examples/binary_classification.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "import sys\n",
    "sys.path.append('..')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Performance of GeOpt on a binary classification task: Breast cancer diagnostic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train size: 113/569 samples\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import sympy\n",
    "sympy.init_printing()\n",
    "import sklearn.datasets\n",
    "X, Y = sklearn.datasets.load_breast_cancer(True)\n",
    "\n",
    "\n",
    "def shuffle_arrays(X, Y):\n",
    "    \"\"\"\n",
    "    Shuffles the first dimension of the given arrays\n",
    "    returns nothing \n",
    "    \"\"\"\n",
    "    rnd_state = np.random.get_state()\n",
    "    np.random.shuffle(X)\n",
    "    np.random.set_state(rnd_state)\n",
    "    np.random.shuffle(Y)\n",
    "\n",
    "\n",
    "shuffle_arrays(X, Y)\n",
    "\n",
    "n = len(X)\n",
    "ntrain = int(n * .2)\n",
    "x_train, y_train = X[:ntrain], Y[:ntrain]\n",
    "x_test, y_test = X[ntrain:], Y[ntrain:]\n",
    "\n",
    "print('train size: %s/%s samples' % (ntrain, n))\n",
    "\n",
    "from geopt.metrics import *\n",
    "\n",
    "\n",
    "def fit(tree):\n",
    "    pred = tree.evaluate(*x_train.T)[0]\n",
    "    if np.isnan(pred).any():\n",
    "        return float('-inf')\n",
    "    return roc_auc_score(y_train, pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ca8ee719981c49b2a7c9c72e23ea610d"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Area under ROC curve for training data: 0.990365448505\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "68caf3e37e4944899715806abdd11ccd"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Area under ROC curve for training data: 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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hcMIPqP62YEIIIYQQmenB9qlbQLr7ELDVqg+Ncg4j3YEcBjyINZ4ex+bZXQZsGsQ7FngW\n671bDnwD+GsQ5uMujdXAWcG1cBeGbbHh0+nYatVB4Euj5E0IIYQQonacA5yHrSrNkzOAn+ecZkja\nLgxHYMOoNwDnAkcW/BxCCCGEEKWyP61Dn3nxe+D4nNP0yboLwzmYzzohhBBCiMawHiOHLMdLD+a3\nbb+c0/XTH20XhmQu3zbYKlW5HBJCCCFE43hbtx+gQ9rtwnAr5mLkDmyOnBBCCCGEEEIIIYQQQggh\nhBBCCCGEEEIIIYQQQoyb/wFqWt1jjXG6jwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$- \\frac{input_{15}}{input_{24}} + \\frac{input_{18} input_{22}}{\\sqrt{input_{29}^{2}}} - input_{2} - input_{24} input_{25} - input_{9}$$"
      ],
      "text/plain": [
       "  input₁₅   input₁₈⋅input₂₂                                    \n",
       "- ─────── + ─────────────── - input₂ - input₂₄⋅input₂₅ - input₉\n",
       "  input₂₄       __________                                     \n",
       "               ╱        2                                      \n",
       "             ╲╱  input₂₉                                       "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from geopt import Evolution\n",
    "from geopt import operations\n",
    "from tqdm import tnrange\n",
    "\n",
    "\n",
    "E = Evolution(30, 100, 1, popsize=20, bestsize=3,\n",
    "              newgen=5, ops=operations.ops)\n",
    "\n",
    "\n",
    "pop = E.bestpop(10, 10, fit, .3, range=tnrange)\n",
    "\n",
    "print('Area under ROC curve for training data:', fit(pop[0]))\n",
    "for _ in tnrange(50):\n",
    "    pop = E.evolve(pop, fit, None)\n",
    "print('Area under ROC curve for training data:', fit(pop[0]))\n",
    "t = pop[0]\n",
    "t.expr[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "matplotlib.rcParams['figure.figsize'] = [16, 8]\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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aAAAATEajROkuSZaNWV4+XDfWU5M8taq+VVULq+rw8ZogAAAAk9dGb999EPuZneSQJDOT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\nTuwR8f8tlQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xab6b940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred = t.evaluate(*x_train.T)[0]\n",
    "fpr, tpr, thresholds = roc_curve(y_train, pred)\n",
    "plt.title('ROC curve of train data')\n",
    "plt.plot(fpr, tpr, color='darkorange',\n",
    "         label='ROC curve (area = %0.2f)' % roc_auc_score(y_train, pred))\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SFp6fLJ732OeW3ZhMm9NnHgAAgE2MldKnYvG8QYSONG1OMuOEPvMAAABsYqyUPlXT5iTH\nXtN7CgAAgE2SlVIAAAC6EaUAAAB0I0oBAADoRpQCAADQjSgFAACgG1EKAABAN6IUAACAbkQpAAAA\n3YhSAAAAuhGlAAAAdCNKAQAA6EaUAgAA0I0oBQAAoBtRCgAAQDeiFAAAgG5EKQAAAN2IUgAAALoR\npQAAAHQjSgEAAOhGlAIAANCNKAUAAKAbUQoAAEA3ohQAAIBuRCkAAADdiFIAAAC6EaUAAAB0I0oB\nAADoRpQCAADQjSgFAACgG1EKAABAN6IUAACAbkQpAAAA3YhSAAAAuhGlAAAAdCNKAQAA6EaUAgAA\n0I0oBQAAoBtRCgAAQDeiFAAAgG5EKQAAAN2MKkqr6oiq+mZVLamq09eyzWuq6uaquqmq5o3tmAAA\nAExEU9e1QVVNSXJeksOSLE3ytaq6tLV284ht9kpyRpKDW2v3VNXPb6iBAQAAmDhGs1J6YJIlrbVb\nW2sPJ5mf5OjVtvmdJOe11u5Jktba3WM7JgAAABPRaKJ05yR3jHi8dPjcSM9O8uyq+tequr6qjljT\njqrq5KpaUFULli1btn4TAwAAMGGM1Y2OpibZK8mhSY5P8hdVtd3qG7XWzm+tzW2tzZ02bdoYvTUA\nAACbqtFE6Z1JdhnxePrwuZGWJrm0tfaT1tq3k3wrg0gFAACAtRpNlH4tyV5VtUdVbZ7kuCSXrrbN\n5zJYJU1V7ZjB6by3juGcAAAATEDrjNLW2sokpyS5PMniJBe11m6qqvdW1VHDzS5Psryqbk5ydZK3\ntdaWb6ihAQAAmBjW+ZEwSdJauyzJZas99+4RX7ckbxn+AgAAgFEZqxsdAQAAwJMmSgEAAOhGlAIA\nANCNKAUAAKAbUQoAAEA3ohQAAIBuRCkAAADdiFIAAAC6EaUAAAB0I0oBAADoRpQCAADQjSgFAACg\nG1EKAABAN6IUAACAbqb2HmCTsfD8ZPG8xz637MZk2pw+8wAAAEwAVkpHa/G8QYSONG1OMuOEPvMA\nAABMAFZKn4xpc5Jjr+k9BQAAwIRhpRQAAIBuRCkAAADdiFIAAAC6EaUAAAB0I0oBAADoRpQCAADQ\njSgFAACgG1EKAABAN6IUAACAbkQpAAAA3YhSAAAAuhGlAAAAdCNKAQAA6EaUAgAA0I0oBQAAoBtR\nCgAAQDeiFAAAgG5EKQAAAN2IUgAAALoRpQAAAHQjSgEAAOhGlAIAANCNKAUAAKAbUQoAAEA3ohQA\nAIBuRCkAAADdiFIAAAC6EaUAAAB0I0oBAADoRpQCAADQjSgFAACgG1EKAABAN6IUAACAbkQpAAAA\n3YhSAAAAuhGlAAAAdCNKAQAA6EaUAgAA0I0oBQAAoBtRCgAAQDeiFAAAgG5EKQAAAN2IUgAAALoR\npQAAAHQjSgEAAOhGlAIAANCNKAUAAKAbUQoAAEA3ohQAAIBuRCkAAADdiFIAAAC6EaUAAAB0I0oB\nAADoZlRRWlVHVNU3q2pJVZ3+BNu9qqpaVc0duxEBAACYqNYZpVU1Jcl5SV6WZGaS46tq5hq22zrJ\naUm+OtZDAgAAMDGNZqX0wCRLWmu3ttYeTjI/ydFr2O59ST6U5MExnA8AAIAJbDRRunOSO0Y8Xjp8\nbpWqek6SXVprXxjD2QAAAJjgnvKNjqrqaUk+luSto9j25KpaUFULli1b9lTfGgAAgE3caKL0ziS7\njHg8ffjco7ZOMivJNVV1W5LnJ7l0TTc7aq2d31qb21qbO23atPWfGgAAgAlhNFH6tSR7VdUeVbV5\nkuOSXProi621Fa21HVtru7fWdk9yfZKjWmsLNsjEAAAATBjrjNLW2sokpyS5PMniJBe11m6qqvdW\n1VEbekAAAAAmrqmj2ai1dlmSy1Z77t1r2fbQpz4WAAAAk8FTvtERAAAArC9RCgAAQDejOn13Ulp4\nfrJ43s8eL7sxmTan3zwAAAATkJXStVk8bxCij5o2J5lxQr95AAAAJiArpU9k2pzk2Gt6TwEAADBh\nWSkFAACgG1EKAABAN6IUAACAbkQpAAAA3YhSAAAAuhGlAAAAdCNKAQAA6EaUAgAA0I0oBQAAoBtR\nCgAAQDeiFAAAgG5EKQAAAN2IUgAAALoRpQAAAHQjSgEAAOhGlAIAANCNKAUAAKAbUQoAAEA3ohQA\nAIBuRCkAAADdiFIAAAC6EaUAAAB0I0oBAADoRpQCAADQjSgFAACgG1EKAABAN6IUAACAbkQpAAAA\n3YhSAAAAuhGlAAAAdCNKAQAA6EaUAgAA0I0oBQAAoBtRCgAAQDeiFAAAgG5EKQAAAN2IUgAAALoR\npQAAAHQjSgEAAOhGlAIAANCNKAUAAKAbUQoAAEA3ohQAAIBuRCkAAADdiFIAAAC6EaUAAAB0I0oB\nAADoRpQCAADQjSgFAACgG1EKAABAN6IUAACAbkQpAAAA3YhSAAAAuhGlAAAAdCNKAQAA6EaUAgAA\n0I0oBQAAoBtRCgAAQDeiFAAAgG5EKQAAAN2IUgAAALoRpQAAAHQjSgEAAOhGlAIAANCNKAUAAKCb\nUUVpVR1RVd+sqiVVdfoaXn9LVd1cVQur6ktVtdvYjwoAAMBEs84oraopSc5L8rIkM5McX1UzV9vs\nG0nmttZmJ7k4yYfHelAAAAAmntGslB6YZElr7dbW2sNJ5ic5euQGrbWrW2s/Hj68Psn0sR0TAACA\niWg0UbpzkjtGPF46fG5tTkryxacyFAAAAJPD1LHcWVX9ZpK5SV6wltdPTnJykuy6665j+dYAAABs\ngkazUnpnkl1GPJ4+fO4xquolSd6Z5KjW2kNr2lFr7fzW2tzW2txp06atz7wAAABMIKOJ0q8l2auq\n9qiqzZMcl+TSkRtU1QFJ/jyDIL177McEAABgIlpnlLbWViY5JcnlSRYnuai1dlNVvbeqjhpu9pEk\nWyX526q6saouXcvuAAAAYJVRXVPaWrssyWWrPffuEV+/ZIznAgAAYBIYzem7AAAAsEGIUgAAALoR\npQAAAHQjSgEAAOhGlAIAANCNKAUAAKAbUQoAAEA3ohQAAIBuRCkAAADdiFIAAAC6EaUAAAB0I0oB\nAADoRpQCAADQjSgFAACgG1EKAABAN6IUAACAbkQpAAAA3YhSAAAAuhGlAAAAdCNKAQAA6EaUAgAA\n0I0oBQAAoBtRCgAAQDeiFAAAgG5EKQAAAN2IUgAAALoRpQAAAHQjSgEAAOhGlAIAANCNKAUAAKAb\nUQoAAEA3ohQAAIBuRCkAAADdiFIAAAC6EaUAAAB0I0oBAADoRpQCAADQjSgFAACgG1EKAABAN6IU\nAACAbkQpAAAA3YhSAAAAuhGlAAAAdCNKAQAA6EaUAgAA0I0oBQAAoBtRCgAAQDeiFAAAgG5EKQAA\nAN2IUgAAALoRpQAAAHQjSgEAAOhGlAIAANCNKAUAAKAbUQoAAEA3ohQAAIBuRCkAAADdiFIAAAC6\nEaUAAAB0I0oBAADoRpQCAADQjSgFAACgG1EKAABAN6IUAACAbkQpAAAA3YhSAAAAuhGlAAAAdCNK\nAQAA6EaUAgAA0I0oBQAAoJupvQcAAADGxk9+8pMsXbo0Dz74YO9RmES22GKLTJ8+PZttttl6ff+o\norSqjkjy8SRTkvxla+2Dq73+9CSfSvLcJMuTHNtau229JgIAANbL0qVLs/XWW2f33XdPVfUeh0mg\ntZbly5dn6dKl2WOPPdZrH+s8fbeqpiQ5L8nLksxMcnxVzVxts5OS3NNa2zPJ2Uk+tF7TAAAA6+3B\nBx/MDjvsIEgZN1WVHXbY4Smtzo/mmtIDkyxprd3aWns4yfwkR6+2zdFJ/nr49cVJXlyb+v8Tfn7O\n4BcAAGxCNvX/DGfT81SPudGcvrtzkjtGPF6a5JfXtk1rbWVVrUiyQ5Lvj9yoqk5OcnKS7Lrrrus5\n8jh54Tm9JwAAAJjwxvXuu62181trc1trc6dNmzaebw0AAIyDKVOmZM6cOZk1a1Ze8YpX5N577131\n2k033ZQXvehF2XvvvbPXXnvlfe97X1prq17/4he/mLlz52bGjBnZZ5998ta3vrXHj/CEvvGNb+Sk\nk07qPcYT+sAHPpA999wze++9dy6//PI1bnPVVVflOc95TmbNmpUTTzwxK1euTJLcc889OeaYYzJ7\n9uwceOCBWbRoUZLk4YcfziGHHLJqu7E0mii9M8kuIx5PHz63xm2qamqSbTO44REAADCJPOMZz8iN\nN96YRYsWZfvtt895552XJHnggQdy1FFH5fTTT883v/nN/Pu//3v+7d/+LX/2Z3+WJFm0aFFOOeWU\nfOYzn8nixYuzaNGi7LnnnmM621gE1VlnnZVTTz11XN/zybj55pszf/783HTTTfmnf/qn/N7v/V5+\n+tOfPmabRx55JCeeeGLmz5+fRYsWZbfddstf//Xgasyzzjorc+bMycKFC/OpT30qp512WpJk8803\nz4tf/OL8zd/8zZjPPJrTd7+WZK+q2iOD+DwuyQmrbXNpkhOTXJfkN5Jc1Ub+lQcAADC+rv7D5O4b\nx3afPz/nSV3mdtBBB2XhwoVJknnz5uXggw/O4YcfniTZcsst86d/+qc59NBD8/u///v58Ic/nHe+\n853ZZ599kiRTp07Nm970psft8/77788f/MEfZMGCBamqvOc978mrXvWqbLXVVrn//vuTJBdffHH+\n8R//MRdeeGFe//rXZ/vtt883vvGNzJkzJ5dcckluvPHGbLfddkmSvfbaK1/5ylfytKc9LW984xtz\n++23J0nOOeecHHzwwY957/vuuy8LFy7M/vvvnyS54YYbctppp+XBBx/MM57xjHzyk5/M3nvvnQsv\nvDBf+MIX8uCDD+ZHP/pRrrrqqnzkIx/JRRddlIceeijHHHNM/viP/zhJ8spXvjJ33HFHHnzwwZx2\n2mk5+eSTR/37uyaf//znc9xxx+XpT3969thjj+y555654YYbctBBB63aZvny5dl8883z7Gc/O0ly\n2GGH5QMf+EBOOumk3HzzzTn99NOTJPvss09uu+22/Nd//Vd22mmnvPKVr8wZZ5yR1772tU9pxtWt\nM0qH14iekuTyDD4S5oLW2k1V9d4kC1prlyb5qySfrqolSX6QQbgCAACT1E9/+tN86UtfWnWq6003\n3ZTnPve5j9nml37pl3L//ffnhz/8YRYtWjSq03Xf9773Zdttt81//Md/JBmcbrou3/rWt3LllVdm\nypQpeeSRR3LJJZfkDW94Q7761a9mt912y0477ZQTTjghb37zm/Mrv/Iruf322/PSl740ixcvfsx+\nFixYkFmzZq16vM8+++TLX/5ypk6dmiuvvDLveMc78nd/93dJkuuuuy4LFy7M9ttvnyuuuCK33HJL\nbrjhhrTWctRRR+Xaa6/NIYcckgsuuCDbb799HnjggTzvec/Lq171quywww6Ped83v/nNufrqqx/3\ncx133HGrAvJRd955Z57//Oevejx9+vTceedjT3Tdcccds3LlyixYsCBz587NxRdfnDvuGNxGaP/9\n98/f//3f51d/9Vdzww035Dvf+U6WLl2anXbaKbNmzcrXvva1df5+P1mj+pzS1tplSS5b7bl3j/j6\nwSSvHtvRAACA9dbpxp0PPPBA5syZk9tuuy3Pfe5zc9hhh43p/q+88srMnz9/1eNnPvOZ6/yeV7/6\n1ZkyZUqS5Nhjj8173/vevOENb8j8+fNz7LHHrtrvzTffvOp7fvjDH+b+++/PVlttteq5u+66KyPv\njbNixYqceOKJueWWW1JV+clPfrLqtcMOOyzbb799kuSKK67IFVdckQMOOCDJYLX3lltuySGHHJJz\nzz03l1xySZLkjjvuyC233PK4KD377LNH95szSlWV+fPn581vfnMeeuihHH744at+f04//fScdtpp\nmTNnTvbbb78ccMABq16bMmVKNt9889x3333Zeuutx2yeUUUpAADAaDx6TemKFSvy8pe/POedd15O\nPfXUzJw5M9dee+1jtr311luz1VZbZZtttsm+++6br3/966tOjX2yRn4syeqfmflzP/dzq74+6KCD\nsmTJkixbtiyf+9zncuaZZyYZXGd5/fXXZ4sttnjCn23kvt/1rnflhS98YS655JLcdtttOfTQQ9f4\nnq21nHEgcQJiAAAIWUlEQVTGGfnd3/3dx+zvmmuuyZVXXpnrrrsuW265ZQ499NA1ft7nk1kp3Xnn\nnVeteibJ0qVLs/POOz/uew866KB8+ctfTjKI5m9961tJkm222Saf/OQnV829xx575Bd/8RdXfd9D\nDz30hL9H62Nc774LAABMDttuu23OPffcfPSjH83KlSvz2te+Nl/5yldy5ZVXJhmsqJ566ql5+9vf\nniR529velrPOOmtVHD3yyCP52Mc+9rj9HnbYYatunpT87PTdnXbaKYsXL151eu7aVFWOOeaYvOUt\nb8mMGTNWrUoefvjh+ZM/+ZNV29144+Ovx50xY0aWLFmy6vGKFStWBd+FF1641vd86UtfmgsuuGDV\nNa933nln7r777qxYsSLPfOYzs+WWW+Y///M/c/3116/x+88+++zceOONj/u1epAmyVFHHZX58+fn\noYceyre//e3ccsstOfDAAx+33d13351kEJkf+tCH8sY3vjFJcu+99+bhhx9OkvzlX/5lDjnkkGyz\nzTZJBtei7rjjjtlss83W+rOuD1EKAABsEAcccEBmz56dz372s3nGM56Rz3/+83n/+9+fvffeO/vt\nt1+e97zn5ZRTTkmSzJ49O+ecc06OP/74zJgxI7Nmzcr3vve9x+3zzDPPzD333JNZs2Zl//33X7WC\n+MEPfjAvf/nL8+IXvzjPetaznnCuY489Np/5zGdWnbqbJOeee24WLFiQ2bNnZ+bMmfnEJz7xuO/b\nZ599smLFitx3331Jkre//e0544wzcvDBBz/uDrcjHX744TnhhBNy0EEHZb/99stv/MZv5L777ssR\nRxyRlStXZvbs2XnXu971mGtB19e+++6b17zmNZk5c2aOOOKInHfeeatOvz3yyCPz3e9+N0nykY98\nJDNmzMjs2bPzile8Ii960YuSJIsXL86sWbOy995754tf/GI+/vGPr9r31VdfnV/7tV97yjOurnrd\nJHfu3LltwYIFXd4bAAAmosWLF2fGjBm9x5jQzj777Gy99db57d/+7d6jjLtf//Vfzwc/+MFVd+0d\naU3HXlV9vbU2d137tVIKAAAwSm9605vy9Kc/vfcY4+7hhx/OK1/5yjUG6VMlSgEAAEZpiy22yG/9\n1m/1HmPcbb755nnd6163QfYtSgEAYALpdXkek9dTPeZEKQAATBBbbLFFli9fLkwZN621LF++/Cl9\nTIzPKQUAgAli+vTpWbp0aZYtW9Z7FCaRLbbYItOnT1/v7xelAAAwQWy22WbZY489eo8BT4rTdwEA\nAOhGlAIAANCNKAUAAKCb6nVnrqpaluQ7Xd589HZM8v3eQzDpOQ7ZGDgO2Vg4FtkYOA7ZGGwKx+Fu\nrbVp69qoW5RuCqpqQWttbu85mNwch2wMHIdsLByLbAwch2wMJtJx6PRdAAAAuhGlAAAAdCNKn9j5\nvQeAOA7ZODgO2Vg4FtkYOA7ZGEyY49A1pQAAAHRjpRQAAIBuJn2UVtURVfXNqlpSVaev4fWnV9Xf\nDF//alXtPv5TMhmM4lh8S1XdXFULq+pLVbVbjzmZ2NZ1HI7Y7lVV1apqQtz1j43LaI7DqnrN8M/E\nm6pq3njPyOQwin8371pVV1fVN4b/fj6yx5xMXFV1QVXdXVWL1vJ6VdW5w2N0YVU9Z7xnHAuTOkqr\nakqS85K8LMnMJMdX1czVNjspyT2ttT2TnJ3kQ+M7JZPBKI/FbySZ21qbneTiJB8e3ymZ6EZ5HKaq\ntk5yWpKvju+ETAajOQ6raq8kZyQ5uLW2b5I/HPdBmfBG+WfimUkuaq0dkOS4JH82vlMyCVyY5Ign\neP1lSfYa/jo5yf8ch5nG3KSO0iQHJlnSWru1tfZwkvlJjl5tm6OT/PXw64uTvLiqahxnZHJY57HY\nWru6tfbj4cPrk0wf5xmZ+EbzZ2KSvC+Dv6B7cDyHY9IYzXH4O0nOa63dkySttbvHeUYmh9Eciy3J\nNsOvt03y3XGcj0mgtXZtkh88wSZHJ/lUG7g+yXZV9azxmW7sTPYo3TnJHSMeLx0+t8ZtWmsrk6xI\nssO4TMdkMppjcaSTknxxg07EZLTO43B4WtAurbUvjOdgTCqj+fPw2UmeXVX/WlXXV9UTrSLA+hrN\nsfhHSX6zqpYmuSzJH4zPaLDKk/1vyI3S1N4DAE9OVf1mkrlJXtB7FiaXqnpako8leX3nUWBqBqeq\nHZrBWSPXVtV+rbV7u07FZHR8kgtbax+tqoOSfLqqZrXWHuk9GGxKJvtK6Z1JdhnxePrwuTVuU1VT\nMzg1Y/m4TMdkMppjMVX1kiTvTHJUa+2hcZqNyWNdx+HWSWYluaaqbkvy/CSXutkRY2w0fx4uTXJp\na+0nrbVvJ/lWBpEKY2k0x+JJSS5KktbadUm2SLLjuEwHA6P6b8iN3WSP0q8l2auq9qiqzTO4QP3S\n1ba5NMmJw69/I8lVzYe7MvbWeSxW1QFJ/jyDIHX9FBvCEx6HrbUVrbUdW2u7t9Z2z+Da5qNaawv6\njMsENZp/N38ug1XSVNWOGZzOe+t4DsmkMJpj8fYkL06SqpqRQZQuG9cpmewuTfK64V14n59kRWvt\nrt5DPVmT+vTd1trKqjolyeVJpiS5oLV2U1W9N8mC1tqlSf4qg1MxlmRwkfFx/SZmohrlsfiRJFsl\n+dvhvbZub60d1W1oJpxRHoewQY3yOLw8yeFVdXOSnyZ5W2vNWUyMqVEei29N8hdV9eYMbnr0eosX\njKWq+mwGfwm34/Da5fck2SxJWmufyOBa5iOTLEny4yRv6DPpU1P+fwMAAEAvk/30XQAAADoSpQAA\nAHQjSgEAAOhGlAIAANCNKAUAAKAbUQoAAEA3ohQAAIBuRCkAAADd/F/v/rcPWabfpwAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc2f62e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred = t.evaluate(*x_test.T)[0]\n",
    "fpr, tpr, thresholds = roc_curve(y_test, pred)\n",
    "plt.title('ROC curve of test data')\n",
    "plt.plot(fpr, tpr, color='darkorange',\n",
    "         label='ROC curve (area = %0.2f)' % roc_auc_score(y_test, pred))\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.947368421053\n"
     ]
    }
   ],
   "source": [
    "print(accuracy(t.evaluate(*x_test.T) >=\n",
    "               optimum_threshold(y_train, t.evaluate(*x_train.T)[0]), y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ensemble learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c5147613eac444c8b11e590d45d2d717"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "classifier_number = 5\n",
    "\n",
    "ens = [max(E.evolvepop(50, E.bestpop(10, 10, fit, .3), fit, None), key=fit) for _ in tnrange(classifier_number)]\n",
    "ens_ths = [optimum_threshold(y_train, t.evaluate(*x_train.T)[0]) for t in ens]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def evaluate(ens, ens_ths, X):\n",
    "    return np.array([t.evaluate(*X.T)[0] >= th for t, th in zip(ens, ens_ths)]).mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0ub4B9Sv4nOez0mbUe89Qfx3R5TTNcy7l2aYKXS7HRr0WGVaf+4qK3Csoeg8G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\nAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left [ input_{28} \\left(- input_{24} - \\frac{input_{27}}{input_{25} - input_{9}}\\right) - \\log{\\left (input_{3}^{2} \\right )}, \\quad - input_{25} \\left(\\frac{input_{13}}{input_{16}} + input_{24}\\right) + \\frac{1}{\\sqrt{input_{2}} \\sqrt{input_{23}}} \\left(- input_{17} input_{9} \\left(input_{2} + input_{7}\\right) + \\frac{input_{18}}{input_{12}}\\right), \\quad \\left(input_{17} - input_{27}\\right) \\left(input_{24} - input_{27} + input_{7} + \\left(- input_{1} input_{12} + input_{12}\\right) \\log{\\left (input_{16} \\right )}\\right), \\quad - input_{2}^{2} input_{27} \\left(- input_{17} - input_{21}\\right)^{2}, \\quad input_{11} - input_{2} - input_{23} \\sqrt{input_{24}} input_{25}\\right ]$$"
      ],
      "text/plain": [
       "⎡                                                                             \n",
       "⎢                                                                             \n",
       "⎢        ⎛               input₂₇     ⎞      ⎛      2⎞            ⎛input₁₃     \n",
       "⎢input₂₈⋅⎜-input₂₄ - ────────────────⎟ - log⎝input₃ ⎠, - input₂₅⋅⎜─────── + in\n",
       "⎢        ⎝           input₂₅ - input₉⎠                           ⎝input₁₆     \n",
       "⎣                                                                             \n",
       "\n",
       "                                             input₁₈                          \n",
       "         -input₁₇⋅input₉⋅(input₂ + input₇) + ───────                          \n",
       "     ⎞                                       input₁₂                          \n",
       "put₂₄⎟ + ───────────────────────────────────────────, (input₁₇ - input₂₇)⋅(inp\n",
       "     ⎠                ________   _________                                    \n",
       "                    ╲╱ input₂ ⋅╲╱ input₂₃                                     \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                            2 \n",
       "ut₂₄ - input₂₇ + input₇ + (-input₁⋅input₁₂ + input₁₂)⋅log(input₁₆)), -input₂ ⋅\n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "                                                                             ⎤\n",
       "                                                                             ⎥\n",
       "                            2                               _________        ⎥\n",
       "input₂₇⋅(-input₁₇ - input₂₁) , input₁₁ - input₂ - input₂₃⋅╲╱ input₂₄ ⋅input₂₅⎥\n",
       "                                                                             ⎥\n",
       "                                                                             ⎦"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[e.expr[0] for e in ens]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy of each one\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA+IAAAAVCAYAAADCZVR3AAAABHNCSVQICAgIfAhkiAAADrNJREFU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\nuNVDfZcAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left [ 0.938596491228, \\quad 0.921052631579, \\quad 0.923245614035, \\quad 0.936403508772, \\quad 0.936403508772\\right ]$$"
      ],
      "text/plain": [
       "[0.938596491228, 0.921052631579, 0.923245614035, 0.936403508772, 0.93640350877\n",
       "2]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Accuracy of each one')\n",
    "[accuracy(evaluate([t], [th], x_test) >= .5, y_test) for t, th in zip(ens, ens_ths)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Frequencies of the votes:\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAnYAAAAWCAYAAABNP9GKAAAABHNCSVQICAgIfAhkiAAAChBJREFU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\ngUAgELDg/4Fwga/kKvohAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left \\{ 0.0 : 144, \\quad 0.2 : 16, \\quad 0.4 : 13, \\quad 0.6 : 26, \\quad 0.8 : 21, \\quad 1.0 : 236\\right \\}$$"
      ],
      "text/plain": [
       "Counter({0.0: 144, 0.2: 16, 0.4: 13, 0.6: 26, 0.8: 21, 1.0: 236})"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from collections import Counter\n",
    "print('Frequencies of the votes:')\n",
    "Counter(evaluate(ens, ens_ths, x_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy of the group\n"
     ]
    },
    {
     "data": {
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      "text/latex": [
       "$$0.956140350877$$"
      ],
      "text/plain": [
       "0.956140350877"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Accuracy of the group')\n",
    "accuracy(evaluate(ens, ens_ths, x_test) >= .5, y_test)"
   ]
  }
 ],
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