0-expected-data-leakage-calculation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 250 original images in each of the 5 classes\n",
    "n_clusters = 250\n",
    "\n",
    "# 5000 images for each of the 5 classes\n",
    "n_total = 5000\n",
    "\n",
    "# typical tran+val / test split is 80/20\n",
    "test_size = 0.2\n",
    "\n",
    "# number of experiments to run to calculate the mean and std of contamination proportion\n",
    "n_experiments = 1000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Single Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4000 1000\n",
      "num_contamenated_clusters 242\n",
      "proportion_contaminated 0.968\n"
     ]
    }
   ],
   "source": [
    "# set for reproducibility in this single test\n",
    "np.random.seed(0)\n",
    "\n",
    "# randomly assign each of the 5000 images to one of the 250 clusters (0, 1, ..., 249)\n",
    "cluster_assignments = np.random.choice(a=n_clusters, size=n_total, replace=True)\n",
    "\n",
    "plt.hist(cluster_assignments, bins=n_clusters)\n",
    "plt.xlabel('Cluster Assignments')\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('Distribution of Cluster Assignments')\n",
    "plt.show()\n",
    "\n",
    "train_val_set, test_set = train_test_split(cluster_assignments, test_size=test_size)\n",
    "print(len(train_val_set), len(test_set))\n",
    "\n",
    "num_contamenated_clusters = len(set(train_val_set).intersection(set(test_set)))\n",
    "print(\"num_contamenated_clusters\", num_contamenated_clusters)\n",
    "\n",
    "proportion_contaminated = num_contamenated_clusters / n_clusters\n",
    "print(\"proportion_contaminated\", proportion_contaminated)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Repeated Tests to Estimate the Mean and Standard Deviation of the Contamination Proportion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean number of contaminated clusters:  245.522\n",
      "Standard deviation of contaminated clusters:  2.0345800549499153\n",
      "\n",
      "Mean proportion of contaminated clusters:  0.982088\n",
      "Standard deviation of proportion of contaminated clusters:  0.008138320219799667\n"
     ]
    }
   ],
   "source": [
    "list_num_contaminated_clusters = []\n",
    "list_proportion_contaminated_clusters = []\n",
    "\n",
    "for i in range(n_experiments):\n",
    "    cluster_assignments = np.random.choice(\n",
    "        a=n_clusters, size=n_total, replace=True)\n",
    "\n",
    "    train_val_set, test_set = train_test_split(\n",
    "        cluster_assignments, test_size=test_size)\n",
    "    \n",
    "    num_contamenated_clusters = len(\n",
    "        set(train_val_set).intersection(set(test_set)))\n",
    "    list_num_contaminated_clusters.append(num_contamenated_clusters)\n",
    "\n",
    "    proportion_contaminated = num_contamenated_clusters / n_clusters\n",
    "    list_proportion_contaminated_clusters.append(proportion_contaminated)\n",
    "\n",
    "print(\"Mean number of contaminated clusters: \", np.mean(list_num_contaminated_clusters))\n",
    "print(\"Standard deviation of contaminated clusters: \", np.std(list_num_contaminated_clusters))\n",
    "print()\n",
    "print(\"Mean proportion of contaminated clusters: \",\n",
    "      np.mean(list_proportion_contaminated_clusters))\n",
    "print(\"Standard deviation of proportion of contaminated clusters: \",\n",
    "      np.std(list_proportion_contaminated_clusters))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting distribution of number of contaminated clusters\n",
    "plt.hist(list_proportion_contaminated_clusters)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "lc25k-cleaning",
   "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": "3.11.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}