2.the_role_of_alpha.ipynb

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    "# Fairness in Biometrics: a figure of merit to assess biometric verification system\n",
    "\n",
    "## The role of alpha\n",
    "\n",
    "The hyper-parameter $\\alpha$ in equation 7 has a crucial role in the computation of $\\text{FDR}(\\tau)$.\n",
    "Such value is a business/application decision. For instance, a bank that deploys a biometric verification system in an ATM might prefer to favor fairness towards False Non-Matches and, for this reason, $\\alpha$ can assume low values.\n",
    "On the other hand, in a border control scenario, where false matches are more critical, decision-makers might decide to favor fairness towards False-Matches.\n",
    "Hence, $\\alpha$ should be high.\n",
    "\n",
    "This example shows how alpha plays the FMR and FNMR trade-offs by observing the FDR values for the synthetiv unfair and fair biometric verification systems.\n",
    "FDR is defined as:\n",
    "\n",
    "$$FDR(\\tau) = 1- (\\alpha A(\\tau) + (1-\\alpha) B(\\tau))$$\n"
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    "%matplotlib widget\n",
    "\n",
    "import plots\n",
    "import experiments\n",
    "import scoring\n",
    "import fairness_metric\n",
    "import numpy as np\n",
    "np.random.seed(10)\n",
    "\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "#################################################\n",
    "## PLAYGROUND: PLAY WITH THE VALUES OF VARIABLES BELOW TO CHANGE THE BEHAVIOUR OF THE FAIR VERIFICATION SYSTEM\n",
    "\n",
    "ALPHA_RANGE = [0, 0.25, 0.5, 0.75, 1]\n",
    "\n",
    "\n",
    "# RANGE OF DECISION THRESHOLDS USED IN THE DEVELOPMENT SET\n",
    "TEN_POWER_OF_X = [0.1, 0.01, 0.001, 0.0001, 0.00001, 0.000001] # BASICALLY, THE FMR THRESHOLDS\n",
    "\n",
    "# NUMBER OF IDENTITIES PER DEMOGRAPHIC\n",
    "IDENTITIES_PER_DEMOGRAPHIC = 300\n",
    "\n",
    "# REPRESENTS HOW A SAMPLES ARE SAMPLED\n",
    "# EACH COLUMN REPRESENTS ONE DEMOGRAPHIC.\n",
    "# THE VALUES REPRESENTS THE AVERAGE EUCLIDEAN DISTANCE BETWEEN EACH IDENTITY\n",
    "# EACH IDENTITY IS SAMPLED IN THE CORNER OF A HYPERCUBE\n",
    "DEMOGRAPHIC_MEAN_DISTANCE_FAIR = [1, 1, 1]\n",
    "# EACH COLUMN REPRESENTS ONE DEMOGRAPHIC.\n",
    "# THE VALUES REPRESENTS THE STANDARD DEVIATIONS OF THE SAMPLES SAMPLED IN THE CORNER OF A HYPERCUBE\n",
    "DEMOGRAPHIC_STD_FAIR = [0.2, 0.2, 0.2]\n",
    "\n",
    "\n",
    "#DEMOGRAPHIC_MEAN_DISTANCE_UNFAIR = [0.8, 1.3, 1.5]\n",
    "DEMOGRAPHIC_MEAN_DISTANCE_UNFAIR = [0.8, 1.5, 2.3]\n",
    "# EACH COLUMN REPRESENTS ONE DEMOGRAPHIC.\n",
    "# THE VALUES REPRESENTS THE STANDARD DEVIATIONS OF THE SAMPLES SAMPLED IN THE CORNER OF A HYPERCUBE\n",
    "#DEMOGRAPHIC_STD_UNFAIR = [0.1, 0.2, 0.4]\n",
    "DEMOGRAPHIC_STD_UNFAIR = [0.1, 0.2, 0.3]\n",
    "\n",
    "#################################################\n",
    "\n",
    "\n",
    "#impostors_per_demographic_dev_fair, genuines_per_demographic_dev_fair, \\\n",
    "#impostors_per_demographic_eval_fair, genuines_per_demographic_eval_fair, n_demographics = experiments.fair_biometric_experiment()\n",
    "#thresholds_raw_fair = scoring.compute_thresholds(impostors_per_demographic_dev_fair, FAR_THRESHOLDS)\n",
    "\n",
    "impostors_per_demographic_dev_fair, genuines_per_demographic_dev_fair, \\\n",
    "impostors_per_demographic_eval_fair, genuines_per_demographic_eval_fair = experiments.generate_uncalibrated_experiment(\n",
    "    DEMOGRAPHIC_DISPLACEMENTS = DEMOGRAPHIC_MEAN_DISTANCE_FAIR,\n",
    "    DEMOGRAPHIC_STD = DEMOGRAPHIC_STD_FAIR,        \n",
    "    DEV_EVAL_IDENTITIES_PER_DEMOGRAPHIC=IDENTITIES_PER_DEMOGRAPHIC\n",
    ")\n",
    "thresholds_raw_fair = scoring.compute_thresholds(impostors_per_demographic_dev_fair, TEN_POWER_OF_X)\n",
    "\n",
    "\n",
    "impostors_per_demographic_dev_unfair, genuines_per_demographic_dev_unfair, \\\n",
    "impostors_per_demographic_eval_unfair, genuines_per_demographic_eval_unfair = \\\n",
    "experiments.generate_uncalibrated_experiment(DEMOGRAPHIC_DISPLACEMENTS=DEMOGRAPHIC_MEAN_DISTANCE_UNFAIR,\n",
    "                                        DEMOGRAPHIC_STD=DEMOGRAPHIC_STD_UNFAIR,\n",
    "                                        DEV_EVAL_IDENTITIES_PER_DEMOGRAPHIC=IDENTITIES_PER_DEMOGRAPHIC)\n",
    "\n",
    "thresholds_raw_unfair = scoring.compute_thresholds(impostors_per_demographic_dev_unfair, TEN_POWER_OF_X)\n",
    "\n",
    "\n",
    "\n",
    "fprs_per_alpha_fair = [fairness_metric.compute_fairness_biometric_verification(impostors_per_demographic_eval_fair,\n",
    "                                                                  genuines_per_demographic_eval_fair, \n",
    "                                                                  thresholds_raw_fair, \n",
    "                                                                  len(TEN_POWER_OF_X),\n",
    "                                                                  n_demographics=3,\n",
    "                                                                  alpha=alpha)\n",
    "                  for alpha in ALPHA_RANGE\n",
    "                 ]\n",
    "    \n",
    "fprs_per_alpha_unfair = [fairness_metric.compute_fairness_biometric_verification(impostors_per_demographic_eval_unfair,\n",
    "                                                                  genuines_per_demographic_eval_unfair, \n",
    "                                                                  thresholds_raw_unfair, \n",
    "                                                                  len(TEN_POWER_OF_X),\n",
    "                                                                  n_demographics=3,\n",
    "                                                                  alpha=alpha)\n",
    "                  for alpha in ALPHA_RANGE\n",
    "                 ]    \n",
    "    \n",
    "    \n",
    "    \n",
    "def fairness_plot_raw_per_alpha(fprs_fair, fprs_unfair , x, alphas):\n",
    "    \n",
    "    transform = lambda x : -1*np.log10(x)\n",
    "    colors = [\"tab:blue\", \"tab:orange\", \"tab:green\", \"tab:red\", \"tab:purple\", \"tab:brown\",\"tab:pink\", \\\n",
    "              \"tab:gray\", \"tab:olive\", \"tab:cyan\"]\n",
    "    colors = colors+colors\n",
    "    \n",
    "    \n",
    "    fig, ax = plt.subplots()\n",
    "    for i, alpha in enumerate(alphas):\n",
    "        \n",
    "        ax.plot(transform(x), fprs_fair[i], label=f\"$\\\\alpha={alpha}$\", color=colors[i])\n",
    "        ax.scatter(transform(x),fprs_fair[i], color=colors[i])\n",
    "        \n",
    "        ax.plot(transform(x),fprs_unfair[i], color=colors[i], linestyle='dashed')        \n",
    "        ax.scatter(transform(x),fprs_unfair[i], color=colors[i], linestyle='dashed')\n",
    "\n",
    "\n",
    "    plt.ylabel('$FDR(\\\\tau)$', fontsize=18)\n",
    "    plt.xlabel('x', fontsize=18)\n",
    "    \n",
    "    plt.xticks(np.arange(len(x)+1), [\"\"]+[f\"$10^{i}$\" for i in range(1, len(x)+1)])\n",
    "    plt.xlim(0.95,len(x)+0.05)\n",
    "    plt.grid(True)\n",
    "    \n",
    "    plt.legend()\n",
    "    plt.show()  \n",
    "    \n",
    "\n",
    "fairness_plot_raw_per_alpha(fprs_per_alpha_fair,fprs_per_alpha_unfair, TEN_POWER_OF_X, ALPHA_RANGE)"
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