supplementary_material_figures.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: brokenaxes in /Users/mathieubazinet/.pyenv/versions/3.12.3/lib/python3.12/site-packages (0.6.2)\n",
      "Requirement already satisfied: matplotlib>3.6 in /Users/mathieubazinet/.pyenv/versions/3.12.3/lib/python3.12/site-packages (from brokenaxes) (3.9.1)\n",
      "Requirement already satisfied: contourpy>=1.0.1 in /Users/mathieubazinet/.pyenv/versions/3.12.3/lib/python3.12/site-packages (from matplotlib>3.6->brokenaxes) (1.2.1)\n",
      "Requirement already satisfied: cycler>=0.10 in /Users/mathieubazinet/.pyenv/versions/3.12.3/lib/python3.12/site-packages (from matplotlib>3.6->brokenaxes) (0.12.1)\n",
      "Requirement already satisfied: fonttools>=4.22.0 in /Users/mathieubazinet/.pyenv/versions/3.12.3/lib/python3.12/site-packages (from matplotlib>3.6->brokenaxes) (4.53.1)\n",
      "Requirement already satisfied: kiwisolver>=1.3.1 in /Users/mathieubazinet/.pyenv/versions/3.12.3/lib/python3.12/site-packages (from matplotlib>3.6->brokenaxes) (1.4.5)\n",
      "Requirement already satisfied: numpy>=1.23 in /Users/mathieubazinet/.pyenv/versions/3.12.3/lib/python3.12/site-packages (from matplotlib>3.6->brokenaxes) (1.26.4)\n",
      "Requirement already satisfied: packaging>=20.0 in /Users/mathieubazinet/.pyenv/versions/3.12.3/lib/python3.12/site-packages (from matplotlib>3.6->brokenaxes) (24.0)\n",
      "Requirement already satisfied: pillow>=8 in /Users/mathieubazinet/.pyenv/versions/3.12.3/lib/python3.12/site-packages (from matplotlib>3.6->brokenaxes) (10.3.0)\n",
      "Requirement already satisfied: pyparsing>=2.3.1 in /Users/mathieubazinet/.pyenv/versions/3.12.3/lib/python3.12/site-packages (from matplotlib>3.6->brokenaxes) (3.1.2)\n",
      "Requirement already satisfied: python-dateutil>=2.7 in /Users/mathieubazinet/.pyenv/versions/3.12.3/lib/python3.12/site-packages (from matplotlib>3.6->brokenaxes) (2.9.0.post0)\n",
      "Requirement already satisfied: six>=1.5 in /Users/mathieubazinet/.pyenv/versions/3.12.3/lib/python3.12/site-packages (from python-dateutil>=2.7->matplotlib>3.6->brokenaxes) (1.16.0)\n",
      "\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m A new release of pip is available: \u001b[0m\u001b[31;49m24.0\u001b[0m\u001b[39;49m -> \u001b[0m\u001b[32;49m24.3.1\u001b[0m\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m To update, run: \u001b[0m\u001b[32;49mpip install --upgrade pip\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "!pip install brokenaxes\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import newton\n",
    "from math import sqrt, log, exp, ceil\n",
    "from functools import partial\n",
    "import numpy as np\n",
    "from brokenaxes import brokenaxes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x, delta):\n",
    "  first = -2*log(1/delta)\n",
    "  second = (2*log((2*sqrt(x))/delta) -1) * exp((-1/x)*log(2*sqrt(x)))\n",
    "\n",
    "  return first + second\n",
    "\n",
    "deltas = [delta*1e-5 for delta in range(1,int(1e4))]\n",
    "\n",
    "soluce = []\n",
    "for delta in deltas:\n",
    "  func_to_optimize = partial(f, delta=delta)\n",
    "  soluce.append(newton(func_to_optimize, 5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 3200x2000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams.update({'font.size': 15})\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8,5),dpi=400)\n",
    "\n",
    "ax.plot(deltas, soluce)\n",
    "\n",
    "# delta = 0.1\n",
    "func_to_optimize = partial(f, delta=0.1)\n",
    "sol = newton(func_to_optimize, 5)\n",
    "ax.annotate(f\"$m^*=${sol:.2f}\", size=15,\n",
    "                xy=(0.1, sol), xytext=(5, 5), textcoords='offset points')\n",
    "ax.plot(0.1, sol, 'ro')\n",
    "\n",
    "# delta = 0.01\n",
    "func_to_optimize = partial(f, delta=0.01)\n",
    "sol = newton(func_to_optimize, 5)\n",
    "ax.annotate(f\"$m^*=${sol:.2f}\", size=15,\n",
    "                xy=(0.01, sol), xytext=(5, 5), textcoords='offset points')\n",
    "ax.plot(0.01, sol, 'ro')\n",
    "\n",
    "# delta = 0.05\n",
    "func_to_optimize = partial(f, delta=0.05)\n",
    "sol = newton(func_to_optimize, 5)\n",
    "ax.annotate(f\"$m^*=${sol:.2f}\", size=15,\n",
    "                xy=(0.05, sol), xytext=(5, 5), textcoords='offset points')\n",
    "ax.plot(0.05, sol, 'ro')\n",
    "\n",
    "#delta = 0.001\n",
    "func_to_optimize = partial(f, delta=0.001)\n",
    "sol = newton(func_to_optimize, 5)\n",
    "ax.annotate(f\"$m^*=${sol:.2f}\", size=15,\n",
    "                xy=(0.001, sol), xytext=(5, 5), textcoords='offset points')\n",
    "ax.plot(0.001, sol, 'ro')\n",
    "\n",
    "#delta = 0.0001\n",
    "func_to_optimize = partial(f, delta=0.0001)\n",
    "sol = newton(func_to_optimize, 5)\n",
    "ax.annotate(f\"$m^*=${sol:.2f}\", size=15,\n",
    "                xy=(0.0001, sol), xytext=(5, 5), textcoords='offset points')\n",
    "ax.plot(0.0001, sol, 'ro')\n",
    "\n",
    "#delta = 0.00001\n",
    "func_to_optimize = partial(f, delta=0.00001)\n",
    "sol = newton(func_to_optimize, 5)\n",
    "ax.annotate(f\"$m^*=${sol:.2f}\", size=15,\n",
    "                xy=(0.00001, sol), xytext=(5, 5), textcoords='offset points')\n",
    "ax.plot(0.00001, sol, 'ro')\n",
    "\n",
    "plt.semilogx()\n",
    "plt.xlabel(r\"$\\delta$\")\n",
    "plt.ylabel(\"$m^*$\")\n",
    "plt.xlim(1e-5-1e-6, 0.11)\n",
    "ax.spines['top'].set_visible(False)\n",
    "ax.spines['right'].set_visible(False)\n",
    "ax.spines['bottom'].set_visible(True)\n",
    "ax.spines['left'].set_visible(True)\n",
    "plt.savefig(\"fig_mstar.jpg\", bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def k(m, delta):\n",
    "  return exp((-1/m)*log(1/delta)) - exp((-1/m)*log(2*sqrt(m)/delta))\n",
    "\n",
    "ks = []\n",
    "for i in range(len(deltas)):\n",
    "  ks.append(k(soluce[i], deltas[i]))\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8,5),dpi=400)\n",
    "\n",
    "ax.plot(deltas, ks)\n",
    "\n",
    "# delta = 0.1\n",
    "func_to_optimize = partial(f, delta=0.1)\n",
    "sol = newton(func_to_optimize, 5)\n",
    "k_sol = k(sol, 0.1)\n",
    "ax.annotate(f\"$K(m^*,\\delta)=${k_sol:.2f}\", size=15,\n",
    "                xy=(0.1, k_sol), xytext=(5, 0), textcoords='offset points')\n",
    "ax.plot(0.1, k_sol, 'ro')\n",
    "\n",
    "# delta = 0.01\n",
    "func_to_optimize = partial(f, delta=0.01)\n",
    "sol = newton(func_to_optimize, 5)\n",
    "k_sol = k(sol, 0.01)\n",
    "ax.annotate(f\"$K(m^*,\\delta)=${k_sol:.2f}\", size=15,\n",
    "                xy=(0.01, k_sol), xytext=(5, -6), textcoords='offset points')\n",
    "ax.plot(0.01, k_sol, 'ro')\n",
    "\n",
    "# delta = 0.05\n",
    "func_to_optimize = partial(f, delta=0.05)\n",
    "sol = newton(func_to_optimize, 5)\n",
    "k_sol = k(sol, 0.05)\n",
    "ax.annotate(f\"$K(m^*,\\delta)=${k_sol:.2f}\", size=15,\n",
    "                xy=(0.05, k_sol), xytext=(5, -5), textcoords='offset points')\n",
    "ax.plot(0.05, k_sol, 'ro')\n",
    "\n",
    "#delta = 0.001\n",
    "func_to_optimize = partial(f, delta=0.001)\n",
    "sol = newton(func_to_optimize, 5)\n",
    "k_sol = k(sol, 0.001)\n",
    "ax.annotate(f\"$K(m^*,\\delta)=${k_sol:.2f}\", size=15,\n",
    "                xy=(0.001, k_sol), xytext=(5, -10), textcoords='offset points')\n",
    "ax.plot(0.001, k_sol, 'ro')\n",
    "\n",
    "#delta = 0.0001\n",
    "func_to_optimize = partial(f, delta=0.0001)\n",
    "sol = newton(func_to_optimize, 5)\n",
    "k_sol = k(sol, 0.0001)\n",
    "ax.annotate(f\"$K(m^*,\\delta)=${k_sol:.2f}\", size=15,\n",
    "                xy=(0.0001, k_sol), xytext=(5, -10), textcoords='offset points')\n",
    "ax.plot(0.0001, k_sol, 'ro')\n",
    "\n",
    "#delta = 0.00001\n",
    "func_to_optimize = partial(f, delta=0.00001)\n",
    "sol = newton(func_to_optimize, 5)\n",
    "k_sol = k(sol, 0.00001)\n",
    "ax.annotate(f\"$K(m^*,\\delta)=${k_sol:.2f}\", size=15,\n",
    "                xy=(0.00001, k_sol), xytext=(5, -12), textcoords='offset points')\n",
    "ax.plot(0.00001, k_sol, 'ro')\n",
    "\n",
    "plt.semilogx()\n",
    "plt.xlabel(\"$\\delta$\")\n",
    "plt.ylabel(\"$K(m^*,\\delta)$\")\n",
    "plt.xlim(1e-5-1e-6, 0.11)\n",
    "plt.ylim(0.05,0.17)\n",
    "ax.spines['top'].set_visible(False)\n",
    "ax.spines['right'].set_visible(False)\n",
    "ax.spines['bottom'].set_visible(True)\n",
    "ax.spines['left'].set_visible(True)\n",
    "plt.savefig(\"fig_k_n_delta.jpg\", bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.figure(figsize=(9,5),dpi=400)\n",
    "# fig, ax = plt.subplots(figsize=(8,5),dpi=400)\n",
    "\n",
    "datasets = [\"MNIST56\", \"MNIST08\", \"MNIST49\", \"MNIST23\", \"MNIST17\", \"MNIST (50%)\", \"MNIST (20%)\", \"MNIST (10%)\", \"AMAZON\"]\n",
    "ns = [10206, 10597, 10612, 10881, 11707, 24000, 42000, 48000, 144000]\n",
    "\n",
    "k_datasets = []\n",
    "for i in range(len(datasets)):\n",
    "  k_datasets.append(k(ns[i], 0.01))\n",
    "k_datasets\n",
    "\n",
    "ax = brokenaxes(xlims=((1000,60000), (120000, 150000),), ylims=((0.0, max(k_datasets)+0.00005),), width_ratios=[2, 1])\n",
    "ax.scatter(ns, k_datasets, color=\"red\")\n",
    "\n",
    "k_all = []\n",
    "for i in range(1, 160000, 100):\n",
    "  k_all.append(k(i, 0.01))\n",
    "ax.plot(range(1, 160000, 100), k_all)\n",
    "\n",
    "for dataset in datasets:\n",
    "  rotation = 0\n",
    "  textcoords = \"data\"\n",
    "  xtext = 20000\n",
    "  if dataset == \"MNIST56\":\n",
    "    xytext = (xtext, 0.00055)\n",
    "    arrowprops = dict(arrowstyle=\"->\", connectionstyle=\"arc3,rad=0.2\")\n",
    "  elif dataset == \"MNIST08\":\n",
    "    xytext = (xtext, 0.00051)\n",
    "    arrowprops = dict(arrowstyle=\"->\", connectionstyle=\"arc3,rad=0.2\")\n",
    "    rotation = 0\n",
    "  elif dataset == \"MNIST49\":\n",
    "    xytext = (xtext, 0.00047)\n",
    "    arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3\")\n",
    "    rotation = 0\n",
    "  elif dataset == \"MNIST23\":\n",
    "    xytext = (xtext, 0.00043)\n",
    "    arrowprops = dict(arrowstyle=\"->\", connectionstyle=\"arc3,rad=-0.2\")\n",
    "    rotation = 0\n",
    "  elif dataset == \"MNIST17\":\n",
    "    xytext = (xtext, 0.00039)\n",
    "    arrowprops = dict(arrowstyle=\"->\", connectionstyle=\"arc3,rad=-0.2\")\n",
    "    rotation = 0\n",
    "  else:\n",
    "    xytext = (5,5)\n",
    "    arrowprops = None \n",
    "    rotation = 45\n",
    "    textcoords = 'offset points'\n",
    "  xy = (ns[datasets.index(dataset)], k_datasets[datasets.index(dataset)])\n",
    "  ax.annotate(dataset, size=15,\n",
    "                xy=xy, xytext=xytext, textcoords=textcoords, rotation=rotation, arrowprops=arrowprops)\n",
    "fig.canvas.draw()\n",
    "\n",
    "# ax.axs[0].set_xticks([10206, 10597, 10612, 10881, 11707])\n",
    "labels = [item.get_text() for item in ax.axs[0].get_xticklabels()]\n",
    "ax.axs[0].set_xticks(ax.axs[0].get_xticks(), labels, rotation=45, ha='right')\n",
    "labels = [item.get_text() for item in ax.axs[1].get_xticklabels()]\n",
    "ax.axs[1].set_xticks(ax.axs[1].get_xticks(), labels, rotation=45, ha='right')\n",
    "ax.set_xlabel(\"Size of the dataset (m)\",labelpad=60)\n",
    "ax.set_ylabel(\"$K(m,\\delta)$\", labelpad=60)\n",
    "plt.savefig(\"fig_kn_datasets.jpg\", bbox_inches='tight')"
   ]
  }
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