bounded_ages), count_epsilon, sensitivity=1)\n",
    "\n",
    "mean_age = summed_ages / count_ages\n",
    "mean_age"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9ca8ed61",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.14528425932627437"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(np.mean(ages) - mean_age) / np.mean(ages)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8aa2763",
   "metadata": {},
   "source": [
    "So far, we've measured sensitivity by figuring out how much one person can affect a result. But there is actually a second dimension to sensitivity: how many different statistics can a user influence? This is called `l0`, while the concept we've been working on up to this point is called `l_inf`. \n",
    "\n",
    "For example, if users are logging in and reading their email and we want to calculate average reading time per email -- a prolific user could end up adding 100s or 1000s or read times per day. Another user might just read one email or less per day. These users have much different privacy loss in the overall average, even if we do bound the reading time of any single email using `linf_sensitivity`.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "471b69d0",
   "metadata": {},
   "source": [
    "### Comparing Laplace and Gaussian Noise\n",
    "\n",
    "Let's take a look at how Laplace and Gaussian noise compare with one another. To do so, we'll want to analyze how many distinct statistics a user can affect (this is also the `l0_sensitivity`). In this example, we'll use a better approximation for the Gaussian noise.\n",
    "\n",
    "NOTE: These functions were built based on [the Google Differential Privacy Library implementation of Gaussian noise.](https://github.com/google/differential-privacy/blob/0e95b99af5fedff95b8cab3739009bbc1366c068/go/noise/gaussian_noise.go)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9d61f88b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def delta_for_gaussian(sigma, l0_sensitivity, linf_sensitivity, epsilon):\n",
    "    l2_sensitivity = linf_sensitivity * sqrt(l0_sensitivity)\n",
    "    a = l2_sensitivity / (2*sigma)\n",
    "    b = epsilon * sigma / l2_sensitivity\n",
    "    c = exp(epsilon)\n",
    "    \n",
    "    if np.isinf(c): \n",
    "        return 0\n",
    "    if np.isinf(b):\n",
    "        return 0\n",
    "    return norm.cdf (a-b) - norm.cdf(-a-b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1259b79b",
   "metadata": {},
   "outputs": [],
   "source": [
    "gaussianSigmaAccuracy = 1e-3\n",
    "\n",
    "def sigma_for_gaussian(l0_sensitivity, linf_sensitivity, epsilon, delta):\n",
    "    if delta >=1:\n",
    "        return 0\n",
    "    \n",
    "    l2_sensitivity = linf_sensitivity * sqrt(l0_sensitivity)\n",
    "    upper_bound = l2_sensitivity\n",
    "    \n",
    "    while delta_for_gaussian(upper_bound, l0_sensitivity, linf_sensitivity, epsilon) > delta:\n",
    "        lower_bound = upper_bound\n",
    "        upper_bound = upper_bound * 2\n",
    "    \n",
    "    while upper_bound - lower_bound > gaussianSigmaAccuracy * lower_bound:\n",
    "        middle = lower_bound * 0.5 + upper_bound * 0.5\n",
    "        if delta_for_gaussian(middle, l0_sensitivity, linf_sensitivity, epsilon) > delta:\n",
    "            lower_bound = middle\n",
    "        else:\n",
    "            upper_bound = middle\n",
    "            \n",
    "    return upper_bound"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7fbc5bfb",
   "metadata": {},
   "outputs": [],
   "source": [
    "epsilon = 1\n",
    "delta = 10**-5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a74e3c8d",
   "metadata": {},
   "outputs": [],
   "source": [
    "l0_sensitivity = 1 # Number of statistics one user influences\n",
    "linf_sensitivity = 5\n",
    "\n",
    "laplace_std_dev = sqrt(2)*l0_sensitivity*linf_sensitivity\n",
    "gauss_std_dev = sigma_for_gaussian(l0_sensitivity, linf_sensitivity, \n",
    "                                   epsilon, delta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f967408e",
   "metadata": {},
   "outputs": [],
   "source": [
    "gauss_std_dev"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b57dd483",
   "metadata": {},
   "outputs": [],
   "source": [
    "laplace_std_dev"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aef90444",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(1., 20, 1)\n",
    "fig,ax= plt.subplots()\n",
    "\n",
    "laplace_stddev = sqrt(2)*x\n",
    "ax.plot(x, laplace_stddev , label='Laplace')\n",
    "\n",
    "\n",
    "gauss_std_dev = [sqrt(sigma_for_gaussian(l0, sensitivity, epsilon, delta)) for l0 in x]\n",
    "ax.plot(x, gauss_std_dev, label='Gaussian')\n",
    "    \n",
    "ax.set_xlabel('l0 sensitivity')\n",
    "ax.set_ylabel('standard deviations')\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96da457d",
   "metadata": {},
   "source": [
    "### Challenge\n",
    "\n",
    "- Use the dataset from the Opacus notebook with the methods in this notebook to calculate anonymous statistics about the reviews. \n",
    "- Find another open review dataset on Kaggle. Compare using the methods from this notebook to the ones from the Laplace notebook. Can you compare the normalized error?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e6929700",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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