{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Gaussian Mechanism Basics #\n",
        "\n",
        "The Gaussian Mechanism adds noise drawn from a Gaussian (normal) distribution to realize $(\\epsilon, \\delta)$ differential privacy.\n",
        "\n",
        "This mechanism has better performance for vector-valued queries than the Laplace Mechanism (queries that return many data points per individual at once).\n",
        "\n",
        "This notebook walks through the basic `eeprivacy` functions for working with the Gaussian Mechanism."
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Preamble: imports and figure settings\n",
        "\n",
        "from eeprivacy import (\n",
        "  GaussianMechanism,\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",
        "})"
      ],
      "outputs": [],
      "execution_count": 1,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2020-09-28T23:30:47.578Z",
          "iopub.execute_input": "2020-09-28T23:30:47.582Z",
          "iopub.status.idle": "2020-09-28T23:30:48.266Z",
          "shell.execute_reply": "2020-09-28T23:30:48.269Z"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Distribution of Gaussian Mechanism Outputs ##\n",
        "\n",
        "For a given ε, noise is drawn from the normal distribution at $\\sigma^2 = \\frac{2s^2 \\log(1.25/\\delta)}{\\epsilon^2}$. The `eeprivacy` function `gaussian_mechanism` draws this noise and adds it to a private value:\n"
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "trials = []\n",
        "for t in range(1000):\n",
        "  trials.append(GaussianMechanism.execute(\n",
        "    value=0,\n",
        "    epsilon=0.1,\n",
        "    delta=1e-12,\n",
        "    sensitivity=1\n",
        "  ))\n",
        "\n",
        "plt.hist(trials, bins=30, color=\"k\")\n",
        "plt.title(\"Distribution of outputs from Gaussian Mechanism\")\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 1800x720 with 1 Axes>",
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "execution_count": 2,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2020-09-28T23:30:48.290Z",
          "iopub.execute_input": "2020-09-28T23:30:48.296Z",
          "iopub.status.idle": "2020-09-28T23:30:48.531Z",
          "shell.execute_reply": "2020-09-28T23:30:48.535Z"
        }
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Gaussian 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.gaussian_mechanism_confidence_interval`.\n",
        "\n",
        "To determine the privacy parameters for a desired confidence interval, employ `eeprivacy.gaussian_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."
      ],
      "metadata": {
        "nteract": {
          "transient": {
            "deleting": false
          }
        }
      }
    },
    {
      "cell_type": "code",
      "source": [
        "trials = []\n",
        "for t in range(100000):\n",
        "  trials.append(GaussianMechanism.execute(\n",
        "    value=0,\n",
        "    epsilon=0.1,\n",
        "    delta=1e-12,\n",
        "    sensitivity=1\n",
        "  ))\n",
        "\n",
        "plt.hist(trials, bins=30, color=\"k\")\n",
        "plt.title(\"Distribution of outputs from Gaussian Mechanism\")\n",
        "plt.show()\n",
        "\n",
        "ci = np.quantile(trials, 0.975)\n",
        "print(f\"95% Confidence Interval (Stochastic): {ci}\")\n",
        "\n",
        "ci = GaussianMechanism.confidence_interval(\n",
        "  epsilon=0.1,\n",
        "  delta=1e-12,\n",
        "  sensitivity=1,\n",
        "  confidence=0.95\n",
        ")\n",
        "print(f\"95% Confidence Interval (Exact): {ci}\")\n",
        "\n",
        "# Now in reverse:\n",
        "epsilon = GaussianMechanism.epsilon_for_confidence_interval(\n",
        "  target_ci=146.288,\n",
        "  delta=1e-12,\n",
        "  sensitivity=1,\n",
        "  confidence=0.95\n",
        ")\n",
        "print(f\"ε for confidence interval: {epsilon}\")"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 1800x720 with 1 Axes>",
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "95% Confidence Interval (Stochastic): 146.00710633910379\n",
            "95% Confidence Interval (Exact): 146.28781668617955\n",
            "ε for confidence interval: 0.09999987468977604\n"
          ]
        }
      ],
      "execution_count": 3,
      "metadata": {
        "collapsed": true,
        "jupyter": {
          "source_hidden": false,
          "outputs_hidden": false
        },
        "nteract": {
          "transient": {
            "deleting": false
          }
        },
        "execution": {
          "iopub.status.busy": "2020-09-28T23:30:48.595Z",
          "iopub.execute_input": "2020-09-28T23:30:48.632Z",
          "iopub.status.idle": "2020-09-28T23:30:49.927Z",
          "shell.execute_reply": "2020-09-28T23:30:49.934Z"
        }
      }
    }
  ],
  "metadata": {
    "kernel_info": {
      "name": "python3"
    },
    "language_info": {
      "name": "python",
      "version": "3.8.5",
      "mimetype": "text/x-python",
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "pygments_lexer": "ipython3",
      "nbconvert_exporter": "python",
      "file_extension": ".py"
    },
    "kernelspec": {
      "argv": [
        "/usr/local/opt/python/bin/python3.7",
        "-m",
        "ipykernel_launcher",
        "-f",
        "{connection_file}"
      ],
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "nteract": {
      "version": "0.24.1"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}