{
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   "cell_type": "markdown",
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   "source": [
    "# Laplace Mechanism Basics #\n",
    "\n",
    "The Laplace Mechanism adds noise drawn from a Laplace distribution to realize differential privacy.\n",
    "\n",
    "This mechanism works well for computing means and histograms, providing accurate results at minimal privacy budgets.\n",
    "\n",
    "This notebook walks through the basic `eeprivacy` functions for working with the Laplace Mechanism."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "execution": {
     "iopub.execute_input": "2020-11-04T00:55:48.510Z",
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   "outputs": [],
   "source": [
    "# Preamble: imports and figure settings\n",
    "\n",
    "from eeprivacy.mechanisms import LaplaceMechanism\n",
    "from eeprivacy.operations import (\n",
    "  PrivateClampedMean,\n",
    "  PrivateHistogram,\n",
    ")\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 = 28\n",
    "LG = 36\n",
    "plt.rcParams.update({\n",
    "    \"figure.figsize\": [25, 10],\n",
    "    \"legend.fontsize\": MD,\n",
    "    \"axes.labelsize\": LG,\n",
    "    \"axes.titlesize\": LG,\n",
    "    \"xtick.labelsize\": LG,\n",
    "    \"ytick.labelsize\": LG,\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nteract": {
     "transient": {
      "deleting": false
     }
    }
   },
   "source": [
    "## Distribution of Laplace Mechanism Outputs ##\n",
    "\n",
    "For a given ε, noise is drawn from the Laplace distribution at `b`=`sensitivity`/ε. The `eeprivacy` class `LaplaceMechanism` draws this noise and adds it to a private value:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "nteract": {
     "transient": {
      "deleting": false
     }
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   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'LaplaceMechanism' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-1-4ba7af56c713>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mtrials\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mt\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1000\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m   trials.append(LaplaceMechanism.execute(\n\u001b[0m\u001b[1;32m      4\u001b[0m     \u001b[0mvalue\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0mepsilon\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'LaplaceMechanism' is not defined"
     ]
    }
   ],
   "source": [
    "trials = []\n",
    "for t in range(1000):\n",
    "  trials.append(LaplaceMechanism.execute(\n",
    "    value=0,\n",
    "    epsilon=0.1,\n",
    "    sensitivity=199/3000\n",
    "  ))\n",
    "\n",
    "plt.hist(trials, bins=30, color=\"k\")\n",
    "plt.title(\"Distribution of outputs from Laplace Mechanism\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nteract": {
     "transient": {
      "deleting": false
     }
    }
   },
   "source": [
    "## Laplace Mechanism Confidence Interval ##\n",
    "\n",
    "With the `eeprivacy` confidence interval functions, analysts can determine how far away the true value of a statistics is from the differentially private result.\n",
    "\n",
    "To determine the confidence interval for a given choice of privacy parameters, employ `eeprivacy.laplace_mechanism_confidence_interval`.\n",
    "\n",
    "To determine the privacy parameters for a desired confidence interval, employ `eeprivacy.laplace_mechanism_epsilon_for_confidence_interval`.\n",
    "\n",
    "The confidence intervals reported below are two-sided. For example, for a 95% confidence interval of +/-10, 2.5% of results will be smaller than -10 and 2.5% of results will be larger than +10.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "execution": {
     "iopub.execute_input": "2020-10-19T20:14:00.067Z",
     "iopub.status.busy": "2020-10-19T20:14:00.024Z",
     "iopub.status.idle": "2020-10-19T20:14:01.051Z",
     "shell.execute_reply": "2020-10-19T20:14:01.061Z"
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     "outputs_hidden": true,
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    "nteract": {
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   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 1800x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% Confidence Interval (Stochastic): 30.05118474953303\n",
      "95% Confidence Interval (Exact): 29.9573227355399\n",
      "ε for confidence interval: 0.100001077329305\n"
     ]
    }
   ],
   "source": [
    "trials = []\n",
    "for t in range(100000):\n",
    "  trials.append(LaplaceMechanism.execute(\n",
    "    value=0,\n",
    "    epsilon=0.1,\n",
    "    sensitivity=1\n",
    "  ))\n",
    "\n",
    "plt.hist(trials, bins=30, color=\"k\")\n",
    "plt.title(\"Distribution of outputs from Laplace Mechanism\")\n",
    "plt.show()\n",
    "\n",
    "ci = np.quantile(trials, 0.975)\n",
    "print(f\"95% Confidence Interval (Stochastic): {ci}\")\n",
    "\n",
    "ci = LaplaceMechanism.confidence_interval(\n",
    "  epsilon=0.1,\n",
    "  sensitivity=1,\n",
    "  confidence=0.95\n",
    ")\n",
    "print(f\"95% Confidence Interval (Exact): {ci}\")\n",
    "\n",
    "# Now in reverse:\n",
    "epsilon = LaplaceMechanism.epsilon_for_confidence_interval(\n",
    "  target_ci=29.957,\n",
    "  sensitivity=1,\n",
    "  confidence=0.95\n",
    ")\n",
    "print(f\"ε for confidence interval: {epsilon}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nteract": {
     "transient": {
      "deleting": false
     }
    }
   },
   "source": [
    "## Examples of Laplace Mechanism Helpers using `eeprivacy` ##\n",
    "\n",
    "The Laplace Mechanism is well-suited for computing means, and `eeprivacy` provides a helper `private_mean_with_laplace` for this use case.\n",
    "\n",
    "The private mean function implemented by `eeprivacy` employs the \"clamped mean\" approach to bound sensitivity. Analysts provide a fixed `lower_bound` and `upper_bound` before computing the mean. For datasets with unknown ranges, an approach like the one described in [Computing Bounds for Clamped Means] can be used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "execution": {
     "iopub.execute_input": "2020-09-28T23:39:57.038Z",
     "iopub.status.busy": "2020-09-28T23:39:57.035Z",
     "iopub.status.idle": "2020-09-28T23:39:57.783Z",
     "shell.execute_reply": "2020-09-28T23:39:57.804Z"
    },
    "jupyter": {
     "outputs_hidden": true,
     "source_hidden": false
    },
    "nteract": {
     "transient": {
      "deleting": false
     }
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1800x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1800x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "N = 500000\n",
    "dataset = np.random.normal(loc=42, size=N)\n",
    "\n",
    "plt.hist(dataset, bins=30, color=\"k\")\n",
    "plt.title(\"Sample Dataset\")\n",
    "plt.xlabel(\"Value\")\n",
    "plt.ylabel(\"Count\")\n",
    "plt.show()\n",
    "\n",
    "trials = []\n",
    "\n",
    "private_mean_op = PrivateClampedMean(\n",
    "  lower_bound = 0,\n",
    "  upper_bound = 50\n",
    ")\n",
    "\n",
    "for i in range(1000):\n",
    "  private_mean = private_mean_op.execute(\n",
    "    values=dataset,\n",
    "    epsilon=0.1,\n",
    "  )\n",
    "  trials.append(private_mean)\n",
    "\n",
    "plt.hist(trials, bins=30, color=\"k\")\n",
    "plt.title(\"Distribution of private mean with Laplace Mechanism\")\n",
    "plt.xlabel(\"Laplace Mechanism Output\")\n",
    "plt.ylabel(\"Count\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nteract": {
     "transient": {
      "deleting": false
     }
    }
   },
   "source": [
    "## Computing Private Histograms ##\n",
    "\n",
    "The Laplace Mechanism is also well-suited for private histograms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "execution": {
     "iopub.execute_input": "2020-09-28T23:39:57.793Z",
     "iopub.status.busy": "2020-09-28T23:39:57.789Z",
     "iopub.status.idle": "2020-09-28T23:39:58.189Z",
     "shell.execute_reply": "2020-09-28T23:39:58.198Z"
    },
    "jupyter": {
     "outputs_hidden": true,
     "source_hidden": false
    },
    "nteract": {
     "transient": {
      "deleting": false
     }
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1800x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "bins = np.linspace(start=0, stop=100, num=30)\n",
    "\n",
    "private_histogram_op = PrivateHistogram(\n",
    "  bins = bins,\n",
    ")\n",
    "\n",
    "private_histogram = private_histogram_op.execute(  \n",
    "  values=dataset,\n",
    "  epsilon=0.001\n",
    ")\n",
    "\n",
    "true_histogram = np.histogram(dataset, bins=bins)\n",
    "\n",
    "bin_centers = (bins[0:-1] + bins[1:]) / 2\n",
    "bin_width = bins[1] - bins[0]\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.bar(\n",
    "  bin_centers, \n",
    "  private_histogram, \n",
    "  width=bin_width/2, \n",
    "  yerr=ci, \n",
    "  color=\"r\", \n",
    "  label=\"Private Count\"\n",
    ")\n",
    "ax.bar(\n",
    "  bin_centers+bin_width/2, \n",
    "  private_histogram, \n",
    "  width=bin_width/2, \n",
    "  color=\"b\", \n",
    "  label=\"True Count\"\n",
    ")\n",
    "\n",
    "plt.title(\"Private histogram of sample dataset\")\n",
    "plt.xlabel(\"Value\")\n",
    "plt.ylabel(\"Count\")\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  }
 ],
 "metadata": {
  "kernel_info": {
   "name": "python3"
  },
  "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": "3.7.8"
  },
  "nteract": {
   "version": "0.25.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}