{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "<CENTER><img src=\"../../images/ATLASOD.gif\" style=\"width:50%\"></CENTER>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Machine Learning for $t\\bar{t}Z$ in ATLAS \n",
    "\n",
    "<CENTER><img src=\"images/feynman_diagrams/ttZ_feynman.png\" style=\"width:100%\"></CENTER>\n",
    "\n",
    "[mybinder.org/v2/gh/atlas-outreach-data-tools/notebooks-collection-opendata/no-root?filepath=13-TeV-examples/uproot_python/ttZ_ML_from_csv.ipynb](https://mybinder.org/v2/gh/atlas-outreach-data-tools/notebooks-collection-opendata/no-root?filepath=13-TeV-examples/uproot_python/ttZ_ML_from_csv.ipynb)\n",
    "\n",
    "Run it yourself: [bit.ly/3sJsuAl](https://bit.ly/3sJsuAl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "This notebook uses ATLAS Open Data http://opendata.atlas.cern to show you the steps to implement Machine Learning in the $t\\bar{t}Z$ Opposite-sign dilepton analysis, loosely following the ATLAS published paper [Measurement of the $t\\bar{t}Z$ and $t\\bar{t}W$ cross sections in proton-proton collisions at $\\sqrt{s}$ = 13 TeV with the ATLAS detector](https://journals.aps.org/prd/pdf/10.1103/PhysRevD.99.072009).\n",
    "\n",
    "The whole notebook takes less than an hour to follow through.\n",
    "\n",
    "Notebooks are web applications that allow you to create and share documents that can contain for example:\n",
    "1. live code\n",
    "2. visualisations\n",
    "3. narrative text\n",
    "\n",
    "Notebooks are a perfect platform to develop Machine Learning for your work, since you'll need exactly those 3 things: code, visualisations and narrative text!\n",
    "\n",
    "We're interested in Machine Learning because we can design an algorithm to figure out for itself how to do various analyses, potentially saving us countless human-hours of design and analysis work.\n",
    "\n",
    "Machine Learning use within ATLAS includes: \n",
    "* particle tracking\n",
    "* particle identification\n",
    "* <span style=\"color:blue\">signal</span>/<span style=\"color:red\">background</span> classification\n",
    "* and more!\n",
    "\n",
    "This notebook will focus on signal/background classification.\n",
    "\n",
    "By the end of this notebook you will be able to:\n",
    "1. run machine learning algorithms to classify <span style=\"color:blue\">signal</span> and <span style=\"color:red\">background</span>\n",
    "2. know some things you can change to improve your machine learning algorithms\n",
    "\n",
    "Feynman diagram pictures are borrowed from our friends at https://www.particlezoo.net"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "## Introduction (from Section 1)\n",
    "\n",
    "Properties of the top quark have been explored by the\n",
    "Large Hadron Collider (LHC) and previous collider experiments in great detail, owing to the large center-of-mass energy and luminosity at the LHC.\n",
    "\n",
    "Measurements of top-quark pairs in association with a Z boson ($t\\bar{t}Z$) provide a direct probe of the\n",
    "weak couplings of the top quark. These couplings\n",
    "may be modified in the presence of physics beyond the\n",
    "Standard Model (BSM). Measurements of the $t\\bar{t}Z$ production cross sections, $\\sigma_{t\\bar{t}Z}$, can be used to\n",
    "set constraints on the weak couplings of the top quark. \n",
    "\n",
    "The production of $t\\bar{t}Z$ is often an important\n",
    "background in searches involving final states with multiple\n",
    "leptons and b-quarks. These processes also constitute an\n",
    "important background in measurements of the associated\n",
    "production of the Higgs boson with top quarks.\n",
    "\n",
    "This paper presents measurements of the $t\\bar{t}Z$ cross section using proton–proton (pp) collision data\n",
    "at a center-of-mass energy $\\sqrt{s}$ = 13 TeV.\n",
    "\n",
    "The final states of top-quark pairs produced in association with a\n",
    "Z boson contain up to 4 leptons. In this analysis, events with 2 opposite-sign\n",
    "(OS) leptons are considered. The dominant <span style=\"color:red\">backgrounds</span>\n",
    "in this channel are Z+jets and $t\\bar{t}$. \n",
    "\n",
    "(In this paper, lepton is used to denote electron or muon, and prompt lepton is used to denote a lepton produced in a Z boson decay, or in the decay of a τ-lepton which arises from a Z boson decay.)\n",
    "\n",
    "## Data and simulated samples (from Section 3)\n",
    "\n",
    "The data were collected with the ATLAS detector at a proton–proton (pp) collision\n",
    "energy of 13 TeV. \n",
    "\n",
    "Monte Carlo (MC) simulation samples are used to model the expected <span style=\"color:blue\">signal</span> and <span style=\"color:red\">background</span> distributions. All samples were processed through the\n",
    "same reconstruction software as used for the data. \n",
    "\n",
    "## Opposite-sign dilepton analysis (from Section 5A)\n",
    "\n",
    "The OS dilepton analysis targets the $t\\bar{t}Z$ process, where both top quarks decay hadronically and the Z boson\n",
    "decays to a pair of leptons (electrons or muons). Events are required to have exactly two opposite-sign leptons.\n",
    "\n",
    "The OS dilepton analysis is affected by large backgrounds from Z+jets or $t\\bar{t}$ production, both characterized\n",
    "by the presence of two leptons. \n",
    "\n",
    "## Contents: \n",
    "\n",
    "[Running a Jupyter notebook](#running) <br />\n",
    "[To setup first time](#setupfirsttime) <br />\n",
    "[To setup everytime](#setupeverytime) <br />\n",
    "[Plot data](#plot_data) <br />\n",
    "[Selections](#selections) <br />\n",
    "[Correlations](#correlations) <br />\n",
    "[Machine Learning setup](#ML_setup) <br />\n",
    "[Overtraining check](#overtraining_check) <br />\n",
    "[Performance](#ROC) <br />\n",
    "[ML_output separation](#ML_output_separation) <br />\n",
    "[ML output data distributions](#ML_output_data) <br />\n",
    "[Going further](#going_further) <br />\n",
    "[Conclusion](#conclusion) <br />\n",
    "\n",
    "<a id='running'></a>\n",
    "\n",
    "## Running a Jupyter notebook\n",
    "\n",
    "To run the whole Jupyter notebook, in the top menu click Cell -> Run All.\n",
    "\n",
    "To propagate a change you've made to a piece of code, click Cell -> Run All Below.\n",
    "\n",
    "You can also run a single code cell, by using the keyboard shortcut Shift+Enter.\n",
    "\n",
    "<a id='setupfirsttime'></a>\n",
    "\n",
    "## First time setup on your computer (no need on mybinder)\n",
    "This first cell only needs to be run the first time you open this notebook on your computer. \n",
    "\n",
    "If you close Jupyter and re-open on the same computer, you won't need to run this first cell again.\n",
    "\n",
    "If you open on mybinder, you don't need to run this cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "!{sys.executable} -m pip install --upgrade --user pip # update the pip package installer\n",
    "!{sys.executable} -m pip install -U pandas sklearn --user # install required packages"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "<a id='setupeverytime'></a>\n",
    "\n",
    "## To setup everytime\n",
    "\n",
    "Cell -> Run All Below\n",
    "\n",
    "to be done every time you re-open this notebook.\n",
    "\n",
    "We're going to be using a number of tools to help us:\n",
    "* [pandas](https://pandas.pydata.org/docs/user_guide/index.html): lets us store data as dataframes, a format widely used in Machine Learning\n",
    "* [numpy](https://numpy.org/doc/stable/): provides numerical calculations such as histogramming\n",
    "* [matplotlib](https://matplotlib.org/stable/contents.html): common tool for making plots, figures, images, visualisations\n",
    "\n",
    "Let's read the csv data into a [pandas DataFrame (df)](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.html) and then display it like a table."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
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       "        type  Channel  NJets     MET    Mll  LepDeltaPhi  LepDeltaR  SumLepPt  \\\n",
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       "3          0        1      3   29.51  91.30         1.87       1.90     87.42   \n",
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       "\n",
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       "2            0  1.00000  \n",
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       "...        ...      ...  \n",
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       "\n",
       "[344579 rows x 10 columns]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd # to store data as dataframes\n",
    "import numpy as np # for numerical calculations such as histogramming\n",
    "import matplotlib.pyplot as plt # for plotting\n",
    "\n",
    "csv_path = \"http://opendata.atlas.cern/release/2020/documentation/visualization/CrossFilter/13TeV_ttZ.csv\"\n",
    "df_all = pd.read_csv(csv_path) # read all data into pandas DataFrame\n",
    "df_all # print as table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "It'd be better to visualise this DataFrame in graphs, rather than a table. \n",
    "\n",
    "Let's start by defining a [dictionary](https://docs.python.org/3/tutorial/datastructures.html#dictionaries) to distinguish between the different processes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "outputs": [],
   "source": [
    "samples_SR = {\n",
    "\n",
    "    0: { # type==0 is measured 'Data'\n",
    "        'name': 'Data'\n",
    "    },\n",
    "    \n",
    "    4: { # type==4 is 'Other' small backgrounds\n",
    "        'name': 'Other',\n",
    "        'color' : 'green'                                                                                                                                                                  \n",
    "    },  \n",
    "    \n",
    "    3: { # type==3 is 'Z' background\n",
    "        'name': 'Z', \n",
    "        'color' : 'red'\n",
    "    }, \n",
    "    \n",
    "    2: { # type==2 is 'tt' (top+antitop) background\n",
    "        'name': 'tt',\n",
    "        'color' : 'lightgrey'\n",
    "    },  \n",
    "    \n",
    "    1: { # type==1 is 'ttZ' (top+antitop+Z) signal\n",
    "        'name': 'ttZ',\n",
    "        'color' : 'blue'\n",
    "    },                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         \n",
    "    \n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "<a id='plot_data'></a>\n",
    "\n",
    "## Plot data\n",
    "\n",
    "We need to define a function to plot any variable, to see the distributions of the simulated and measured data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "outputs": [],
   "source": [
    "def plot_data(data, x_variable, samples_to_plot=samples_SR):\n",
    "     \n",
    "    min_x = min(data[x_variable]) # minimum x-value for this variable\n",
    "    max_x = max(data[x_variable]) # maximum x-value for this variable\n",
    "    step_x = (max_x-min_x)/10 # step size in x-value for this variable\n",
    "    \n",
    "    bin_edges = np.arange(start=min_x, # The interval includes this value\n",
    "                          stop=max_x+step_x, # The interval doesn't include this value\n",
    "                          step=step_x ) # Spacing between values\n",
    "    bin_centres = (bin_edges[:-1] + bin_edges[1:]) / 2\n",
    "\n",
    "    mc_x = [] # define list to hold the MC x values\n",
    "    mc_weights = [] # define list to hold the MC weights\n",
    "    mc_colors = [] # define list to hold the MC bar colors\n",
    "    mc_labels = [] # define list to hold the MC legend labels\n",
    "\n",
    "    mc_stat_err_squared = np.zeros(len(bin_centres)) # define array to hold the MC statistical uncertainties\n",
    "    for s in samples_to_plot: # loop over samples\n",
    "        if s!=0: # if not data\n",
    "            mc_x.append(data[data['type']==s][x_variable])\n",
    "            mc_weights.append(data[data['type']==s]['weight'])\n",
    "            mc_colors.append( samples_to_plot[s]['color'] ) # append to the list of Monte Carlo bar colors\n",
    "            mc_labels.append( samples_to_plot[s]['name'] ) # append to the list of Monte Carlo legend labels \n",
    "            weights_squared,_ = np.histogram(data[data['type']==s][x_variable], bins=bin_edges,\n",
    "                                             weights=data[data['type']==s]['weight']**2) # square the weights\n",
    "            mc_stat_err_squared = np.add(mc_stat_err_squared,weights_squared) # add weights_squared for s \n",
    "\n",
    "    # plot the Monte Carlo bars\n",
    "    mc_heights = plt.hist(mc_x, bins=bin_edges, \n",
    "                          weights=mc_weights, stacked=True, \n",
    "                          color=mc_colors, label=mc_labels )\n",
    "\n",
    "    mc_x_tot = mc_heights[0][-1] # stacked background MC y-axis value\n",
    "    mc_x_err = np.sqrt( mc_stat_err_squared ) # statistical error on the MC bars\n",
    "\n",
    "    # histogram the data\n",
    "    data_x,_ = np.histogram(data[data['type']==0][x_variable], bins=bin_edges ) \n",
    "\n",
    "    # statistical error on the data\n",
    "    data_x_errors = np.sqrt(data_x)\n",
    "\n",
    "    # plot the data points\n",
    "    plt.errorbar(x=bin_centres, \n",
    "                 y=data_x, \n",
    "                 yerr=data_x_errors,\n",
    "                 fmt='ko', # 'k' means black and 'o' is for circles \n",
    "                 label='Data')\n",
    "\n",
    "    # plot the statistical uncertainty\n",
    "    plt.bar(bin_centres, # x\n",
    "            2*mc_x_err, # heights\n",
    "            alpha=0.5, # half transparency\n",
    "            bottom=mc_x_tot-mc_x_err, color='none', \n",
    "            hatch=\"////\", width=step_x, label='Unc.' )\n",
    "\n",
    "    # x-axis label\n",
    "    plt.xlabel(x_variable)\n",
    "\n",
    "    # y-axis label\n",
    "    plt.ylabel('Events')\n",
    "\n",
    "    # draw the legend\n",
    "    plt.legend() # number of columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "Let's take a look at the variable `Mll`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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": [
    "plot_data(df_all, x_variable='Mll')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "We can't see <span style=\"color:blue\">signal</span> anywhere..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a id='selections'></a>\n",
    "\n",
    "## Selections\n",
    "\n",
    "We make selections to focus on <span style=\"color:blue\">signal</span>, then print the selected DataFrame's rows.\n",
    "\n",
    "<CENTER><img src=\"images/selections_meme.jpeg\" style=\"width:80%\"></CENTER>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>type</th>\n",
       "      <th>Channel</th>\n",
       "      <th>NJets</th>\n",
       "      <th>MET</th>\n",
       "      <th>Mll</th>\n",
       "      <th>LepDeltaPhi</th>\n",
       "      <th>LepDeltaR</th>\n",
       "      <th>SumLepPt</th>\n",
       "      <th>NBJets</th>\n",
       "      <th>weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>25.80</td>\n",
       "      <td>91.90</td>\n",
       "      <td>2.35</td>\n",
       "      <td>2.39</td>\n",
       "      <td>37.51</td>\n",
       "      <td>1</td>\n",
       "      <td>1.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>12.21</td>\n",
       "      <td>92.20</td>\n",
       "      <td>2.94</td>\n",
       "      <td>2.94</td>\n",
       "      <td>37.22</td>\n",
       "      <td>1</td>\n",
       "      <td>1.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>25.10</td>\n",
       "      <td>88.14</td>\n",
       "      <td>2.15</td>\n",
       "      <td>2.59</td>\n",
       "      <td>46.19</td>\n",
       "      <td>2</td>\n",
       "      <td>1.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>124</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>49.99</td>\n",
       "      <td>92.49</td>\n",
       "      <td>0.57</td>\n",
       "      <td>1.50</td>\n",
       "      <td>145.59</td>\n",
       "      <td>1</td>\n",
       "      <td>1.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>182</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>42.82</td>\n",
       "      <td>91.80</td>\n",
       "      <td>2.84</td>\n",
       "      <td>2.84</td>\n",
       "      <td>14.16</td>\n",
       "      <td>2</td>\n",
       "      <td>1.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>344416</th>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>31.92</td>\n",
       "      <td>90.50</td>\n",
       "      <td>1.27</td>\n",
       "      <td>2.26</td>\n",
       "      <td>62.63</td>\n",
       "      <td>1</td>\n",
       "      <td>0.22986</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>344448</th>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>59.72</td>\n",
       "      <td>94.34</td>\n",
       "      <td>2.63</td>\n",
       "      <td>2.76</td>\n",
       "      <td>73.35</td>\n",
       "      <td>1</td>\n",
       "      <td>0.25186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>344478</th>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>41.16</td>\n",
       "      <td>92.18</td>\n",
       "      <td>1.40</td>\n",
       "      <td>1.53</td>\n",
       "      <td>115.42</td>\n",
       "      <td>1</td>\n",
       "      <td>0.22737</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>344552</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>14.24</td>\n",
       "      <td>89.51</td>\n",
       "      <td>1.61</td>\n",
       "      <td>1.69</td>\n",
       "      <td>93.50</td>\n",
       "      <td>1</td>\n",
       "      <td>0.36640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>344562</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "      <td>53.60</td>\n",
       "      <td>83.31</td>\n",
       "      <td>1.88</td>\n",
       "      <td>2.58</td>\n",
       "      <td>53.33</td>\n",
       "      <td>1</td>\n",
       "      <td>0.55433</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>13600 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        type  Channel  NJets    MET    Mll  LepDeltaPhi  LepDeltaR  SumLepPt  \\\n",
       "7          0        1      6  25.80  91.90         2.35       2.39     37.51   \n",
       "40         0        1      5  12.21  92.20         2.94       2.94     37.22   \n",
       "44         0        1      5  25.10  88.14         2.15       2.59     46.19   \n",
       "124        0        0      7  49.99  92.49         0.57       1.50    145.59   \n",
       "182        0        0      5  42.82  91.80         2.84       2.84     14.16   \n",
       "...      ...      ...    ...    ...    ...          ...        ...       ...   \n",
       "344416     4        0      5  31.92  90.50         1.27       2.26     62.63   \n",
       "344448     4        0      7  59.72  94.34         2.63       2.76     73.35   \n",
       "344478     4        0      5  41.16  92.18         1.40       1.53    115.42   \n",
       "344552     4        1      7  14.24  89.51         1.61       1.69     93.50   \n",
       "344562     4        1      8  53.60  83.31         1.88       2.58     53.33   \n",
       "\n",
       "        NBJets   weight  \n",
       "7            1  1.00000  \n",
       "40           1  1.00000  \n",
       "44           2  1.00000  \n",
       "124          1  1.00000  \n",
       "182          2  1.00000  \n",
       "...        ...      ...  \n",
       "344416       1  0.22986  \n",
       "344448       1  0.25186  \n",
       "344478       1  0.22737  \n",
       "344552       1  0.36640  \n",
       "344562       1  0.55433  \n",
       "\n",
       "[13600 rows x 10 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_selected = df_all[(df_all['Channel']!=2) & # select events that aren't in the Channel 'emu'\n",
    "                     (df_all['NJets']>=5) & # at least 5 jets\n",
    "                     (df_all['NBJets']>=1) & # at least 1 b-tagged jets\n",
    "                     (df_all['Mll']>81.12) & # Z-boson mass - 10 GeV\n",
    "                     (df_all['Mll']<101.12) # Z-boson mass + 10 GeV\n",
    "                    ]\n",
    "df_selected # print as table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "Now if we take another look at `Mll`, we can see the <span style=\"color:blue\">signal</span> a bit easier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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": [
    "plot_data(df_selected, x_variable='Mll')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "We can also look at other variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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": [
    "plot_data(df_selected, x_variable='NJets')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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": [
    "plot_data(df_selected, x_variable='MET')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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": [
    "plot_data(df_selected, x_variable='LepDeltaPhi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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": [
    "plot_data(df_selected, x_variable='LepDeltaR')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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": [
    "plot_data(df_selected, x_variable='SumLepPt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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": [
    "plot_data(df_selected, x_variable='NBJets')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "They look nice, but there's a problem.\n",
    "\n",
    "Wherever you may see a bit of <span style=\"color:blue\">signal</span>, it's covered by the Uncertainty band. \n",
    "\n",
    "This means that the extra area covered by the <span style=\"color:blue\">signal</span> could just be statistical fluctuations of the background processes. Hmm..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a id='separations'></a>\n",
    "\n",
    "## Separation\n",
    "\n",
    "Let's see how well <span style=\"color:blue\">signal</span> & <span style=\"color:red\">background</span> are separated for each variable, using simulation.\n",
    "\n",
    "<CENTER><img src=\"images/separation_meme.jpeg\" style=\"width:70%\"></CENTER>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "outputs": [],
   "source": [
    "def plot_separation(data, x_variable, samples_to_plot=samples_SR):\n",
    "    \n",
    "    min_x = min(data[x_variable]) # minimum x-value for this variable\n",
    "    max_x = max(data[x_variable]) # maximum x-value for this variable\n",
    "    step_x = (max_x-min_x)/10 # step size in x-value for this variable\n",
    "    \n",
    "    bin_edges = np.arange(start=min_x, # The interval includes this value\n",
    "                          stop=max_x+step_x, # The interval doesn't include this value\n",
    "                          step=step_x ) # Spacing between values\n",
    "\n",
    "    # clip signal underflow and overflow into x-axis range\n",
    "    signal_x = data[data['type']==1][x_variable]\n",
    "\n",
    "    mc_x = [] # define list to hold the MC histogram entries\n",
    "    for s in samples_to_plot: # loop over samples\n",
    "        if s!=0 and s!=1: # if not data nor signal\n",
    "            mc_x = [*mc_x, # mc_x for previous sample\n",
    "                    *data[data['type']==s][x_variable] ] # this sample\n",
    "\n",
    "\n",
    "    main_axes = plt.gca() # get current axes\n",
    "\n",
    "    # plot the background Monte Carlo distribution\n",
    "    mc_heights = plt.hist(mc_x, \n",
    "                          bins=bin_edges,\n",
    "                          density=True, # normalise the histogram\n",
    "                          histtype='step', color='red', \n",
    "                          label='background' )\n",
    "\n",
    "    # plot the signal distribution\n",
    "    signal_heights = plt.hist(signal_x,  \n",
    "                              bins=bin_edges,\n",
    "                              density=True, # normalise the histogram \n",
    "                              histtype='step', color='blue', \n",
    "                              label='signal', \n",
    "                              linestyle='--' ) # dashed line\n",
    "\n",
    "    bin_width = (max(data[x_variable])-min(data[x_variable]))/10\n",
    "    separation = 0 # start separation counter at 0\n",
    "    nstep  = 10 # number of bins\n",
    "    nS     = sum(signal_heights[0])*bin_width # signal integral\n",
    "    nB     = sum(mc_heights[0])*bin_width # background integral\n",
    "    for bin_i in range(nstep): # loop over each bin\n",
    "        s = signal_heights[0][bin_i]/nS # normalised signal in bin_i\n",
    "        b = mc_heights[0][bin_i]/nB # normalised background in bin_i\n",
    "        if (s + b > 0): separation += (s - b)*(s - b)/(s + b) # separation\n",
    "    separation *= 0.5*bin_width # multiply by 0.5 x bin_width \n",
    "\n",
    "    # x-axis label\n",
    "    plt.xlabel(x_variable )\n",
    "\n",
    "    # y-axis label\n",
    "    plt.ylabel('Normalised units') \n",
    "\n",
    "    # draw the legend\n",
    "    plt.legend() # no box around the legend\n",
    "    \n",
    "    plt.title(str(round(separation*100,1))+'% Separation between signal and background')\n",
    "    \n",
    "    plt.show() # show the Signal and background distributions\n",
    "    \n",
    "    \n",
    "    # *************\n",
    "    # Signal to background ratio\n",
    "    # *************\n",
    "    plt.figure() # start new figure\n",
    "    SoverB = [] # list to hold S/B values\n",
    "    for cut_value in bin_edges: # loop over bins\n",
    "        signal_weights_passing_cut = sum(data[(data['type']==1) & (data[x_variable]>cut_value)].weight)\n",
    "        background_weights_passing_cut = 0 # start counter for background weights passing cut\n",
    "        for s in [2,3,4]: # loop over background samples\n",
    "            background_weights_passing_cut += sum(data[(data['type']==s) & (data[x_variable]>cut_value)].weight)\n",
    "        if background_weights_passing_cut!=0: # some background passes cut\n",
    "            SoverB_value = signal_weights_passing_cut/background_weights_passing_cut\n",
    "            SoverB_percent = 100*SoverB_value # multiply by 100 for percentage\n",
    "            SoverB.append(SoverB_percent) # append to list of S/B values\n",
    "\n",
    "    plt.plot( bin_edges[:len(SoverB)], SoverB ) # plot the data points\n",
    "    plt.ylim( bottom=0 ) # set the x-limit of the main axes\n",
    "    plt.ylabel( 'S/B (%)' ) # write y-axis label for main axes\n",
    "    plt.title('signal:background ratio for different '+x_variable+' selection values')\n",
    "    plt.xlabel( x_variable ) # x-axis label \n",
    "\n",
    "    plt.show() # show S/B plot\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "Let's take a look at those input variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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"
    },
    {
     "data": {
      "image/png": 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SUoEQEZG0VCBERCQtFQgREUlLBUJERNJSgRARkbRUIEREJC0VCBERSUsFQkRE0lKBEBGRtFQgREQkLRUIERFJSwVCRETSUoEQEZG0VCBERCQtFQgREUlLBUJERNJSgRARkbRUIEREJC0VCMkqd2fGp2tw99BRRCQDFQjJqjvGfMgJd73Oz5+bqiIhknAqEJI1f5uwgHtenUW39oU89L+53PnyzNCRRKQWKhCSFWPnLOfapyZz2J7tGXPVkZzdvzN3vzKTEa9/FDqaiNQgL8RIzewqYBjgwPvAxe6+MUQWaXhzl67jW4+Mp0u7Qv5wfj/y83L41Rl9WVe+hV++MJ2igjzOH9g1dEwRqSbrWxBm1gm4Aujv7n2AXOAb2c4h2bFq/WaGjhqHAw8OHkDrwmYA5OYYd55zAMfs3YHrn/6ApycuDBtURL4gVBNTHtDCzPKAQuCTQDmkAW3eUsm3H53A/OXr+dMF/ehWUrRV9/y8HH5//kEM7N6Oq//6HmOmfBooqYikk/UC4e4LgduBecAiYJW7j6nen5ldambjzWx8WVlZtmPKDnJ3bnj6A978aBm3ndGXgXu0T9tf82a53D94AH06tebyxyby35lLs5xURGoSoompLXAa0B3YDSgyswuq9+fuI9y9v7v3Ly0tzXZM2UH3vTGbJ8bN57tH78nX+3Wutd+WBXmMungAe5QW8c2HxzN+7vIspRSR2oRoYjoOmOPuZe6+GXgKOCxADmkgL035lF/9czon7rcLVx/fq07vaVOYz8OXHMwurZtz8UPj+GDhqgZOKSKZhCgQ84BDzKzQzAw4FpgWIIc0gA8WruL7T0yib+c2/O7sA8jJsTq/t0Nxc0YPG0irFs246MGxzFqypgGTikgmIfZBvAM8CbxLdIhrDjAi2zmk/n26aiOXjBpHu6J87ruoH82b5W7zMDq1acHoYQPJMeP8+99h/vL1DZBUROoiyFFM7n6ju+/t7n3c/UJ3Lw+RQ+rP+k0VXDJqHGs3VnD/4P50KG6+3cPqXlLE6GEHs3FzJefd/zafrtIpMiIh6Exq2WGVlc73n5jEtEWruee8g9hn11Y7PMy9d2nFqKEHs3ztJi544B2WrdU6hEi2qUDIDvv1i9MZM3UxN5zcm6P37lBvwz2gSxseGDKA+cvXc9GDY1m9cXO9DVtEMlOBkB3yxNh5/On12Vx4SFeGHNat3od/yB7t+eOF/fhw8RqGPjSO9Zsq6n0cIpKeCoRstzdnLeX6pz/giL1KufGU3kQHpdW/o3t14K5zDuTdeSv41iMTKK/Y0iDjEZGtqUDIdpm1ZC2XjZ5A95Ii7jnvQPJyG3ZWOqnvrtz29b68MXMp33tsIhVbKht0fCKiAiHbYfm6TVwyahzNcnN4cMgAWjVvlpXxnt2/Czee0psxUxfzoycnU1mpGw6JNKQgl/uWxqu8YguXPTKBRas28vg3D6FLu8Ksjv/iL3VnXXkFt4/5kML8XG45vU+DNW2JNHUqEFJn7s51T73P2LnLufvcA+nXtW2QHN89ugdry7fwx/98RMuCPK796t4qEiINQAVC6uz3r33EU+8u5Krj9uLU/XcLlsPM+PGgXqwt38yfXp9NcfM8Lj+mZ7A8IjsrFQipk+cnL+K3L83g9AN244pje4SOg5nx81P7sL58S9zclMfQw7uHjiWyU1GBkIwmzV/JD/4yiX5d23Lb1/smpjknJ8f4zZl9Wbepgp8/N5WWBXmcPaBL6FgiOw0dxSS1WrhyA8NGjadDqwJGXLh9F+BrSHm5Odx97oF8uWcJ1z41mecm6+aEIvVFBUJqtLa8gktGjqN88xYeHDyA9i0LQkdKqyAvlz9d2I9+Xdvy/Scm8er0JaEjiewUVCAkrYotlXzvsXeZuWQtv7/gIHp2LA4dqVaF+Xk8MGQAe+9azGWjJ/DWR8tCRxJp9FQgJK1bnp/GqzPKuPnUfflyz8Zxy9dWzZvx8NCB7N6ukGGjxjFx3orQkUQaNRUI+YJH3prLyDfncsnh3bngkK6h42yTdkX5jB42kPYtCxjy0DimLVodOpJIo6UCIVv5z4dl3PTsVI7bpwM/OXGf0HG2S8dWzXl02EBaNMvlwgfGMrtsbehIIo2SCoR85sPFa7j80XfZq2Mxw79xILnbcD/ppOnSrpDRwwZS6c4F97/DwpUbQkcSaXRUIASApWvLGTpyHC3yc3lgcH+KChr/KTI9OrTk4aEHs6a8gvPve5sla3TrUpFtoQIhbNy8hUsfHs/SteXcP7g/u7VpETpSvenTqTUjLx7A4tXlXPTAWFau3xQ6kkijoQLRxLk71zw5mXfnreSucw6gb+c2oSPVu35d23HfRf2ZXbaOwQ+OZW257konUhcqEE3cXS/P5Jn3PuGaQb0Y1GfX0HEazOE9S7j3/IP44JPVXDJyHBs36650IpmoQDRhT09cyPBXZnJWv858+8g9Q8dpcMf37sjvzt6fsXOX8+3RE9hUobvSidRGBaKJGj93Odc8OZmB3dtx69f2S8wF+BraaQd04tbT9+PVGWVc9edJbNFd6URq1PgPVZFtNm/Zei59ZAKd2rbgjxf0Iz+vaa0nnDdwd9aWb+aXL0ynU9sWjfZ8D5GGpgLRxKzasJmho8axpdJ5cMgA2hblh44UxKVH7MmCFRsY8fpsurUv4ryBu4eOJJI4KhBNyOYtlVz+2Lt8vGwdDw8dSPeSotCRgvrZyb35eNl6bvjHB+zerpDDe5aEjiSSKE2rbaGJu/nZKbwxcym3fm0/Dt2zfeg4weXl5nDPeQfSo7Ql3350AjMXrwkdSSRRVCCaiFenL2H02/P41hF7cHZ/3XWtSnHzZjwwpD8FebkMHTWOZWvLQ0cSSQwViCZgU0UlP39uKnuUFHH1V3qFjpM4ndsWcv/g/ixZXc6lj0zQORIiMRWIJuCh/81hztJ13HBK7yZ3xFJdHdClDXeecwATPl7BNU9Oxl2Hv4poabGTW7J6I3e/MpNj9+7A0b06hI6TaCfutys/OqEXz7z3CXe9PDN0HJHgghQIM2tjZk+a2XQzm2Zmh4bI0RTc9uJ0Nm9xbji5d+gojcJ3jtqTM/t1ZvgrM3l64sLQcUSCCnWY63DgRXc/08zygcJAOXZqEz5ewVPvLuQ7R+1JtyZ+SGtdmRm//Np+zF++nmuenEynti0Y0K1d6FgiQWTcgjCzQ83sXjObbGZlZjbPzF4ws++aWettHWH8niOABwDcfZO7r9zm5FKrykrnpmem0LFVAd89ukfoOI1Kfl4Of7qwH53atuBbj0zg42XrQkcSCaLWAmFm/wSGAS8Bg4Bdgd7A9UBz4B9mduo2jrM7UAY8ZGYTzex+M/vC6q2ZXWpm481sfFlZ2TaOQv46YT7vL1zFT07cZ6e4+U+2tSnM58EhA6h0Z+jIcaxavzl0JJGss9qO1jCzEndfWusA6tBPtf77A28DX3L3d8xsOLDa3W+o6T39+/f38ePH13UUTd6qDZs55vbX6F5SxF8vO7TJXIivIbw9exkXPvAOA7q1Y9TQg2mWq+M6pPEwswnu3n9731/r3J5uwW9mx5rZKWbWrKZ+MlgALHD3d+LnTwIHbeMwpBbDX57J8vWbuOnUfVUcdtAhe7TnV2f05c2PlnH93z/Q4a/SpGzT6pCZ3QF8Cdgf+Mf2jNDdPwXmm1nVGVvHAlO3Z1jyRTMXr2HUW3M59+Dd6dNpm3cRSRpn9uvM5Uf34M/j5zPi9dmh44hkTa2N03FB+EXKTuTdgbPjx+/vwHi/BzwaH8E0G7h4B4YlMXfnpmenUJSfyw91xnS9+sHxezFn2Tpue3E6XdsXMajPLqEjiTS4TFsQTwFPmNkVZpYLPAy8CrwF3Le9I3X3Se7e3937uvvp7r5ie4cln3tpymL+N2sZV3+lF+2a6GW8G0pOjnHHWfuzf+c2fP/PE3l/warQkUQaXKZ9EP9z90HAcqIjmczdj3L3Q9x9eFYSSp1s3LyFW56fSq+OxZyvexs0iObNcrnvov60LyrgklHj+GTlhtCRRBpUpsNc88zsJGAJcDqwv5k9Y2b7ZyOc1N2f/jObBSs2cOOpvcnTkTYNprS4gAeHDGD9pi1cMmo8a8srQkcSaTCZliRPAwcARwL3uvsvgMuA75nZdjcxSf1asGI9v39tFifttyuH7amb3jS0XrsUc+/5B/Hh4jVc8fhE3ddadlqZCkRXd78VuBnYD8DdP3H3YcC9DR1O6uZXL0zHDK47ce/QUZqMI/cq5aZT9+Xf05dw6/PTQscRaRCZTrEdYWZvxY9/l9rB3Sc1SCLZJm9+tJTn31/EVcftRee2uqRVNl14SFdml63lwf/NoXtJIRce2i10JJF6VWuBcPf/A/4vS1lkG1VsqeTmZ6bSuW0LvnXkHqHjNEnXnxTd1/qmZ6fSpV0hR+mS6rITybST+noza1tL92PM7OT6jyV18eg785ixeA3Xn9Sb5s1yQ8dpknJzjLvPPZC9OhZz+WMTmfGp7mstO49M+yDeB54zs1fM7Ldmdo2Z/czMHjGz94FTgHcyDEMawPJ1m7hjzAwO71HCCft2DB2nSWtZkMcDg/tTmJ/L0JHjKFuj+1rLziHTeRD/cPcvER25NAXIBVYDo4GD3f0qd9elVgO4fcwM1m3awo2n9Nb1lhJgtzYteGDwAJav28Q3Hx6v+1rLTqFOB8y7+0x3H+nuv3L3u9z9JXfXWUKBfLBwFY+PncfgQ7vRs2Nx6DgS269za+485wDeW7CSq//yHpU6/FUaOZ1R1ci4RzcCaleYz5XH9QwdR6oZ1GcXrh20N8+/v4jf/evD0HFEdojuJNPIPPPeJ4z/eAW//vp+tG7RLHQcSePSI/ZgztJ13PPqLLqVFHFmv86hI4lsF21BNCLryiv45QvT6Nu5NWf16xI6jtTAzPjF6X04bM/2XPfUZN6evSx0JJHtkukw1+ZmNtjMTrXIj83sOTMbbma6pkOW3fvqLBavLufGU/YlJ0c7ppOsWW4Ofzi/H7u3K+Sy0ROYs1T3tZbGJ9MWxMPAV4ChwGtE94O4B1gDjGzIYLK1uUvXcf8bczjjoE7061rjqSmSIK0Lm/HgkAEYMHTkOFau3xQ6ksg2yVQgerv7+cCZQC93/667v+ju1wNq48iiW56fSrNc49pBut5SY9K1fREjLurPwhUb+NYjE9hUURk6kkidZSoQmwDcvQL4pFo3HeidJa/OWMLL05ZwxbE96dCqeeg4so0GdGvHb87syztzlnPdU+/rvtbSaGQ6iqmzmd0NWMpj4uedGjSZALCpopJfPDuVPUqKuPhL3UPHke10+oGdmLN0HcNfmckepUV89+geoSOJZJSpQPwo5fH4at2qP5cGMPLNOcxeuo6HLh5Afp4OOmvMvn9cT+YsXcdvX5pB95IiTtxv19CRRGqVqUB0Av7p7hOzEUa2tmT1Roa/PJPj9unA0bpKaKNnZvzmzL4sXLmBq/48id3atOCALm1CxxKpUaZV0o+AK81sopmNNLNzaru6q9Sv216czuYtzvUn9Q4dRepJ82a5jLiwHx1aFTBs1HgWrFgfOpJIjTJdrO/P7j7E3Q8EhgN7AE+Z2evxVV0PzkrKJmjCxyt46t2FDPtyd7qVFIWOI/WofcsCHhw8gPKKLVwycjxrNm4OHUkkrTo3arv7xPhifUcDJxNd3XVYgyVrwioro+stdWxVoJ2ZO6meHYv5w/n9mFW2lh//bXLoOCJpZTqTeoCZ7ZLy/CIz+wdwC/Cqu1/a0AGbor9OmM/7C1fxkxP3oahAl8vaWR3es4Sz+3fhvzOXho4iklamLYg/EZ8LYWZHALcRnV29ChjRsNGaplUbNvObF2fQv2tbTt1/t9BxpIF1btuC1RsrdP8ISaRMBSLX3ZfHj88BRrj739z9BkBtHw1g+MszWb5+Ezeduq9uBNQElLYsAGDpWt2FTpInY4Ews6o2jmOBf6d0U9tHPZu5eA2j3prLuQfvTp9OrUPHkSwoLY4KhG5TKkmUaSH/OPAfM1sKbADeADCzHkTNTFJP3J2bnp1CUX4uP/xKr9BxJEtUICTJai0Q7n6rmb0C7AqM8c8vIpMDfK+hwzUlL01ZzP9mLePmU/elXVF+6DiSJZ8VCDUxSQJlbCZy97fTvKZ7KdajjZu3cMvzU+nVsZjzB+4eOo5kUbuifMy0BSHJpP0ICTDi9dksWLGBx745kLxcXW+pKWmWm0O7wnwVCEkkLY0CW7hyA79/bRYn7bcrh+2pm/Q1RaXFBSoQkkjBCoSZ5cbXeHouVIYk+OUL0wD4yUn7BE4ioZQWF2gfhCRSyC2IK4FpAccf3FsfLeP5yYv4zlE96NSmReg4EkhpS21BSDIFKRBm1hk4Cbg/xPiToGJLJTc/O4XObVtw6RF7hI4jAVU1MelOc5I0obYg7gKuAWq8Qa+ZXWpm481sfFlZWdaCZctjY+cx/dM1XH9Sb5o3yw0dRwIqLS6gvKKSNeUVoaOIbCXrBcLMTgaWuPuE2vpz9xHu3t/d+5eWlmYpXXYsX7eJO8Z8yOE9Sjhh346h40hgOllOkirEFsSXgFPNbC7wBHCMmY0OkCOYO8bMYG15BTee0lvXW5LPrsekAiFJk/UC4e7XuXtnd+8GfAP4t7tfkO0coXywcBWPjZ3H4EO70bNjceg4kgDagpCk0nkQWeTu3PzsFNoV5nPlcT1Dx5GEUIGQpApaINz9NXc/OWSGbHrmvU8YN3cF1wzqResWzULHkYRo3aIZzXKNJSoQkjDagsiSdeUV/PKFafTt3Jqz+nUJHUcSxMx0LoQkkgpEltz76iwWry7nxlP2JSdHO6ZlazqbWpJIBSIL5i5dx/1vzOGMgzrRr2vb0HEkgXQ9Jkminfpqrr8bM4P3FoS/r9HHy9bRLNe4dtDeoaNIQpUWFzBpfvh5VSTVTl0g1pZvYeWGzaFj0KYwnx+e0IsOrZqHjiIJVdqygOXrytlS6eSqCVISYqcuED87pXfoCCJ1UlpcQKXDsnXldCjWioQkg/ZBiCSAzoWQJFKBEEkAFQhJIhUIkQQobRk1K6lASJKoQIgkQElxPoDOhZBEUYEQSYDC/DxaFuRpC0ISRQVCJCF0spwkjQqESELoekySNCoQIglR2krXY5JkUYEQSQhtQUjSqECIJERpcQFrNlawcfOW0FFEABUIkcTQyXKSNCoQIgnxWYHQfghJCBUIkYQobaktCEkWFQiRhOigJiZJGBUIkYRoV5SPmQqEJIcKhEhC5OXm0L4oX/sgJDFUIEQSpETnQkiCqECIJIiuxyRJogIhkiAqEJIkKhAiCVJaHF2Pyd1DRxFRgRBJktKWBWyqqGT1xorQUURUIESSRJfbkCRRgRBJEBUISRIVCJEE6aDrMUmCqECIJEhpy+aAtiAkGVQgRBKkVYs88nNzVCAkEbJeIMysi5m9amZTzWyKmV2Z7QwiSWVmOhdCEiMvwDgrgKvd/V0zKwYmmNm/3H1qgCwiiVNSrHtTSzJkfQvC3Re5+7vx4zXANKBTtnOIJJXuTS1JEXQfhJl1Aw4E3gmZQyRJ1MQkSRGsQJhZS+BvwPfdfXWa7pea2XgzG19WVpb9gCKBlBYXsHxdOVsqdbkNCStIgTCzZkTF4VF3fypdP+4+wt37u3v/0tLS7AYUCai0uIBKh2XrtBUhYYU4ismAB4Bp7v67bI9fJOmq7k29ZLUKhIQVYgviS8CFwDFmNin+OzFADpFEKtXZ1JIQWT/M1d3/C1i2xyvSWHTQ9ZgkIXQmtUjClLRUgZBkUIEQSZgW+bkUF+SpQEhwKhAiCVSqs6klAVQgRBKoRCfLSQKoQIgkUGlxAUtVICQwFQiRBNL1mCQJVCBEEqi0uIA15RVs2LQldBRpwlQgRBKo6mS5pdpRLQGpQIgkUFWBWKJmJglIBUIkgUp1spwkgAqESAJ10PWYJAFUIEQSqF1RPmbagpCwVCBEEigvN4f2RfkqEBKUCoRIQpXoXAgJTAVCJKF0PSYJTQVCJKF0uQ0JTQVCJKFK4wv2uXvoKNJEqUCIJFRpywI2balk9YaK0FGkiVKBEEmoz+9NvTFwEmmqVCBEEkqX25DQVCBEEuqzs6lVICQQFQiRhCpt2RxQgZBwVCBEEqpVizzyc3N0LoQEowIhklBm9tmhriIhqECIJFiJCoQEpAIhkmC6N7WEpAIhkmClxQW67agEowIhkmClxQUsW7eJii2VoaNIE6QCIZJgpcUFuMPydZtCR5EmSAVCJMGq7k2ts6klBBUIkQQr1b2pJSAVCJEE0+U2JCQVCJEEK2mpAiHhBCkQZjbIzGaY2SwzuzZEBpHGoEV+LsUFeSoQEkTWC4SZ5QL3Al8FegPnmlnvbOcQaSx0b2oJJcQWxMHALHef7e6bgCeA0wLkEGkUSooLKFutAtHU/PP9Rez7sxeZtWRtsAx5AcbZCZif8nwBMLB6T2Z2KXBp/HStmc3YzvGVAEu3870NKYm5kpgJkpkr65ns23XqTdOq7hpFrp6/2KFhdd2RN4coEHXi7iOAETs6HDMb7+796yFSvUpiriRmgmTmSmImSGauJGYC5aqLEE1MC4EuKc87x6+JiEiChCgQ44CeZtbdzPKBbwDPBMghIiK1yHoTk7tXmNnlwEtALvCgu09pwFHucDNVA0liriRmgmTmSmImSGauJGYC5crI3D10BhERSSCdSS0iImmpQIiISFo7dYEws7lm9r6ZTTKz8aHzAJhZGzN70symm9k0Mzs0AZl6xdOo6m+1mX0/AbmuMrMpZvaBmT1uZs1DZwIwsyvjTFNCTicze9DMlpjZBymvtTOzf5nZzPh/2wRkOiueVpVmFuTwzRpy/Tb+HU42s7+bWZsEZPpFnGeSmY0xs92ymam6nbpAxI529wOSclwxMBx40d33BvYHpgXOg7vPiKfRAUA/YD3w95CZzKwTcAXQ3937EB3Q8I2QmQDMrA/wTaIrAuwPnGxmPQLFGQkMqvbatcAr7t4TeCV+HjrTB8AZwOtZzpJqJF/M9S+gj7v3BT4ErktApt+6e9/4t/gc8LMsZ9pKUygQiWFmrYEjgAcA3H2Tu68MGuqLjgU+cvePQwchOsquhZnlAYXAJ4HzAOwDvOPu6929AvgP0cIv69z9dWB5tZdPA0bFj0cBp4fO5O7T3H17r4RQL2rINSb+DgHeJjonK3Sm1SlPi4CgRxHt7AXCgTFmNiG+dEdo3YEy4CEzm2hm95tZUehQ1XwDeDx0CHdfCNwOzAMWAavcfUzYVEC0NvxlM2tvZoXAiWx94mdoHd19Ufz4U6BjyDCNyFDgn6FDAJjZrWY2HzgfbUE0qMPd/SCiK8d+18yOCJwnDzgI+IO7HwisI/tNADWKT1w8FfhrArK0JVob7g7sBhSZ2QVhU0Vrw8CvgTHAi8AkYEvITDXx6Bh2HceegZn9FKgAHg2dBcDdf+ruXYjyXB4yy05dIOK1UNx9CVGb+sFhE7EAWODu78TPnyQqGEnxVeBdd18cOghwHDDH3cvcfTPwFHBY4EwAuPsD7t7P3Y8AVhC1XyfFYjPbFSD+vyRwnkQzsyHAycD5nryTwh4Fvh4ywE5bIMysyMyKqx4DXyFqHgjG3T8F5ptZr/ilY4GpASNVdy4JaF6KzQMOMbNCMzOiaRV8hz6AmXWI/+9OtP/hsbCJtvIMMDh+PBj4R8AsiWZmg4BrgFPdfX3oPABm1jPl6WnA9FBZYCc+k9rM9uDzI3HygMfc/daAkQAwswOA+4F8YDZwsbuvCBqKz4roPGAPd18VOg+Amd0MnEO0+T8RGObuwW+MYGZvAO2BzcAP3P2VQDkeB44iujz0YuBG4GngL8DuwMfA2e5efUd2tjMtB/4PKAVWApPc/YRsZaol13VAAbAs7u1td78scKYTgV5AJdH3d1lVS0gIO22BEBGRHbPTNjGJiMiOUYEQEZG0VCBERCQtFQgREUlLBUJERNJSgRBJYWZuZnekPP+hmd0UP77JzH6Y4f2nm1nvBo4pkhUqECJbKwfOMLOS7Xz/6YAKhOwUVCBEtlZBdE/gq2rrycz2NLMX4wtBvmFme5vZYUTXsvptfD3/Pc3sCjObGl/j/4lsfACR+pIXOoBIAt0LTDaz39TSzwiis1xnmtlA4PfufoyZPQM85+5PApjZtUB3dy/P9g1pRHaUCoRINe6+2sweJrph0Ybq3c2sJdGFA/8aXSYKiC7ZkM5k4FEze5roMhgijYYKhEh6dwHvAg+l6ZYDrIzv+pXJSUQ3iToF+KmZ7ZdykxqRRNM+CJE04gvc/QW4JE231cAcMzsLwCL7x53XAFVXEc4Burj7q8CPgdZAyyzEF6kXKhAiNbuD6EqbVfKIjnKC6G5fl5jZe8AUokszAzwB/MjMJgI9gdFm9j7R1WjvTuAtZkVqpKu5itSRmf0duM/dXwidRSQbtAUhUgfxVkAl0a1GRZoEbUGIiEha2oIQEZG0VCBERCQtFQgREUlLBUJERNJSgRARkbT+H3m+LV/6hFXrAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_separation(df_selected, x_variable='NJets')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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"
    },
    {
     "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": [
    "plot_separation(df_selected, x_variable='MET')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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"
    },
    {
     "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": [
    "plot_separation(df_selected, x_variable='Mll')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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"
    },
    {
     "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": [
    "plot_separation(df_selected, x_variable='SumLepPt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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"
    },
    {
     "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": [
    "plot_separation(df_selected, x_variable='LepDeltaPhi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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"
    },
    {
     "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": [
    "plot_separation(df_selected, x_variable='LepDeltaR')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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"
    },
    {
     "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": [
    "plot_separation(df_selected, x_variable='NBJets')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "Hmm... some of those separations and <span style=\"color:blue\">S</span>/<span style=\"color:red\">B</span> are helpful, but could we achieve higher separation and <span style=\"color:blue\">S</span>/<span style=\"color:red\">B</span>?\n",
    "\n",
    "With Machine Learning, the answer is yes!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a id='correlations'></a>\n",
    "\n",
    "## Correlations\n",
    "\n",
    "It'd be nice if we could use all variables in our ML technique.\n",
    "\n",
    "But, we can't use `Mll` since we selected values around the Z mass; using it &#8594; overtraining.\n",
    "\n",
    "To be sure we can use all the others, we need to check the correlations between them.\n",
    "\n",
    "If a pair of variables is fully correlated (=1.0), using both wouldn't add any new info.\n",
    "\n",
    "<CENTER><img src=\"images/correlation_meme.jpeg\" style=\"width:80%\"></CENTER>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "outputs": [],
   "source": [
    "ML_inputs = ['NJets','NBJets','MET','LepDeltaPhi','LepDeltaR','SumLepPt']\n",
    "\n",
    "def correlations(data):\n",
    "    \"\"\"Calculate pairwise correlation between features.\n",
    "    \n",
    "    Extra arguments are passed on to DataFrame.corr()\n",
    "    \"\"\"\n",
    "    # simply call df.corr() to get a table of\n",
    "    # correlation values if you do not need\n",
    "    # the fancy plotting\n",
    "    corrmat = data.corr()\n",
    "    \n",
    "    heatmap1 = plt.pcolor(corrmat) # get heatmap\n",
    "    plt.colorbar(heatmap1) # plot colorbar\n",
    "\n",
    "    plt.title(\"correlations\") # set title\n",
    "\n",
    "    x_variables = corrmat.columns.values # get variables from data columns\n",
    "    \n",
    "    plt.xticks(np.arange(len(x_variables))+0.5, x_variables, rotation=60) # x-tick for each label\n",
    "    plt.yticks(np.arange(len(x_variables))+0.5, x_variables) # y-tick for each label"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AF1uO3a7t2AvGGlDT7uOJiAhK4pm/cNKwywhcCjxX0kaSlgH2pFQA/4OkqS1Pd+HJa+tnAztJWk3SasBOLFqktUS6PmSO7X26/ZoREf2oE8UFtudLOoCSMCYDJ9i+WtLhwJx6nfugWmg1H7gP2Kcee5+kz1KSF8DhA4UGY5Gx2iIiGqiTE8HZPhM4s23dp1sefxz4+BDHngCc0JFAqiSeiIiG6tchcYaTxBMR0USeuKNTJ/FERDTQRJ4WIYknIqKBylhtE7PwOIknIqKhnBZPRER0U4oLIiKia5zigoiI6LZ0tUVERBeJBSkuiIiIbkk5dYBgyDG4G0h9OLlDv/2NbbH0Cr0OYdSufuLhXocwakutsUavQxi9eR04h8t1nokoiScioqFS1RYREV1jUlwQERFd1bnRqZsmiScioqEWLkziiYiILrHT1RYREV2WrraIiOiqlFNHRERXpastIiK6xmjCJp4+uhc/IuJppI5OPdwyEpJ2lnSdpBslHTrI9o9IukbSFZLOk7RBy7YFkubWZXYn3lpaPBERTdWBazySJgPfBHYE7gAulTTb9jUtu/0BmG77YUkfBL4I7FG3PWJ72tgjeVJaPBERDWVr2GUEtgFutH2z7ceBU4FdF30dn297YCC/S4B1O/pG2iTxREQ0lD38AkyRNKdl2bftNOsAt7c8v6OuG8p7gZ+3PF+unvcSSTM68LaGTzyS/j7WF5G0naS/SfpD7Wf8taQ3jeC4fSR9oz6eIWnzERxzmKQ7a3/kVZJ2qetnSdptkP3XlnT6kryviIjxMjBW2whaPPNsT29ZZi7pa0r6J2A68KWW1RvYng68A/iKpI3H8r6gu9d4LrT9JgBJ04AfS3rE9nkjPH4G8DPgmmH2Azja9pGSNgMulPTMoXa0/SfgKQkpIqKnDO7MkDl3Auu1PF+3rluEpB2ATwCvtv3YP8Kw76z/3izpAuCFwE1jCWiJutokbSzpLEmXSbpQ0qZ1/SxJx9Zm2fVDtWpszwUOBw6ox60p6QxJl9bl5W2v9zJgF+BLtSWzsaT3130vr8c+ZXIU29cC84EpddWrJF0s6eaB1o+kDSVdtSQ/h4iIceURLMO7FHiupI0kLQPsCSxSnSbphcC3gV1s39OyfjVJy9bHU4CXM7Iv/4u1pNd4ZgIH2n4x8FHgmJZtG1IuZr0ROFbSckOc4/fApvXxVymtlK2BtwHHte5o+2LKD+oQ29Ns3wT8yPbWtl8AXEvpl1yEpJcAC4G/1FVTgVcAbwKOGO5NStp3oN90/kMPDbd7REQHDd/NNpLiAtvzKV/yz6Z8Vp5m+2pJhw9ciqB0ra0E/LCtbHozYI6ky4HzgSPaquGWyKi72iStBLysBjiwetmWXU6zvRC4QdLNPJlcnnKqlsc7AJu3nO8Z9XUW5/mSPgesSvmBnd2y7eDaV/kgsIdt13P/uMZ2jaS1hjk/ta90JsDya683QQeviIjG6tCnju0zgTPb1n265fEOQxx3MbBlZ6J40pJc45kE3L+Yuu72H9VQP7oXUrLvwDm3tf1o6w4tiWgws4AZti+XtA+wXcu2o20fOcgxj7U8npi3BEfExDCBR6cedVeb7QeAWyTtDqDiBS277C5pUq18eDZwXfs5JG0FfIpyUxPAL4ADW7ZPG+SlHwRWbnm+MnCXpKWBd472fURENF5nrvE0zkgSzwqS7mhZPkL5oH9v7fe7mkVvRroN+B2lDny/llbMKwfKqSkJ56CWiraDgOl1uIZrgP0GieNU4JB6jo0pieu3wEXA/43qXUdE9ANr+KUPDdvVZnuo5LTzEOvPtb1I4rB9AbDKYl5jHk8Oz9C6fhalSw3bFwGt9/F8qy7txxw2xGvs0/Z8pfrvH4HnDxVbRETP9GmLZjgZqy0ioolM37ZohtPRxNPeqoiIiCWXieAiIqK7kngiIqKb1JkhcxoniScioon6uFx6OEk8ERGN1L/l0sNJ4omIaKq0eCIioquSeCIioquSeCIiomucqraIiOi2CdriWdKJ4CIiIpZIWjwREQ2lCdriSeIZoYVLwWNrLux1GCO2cHKvIxi9m9/27V6HMCqbHvfBXocwen14yWD+J/rw0/fgDp0n9/FERETXTOCRC3KNJyKiobRw+GVE55F2lnSdpBslHTrI9mUl/aBu/62kDVu2fbyuv07S6zrxvpJ4IiKaqgNTX0uaTJn1+fWUyTT3krR5227vBf5q+znA0cAX6rGbA3sCW1Am/zymnm9MkngiIpqqA4kH2Aa40fbNth8HTgV2bdtnV+DE+vh04LWSVNefavsx27cAN9bzjUkST0REA8kjW0ZgHeD2lud31HWD7mN7PvA3YI0RHjtqKS6IiGiqkVW1TZE0p+X5TNszxymijkjiiYhoqBEWD8yzPX0x2+8E1mt5vm5dN9g+d0haClgFuHeEx45autoiIpqqM9d4LgWeK2kjSctQigVmt+0zG9i7Pt4N+KVt1/V71qq3jYDnAr8by1uCtHgiIppp5NdwFn8ae76kA4CzgcnACbavlnQ4MMf2bOB44HuSbgTuoyQn6n6nAdcA84EP2V4w1piSeCIimqpDN5DaPhM4s23dp1sePwrsPsSxnwc+35lIiiSeiIimmqAjFyTxREQ0VAYJjYiI7pqgiaevq9okWdLJLc+XkvQXST+rz/epz+e2LC9oeXyfpFvq43N7904iItp07gbSxun3Fs9DwPMlLW/7EWBHnlpj/gPbB7StmwYgaRbwM9unj3egERGj1qeJZTh93eKpzgTeWB/vBZzSw1giIjqnM/fxNM5ESDynUm5wWg7YCvht2/Y92rralh/piSXtK2mOpDkL/v5QJ2OOiFgska62xrJ9RZ07Yi/a6tSrwbraRnrumcBMgGXXX69P/4sjom9N0E+dvk881WzgSGA7yoiqERH9zSOf6K3fTJTEcwJwv+0rJW3X41giIjojLZ7msn0H8LUhNu8h6RUtz/e3fXEXwoqIGJN+vYYznL5OPLZXGmTdBcAF9fEsYNZijt9nXAKLiOiEJJ6IiOiaPi6XHk4ST0REQ6W4ICIiuirXeCIioruSeCIiomtyjSciIrpJdZmIkngiIpoqLZ6IiOimiVrVNhFGp46ImJi6MC2CpNUlnSPphvrvaoPsM03SbyRdLekKSXu0bJvVMqHmXEnThnvNJJ6IiCbq3gykhwLn2X4ucF593u5h4F22twB2Br4iadWW7YfYnlaXucO9YBJPRERTdWciuF2BE+vjE4EZTwnDvt72DfXxn4B7gDWX9AWTeCIiGqpLLZ61bN9VH/8ZWGuxMUnbAMsAN7Ws/nztgjta0rLDvWCKCyIimmpkiWWKpDktz2fWSSz/QdK5wLMGOfYTi7ycbWnodCZpKvA9YG/bA6UPH6ckrGUoE2d+DDh8cQEn8YzUZLNw1Sd6HcWI3bzTCb0OYdSefcYHeh3CqCzbh6Wu7scbQ/rw59wRI58Ibp7t6Ys9lb3DUNsk3S1pqu27amK5Z4j9ngH8D/AJ25e0nHugtfSYpO8CHx0u4HS1RUQ0VXeu8cwG9q6P9wZ+0r6DpGWA/wZOsn1627ap9V9Rrg9dNdwLJvFERDSQ6No1niOAHSXdAOxQnyNpuqTj6j5vB14F7DNI2fT3JV0JXAlMAT433Aumqy0ioqm60M1o+17gtYOsnwO8rz4+GTh5iOO3H+1rJvFERDSUPDEvcCXxREQ00ciLC/pOEk9ERFNNzAZPEk9ERFNlBtKIiOiuJJ6IiOiazpVLN04ST0REUyXxREREtwjQwomZeZJ4IiIaKl1tERHRPZ0bi61xGjVWmyRLOqrl+UclHVYfHybpzjpG0P9J+pakSXXbLEm7DXPufSStPa5vICKig7Rw+KUfNSrxAI8Bb5U0ZYjtR9ueBmwObAm8ehTn3gdI4omI/tGd0am7rmmJZz5lIqGDh9lvGWA54K/tGyS9WNKvJF0m6WxJU2traDplFNW5kpaXdISka+qseUd2/J1ERIyFS3HBcEs/alriAfgm8E5Jqwyy7WBJc4G7gOttz23dKGlp4OvAbrZfDJwAfL7OHzEHeGdtMa0AvAXYwvZWjGAY74iIbuvStAhd17jEY/sB4CTgoEE2D3S1PRNYUdKebds3AZ4PnFMT1CeBdQc5z9+AR4HjJb0VeHiwWCTtK2mOpDkLHnxoSd5ORMSSS1dbV30FeC+w4mAbbT8BnEWZmKiVgKttT6vLlrZ3GuT4+cA2wOnAm+q5Bnudmban254+eeVBQ4mIGBddnAiu6xqZeGzfB5xGST5PUadYfTlwU9um64A1Jb207re0pC3qtgeBlev6lYBVbJ9JuZ70go6/iYiIsbBHtvShRiae6ijKNKqtBq7xXAVMBo6p65cCHrP9OLAb8AVJlwNzgZfVfWYBx9bjVwZ+JukK4H+Bj4zbu4iIWEITtcXTqBtIba/U8vhuShHAwPPDgMPaj6n38mxGbf3UgoP2LjhsnwGc0bJqm85EHRExPvr1Pp3hNLnFM6x6Q+hVwCW2r+l1PBERHWNgoYdf+lCjWjyjZftPlJtJIyImni7kFUmrAz8ANgT+CLzd9mD3SC4ArqxPb7O9S12/EXAqsAZwGfDP9bLHkPq6xRMRMZF16RrPocB5tp8LnFefD+aRlorhXVrWf4Fyq8tzKDf1D1oU1iqJJyKiqbpT1bYrcGJ9fCIwY6QH1grj7Sm3poz4+CSeiIiG6lKLZy3bd9XHfwbWGmK/5eoN9ZdImlHXrQHcX++NBLgDWGe4F+zrazwREROVPOKJ4KZImtPyfKbtmYucSzoXeNYgx36i9YltS0Omsw1s3ynp2cAvJV1JGQVm1JJ4IiKaamTl1PNsT1/cDrZ3GGqbpLslTbV9l6SpwD1DnOPO+u/Nki4AXki5RWVVSUvVVs+6wJ3DBZyutoiIhpI97NIBs4G96+O9gZ88JQ5pNUnL1sdTKCPHXGPbwPmUG/eHPL5dEk9ERBONZIDQzlzjOQLYUdINwA71OZKmSzqu7rMZMKeOCHM+cETLvZMfAz4i6UbKNZ/jh3vBdLVFRDRSd8Zis30v8NpB1s8B3lcfX0yZfHOw429mlCPBJPFERDRUv070NpwknoiIJvLEHastiScioqn6dNqD4STxjNCWz5jH73Y6oddhjNizf/GeXocwapMW9DqC0Zm02NGomqkfv0E/vmaf/WJ00sTMO0k8ERFN1aFy6cZJ4omIaKoknoiI6BbZaEEST0REdFNaPBER0VVJPBER0TVmpIOE9p0knoiIhkpVW0REdFcST0REdI0NCydmX1sST0REU03MvJPEExHRVLnGExER3ZXEExERXWMg8/FERET3TNzigkm9DmCkJFnSUS3PPyrpsPr4MEkfHeb4GZI2H+cwIyI6xx5+6UN9k3iAx4C3SpqyhMfPAJJ4IqI/DHS1Dbf0oX5KPPOBmcDBi9tJ0saSzpJ0maQLJW0q6WXALsCXJM2t+xwk6RpJV0g6tRtvICJi5AxeOPwyRpJWl3SOpBvqv6sNss9r6mfnwPKopBl12yxJt7Rsmzbca/bbNZ5vAldI+uJi9pkJ7Gf7BkkvAY6xvb2k2cDPbJ8OIOlQYCPbj0ladbATSdoX2Bdg/XX67UcVEX2vO11phwLn2T6ifi4eCnxs0TB8PjANSqICbgR+0bLLIQOfrSPRTy0ebD8AnAQcNNh2SSsBLwN+KGku8G1g6hCnuwL4vqR/orSmBnu9mban256+5hqTxxp+RMTIda+rbVfgxPr4RMplicXZDfi57YeX9AX7KvFUXwHeC6w4yLZJwP22p7Usmw1xnjdSWlAvAi6VlCZNRDTLwoXDLzBF0pyWZd9Rvspatu+qj/8MrDXM/nsCp7St+3y9bHG0pGWHe8G+Szy27wNOoySf9m0PALdI2h1AxQvq5geBlev6ScB6tfn4MWAVYKUuhB8RMUIjqGgrXXHzBnpm6jKz/UySzpV01SDLrou8ou3ywoOTNBXYEji7ZfXHgU2BrYHVaeumG0y/fss/Cjig5flSlKo3gHcC35L0SWBp4FTg8vrvdyQdRMnYx0taBRDwNdv3dyn2iIjhmY7dx2N7h6G2Sbpb0lTbd9XEcs9iTvV24L9tP9Fy7oHW0mOSvgss9tYW6KPEY3ullsd3Ayu0bN4CuLhuuwXYeZDjL2LRcupXjE+kEREd0p3igtnA3sAR9d+fLGbfvSgtnH9oSVqiXB+6argX7LuutnaSrqSM4fqL4faNiOgr3bmB9AhgR0k3ADvU50iaLum4gZ0kbQisB/yq7fjv18/hK4EpwOeGe8G+afEMxfaWvY4hIqLzunODqO17gdcOsn4O8L6W538E1hlkv+1H+5p9n3giIiYkgxcs6HUU4yKJJyKiqfp0LLbhJPFERDRRpr6OiIiuS4snIiK6yWnxRERE19iwIIknIiK6qQPTHjRREk9ERAMZcJ9O9DacJJ6IiCay0+KJiIjumqgtHnmClut1mqS/ALeOw6mnAPPG4bzjKTGPv36LF/ov5vGMdwPba47lBJLOosQ4nHm2nzIwcpMl8fSYpDm2p/c6jtFIzOOv3+KF/ou53+KdSPp+dOqIiOgvSTwREdFVSTy995RpavtAYh5//RYv9F/M/RbvhJFrPBER0VVp8URERFcl8URERFcl8URERFcl8TSMJPU6hiXV1NglLSvpo5Im9zqWTpN0gKSVex3HSEnKZ04k8TSJpGe4j6o9Bj5EBj74Ghz7Zyl3ki9oanJcEpKWBh61/aCkQyQt2+uYBiNpDUmvlrSeXQYfa/r/w0B8kvaUtHmv45loknh6bOBbuKRXAd9q//Bo8h/owIcI8EVJr2nd1pRvtpKeB7wFOAoanRxHzfYTto+TtAawE/BrSe/pdVyDOAP4GHCjpCOg2f8PkjYEPifpQOBA29fU9ROuxdwrjfhweDqzvaA+PAo41fZjkt4oaf+6vZF/oC2tnX2B9W2fL2nl2qU1rSUp9doXgAXAqyW9RNLyvQ6oE1q/kNi+1/aOwH8C75L0c0nb9y66J0k6CLjL9huAzYFNJG0r6cWSVpf0kh6H+BS2/wj8CvgEsIqkNev6BZKWkrR6L+ObCJJ4GkDSi4Dbbf9U0keB9wAHSvqSpEaOIN6SWHYEPilpM8oH3w7AqZI26llwlaS3AKsB7we2ofxcd5f0vKa0yJbUwBcSSS+T9EFJG9n+MfBa4Bzg+Pp/0jOSlgP2BX4raTnbNwHXAd8GZgMnAbMkPb+HYS5C0otq78MzKTF+FzhP0pfrLu8D/rlX8U0Uff3H18/aPvj+Aqwn6SpgKuUD8vXA82zP70V8i9MW+1mUP9DvAOfVUXKvBNbpRWxtNgCOsH0h8P+A/6V8MO8LvEHSer0MbknVrjUkvRqYBbwYuFzSN4CFtr8MTLd9be+iBGAVSjfb2sCHJb0WeB3wIdvrAAcAW9u+qgldypK2oiSag4AXAn+0fRTwTmANSTcB+wM/qPv3POZ+lZELeqS2CP4IHAGcVbuq3lxbPZOBnwJn2D5e0qSmdF3VboYHKB/qn7e9p6TplN+lSyW9A9jP9qt6HOfelA+OX7X+/CStBfwT8CrgJ7ZP6GWcoyXpmcBHgF8AuwE/r78z61CGgHk58Enb3+hhmP9QW+w7UuJ6EbAS8Dbbf+lpYIOQdDolkf8c2JXyBeUA2zfW7c8FVrB9uaTJLd3kMUpJPD0gaQqwB/ACyjfwN9i+rmX7rsD7bb+pRyEOSdIulNbY5sBvbB/asm014BjgeNvn9uqPU9IqwBzgLfXb9Nq2/9SWgKYD99i+rdvxjYWkqcCBwLrAcsDvgW/b/mvd/iZKS/nLQ59l/LV/WardbtsBOwMPA3cA37P9YG8iXJSkHYGzgefYvrmu+znwddtnSlJTr7f2o0ZeP5jobM+T9D/AO4AHgVfW7pNL6h/rnXUbTftmZXu2pBcCuwPXSnoxcKPtvwGbAvsPfAj2MO7PASfVpDMN+J6k6bYfG9jB9pwexbbEJK0KPINSMLEhpQtoG+AOSXOB623/rGX/nrSUB15X0orAB4HHgD8DZwKXUn63pzYl6QDYPkfSF4BLJZ1GafUsZfvMuj1Jp4PS4umytm/dmwMLKX+cywO/pLSEHrC9d++iXLyaJJ9F+Qb7dsp1nj8APwQ2tX1nD2N7DqUV8Lb6YXISMMf21+r21ShVeJf3KsYlJemXlA/xlwNftn2YpD0prYh7KR/qP7X9UA/DZKB1IOmbwHxgBWArSmHBibbPk7SS7b83oRu57W/ymcCxwAzgZNvv6mVsE1WKC7qs5Rf8ncA+wNbAwcBFwHTgduCjdZ/G/P/oyfuNtgNeA+wFnEK52LoxsAvwMdt39vh+hwWUD46dJZ0CbDWQdKrjgJf1JLIxqGXJd9t+PeVaya6SXm/7VMrvy33A5r1OOlBaByr3T73Y9oeBjYDjgb8BR0s6yPbf6749v3bZ8jf5DNv32H4rpSt5M0k3SnpDbyOceNLi6aKWLoiPUKpmLgI+DazT3pRvwjfBAS3fYJenxPwF4DBKxdiJdZ+lbT/Run8P4nw2pULwUWB74G2UKsFT6jIN+GqvCx9Gq14fmUOpHPy27UclHQKsaPuwlv2Wt/1IE353JG1NqWp7hFLs8PraRfth4FDbf27CdZOBrmxJO1FKpVen3MNzpu3LJP0LsJ7t/9fLOCeaXOPpopp0VgL2pHwwfhE4sn6ovwO4z/ZZA/v2MNRFtHw4fBz4L2AucL/tE+uF/N2BU4En2vbvtnMpLcav2z5d0v9SRi3YltKa3A34lx7FNhYDZcnrUMqS51C6ZAeuAy5r+zHbj0Dvfndqi+GBet3vEeBy4NmAa+n6O4CHbf+5xtnzb70t1yE/R/kytTyl/Ht/SV+0/ZWBfZuQ0CeKxnTlTHQD3Wa1i+G/KeWaG7ZUH+0P9PwPsZ0WHcLnt5RrCUcAh9d1bwPePNB10gsqlqFc2wF4W71AvK3tk4GvAPOAn9n+UY/CXGK276aMN3c+sDLlnqSHKWXttBZN9Er9QrWjyk27pwBTbD9u+/+Am4DzgPUpowE0oht54D4cSTOAebbPtH0GcCLlZ/sRScsP7Jek0znpauuC2oyfBvyP7aslfRg4Eviu7X0lfZJyI92uvYyzXe1aex8l4VxF+eb9E8o9PNtSurR+SrnX4ZJefyOUtAFwCOUG1rspVV93UlpANw20DHoV35IYpiz5IUpZ8slNqBCTtDPwdUpBwT8Bd9SkiaT1gXttP9Tr35NWKgOtHkK5mfV04Gjbt0h6BfAZl6GIosOSeLpA0u6UGxYfplQe/ZhS5XMUpbvzauArtv+vSeXTteruU8D9wCWUctgVKIUF7wcuppRS/3sv++slLWP78fr45cB/ULr+LqEUPbwB+JTtX/QiviU1TFnycpSuq2fa/lQPw0RlvLXtKNegXkf53V4LuBb4GaWA5qW2P9irGBenttZeRXkPG1K6CVenVA6e33r9MjojiWec1ftIrgamUK43PJ/SXXWW7YskreJyD0zPLsovTq1QezvlG/Z9lJLv3wF/BRYMJMke3jOyNfBvlGF7bqO0wu6nJMevUrpMXgL8tg9bO31Rlqxy0+rrKF33v7F9ci0keA+wLKUK7z9tn9GE3/GWgoINgJdSbsb9b8r1nZdS/k7/DMyy/eveRTpxJfGMI0nPoly0vBOYXatktqRc31kHuJkyvtnvm/AH2UrSHpQPuotsX69yx/yelIv0N1FusPu9y2javWzt7E0ZX+su4F8po0HsQPkw+ZbtzzTtZzsatSz5JNvbSjoXOA3YEng1cJwXLRXvmdo6fiklyT8EfN/2HJX7qnAddqZJJF1EKa//InCM7c/U9c+n/A69lFIFeXHvopyYknjGUb0wvxPlw3AdyjfVnwC3Un6xXwMsQ2nS9+ymy3YqNyUeTEmYKwHvorQcHgPWAz5AuVB8ilvulO+VWln3HWAzSuXaLZTEY9u39DK2seqXsuQBkjYB3gxsQqkw/JHtq3ob1VNJejPwdtv/LOkSYK96bWd/yheZZ1CGHrqwp4FOUEk846TtvpblKUlmW0p3xJWUi/KTKN+2HgD+rUEXXC8G9nUZcua/6+rHKXF+ta6fQbkou3dTvs3Wbs0fARcCH7Z9f08DWkJtZcmPAddTypK/TEn6B1Hu4dm/h2G2dlntQLkv7dWU34m7KSNmv4nS9XZqD8McVC0e2JzSQrvH9sclvQD4HrCN7Ud7GuAE1/OSxomoXhc5UtJ/SPpnSgnp3yhdVytS7jQ/tpYg3w6s3qCksx+wKnBnvaj9IsoNo9+kXJvaC8Bl7pc1Kdd9GsH2XMooCmcB90jaq7cRjV4/lSXXpDOJkhDPpbQ4d7F9n+1zgM9QugabOIXAtTxZUHCMymjxn+XJG3Rzj+M4SotnHNTuhrmUC6sDH+QbUoZz2YKS8O+z/db6B7lMUy58S3oj8EZKN9sOwNW2D6jbNqcMfTLD9t2SntOU1k672s25su15vY5ltPqpLFnSAZQbLo+hjNX3Ckr38acpXciNm/5gQC0uOILy93kP8ODA73qMrySecVK/MR1EudnvPbbPrutXtv1ga9l0U/ro67WDgQq8XSmVbFcBv7Z9dr3faKrtDzXhQ2+i6ceyZJXZc7emfFmZZftHKtN6HGT7tb2Nrqj36uxI6fb76yDbnwM8MnCdNb/b4y+JZ5ypjOR8MuUDZH/bl/Q4pEENUYG3GWVkgjUooyrsCrywXn/IH2eH9UtZcm2lL19jup8ynM/A4KVrA58HPlHLvXt+X5qkbSnTbf8K+D5wee1OW9r2E5I+BqzmlrmlYnwl8XSJyrS6ZwFn2353r+NpN0gF3vWUG11vpUxWtyfwK9snNeHDZKJqellyrQbbhVI1OJkyGsdXa5fbuyjTi99u++gehvkUKnMZHUKZUuKXwGkuN2yvBVwGvLJWtTWi92GiS+LpovpN8dkuw7c05hd8BBV4P6b8rqTSp0uaWJYsaVPKsDL/RplHaj6lO3l5yigK97sOVFr373mruP1Lksr01R+lXHP9NvBuygR6/y9fqLoniedprlbgfZny7fpaygfdzyl3b0+mXCz+P+BDth/oVZwTWb+UJavMb3S+7Zkt61YFPkSpvju4V7ENZuDLncoAsh+g3GR8rct4ia8BPkZpuW3lMjRRY74MTnRJPE9zo6nA602ETw+1LHkusDelVTHT9hfqtlUps9L27MOxJsXZwJquk83pybHkXkapwnuj65QHTdCSeI6kFEDcBPydcoPx6bZvl7SO6+SFae10T2rVn+ZsXydpZUqXyWcoFXhfhEUr8Orz/HGOn/0plWt/oZT2Hlm7PQfKkhdCT+eweYBSLn28pHNtH9cS08WS7gaeSRnjrOdaks6KlHvnXkNpwb+FUgTxGUk/sn0mLDIvT3RBbiANbM93mRdoK+BfJP1e0rauQ+0P/FHmj3NcXUwp5DgG+FL9We9EuYu+CffCXAocShkZYntJ/yXpdfCP+WyWt31FD+NbREuCnk4ZaXpv20/YPg2YSZmkrnFD+TxdpKstnqLpFXgTRb+VJQ9QmU30jZR7Y+6i3Gj8Ltu/a0KcLV2AM4AvUVqSH6Bcu/xAP95UPNEk8cSgmlqBN1H0S1lyS+HDiygJZnNKi+Fmyr1pHwIW2t6vab8nkr4N/ND2uSoT6B1DmRzwS7Y/2bR4n06SeCK6rE/Lkq8FjgU2Ap4LzLX9CUkrAE/UGzF7HucASa+k3BB9M+Wm2+vr+mmUKraTehje014ST0SX9UtZckuX1faUopN/qus3BE6iVIY1Yj4gWHToqZoQd6MMQXQbpWLwf1u72dLi6Z0UF0R0US1L3pUydMvAukkuUzicD7yqDl/UczXpLEcZsmcLSbtKWtX2Hykjlm/b0wDbtCSdj1LmK/o+cBhlLqMdgA9LmtK+f3RfEk9Ed7WWJb8Pygd8/fdiyk2jz+xdeE+qCfFRyqClv6YUFLxDZdbXD1FGtBi4CbkR6rXJP1CmaPgpsGW9H+pU4NYUFjRDutoiuqh+MD4LeCUwo64+0WX07xmUCexe06PwgEUKClajzLm0fr1AvzdlxPINgLOBo1zmlGqUejPuGsD2wHspN4x+2fZ1dXu62HosiSeiR/qgLPl/KC2dQ4DP2f6Kymjr/0wZ2udW4Du2b+9hmK0ztr4UwPZv6vplKaOrHwicYfvIHoYZLdLVFtEFLaM/vEjSv0qaBaxH6a46nDJ52gU16agBSWc34GHgK5ShZn6uMsfUZra/QimpXtCApLMt8ElJUynXnGZL+pqkNV0mV7yUMsfU1+v+TZsJ9WkpLZ6ILuqXsmSVKdtvo0wjsKbtgyVtARxFmYG2ESOVS/oF8GPbx9Tn6wPfBVYBfgDsQbmX5wtN+LlGkbHaIsZZW1nyZba/WtdvCJwk6aDWsuSGfDheDvwX8CzbA5Vg/w6c4zKJ2lK25/cuPJD0dgDbx9QW5XbAB4FrKAlzDeCztn9S92vCzzVIV1vEuGt6WfJA95OkpQYe13HX9gdulfQ7SccCK9o+qm7vadKplgH+VB/vTRkW52+UqsFfAz8YSDrpYmuWdLVFjLOWFs+rgbdSRiiYS5kDaQ9glu3TelVQUKvAnuk6pYHK/DXzB1oIknYF7gBuqBfxe174UONaHfgaZRDQbSj37sx2GVH9O8AfbX++lzHG4NLVFjFOWj6gV5G0JrC07Q8PUpbc66H5NwF+L+lrtj9m+/Ea/4ouc+8sBTzP9mU9jnMRtu+T9HHg2ZSf7bnwj1ELtqa0JlM+3UDpaosYJy0f0CdT5oE5VdK/2D4ROAA4jfKh+a+1tLonbF8LPAN4SNJdNTFi+yFJz6RMEX1Zr+JbHNu32/5VS9JZFTiOci3qxtraTNJpmCSeiHHUL2XJLnPVHA48H9hdZU6m9YGPA9+3fX3tkmusgS5DytxG/1ZXJ+k0UK7xRIyjfilLbifpBZT5a55FmeTtsX7psmq5ptYX8T4dJfFEjCOVSfUWKUuWdDrwG9tHNaEseSi1Emx927c2Oc7oP0k8ER0y8A27dqUtaBkt+VXA0cAC4PfABrZf38NQI3oqiSeiQ/q1LDmi2xp9sTCiz2wC3CLpCwC2H6/XGlas2wfKkh+o25N04mkpiSeiQ/q5LDmim9LVFjEO6vQBJwJrU+bdORiYVG8gzWCV8bSWxBMxjvq5LDlivCTxRIyzlCVHLCqJJyIiuirFBRER0VVJPBER0VVJPBER0VVJPBER0VVJPBER0VVJPBER0VX/HwePV39UNXTuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "correlations(df_selected[ML_inputs]) # plot correlation matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "No variable pair is correlated > ~0.75, so we can use each variable :)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a id='ML_setup'></a>\n",
    "\n",
    "## Machine Learning setup\n",
    "\n",
    "Now we need to organise data ready for ML.\n",
    "\n",
    "<CENTER><img src=\"images/ML_meme.jpeg\" style=\"width:60%\"></CENTER>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "outputs": [],
   "source": [
    "df_measured = df_selected[df_selected['type']==0] # measured data has type==0\n",
    "df_simulated = df_selected[df_selected['type']!=0] # simulated data has type!=0\n",
    "\n",
    "# for sklearn data is usually organised                                                                                                                                           \n",
    "# into one 2D array of shape (n_samples x n_features)                                                                                                                             \n",
    "# containing all the data and one array of categories                                                                                                                             \n",
    "# of length n_samples  \n",
    "\n",
    "X = df_simulated[ML_inputs] # concatenate the list of MC dataframes into a single 2D array of features, called X\n",
    "y = np.concatenate([np.ones(df_simulated[df_simulated['type']==1].shape[0]), \n",
    "                    np.zeros(df_simulated[df_simulated['type']!=1].shape[0])]) # concatenate the list of lables into a single 1D array of labels, called y\n",
    "\n",
    "# One of the first things to do is split your data into a training and testing set. \n",
    "# This will split your data into train-test sets: 75%-25%. \n",
    "# It will also shuffle entries so you will not get the first 75% of X for training and the last 25% for testing. \n",
    "# This is particularly important in cases where you load all signal events first and then the background events.\n",
    "\n",
    "# Here we split our data into two independent samples. \n",
    "# The split is to create a training and testing set. \n",
    "# The first will be used for training the classifier and the second to evaluate its performance.\n",
    "\n",
    "# We don't want to test on events that we used to train on, \n",
    "# this prevents overfitting to some subset of data so the network would be good for the test data but much worse at any *new* data it sees.\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "# make train and test sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, \n",
    "                                                    random_state=7 )\n",
    "\n",
    "# A neural network may have difficulty converging before the maximum number of iterations if the data is not \n",
    "# normalized. \n",
    "# Multi-layer Perceptron is sensitive to feature scaling, so it is highly recommended to scale your data. \n",
    "# Note that you must apply the same scaling to the test set for meaningful results. \n",
    "# There are a lot of different methods for normalization of data, \n",
    "# we will use the built-in StandardScaler for standardization.\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler() # initialise StandardScaler\n",
    "\n",
    "# Fit only to the training data\n",
    "scaler.fit(X_train)\n",
    "\n",
    "# Now apply the transformations to the data:\n",
    "X_train = scaler.transform(X_train)\n",
    "X_test = scaler.transform(X_test)\n",
    "X = scaler.transform(X)\n",
    "\n",
    "# We'll use SciKit Learn (sklearn) in this tutorial. Other possible tools include keras and pytorch. \n",
    "\n",
    "# After initialising our MLPClassifier, call the .fit() method with the training sample as an argument. \n",
    "# This will train the tree. \n",
    "\n",
    "from sklearn.neural_network import MLPClassifier\n",
    "\n",
    "ml_classifier = MLPClassifier(random_state=7) # initialise classifier\n",
    "ml_classifier.fit(X_train, y_train) # fit MVA to training set\n",
    "\n",
    "# Now we are ready to evaluate the performance on the held out testing set.\n",
    "\n",
    "df_with_ML = df_selected.copy() # copy selected DataFrame to be able to add new column\n",
    "ml_output_list = [] # start list to hold ML outputs\n",
    "for s in [0,1,2,3,4]: # loop over samples\n",
    "    X_s = df_selected[df_selected['type']==s][ML_inputs] # get the MVA input features\n",
    "    X_s = scaler.transform(X_s) # apply scaling\n",
    "    ml_output_on_X_s = ml_classifier.predict_proba(X_s)[:, 1] # get decision function for this sample\n",
    "    ml_output_list.append(ml_output_on_X_s) # append to list of ML outputs\n",
    "ml_output_array = np.concatenate(ml_output_list) # concatenate into one array\n",
    "df_with_ML['ML_output'] = ml_output_array # save new column"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a id='overtraining_check'></a>\n",
    "\n",
    "## Overtraining check\n",
    "\n",
    "In this section we will check whether there has been any overtraining.\n",
    "\n",
    "<CENTER><img src=\"images/overtraining_meme.jpeg\" style=\"width:40%\"></CENTER>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "outputs": [],
   "source": [
    "def compare_train_test(clf, X_train, y_train, X_test, y_test):\n",
    "    decisions = [] # list to hold decisions of classifier\n",
    "    for X,y in ((X_train, y_train), (X_test, y_test)): # train and test\n",
    "        d1 = clf.predict_proba(X[y>0.5])[:, 1] # signal\n",
    "        d2 = clf.predict_proba(X[y<0.5])[:, 1] # background\n",
    "        decisions += [d1, d2] # add to list of classifier decision\n",
    "        \n",
    "    low = min(np.min(d) for d in decisions) # get minimum score\n",
    "    high = max(np.max(d) for d in decisions) # get maximum score\n",
    "    low_high = (low,high) # tuple holding score range\n",
    "    \n",
    "    # plot the test set background\n",
    "    background_test_heights = plt.hist(decisions[3], # background in test set\n",
    "                                       range=low_high, # lower and upper range of the bins\n",
    "                                       density=True, # area under the histogram will sum to 1\n",
    "                                       color='red', label='B (test)', # Background (test)\n",
    "                                       alpha=0.5 ) # half transparency\n",
    "    \n",
    "    # plot the test set signal\n",
    "    signal_test_heights = plt.hist(decisions[2], # signal in test set\n",
    "                                   range=low_high, # lower and upper range of the bins\n",
    "                                   density=True, # area under the histogram will sum to 1\n",
    "                                   color='blue', label='S (test)', # Signal (test)\n",
    "                                   alpha=0.5 ) # half transparency\n",
    "\n",
    "    # histogram the training set background\n",
    "    background_train_hist, bin_edges = np.histogram(decisions[1], # training background\n",
    "                                                    range=low_high, # lower & upper range of the bins\n",
    "                                                    density=True ) # area under the histogram will sum to 1\n",
    "    \n",
    "    # get scale between raw and normalised training background\n",
    "    background_scale = len(decisions[1]) / sum(background_train_hist) \n",
    "    \n",
    "    # get statistical error on background training set\n",
    "    background_train_err = np.sqrt(background_train_hist * background_scale) / background_scale\n",
    "    \n",
    "    center = (bin_edges[:-1] + bin_edges[1:]) / 2 # bin centres\n",
    "    \n",
    "    # plot training set background\n",
    "    plt.errorbar(x=center, y=background_train_hist, yerr=background_train_err, fmt='ro', # red circles\n",
    "                 label='B (train)' ) # Background (train)\n",
    "\n",
    "    # histogram the training set signal\n",
    "    signal_train_hist, bin_edges = np.histogram(decisions[0], # training signal\n",
    "                                                range=low_high, # lower & upper range of the bins\n",
    "                                                density=True ) # area under the histogram will sum to 1\n",
    "    \n",
    "    # get scale between raw and normalised training signal\n",
    "    signal_scale = len(decisions[0]) / sum(signal_train_hist) \n",
    "    \n",
    "    # get statistical error on signal training set\n",
    "    signal_train_err = np.sqrt(signal_train_hist * signal_scale) / signal_scale\n",
    "    \n",
    "    # plot training set signal\n",
    "    plt.errorbar(x=center, y=signal_train_hist, yerr=signal_train_err, fmt='b*', # blue stars\n",
    "                 label='S (train)' ) # Signal (train)\n",
    "\n",
    "    plt.xlabel(\"ML output\") # write x-axis units\n",
    "    plt.ylabel(\"Normalised units\") # write y-axis units\n",
    "    plt.legend() # draw legend\n",
    "    plt.title('overtraining check') # add title to plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "compare_train_test(ml_classifier, X_train, y_train, X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "If overtraining were present, the dots (test set) would be very far from the bars (training set).\n",
    "\n",
    "Within uncertainties, our dots are in reasonable agreement with our bars, so we can proceed :)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a id='ROC'></a>\n",
    "\n",
    "## Performance\n",
    "\n",
    "A useful plot to judge the performance of a classifier is to look at the ROC curve directly.\n",
    "\n",
    "<CENTER><img src=\"images/ROC_meme.jpeg\" style=\"width:100%\"></CENTER>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import roc_curve\n",
    "\n",
    "# define function to plot ROC curve\n",
    "def roc(clf, X_train, y_train, X_test, y_test): \n",
    "    train_decisions = clf.predict_proba(X_train)[:, 1] # get probabilities on train set\n",
    "    test_decisions = clf.predict_proba(X_test)[:, 1] # get probabilities on test set\n",
    "        \n",
    "    # Compute ROC curve for training set\n",
    "    train_fpr, train_tpr, _ = roc_curve(y_train, # actual\n",
    "                                        train_decisions ) # predicted\n",
    "    \n",
    "    # plot train ROC curve\n",
    "    plt.plot(train_fpr, # x\n",
    "             train_tpr, # y\n",
    "             label='Train', color='orange' )\n",
    "\n",
    "    # Compute ROC curve for test set\n",
    "    test_fpr, test_tpr, _ = roc_curve(y_test, # actual\n",
    "                                      test_decisions ) # predicted\n",
    "    \n",
    "    # plot test ROC curve\n",
    "    plt.plot(test_fpr, # x\n",
    "             test_tpr, # y\n",
    "             label='Test', color='purple' )\n",
    "    \n",
    "    plt.xlabel('False Positive Rate') # add x-axis label\n",
    "    plt.ylabel('True Positive Rate') # add y-axis label\n",
    "    plt.title('ROC curve') # add title\n",
    "    plt.legend() # draw legend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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": [
    "roc(ml_classifier, X_train, y_train, X_test, y_test) # plot ML ROC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "The fact that the <span style=\"color:orange\">train</span> and <span style=\"color:purple\">test</span> curves overlap is another indication that overtraining isn't present.\n",
    "\n",
    "The better the classifier, the more the curves will lie towards the top left."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a id='ML_output_separation'></a>\n",
    "\n",
    "## ML_output separation\n",
    "\n",
    "Let's look at how well `ML_output` separates between <span style=\"color:blue\">signal</span> and <span style=\"color:red\">background</span>.\n",
    "\n",
    "<CENTER><img src=\"images/ML_output_separation_meme.jpeg\" style=\"width:40%\"></CENTER>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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"
    },
    {
     "data": {
      "image/png": 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TniOSJjIREen5kvI+WCIi0v0l+oaGnTJkyBAfM2ZM1GGIiHQrRUVFW9x9aFTL7xYJZsyYMSxYsCDqMEREuhUzO5i7Vxw0NZGJiEhcKMGIiEhcKMGIiEhcKMGIiEhcKMGIiEhcKMGIiEhcKMGIiEhcKMGIiCShLbv2cuW9b7CouDLqUDpNCUZEJAn99d2NvLV2G1lpHX3ycfJQghERSTLuzuwFJUwtyObQ4e15CGpyUoIREUkySzfuYGX5TmbNLIw6lIOiBCMikmRmFxWTltqHi4484NOyk54SjIhIEqmpa+DJRaV88vARZGf1jTqcg6IEIyKSROat2ExVdR2zZhREHcpBU4IREUkis4uKycvO4MQJQ6IO5aApwYiIJIlNVTW88kEFl07PJ6WPRR3OQVOCERFJEk+8W0Kjw6wZ3fvssSZKMCIiScDdmVNUwszRgxg7pF/U4XQJJRgRkSSwcEMlayp2c/nM7t+530QJRkQkCcwpKiazbwrnd/NrX2IpwYiIRKy6toGnF5dx7hEj6J+eGnU4XUYJRkQkYs8t28TOvfU94tqXWEowIiIRm11UTMGgTI4bOzjqULqUEoyISIRKtu/h9dVbmTWjgD494NqXWEowIiIRemLhRtzhsuk9q3kMlGBERCLT2Bhc+3L8uMEU5mZFHU6XU4IREYnI2+u2sWHbnh517UssJRgRkYjMXlBC//RUzp2SF3UocaEEIyISgd1763l2aRkXHJlHZlpK1OHEhRKMiEgE/v5eGXtqG3rctS+xlGBERCIwZ0EJ44b0Y8boQVGHEjdKMCIiCbZuy27eXreNy2YUYNazrn2JpQQjIpJgjy8soY/1zGtfYinBiIgkUEOj83hRCSceMpQR2RlRhxNXSjAiIgn0+uotlFbVcHkP7txvogQjIpJAc4pKGJiRylmTh0cdStzFLcGYWaGZzTez5Wa2zMy+Hg7PNbMXzGxV+L/nnkIhIhKjqrqOfyzdxMXT8sno2zOvfYkVzxpMPXCLu08GjgO+bGaTgduAee5+CDAvfC8i0uM9vaSUvfWNPfral1hxSzDuXubuC8PXO4EVQD5wMfCncLI/AZfEKwYRkWQye0EJhw7vz5EF2VGHkhAJ6YMxszHAUcBbwHB3LwtHbQJabIg0s5vMbIGZLaioqEhEmCIicfPh5p0sKq7k8hmFPfral1hxTzBm1h94HPiGu++IHefuDnhLn3P3+9x9prvPHDp0aLzDFBGJq9lFJaT0MS45Kj/qUBImrgnGzPoSJJf/c/cnwsHlZpYXjs8DNsczBhGRqNU3NPLEwo2cdthQhg5IjzqchInnWWQG/AFY4e6/jBn1FHBd+Po64Ml4xSAikgxeWVVBxc69zJpRGHUoCZUax3l/ArgWeM/MFoXDvgP8DHjMzD4PrAeuiGMMIiKRm1NUQm6/NE6fOCzqUBIqbgnG3V8DWuvJOiNeyxURSSbbd9cyd/lmPnPcaNJSe9e17b3r24qIJNiTizZS29B7rn2JpQQjIhJHs4tKOHzkQCaPHBh1KAmnBCMiEifLS3ewrHRHr7ixZUuUYERE4mROUQl9U4yLp/Wea19iKcGIiMRBbX0jf120kTMnDWdQv7Sow4mEEoyISBzMX7mZbbtruXxm72weAyUYEZG4mL2ghGED0jn5kN57qyslGBGRLlaxcy/zV27mU9PzSU3pvbvZ3vvNRUTi5K/vbqSh0Xvt2WNNlGBERLqQuzOnqIRphTlMGDYg6nAipQQjItKF3ttYxcrynb26c7+JEoyISBeavaCE9NQ+XHDkyKhDiZwSjIhIF6mpa+DJRRv55OEjyM7sG3U4kVOCERHpInNXlLOjpl7NYyElGBGRLjJ7QQkjszM4YfyQqENJCkowIiJdYFNVDa+uquCyGQWk9GntUVi9ixKMiEgXeHxhCY0Ol01X81gTJRgRkYPk7jxeVMIxY3IZM6Rf1OEkDSUYEZGDtHDDdtZs2c0sde7vRwlGROQgzV5QQlZaCucfkRd1KElFCUZE5CBU1zbw9JIyzp2SR7/01KjDSSpKMCIiB+Efy8rYtVfXvrRECUZE5CDMXlDCqNwsjh2bG3UoSUcJRkSkk4q37eH11VuZNaMAM1370pwSjIhIJz2xcCNmcOn0/KhDSUpKMCIindDY6MxZWMwJ4wdTMCgr6nCSkhKMiEgnvLV2G8Xbqrl8RmHUoSQtJRgRkU6YXVTMgPRUPnn4iKhDSVpKMCIiHbRrbz3PvreJC6bmkZmWEnU4SUsJRkSkg55ZUkZ1XQOz1Dx2QEowIiIdNLuomHFD+zF9VE7UoSQ1JRgRkQ5Yu2U376zbzuUzCnXtSxuUYEREOuDxohL66NqXdlGCERFpp4ZG5/GFJZx86FCGD8yIOpykpwQjItJO//xwC2VVNbr2pZ3ilmDM7I9mttnMlsYM+4GZbTSzReHfefFavohIV5tdVEJ2Zl/OnDws6lC6hXjWYO4Hzmlh+K/cfVr490wcly8i0mWqqut4btkmLp42kvRUXfvSHnFLMO7+CrAtXvMXEUmkvy0upba+Uc1jHRBFH8xXzGxJ2IQ2KILli4h02OyiEiaOGMCU/IFRh9JtJDrB/A8wHpgGlAG/aG1CM7vJzBaY2YKKiooEhSci8nGryneyuLhSz33poIQmGHcvd/cGd28Efgccc4Bp73P3me4+c+jQoYkLUkSkmTlFJaT2MS45Ste+dERCE4yZ5cW8/RSwtLVpRUSSQX1DI0+8u5HTJg5jSP/0qMPpVlLjNWMzexg4FRhiZiXA94FTzWwa4MA64AvxWr6ISFd4+YMKKnbu5fIZBVGH0u3ELcG4+9UtDP5DvJYnIhIPc4pKGNwvjdMm6tqXjtKV/CIirdi2u5a5K8q55Kh8+qZod9lRKjERkVY8uWgjdQ3O5TPVPNYZbTaRmdnxwGeAk4A8oJqgc/7vwEPuXhXXCEVEIjJ7QQlH5GczcYSufemMA9ZgzOxZ4AbgOYLbvuQBk4HvARnAk2Z2UbyDFBFJtGWlVSwv26Hay0FoqwZzrbtvaTZsF7Aw/PuFmQ2JS2QiIhGaU1RCWkofLpo6MupQuq0D1mBaSC6Y2RlmdqGZ9W1tGhGR7qy2vpEnF5Vy1uTh5GSlRR1Ot9WhTn4z+wXwCWAq8GRcIhIRidiL75ezbXcts9Q8dlAO2EQWJpT/dPfKcNAo4Irw9XtxjEtEJDJzikoYPjCdkw/RbaoORls1mCeAR8zsa2aWAjwAzAfeILiXmIhIj/LOum3MX1nBpdMLSOmjG1sejLb6YP7p7ucQPNflOcDc/VR3P87d70xIhCIiCbKpqoYvPrSQUblZ3HzK+KjD6fbaOk051czOBzYDlwBTzewpM5uaiOBERBJlb30DNz9UxJ7aeu69dgbZmX2jDqnba+s05b8SNIdlAZ929+vMbCTwIzNzd78x3gGKiCTCD55azqLiSv7n09M5dPiAqMPpEdpKMKPd/QIzSwPeBHD3UuCG8K7IIiLd3p/f2sDDb2/gS6eO59wj8tr+gLRLWwnmPjN7I3z9y9gR7r4oLhGJiCTQwg3b+f5TSzn50KHccvZhUYfToxwwwbj7b4DfJCgWEZGE2ryzhi8+VERediZ3XTVNZ411sbY6+b9nZoMOMP50M7ug68MSEYmv2vpGvvx/C9lRHXTq64r9rtdWE9l7wNNmVkNw77EKgptcHgJMA+YCP41ngCIi8fDjvy/nnXXbuevqo5iUp7slx0NbTWRPEtwx+RCCW8TkATuAh4Cb3L06/iGKiHSt2QuKeeCN9dx40ljdzDKO2vXIZHdfBayKcywiInG3pKSS7/51KSeMH8y3zpkYdTg9mp5oKSK9xtZde7n5wSKG9k/n7mumk6rHIMdVu2owIiLdXX1DI1/+80K27q7l8S+eQG4/derHmxKMiPQKtz/7Pm+u2cYvr5jKlPzsqMPpFdo6TTnDzK4zs4ss8C0ze9rM7tSTLEWku3hy0Ub+8Nparj9hDJdO1zNeEqWtBsgHgLOBzwEvETwP5m5gJ3B/PAMTEekKy0qr+NbjSzhmbC7fPX9S1OH0Km01kU129ylmlgqUuPsp4fB/mNniOMcmInJQtu+u5QsPFpGTmcZ/XzOdvurUT6i2SrsWwN3rgdJm4xriEpGISBdoaHS+9si7bN6xl3uuncHQAelRh9TrtFWDKTCzuwCLeU34Pj+ukYmIHIQ7nlvJq6u28PPLjmBaYU7U4fRKbSWYW2NeL2g2rvl7EZGk8PclZdzz8mo+feworjx6VNTh9FptJZh84Fl3fzcRwYiIHKyVm3Zy65zFzBg9iO9feHjU4fRqbSWY1cDXw0ckLwaeBZ539+1xj0xEpIOq9tRx04ML6Jeeym8/PZ20VHXqR6mtm10+CjwKYGZHAecAT5hZCsGdlP/h7m/HPUoRkTY0NjrfePRdSiurefjG4xg+MCPqkHq9dqd3d3/X3W9399OAC4BlwA1xi0xEpAN+PfcD5q+s4PsXHs7MMblRhyO0UYMxs6OBYnffFL7/LHAZsB74gbs/Hv8QRUQO7Lllm7jrxQ+5YmYBnz5WnfrJoq0azL2E18KY2cnAzwiu7q8C7otvaCIibftw8y5ueWwxUwuy+dHFUzDTY4+TRVud/Cnuvi18fSVwX1hredzMFsU1MhGRNuysCTr1M/r24X8+M4OMvilRhyQx2qrBpIS3iQE4A3gxZlxbzWt/NLPNZrY0Zliumb1gZqvC/4M6F7aI9HaNjc6/PraY9Vv3cPc10xmZkxl1SNJMWwnmYeBlM3sSqAZeBTCzCQTNZAdyP8FZZ7FuA+a5+yHAvPC9iEiH3T3/Q15YXs73zp/EceMGRx2OtKCt05R/YmbzgDyC6188HNUH+Gobn33FzMY0G3wxcGr4+k8Ed2j+VsdCFpHe7sX3y/nV3A+49Kh8rj9hTNThSCvafOCYu7/ZwrAPOrm84e5eFr7eBAzv5HxEpJdau2U3X39kEZPzBvLTS49Qp34Si+wy17A25K2NN7ObzGyBmS2oqKhIYGQikqx2763npgcWkNrHuPdadeonu0QnmHIzywMI/29ubUJ3v8/dZ7r7zKFDhyYsQBFJTu7OrXMWs7piF3dfM52CQVlRhyRtSHSCeQq4Lnx9HfBkgpcvIt3UPS+v4Zn3NvHtcyfxiQl6Ynt3ELcEY2YPA28Ah5lZiZl9nuBCzbPMbBVwZvheROSAXvmggjuee58Lp47khpPGRh2OtFObnfyd5e5XtzLqjHgtU0R6ng1b9/DVh9/l0OED+Pll6tTvTnQvaxFJWtW1DXzhoSIA7r12BllpcTsmljjQ2hKRpOTu3PbEEt7ftIP/vf5oRg/uF3VI0kGqwYhIUvrDa2t5clEp3zz7ME49bFjU4UgnKMGISNJ5ffUWbn/2fc6dMoIvnTo+6nCkk5RgRCSpbKys5it/fpdxQ/pxx+VT1anfjSnBiEjSqKlr4OYHi6irb+Tea2fQP13dxN2Z1p6IRK6mroHXVm3hT2+s472NVfzhupmMG9o/6rDkICnBiEgktu+uZd77m3l+2SZeXbWF6roGBqSn8h8XTOaMSboPbk+gBCMiCbNh6x6eX76JF5aX8866bTQ6jBiYweUzCzhr8nCOHTuYtFS13PcUSjAiEjfuztKNO/Yllfc37QRg4ogBfPm0CZw9eQRT8geqI7+HUoIRkS5VW9/IW2u38vyycuauKKesqoY+BkePyeV750/i7MkjGDVYd0LuDZRgROSg7ayp46WVFTy/vJyX3t/Mzr31ZPTtwymHDuWWsw/j9InDyO2XFnWYkmBKMCLSKZuqanhhRTkvLC/njdVbqGtwBvdL49wjRnD25BGceMgQPRCsl1OCEZF2cXc+KN/FC2F/yuKSKgDGDM7iXz4xlrMmD2f6qEGk9FF/igSUYESkVQ2NTtH67Ty/bBMvrChn/dY9AEwtzOHWTx7G2ZOHM2FYf3XSS4uUYERkP9W1Dby6KuhPefH9zWzbXUtaSh+OHz+Ym04ex5mThjN8YEbUYUo3oAQjIlTtqeO5sOnr1VUV1NQ1MiAjldMnDuOsycM55dChDMjoG3WY0s0owYj0Ylt37eX3r63lgdfXsbu2gbzsDK6cWchZk0dwzNhcXfQoB0UJRqQX2ryzht+9soaH3txATX0D5x2Rx40njWNqQbb6U6TLKMGI9CKbqmq45+XVPPz2BuoaGrlo6ki+cvoEJgwbEHVo0gMpwYj0AiXb93DPy6t57J0SGty59Kh8vnTaBMYO0WOIJX6UYER6sPVbd/Pb+at5fGEJZjBrRiFfOnU8hbm6VYvEnxKMSA+0pmIXd8//kCcXlZLSx7jm2FF84ZTx5OdkRh2a9CJKMCI9yAflO7n7xQ95ekkpaal9uO74MXzhlHG6bkUioQQj0gMsL93B3fNX8ezSTWT2TeHGk8Zxw0njGDogPerQpBdTghHpxt4rqeKuF1fxwvJy+qen8uVTJ/C5E8fqzsWSFJRgRLqhhRu285t5q5i/soKBGal848xD+JcTxpKdpavtJXkowYh0I2+v3cZd81bx2odbGJTVl1s/eRifPX60buMiSUkJRiTJuTtvrN7KnfNW8dbabQzpn8a3z53IZ44bTb90/YQleWnrFElS7s4rq7Zw17xVFK3fzrAB6fzHBZO5+phRZKbpQV6S/JRgRJKMuzNvxWZ+8+IqFpdUMTI7g/+8+HAun1moJ0RKt6IEI5IkGhud55dv4jcvfsiy0h0U5mZy+6VHcNn0At3VWLolJRiRiDU0Os+8V8bdL37IyvKdjB3SjztmHcklR+XTN0WJRbovJRiRiKzdspu5y8t55J0NrK7YzYRh/bnzqmmcf0QeqUos0gMowYgkSEOjs3DDduYuL+eFFeWsqdgNwBH52dx9zVGcOyWPlD56Fov0HEowInG0a289r35QwdwVm5m/Mni+fd8U47hxg7nu+DGcMWkYBYN0Z2PpmSJJMGa2DtgJNAD17j4zijhE4qGsqpq5KzYzd3k5b6zeSm1DI9mZfTl94jDOmDSMkw8dykBdGCm9QJQ1mNPcfUuEyxfpEu7OstIdvLC8nLkryllWugOAMYOz+Ozxozlz8nBmjh6kfhXpddREJtIJNXUNvLFmK/NWlDNvxWbKqmowgxmjBnHbuRM5c9Jwxg/tp+fbS68WVYJx4Hkzc+Bed7+v+QRmdhNwE8CoUaMSHJ7Ix23dtZf5KyuYu7ycV1ZVsKe2gay0FE4+ZCj/etYwTp84jMH9dXt8kSZRJZgT3X2jmQ0DXjCz9939ldgJwqRzH8DMmTM9iiCld3N3VlfsZu6KcuYuL2fhhu00OgwfmM6njsrnzMnDOX7cYF1dL9KKSBKMu28M/282s78AxwCvHPhTIvFX39DIgvXbmbeinLkrNrN2S3Aq8eEjB/LV0w/hrMnDOXzkQDV9ibRDwhOMmfUD+rj7zvD12cCPEh2HSJOdNXW88sEW5q4o58X3N1NVXUdaSh+OHz+Yz504ljMmDmOknmUv0mFR1GCGA38JjwBTgT+7+z8iiEN6qfqGRlaW7+SdtduY9/5m3lyzlboGZ1BWX86YNIyzJg3npEOH0l+3whc5KAn/Bbn7GmBqopcrvZO7U7ytmkUllSwuDv6WllZRU9cIwLih/fjcJ8Zy5uThTB81SFfSi3QhHaJJj7Jtdy2Lw2SyKEwo2/fUAZCe2ocp+dlcc8xophZmc1ThIEYN1lX0IvGiBCPdVnVtA8tKq4JEUlLF4uJKNmzbA4AZHDpsAGdNHs7UwhymFuRw2IgBujuxSAIpwUi30NDorNq8M6yZBMlkZflOGhqDM9jzczKZWpjNp48dxdTCHKbkZ6sPRSRi+gVK0nF3NlZWs7i4isUlQVPX0o1V7KltAGBgRipTC3P40qTxTC3I4cjCbIYNyIg4ahFpTglGIle5p3ZfE9fi4koWl1SyZVctAGkpfZg8ciBXzCxkamE2UwtyGDO4H33UGS+S9JRgJKFq6hpYXrZjXzJZVFzJuq0f9ZuMH9qfUw4dxrTCbKYW5jBxxEA9Llikm1KCkbhpaHTWVOwKO+ErWVxcxYqyHdSH/SYjBmYwtTCbK44uZFpBDlMKsnUbe5EeRAlGuoS7U1ZVE9RKwtOEl27cwa699QAMSE/lyMJsbjp5HEcW5DCtMIcR2eo3EenJlGCkU6qq61iy73qToDO+YudeAPqmGJPzBnLp9HymFuQwtTCHcUPUbyLS2yjBSJtq6hpY0dRvEnbGrwlvAgnB1fAnTRgSXG9SmMOkvAGkp+oOwyK9nRKM7Kex0VmzZde+a00Wl1SyomwHdQ1Bv8mwAelMK8zhshkFTC3I4YiCbLIz1W8iIh+nBNPLbaqqiemEr+S9kip2hv0m/dNTObIgmxtOGsdU9ZuISAcpwfQilXtqWVa6Y989uhaXVFK+46N+k0l5A7nkqHymFuYwrTCbcUP6q99ERDpNCaYHqWtopKyyhg3b9uz7K962h/XbdrNh6x521NTvm3bckH6cMH4IUwuyw36TgXoyo4h0KSWYbsTdqaqu+1gCaXpdWlmz795cEFwFX5CbyajcLKaPGkThoCwm5g3gyPwcsrPUbyIi8aUEk2Rq6xspraxuMYFs2LaHnTG1EIAh/dMoDBPIJdOyKMzNYnRuFqMGZzF8QIaauEQkMkowCebuVO5puRayfuseyqqqiamEkJbah8JBQS1k5uhBFOZmMSpMIIWDsuinOwaLSJLS3qmLNTY6W3fXUlpZTVlVNRsrayirrKZke/W+ZNJ0llaTIf3TGZWbydFjBjEqN59Rg/sFSSQ3i2ED0lULEZFuSQmmg3bW1FFaWUNpVXWQRCprKK2sprSqmrKqGsoqa6htaNzvMxl9+5Cfk8nowf04ZmzuR7WQ3CwKczPJStNqEJGeR3u2GHvrG9hUVRMkkLAGUlpVs18iaV77SOljjBiYQV52BlMLcjhnSgYjszMZmZNJXnYG+TmZ5GT1xUy1EBHpXXpNgmlsdCp27Q0TR1jriEkkGytr2LJr78c+N7hfGnk5GYwenMXx4weTl53ByJxMRuYE/4f2TydVj+EVEfmYHp1gHnhjHU8vKaO0spryHTX7bnfSJCstJUwWmUzKG0he9keJo6kGomtDREQ6p0cnmD21DeAwc/Qg8sKkMbKpBpKdycDMVDVdiYjESY9OMDefMp6bTxkfdRgiIr2SOg9ERCQulGBERCQulGBERCQulGBERCQulGBERCQulGBERCQulGBERCQulGBERCQulGBERCQulGBERCQulGBERCQuIkkwZnaOma00sw/N7LYoYhARkfhKeIIxsxTgv4FzgcnA1WY2OdFxiIhIfEVRgzkG+NDd17h7LfAIcHEEcYiISBxFcbv+fKA45n0JcGzziczsJuCm8O0uM1uZgNgAhgBbErSsjkjWuCB5Y0vWuCB5Y0vWuCB5Y0vmuEZHGUDSPg/G3e8D7kv0cs1sgbvPTPRy25KscUHyxpascUHyxpascUHyxpbkcY2JMoYomsg2AoUx7wvCYSIi0oNEkWDeAQ4xs7FmlgZcBTwVQRwiIhJHCW8ic/d6M/sK8ByQAvzR3ZclOo4DSHizXDsla1yQvLEla1yQvLEla1yQvLEprlaYu0cdg4iI9EC6kl9EROJCCUZEROKi1yaYtm5XY2Ynm9lCM6s3s1lJFNe/mtlyM1tiZvPMLGHnubcjtpvN7D0zW2RmryXqDg3tvfWQmV1mZm5mCTmltB3ldb2ZVYTltcjMbkhEXO2JLZzminBbW2Zmf06GuMzsVzHl9YGZVSYirnbGNsrM5pvZu+Hv87wkiWt0uK9YYmYvmVlBIuICwN173R/ByQWrgXFAGrAYmNxsmjHAkcADwKwkius0ICt8/UXg0SSKbWDM64uAfyRDXOF0A4BXgDeBmckQF3A9cHci1l8nYjsEeBcYFL4flgxxNZv+qwQnCSVLmd0HfDF8PRlYlyRxzQauC1+fDjyYqG2tt9Zg2rxdjbuvc/clQGOSxTXf3feEb98kuI4oWWLbEfO2H5CIM0jae+uh/wR+DtQkIKaOxBWF9sR2I/Df7r4dwN03J0lcsa4GHk5AXNC+2BwYGL7OBkqTJK7JwIvh6/ktjI+b3ppgWrpdTX5EscTqaFyfB56Na0QfaVdsZvZlM1sN/H/A15IhLjObDhS6+98TEE+74wpdFjZdzDGzwhbGx0N7YjsUONTM/mlmb5rZOUkSFxA0+wBj+WjHGW/tie0HwGfMrAR4hqCGlQxxLQYuDV9/ChhgZoMTEFuvTTDdnpl9BpgJ3BF1LLHc/b/dfTzwLeB7UcdjZn2AXwK3RB1LC/4GjHH3I4EXgD9FHE+sVIJmslMJagq/M7OcKANq5ipgjrs3RB1IjKuB+929ADgPeDDc/qL2TeAUM3sXOIXgzikJKbdk+PJRSNbb1bQrLjM7E/gucJG7702m2GI8AlwSz4BCbcU1AJgCvGRm64DjgKcS0NHfZnm5+9aY9fd7YEacY2p3bARHwk+5e527rwU+IEg4UcfV5CoS1zwG7Yvt88BjAO7+BpBBcMPJSONy91J3v9TdjyLYb+DulXGOa9/Ce90fwdHZGoIqdlPH2OGtTHs/ievkbzMu4CiCTr1Dkq3MYmMCLgQWJENczaZ/icR08renvPJiXn8KeDOJ1uU5wJ/C10MImmEGRx1XON1EYB3hheJJVGbPAteHrycR9MHENcZ2xjUE6BO+/gnwo4SVW6IWlGx/BFXYD8Kd9XfDYT8iqBUAHE1wFLcb2AosS5K45gLlwKLw76kkKrM7gWVhXPMPtKNPZFzNpk1Igmlned0eltfisLwmJtG6NIKmxeXAe8BVyRBX+P4HwM8SVVYdKLPJwD/D9bkIODtJ4poFrAqn+T2Qnqgy061iREQkLnprH4yIiMSZEoyIiMSFEoyIiMSFEoyIiMSFEoyIiMSFEoyIiMSFEoz0WOGt+R+KeZ8a3h7/6fD99WZ2d5yWfcnBPK7AzHLM7EtdGZNIoinBSE+2G5hiZpnh+7NI3C2BLiG48K6zcgAlGOnWlGCkp3sGOD983enbu5vZ1eHD1Jaa2c9jhu+KeT3LzO43sxMInodzR/hgrPHhg57uDN8vNbNjws/8wMy+GTOPpWY2BvgZMD6cPqluaCrSXkow0tM9AlxlZhkED5B7q6MzMLORBM+SOR2YBhxtZpe0Nr27vw48Bdzq7tPcfXU4KsvdpxHUTP7YxmJvA1aHn7+1ozGLJAMlGOnRPHho3BiC2ssznZzN0cBL7l7h7vXA/wEnd2I+D4cxvQIMTLLb34t0udSoAxBJgKeA/yJ4tklXP2gp9mZ+GR2Ytul9Pfsf6LU1D5FuQzUY6Q3+CPzQ3d/r5OffJnhg0xAzSyGoDb0cjis3s0nhg6U+FfOZnQTPool1JYCZnQhUuXsVwW3np4fDpxPcdr21z4t0K0ow0uO5e4m739XK6OvNrCTmr6CFz5cR9InMJ7gVe5G7PxmOvg14GngdKIv52CPArWb2rpmND4fVhE8VvIfg4VQAjwO5ZrYM+ArBLdVx963AP8NOf3XyS7ek2/WLJICZvQR8090XRB2LSKKoBiMiInGhGoxIDDN7C0hvNvjag+i/Eem1lGBERCQu1EQmIiJxoQQjIiJxoQQjIiJxoQQjIiJx8f8DUhC/ctgt/OsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_separation(df_with_ML, x_variable='ML_output')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "This separation and <span style=\"color:blue\">S</span>/<span style=\"color:red\">B</span> is better than any of the individual variables could ever have achieved, nice!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<a id='ML_output_data'></a>\n",
    "\n",
    "## ML_output data distributions\n",
    "\n",
    "Now we can take a look at the combined measured & simulated `ML_output` distribution.\n",
    "\n",
    "<CENTER><img src=\"images/ML_output_data_meme.jpeg\" style=\"width:50%\"></CENTER>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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": [
    "plot_data(df_with_ML, x_variable='ML_output')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "Hmm... <span style=\"color:blue\">signal</span> is still covered by the Uncertainty..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## How does $t\\bar{t}Z$ look?\n",
    "\n",
    "Looking at the diagram for <span style=\"color:blue\">signal</span>, we expect at least 6 jets, including at least 2 b-jets.\n",
    "\n",
    "<CENTER><img src=\"images/feynman_diagrams/ttZ_diagram.png\" style=\"width:27%\"></CENTER>\n",
    "\n",
    "Let's make a further selection for >=6 jets & >=2 b-jets, then see how `ML_output` looks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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": [
    "post_selected_df = df_with_ML[(df_with_ML['NJets']>=6) & # select at least 6 jets\n",
    "                              (df_with_ML['NBJets']>=2)] # select at least 2 b-jets\n",
    "\n",
    "plot_data(post_selected_df, x_variable='ML_output')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "We can finally see a little bit of <span style=\"color:blue\">signal</span> not covered by Uncertainty between 0.8-0.9 in `ML_output`\n",
    "\n",
    "We can completely eliminate <span style=\"color:gray\">tt background</span> and achieve <span style=\"color:blue\">S</span>/<span style=\"color:red\">B</span>~15% by selecting `ML_output>0.8`.\n",
    "\n",
    "<a id='going_further'></a>\n",
    "\n",
    "## Going further\n",
    "\n",
    "Improvement can be made, but this technique of isolating <span style=\"color:blue\">signal</span> at high `ML_output` will allow us to make precise measurements of the <span style=\"color:blue\">signal</span> process.\n",
    "\n",
    "Maybe you'd like to try some of these improvements?\n",
    "\n",
    "There are a number of things you could try: \n",
    "\n",
    "* **Try different selections** in '[Selections](#selections)'. \n",
    "* **Add `Mll` in `ML_inputs`** in '[Correlations](#correlations)'. Does it lead to overtraining? \n",
    "* **Try a different train_test_split** than the default 75% in '[Machine Learning setup](#ML_setup)'. You may find the [sklearn documentation on train_test_split](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html) helpful. Does it change the results?\n",
    "* **Try a different scaler** than `StandardScaler` in '[Machine Learning setup](#ML_setup)'. You may find the [sklearn documentation on preprocessing](https://scikit-learn.org/stable/modules/preprocessing.html) helpful.\n",
    "* **Try other machine learning algorithms** than `MLPClassifier` in '[Machine Learning setup](#ML_setup)'. You may find [sklearn documentation on supervised learning](https://scikit-learn.org/stable/supervised_learning.html#supervised-learning) helpful.\n",
    "* **Modify classifier hyperparameters** in '[Machine Learning setup](#ML_setup)'. For `MLPClassifier`, you may find [sklearn documentation on `MLPClassifier`](https://scikit-learn.org/stable/modules/generated/sklearn.neural_network.MLPClassifier.html) helpful.\n",
    "\n",
    "With each change, keep an eye on the data distributions, separations, correlations, overtraining and ROC. \n",
    "\n",
    "Let us know if you find high separations and performance! As long as there isn't overtraining of course ;)\n",
    "\n",
    "<a id='conclusion'></a>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Conclusion\n",
    "\n",
    "Chucking everything into machine learning means we only have 1 variable to optimise. \n",
    "\n",
    "<span style=\"color:blue\">Signal</span> and <span style=\"color:red\">background</span> distributions are separated more when looking at ML output. \n",
    "\n",
    "Machine learning achieves higher <span style=\"color:blue\">S</span>/<span style=\"color:red\">B</span> than individual variables, because it finds multi-dimension correlations that give better <span style=\"color:blue\">S</span>/<span style=\"color:red\">B</span> classification.\n",
    "\n",
    "Hope you've enjoyed this notebook on Machine Learning <span style=\"color:blue\">signal</span> v <span style=\"color:red\">background</span> classification!\n",
    "\n",
    "<CENTER><img src=\"images/conclusion_meme.jpeg\" style=\"width:100%\"></CENTER>"
   ]
  }
 ],
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