piyush01123 · November 12, 2019 14:14
diff --git a/ensemble_error_limit.ipynb b/ensemble_error_limit.ipynb
 {
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import binom\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ensemble_error(N, eps):\n",
    "    # for N=11, we will misclassify if at least 6 go wrong (11//2+1)\n",
    "    # similarly for 12, at least 7 must go wrong\n",
    "    errors = [binom.pmf(i, N, eps) for i in range(N//2+1, N+1)]\n",
    "    return sum(errors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 11\n",
    "\n",
    "model_accuracies = np.arange(0,1,.01)\n",
    "ensemble_accuracies = [1-ensemble_error(N, 1-acc) for acc in model_accuracies]\n",
    "\n",
    "plt.plot(model_accuracies, ensemble_accuracies, 'b')\n",
    "plt.title(\"Ensemble Accuracy vs Model Accuracy\")\n",
    "plt.plot([0, 1], [0, 1],'r--')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
 }
	{
	"cells": [
	{
	"cell_type": "code",
	"execution_count": 1,
	"metadata": {},
	"outputs": [],
	"source": [
	"import numpy as np\n",
	"from scipy.stats import binom\n",
	"import matplotlib.pyplot as plt"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 2,
	"metadata": {},
	"outputs": [],
	"source": [
	"def ensemble_error(N, eps):\n",
	" # for N=11, we will misclassify if at least 6 go wrong (11//2+1)\n",
	" # similarly for 12, at least 7 must go wrong\n",
	" errors = [binom.pmf(i, N, eps) for i in range(N//2+1, N+1)]\n",
	" return sum(errors)"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 3,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"image/png": 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\n",
	"text/plain": [
	"<Figure size 432x288 with 1 Axes>"
	]
	},
	"metadata": {
	"needs_background": "light"
	},
	"output_type": "display_data"
	}
	],
	"source": [
	"N = 11\n",
	"\n",
	"model_accuracies = np.arange(0,1,.01)\n",
	"ensemble_accuracies = [1-ensemble_error(N, 1-acc) for acc in model_accuracies]\n",
	"\n",
	"plt.plot(model_accuracies, ensemble_accuracies, 'b')\n",
	"plt.title(\"Ensemble Accuracy vs Model Accuracy\")\n",
	"plt.plot([0, 1], [0, 1],'r--')\n",
	"plt.show()"
	]
	}
	],
	"metadata": {
	"kernelspec": {
	"display_name": "Python 3",
	"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": "3.7.5"
	}
	},
	"nbformat": 4,
	"nbformat_minor": 2
	}