chrisburr/Example.ipynb

## Example.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Welcome to JupyROOT 6.14/04\n"
     ]
    }
   ],
   "source": [
    "# It's generally considered a good practice to put all imports at the top the file\n",
    "from matplotlib import pyplot as plt\n",
    "import root_pandas\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.ensemble import GradientBoostingClassifier\n",
    "from sklearn.metrics import roc_curve, auc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Examples\n",
    "\n",
    "You can change the cell type to markdown to add fancy stuff inline.\n",
    "It even supports LaTeX!\n",
    "\n",
    "$D^0 \\rightarrow \\phi \\gamma$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Read the mass, eta and all momentum components from root file into a pandas DataFrame (df)\n",
    "# df = root_pandas.read_root('something.root', key='dir/my_tree', columns=['D0_M', 'D0_P*'])\n",
    "\n",
    "# As I don't have one to hand, I make some fake data instead\n",
    "def make_fake_data(size, *, smear=None, mass_peak=None):\n",
    "    df = pd.DataFrame({\n",
    "        'D0_PX': np.random.exponential(100, size=size),\n",
    "        'D0_PY': np.random.exponential(110, size=size),\n",
    "        'D0_PZ': np.random.exponential(50000, size=size),\n",
    "    })\n",
    "\n",
    "    for col in df:\n",
    "        df[col] *= np.random.choice([1, -1], replace=True, size=size)\n",
    "        if smear is not None:\n",
    "            df[col] *= np.random.normal(1, smear, size=size)\n",
    "    \n",
    "    df['D0_VERTEX_CHI2'] = np.random.normal(3, smear or 1, size=size)\n",
    "        \n",
    "    if mass_peak is None:\n",
    "        df['D0_M'] = 1790+np.random.exponential(100, size=size)\n",
    "    else:\n",
    "        df['D0_M'] = np.random.normal(mass_peak, 5, size=size)\n",
    "\n",
    "    # It would be better to use hepvector here:\n",
    "    # https://hepvector.readthedocs.io/en/latest/\n",
    "    df.eval('D0_P = sqrt(D0_PX**2 + D0_PY**2 + D0_PZ**2)', inplace=True)\n",
    "    df.eval('D0_PT = sqrt(D0_PX**2 + D0_PY**2)', inplace=True)\n",
    "    df.eval('D0_PE = sqrt(D0_M**2 + D0_P**2)', inplace=True)\n",
    "    df.eval('D0_ETA = 0.5 * log((D0_PE+D0_PZ)/(D0_PE-D0_PZ))', inplace=True)\n",
    "    return df\n",
    "\n",
    "df_data = pd.concat([make_fake_data(10000, mass_peak=1860),\n",
    "                     make_fake_data(100000, smear=2)])\n",
    "df_1 = make_fake_data(10000, smear=2)\n",
    "df_2 = make_fake_data(10000, mass_peak=1860)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variable plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, '$D^0$ mass')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make 100 uniform bins between 1820 and 1910 (101 points as these are the edges)\n",
    "mass_bins = np.linspace(1820, 1910, 101)\n",
    "# Create the plot, it will be automatically show when you run this cell\n",
    "plt.hist(df_data['D0_M'], bins=mass_bins)\n",
    "plt.xlabel('$D^0$ mass')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, '$D^0$ mass')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We can also do things slightly differently to compare two histograms\n",
    "plt.hist(df_1['D0_M'], range=[1800, 1910], bins=100, histtype='step', label='Sample 1')\n",
    "plt.hist(df_2['D0_M'], range=[1800, 1910], bins=100, histtype='step', label='Sample 2')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('$D^0$ mass')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JtAFTImJvRGwCiIg/AtuBMUXGWgl8sGeHZmZmlVBOohgD7C7Yb+e1F/VT2kTEceAQMLKcvuky1SXAhlT0xojYm7Z/B7yxjBjNzKyPDOhktqRzge8Cn42IP3Suj4gAokTfGyW1Smrdt29fH0dqZnbmKidR7AHGFuzXp7KibSTVAMOB/Xl9JQ0lSxL3RcQDBW1+L2l0ajMaeKFYUBGxLCKaIqKprq6ujMMwM7OeKCdRbATGSWqUdDbZ5HRLpzYtwOy0fR2wPr0baAGa011RjcA44Mk0f3EPsD0ivpwz1mzg+909KDMzq5yarhpExHFJc4F1wBBgeURslXQb0BoRLWQv+t+U1Aa8RJZMSO1WA9vI7nS6OSJOSLoC+AjwjKTN6am+EBFrgUXAaklzgN8Cf13JAzYzs+7pMlEApBfwtZ3Kbi3YPgpcX6LvQmBhp7LHAJVovx+4qpy4zMys7/mT2WZmlsuJwszMcjlRmJlZLicKMzPL5URhZma5nCjMzCyXE4WZmeVyojAzs1xOFGZmlsuJwszMcjlRmJlZLicKMzPL5URhZma5nCjMzCyXE4WZmeVyojAzs1xOFGZmlsuJwszMcjlRmJlZLicKMzPL5URhZma5ykoUkmZI2iGpTdK8IvW1ku5P9RskNRTUzU/lOyRNLyhfLukFSVs6jbVA0h5Jm9PjfT0/PDMz660uE4WkIcBS4BpgPHCDpPGdms0BDkTEBcASYHHqOx5oBiYAM4C70ngAK1JZMUsiYnJ6rO3eIZmZWSWV845iCtAWEc9FxCvAKmBmpzYzgZVpew1wlSSl8lURcSwidgJtaTwi4mfASxU4BjMz60PlJIoxwO6C/fZUVrRNRBwHDgEjy+xbzFxJT6fLU+cVayDpRkmtklr37dtXxpBmZtYT1TiZ/TXg7cBkYC/wr8UaRcSyiGiKiKa6urr+jM/M7IxSTqLYA4wt2K9PZUXbSKoBhgP7y+zbQUT8PiJORMSfgf8kXaoyM7OBUU6i2AiMk9Qo6WyyyemWTm1agNlp+zpgfUREKm9Od0U1AuOAJ/OeTNLogt0PAVtKtTUzs75X01WDiDguaS6wDhgCLI+IrZJuA1ojogW4B/impDayCerm1HerpNXANuA4cHNEnACQ9G1gKjBKUjvwpYi4B7hT0mQggF3Axyt5wGZm1j1dJgqAdIvq2k5ltxZsHwWuL9F3IbCwSPkNJdp/pJyYzE4rSybCoedPKW6PUdQPQDhmhcpKFGbWxw49DwsOnVJ8xbwfsqv/ozHroBrvejIzsyriRGFmZrmcKMzMLJcThZmZ5XKiMDOzXE4UZmaWy4nCzMxyOVGYmVkuJwozM8vlRGFmZrmcKMzMLJfXejIbhNpjFPULhp9aMfwt8PfP9H9AdlpzojAbhK449u/sWnTtqRXFkodZL/nSk5mZ5XKiMDOzXE4UZmaWy4nCzMxyOVGYmVku3/VkViUa5v3wlLIxI84ZgEjMOiorUUiaAXwFGAJ8PSIWdaqvBe4FLgX2A7MiYleqmw/MAU4An46Idal8OfB+4IWIuLhgrPOB+4EGYBfw1xFxoMdHaDZIFL3d1awKdHnpSdIQYClwDTAeuEHS+E7N5gAHIuICYAmwOPUdDzQDE4AZwF1pPIAVqayzecAjETEOeCTtm5nZAClnjmIK0BYRz0XEK8AqYGanNjOBlWl7DXCVJKXyVRFxLCJ2Am1pPCLiZ8BLRZ6vcKyVwAe7cTxmZlZh5SSKMcDugv32VFa0TUQcBw4BI8vs29kbI2Jv2v4d8MYyYjQzsz5S1Xc9RUQAUaxO0o2SWiW17tu3r58jMzM7c5STKPYAYwv261NZ0TaSaoDhZJPa5fTt7PeSRqexRgMvFGsUEcsioikimurq6so4DDMz64lyEsVGYJykRklnk01Ot3Rq0wLMTtvXAevTu4EWoFlSraRGYBzwZBfPVzjWbOD7ZcRoZmZ9pMtEkeYc5gLrgO3A6ojYKuk2SR9Ize4BRkpqA/6BdKdSRGwFVgPbgB8DN0fECQBJ3wYeB94hqV3SnDTWImCapGeBv0r7ZmY2QMr6HEVErAXWdiq7tWD7KHB9ib4LgYVFym8o0X4/cFU5cZmdqcaMOKfoB/R2DRuAYOy0509mmw1Cv5h3ZfGKBf0ahp0hqvquJzMzG3hOFGZmlsuJwszMcjlRmJlZLicKMzPL5URhZma5nCjMzCyXE4WZmeVyojAzs1xOFGZmlsuJwszMcjlRmJlZLicKMzPL5URhZma5nCjMzCyXE4WZmeVyojAzs1xOFGZmlsuJwszMcpWVKCTNkLRDUpukeUXqayXdn+o3SGooqJufyndImt7VmJJWSNopaXN6TO7dIZqZWW/UdNVA0hBgKTANaAc2SmqJiG0FzeYAByLiAknNwGJglqTxQDMwAXgz8LCkC1OfvDE/HxFrKnB8ZmbWS+W8o5gCtEXEcxHxCrAKmNmpzUxgZdpeA1wlSal8VUQci4idQFsar5wxzcysCpSTKMYAuwv221NZ0TYRcRw4BIzM6dvVmAslPS1piaTaMmI0M7M+Uo2T2fOBdwLvAs4HbinWSNKNklolte7bt68/4zMzO6OUkyj2AGML9utTWdE2kmqA4cD+nL4lx4yIvZE5BnyD7DLVKSJiWUQ0RURTXV1dGYdhZmY9UU6i2AiMk9Qo6WyyyemWTm1agNlp+zpgfUREKm9Od0U1AuOAJ/PGlDQ6/Svgg8CW3hygmZn1Tpd3PUXEcUlzgXXAEGB5RGyVdBvQGhEtwD3ANyW1AS+RvfCT2q0GtgHHgZsj4gRAsTHTU94nqQ4QsBn4ROUO18zMuqvLRAEQEWuBtZ3Kbi3YPgpcX6LvQmBhOWOm8ivLiclssLl80Xr2HDxStG7XsH4OxqwbykoUZtZ7ew4eYdeia4tXLujXUMy6pRrvejIzsyriRGFmZrl86cnsNNMw74dFy8eMOIdfzPMUoHWfE4XZaabUPEipBGLWFScKs37yWO2nYcHfFK8c/pb+DcasG5wozPpJvV6EBYcGOgyzbnOiMDudDH8LLBhetOqx2lFAidtzzXI4UZidTv7+mZJV9SUSiFlXfHusmZnlcqIwM7NcvvRkVmGl1nTyek42WDlRmFVYyTWdFvR7KKco9lkKfxDPuuJEYXYGKZbA/EE864rnKMzMLJcThZmZ5XKiMDOzXJ6jMOuhUnc3jRlxzgBEY9Z3nCjMeij3G+sGkTEjzvHdUJbLicKs0pZMhEPPn1pepSvElkoGvhvKTiorUUiaAXwFGAJ8PSIWdaqvBe4FLgX2A7MiYleqmw/MAU4An46IdXljSmoEVgEjgaeAj0TEK707TLOe6/YlpkPPV+cqsaUWDBz+lqJrRPmdhp3UZaKQNARYCkwD2oGNkloiYltBsznAgYi4QFIzsBiYJWk80AxMAN4MPCzpwtSn1JiLgSURsUrS3Wnsr1XiYM3y5CWE0+ESU8kFA0ssFuh3GnZSOe8opgBtEfEcgKRVwEygMFHM5LXPna4BvipJqXxVRBwDdkpqS+NRbExJ24ErgZPf7rIyjetEYRVRKhnAaZQQ+pjfaZx5ykkUY4DdBfvtwLtLtYmI45IOkV06GgM80anvmLRdbMyRwMGIOF6kvdkp8l74i6loMhhkcxEldfOSVKlkcPmi9RV7t+GkU10G7WS2pBuBG9PuYUk7utF9FPBi5aPqE4MpVqjyeH8LaP6ru30U6xb4B1V+2H7/2fbqOHoVa6f/p75W1edsEZWM963lNConUewBxhbs16eyYm3aJdUAw8kmtfP6FivfD4yQVJPeVRR7LgAiYhmwrIz4TyGpNSKaetK3vw2mWGFwxTuYYoXBFa9j7TsDEW85n8zeCIyT1CjpbLLJ6ZZObVqA2Wn7OmB9REQqb5ZUm+5mGgc8WWrM1OfRNAZpzO/3/PDMzKy3unxHkeYc5gLryG5lXR4RWyXdBrRGRAtwD/DNNFn9EtkLP6ndarKJ7+PAzRFxAqDYmOkpbwFWSbod+O80tpmZDRBlf8SfWSTdmC5dVb3BFCsMrngHU6wwuOJ1rH1nIOI9IxOFmZmVz6vHmplZrtM6UUj6nKSQNCrtS9K/S2qT9LSkvyxoO1vSs+kxu6D8UknPpD7/nj5IWMkY/1+KZbOkn0h6cxXH+s+SfpXi+Z6kEQV189Pz7pA0vaB8RiprkzSvoLxR0oZUfn+6qaGiJF0vaaukP0tq6lRXdfHmHEfRmPqbpOWSXpC0paDsfEkPpXPxIUnnpfJun78VjnWspEclbUvnwGeqNV5JwyQ9KemXKdZ/SuVFzzllNwfdn8o3SGooGKvoed1rEXFaPshuv11Hdkv2qFT2PuBHgIDLgA2p/HzgufTveWn7vFT3ZGqr1PeaCsf5hoLtTwN3V3GsVwM1aXsxsDhtjwd+CdQCjcBvyG5SGJK23wacndqMT31WA81p+27gk31wDlwEvAP4KdBUUF6V8ZY4hpIxDcDv1P8E/hLYUlB2JzAvbc8rOCe6ff5WONbRwF+m7dcDv07/71UXb3rOc9P2UGBDiqHoOQfcxGuvE83A/XnndSViPJ3fUSwB/i9QOAkzE7g3Mk+QfWZjNDAdeCgiXoqIA8BDwIxU94aIeCKy/4l7gQ9WMsiI+EPB7l8UxFuNsf4kXvvU/BNkn3M5GeuqiDgWETuBk0u1vLr8S2QLO55cqkVkS7WsSf1XVjrWFO/2iCj2QcyqjLeEojH103N3EBE/I7ursdBMsp8HdPy5dOv87YNY90bEprT9R2A72SoPVRdves7DaXdoegSlz7nCY1gDXJXO0VLnda+dlolC0kxgT0T8slNVseVIxnRR3l6kvNLxLpS0G/gwcGs1x1rgo2R/gdFFTMXKB3qplsEUb6mYqsUbI2Jv2v4d8Ma03d2fcZ9Jl2YuIftLvSrjlTRE0mbgBbJk9BtKn3MdlkwCCpdM6pNYB/MSHg8DbypS9UXgC2SXSapCXqwR8f2I+CLwRWVLss8FvtSvARboKtbU5otkn4u5rz9jK6aceK1/RERIqqrbKCWdC3wX+GxE/EEF03bVFG9kny+bnOb9vge8c4BD6mDQJoqI+Kti5ZImkl2f+2U6KeqBTZKmUHpJkT3A1E7lP03l9UXaVyTWIu4D1pIliqqMVdL/Ad4PXJUucZETKyXKy16qpbfxljBg8fZAOUvoDKTfSxodEXvTpZoXUnl3z9+KkzSULEncFxEPVHu8ABFxUNKjwHsofc71ZMmkXgd2Wj+AXbw2mX0tHSesnozXJqx2kk1WnZe2z091nSeI31fh+MYVbH8KWFPFsc4g+5R9XafyCXScRHuObBK2Jm038tpE7ITU5zt0nKi7qQ/PgZ/ScTK7quPtFHvJmAbiATTQcTL7n+k4OXxnT8/fCscpsnm6f+tUXnXxAnXAiLR9DvBzsj/Gip5zwM10nMxenXdeVyTGgTrh+vHE3sVriUJkX5j0G+CZTi8eHyWb/GkD/q6gvAnYkvp8lfQhxQrG9900/tPAD4AxVRxrG9k10M3pcXdB3RfT8+6g4G4rsrtJfp3qvlhQ/jayxNaWfiFq++D//kNk12mPAb8H1lVzvDnHUTSm/n4A3wb2An9KP9c5ZNfGHwGeBR7mtT9aun3+VjjWK8gmhJ8uOF/fV43xApPIlit6Ov3+3pp3zgHD0n5bqn9bV+d1bx/+ZLaZmeU6Le96MjOzynGiMDOzXE4UZmaWy4nCzMxyOVGYmVkuJwozM8vlRGFmZrkG7RIeZtVE0l8AdwGvAD+NiAFfB8usUvyOwqxMkj4uaa+yL5n6paTvSGpM1f+bbPmVjwEfKNH/ROq7JfV9XfqCnZ2Szk9tzkv7Df1yUGZlcKIwK99EsuUVJkfE/yBbCuKB9F0A9by2xPOJEv2PpL4Xk73z+ERE7Aa+BixKbRYByyJiV18dhFl3OVGYlW8S2Vo8AETE3WRLnI8lW/vo5Oq95fxe/Ry4IG0vAS6T9FmyNYr+pVIBm1WC5yjMyncxsLVT2RGyVUUfAL4q6VqyxR1LSktDXwP8GCAi/iTp82n/6oj4U6UDN+sNJwqzMkgaCxyOgq+uTd93MBp4LiJeBv6ui2HOSd9iBtk7insK6q4hW5n1YrJvODOrGk4UZuWZSMEvJwb+AAAArUlEQVRlp+TvgPWRfSdzOY5ExOTOhZImA9PIvgfhMUmr4rWv6zQbcJ6jMCtPh/kJSVcD84F/7M2gaSL8a2Rf1fk82RfreI7CqooThVl5JgIflvSUpE3AbGBGRGzv5bgfA56PiJOXm+4CLpL0v3o5rlnF+IuLzMwsl99RmJlZLicKMzPL5URhZma5nCjMzCyXE4WZmeVyojAzs1xOFGZmlsuJwszMcjlRmJlZrv8P/+7Y+9q2n+IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for var in df_1.columns:\n",
    "    if var == 'Dp_M':\n",
    "        continue\n",
    "\n",
    "    # Compute the bins we should use\n",
    "    x_low = min(df_1[var].min(), df_2[var].min())\n",
    "    x_high = max(df_1[var].max(), df_2[var].max())\n",
    "    bins = np.linspace(x_low, x_high)\n",
    "    \n",
    "    # We can put the histogram arguments into a dictionary to avoid typing them every time\n",
    "    hist_kwargs = dict(histtype='step', bins=bins, density=1)\n",
    "\n",
    "    # We run figure so a new plot is made for each iteration of the loop\n",
    "    plt.figure()\n",
    "    plt.hist(df_1[var], label='Sample 1', **hist_kwargs)\n",
    "    plt.hist(df_2[var], label='Sample 2', **hist_kwargs)\n",
    "    pretty_var_name = var.replace('D0_', '$D^0$ ')\n",
    "    plt.xlabel(pretty_var_name)\n",
    "    plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training your first classifier\n",
    "\n",
    "Here I use an GradientBoostingClassifier BDT which is documented [here](http://scikit-learn.org/stable/modules/generated/sklearn.ensemble.GradientBoostingClassifier.html).\n",
    "\n",
    "The fit method used for \"training\" in scikit-learn takes two arguments:\n",
    " - `X`: The data to train using\n",
    " - `y`: The true \"class\" of each sample, typically we use 0 for background and 1 for signal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 2.82 s, sys: 11 ms, total: 2.84 s\n",
      "Wall time: 2.83 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "training_columns = ['D0_P', 'D0_PT', 'D0_ETA', 'D0_VERTEX_CHI2']\n",
    "\n",
    "# For X we just concatenate the dataframes of the relevent columns to get a new DataFrame\n",
    "X = pd.concat([df_1[training_columns], df_2[training_columns]])\n",
    "\n",
    "# For y we need an array of zeros and ones\n",
    "y = np.concatenate([np.zeros(len(df_1)), np.ones(len(df_2))])\n",
    "\n",
    "# Train the classifer\n",
    "bdt = GradientBoostingClassifier(max_depth=3, n_estimators=200)\n",
    "bdt.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the decision function for each class\n",
    "def plot_decision_function(classifier, X, y_true):\n",
    "    y_scores = classifier.decision_function(X)\n",
    "\n",
    "    hist_kwargs = dict(\n",
    "        range=[y_scores.min(), y_scores.max()], bins=50,\n",
    "        histtype='step', linewidth=1.5, density=1\n",
    "    )\n",
    "\n",
    "    plt.figure()\n",
    "    for i in np.unique(y_true):\n",
    "        plt.hist(y_scores[y_true == i], label=f'Class {i:.0f}', **hist_kwargs)\n",
    "    plt.xlim(*hist_kwargs['range'])\n",
    "    plt.xlabel('Classifier response')\n",
    "    plt.ylabel('Arbitary units')\n",
    "    plt.legend(loc='upper left')\n",
    "\n",
    "plot_decision_function(bdt, X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot a ROC curve\n",
    "def plot_roc(classifier, X, y_true):\n",
    "    y_score = classifier.decision_function(X)\n",
    "    fpr, tpr, thresholds = roc_curve(y_true, y_score)\n",
    "    area = auc(fpr, tpr)\n",
    "\n",
    "    plt.figure()\n",
    "\n",
    "    plt.plot([0, 1], [0, 1], color='grey', linestyle='--')\n",
    "    plt.plot(fpr, tpr, label=f'ROC curve (area = {area:.2f})')\n",
    "\n",
    "    plt.xlim(0.0, 1.0)\n",
    "    plt.ylim(0.0, 1.0)\n",
    "    plt.xlabel('False Positive Rate')\n",
    "    plt.ylabel('True Positive Rate')\n",
    "    plt.legend(loc='lower right')\n",
    "    plt.gca().set_aspect('equal', adjustable='box')\n",
    "\n",
    "\n",
    "plot_roc(bdt, X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apply the classifier to the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fb3357cffd0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_data['BDT_score'] = bdt.decision_function(df_data[training_columns])\n",
    "cut = -1\n",
    "\n",
    "hist_kwargs = dict(bins=mass_bins, histtype='step', density=None)\n",
    "plt.hist(df_data['D0_M'], label='Before', **hist_kwargs)\n",
    "plt.hist(df_data.query(f'BDT_score > {cut}')['D0_M'], label='After', **hist_kwargs)\n",
    "plt.xlabel('$D^0$ mass')\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Further improvements\n",
    "\n",
    "This example needs expanding, ask me about each of these things:\n",
    " - Split the data into training and testing data\n",
    " - Use k-folding to get testing and training data\n",
    " - Plot the figure of merit\n",
    " - Consider using other kinds of classifer (XGBoost is great!)\n",
    " - Hyperparameter optimisation"
   ]
  }
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