Initial commit

[python_dp.git] / Incomplete / renyi.ipynb

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   "source": [
    "# Renyi Differential Privacy\n",
    "\n",
    "By [Armaan Bhojwani](https://armaanb.net) under [Praneeth Vepakomma](https://praneeth.mit.edu/)\n",
    "\n",
    "This notebook features some examples of using the dp_accounting Renyi accountant to translate between epsilon, delta and alpha, rho interpretations of Renyi DP, and for usk in compositions.\n",
    "\n",
    "### Dependencies\n",
    "- matplotlib\n",
    "- dp_accounting\n",
    "\n",
    "### Status\n",
    "Incomplete"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "378ba024",
   "metadata": {},
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "id": "062e3b39",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Privacy parameters\n",
    "# (https://github.com/google/differential-privacy/blob/main/python/dp_accounting/rdp/rdp_privacy_accountant.py#L781)\n",
    "custom_orders = False # Set to array of custom orders, otherwise use defaults\n",
    "\n",
    "sensitivity = 99  # Sensitivity of the function\n",
    "epsilon = 2    # Privacy garuntee\n",
    "delta = 10e-7\n",
    "\n",
    "# Data parameters\n",
    "data_len = 1500  # Length of dataset\n",
    "data_low = 0     # Lowest value of dataset\n",
    "data_high = 99   # Highest value of dataset\n",
    "\n",
    "# Initialize Numpy RNG\n",
    "rng = np.random.default_rng()\n",
    "\n",
    "# Increment data_high so that it includes the value specified\n",
    "data_high += 1\n",
    "\n",
    "# Create dataset as defined by above parameters\n",
    "x = rng.integers(low=data_low, high=data_high, size=(data_len))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25510bc4",
   "metadata": {},
   "source": [
    "## Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "a74d9ba6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "found noise multiplier: 2.382578592961857\n"
     ]
    }
   ],
   "source": [
    "import dp_accounting as dpa\n",
    "import dp_accounting.rdp as rdpa\n",
    "\n",
    "# noise_multiplier is the ratio of the standard deviation of the Gaussian\n",
    "# noise to the l2-sensitivity of the function to which it is added\n",
    "noise_multiplier = dpa.calibrate_dp_mechanism(rdpa.RdpAccountant,\n",
    "                                              dpa.GaussianDpEvent, epsilon,\n",
    "                                              delta)\n",
    "\n",
    "print(f\"found noise multiplier: {noise_multiplier}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "7451e486",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "found epsilon: 1.9999992100966923\n",
      "found delta:   1.0000000000000023e-06\n",
      "────────────────────────────────────────\n",
      "found alpha:   12.0\n",
      "found rho:     1.0569556863430245\n"
     ]
    }
   ],
   "source": [
    "from common import *\n",
    "\n",
    "accountant = rdpa.RdpAccountant(\n",
    "    orders=custom_orders) if custom_orders else rdpa.RdpAccountant()\n",
    "\n",
    "event = dpa.GaussianDpEvent(noise_multiplier)\n",
    "accountant = accountant.compose(event)\n",
    "\n",
    "t_epsilon, alpha = accountant.get_epsilon_and_optimal_order(delta)\n",
    "t_delta = accountant.get_delta(t_epsilon)\n",
    "\n",
    "alpha_idx = np.where(accountant._orders == alpha)\n",
    "rho = accountant._rdp[alpha_idx][0]\n",
    "\n",
    "print(f\"found epsilon: {t_epsilon}\")\n",
    "print(f\"found delta:   {t_delta}\")\n",
    "print_hline(40)\n",
    "print(f\"found alpha:   {alpha}\")\n",
    "print(f\"found rho:     {rho}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "id": "6c295418",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using sigma: 2.382578592961857\n",
      "non-private sum: 75550\n",
      "private sum:     75548\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def gaussian_mech_RDP(x, sensitivity, alpha, rho, sigma=0):\n",
    "    sigma = np.sqrt((sensitivity**2 * alpha) / (2 * rho)) if sigma == 0 else sigma\n",
    "    print(f\"Using sigma: {sigma}\")\n",
    "    return x + np.random.normal(loc=0, scale=sigma)\n",
    "\n",
    "# https://programming-dp.com/ch6.html#vector-valued-functions-and-their-sensitivities\n",
    "l2_sensitivity = sensitivity ** 0.5\n",
    "\n",
    "sum_x = np.sum(x)\n",
    "sigma = noise_multiplier * l2_sensitivity\n",
    "sum_X = round(gaussian_mech_RDP(sum_x, l2_sensitivity, alpha, rho, sigma=sigma))\n",
    "\n",
    "print(f\"non-private sum: {sum_x}\")\n",
    "print(f\"private sum:     {sum_X}\")"
   ]
  }
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