{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Classification with a control channel: Don't cheat yourself!\n",
    "\n",
    "Gilles Louppe -- [@glouppe](https://twitter.com/glouppe) <br />\n",
    "Tim Head -- [@betatim](https://twitter.com/betatim)\n",
    "\n",
    "Last changed on August 4, 2015."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note\n",
    "\n",
    "The conclusions here apply when following the protocol used in the Kaggle [Flavours of physics](https://www.kaggle.com/c/flavours-of-physics/) challenge.\n",
    "\n",
    "\n",
    "# Abstract\n",
    "\n",
    "In High Energy Physics classifiers are often trained on a mixture of simulated and real samples/events. In this notebook we show how and why checks on control channels to compare the classifier's response on real and simulated events/samples can be bypassed (accidentally or on purpose). Overall, this study calls for caution: the obtained classifier might not be as reliable as estimated, even if tests on control channels pass. In particular, a passing control channel test does not guarantee that the classifier does not leverage discriminative simulation imperfections."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Notation\n",
    "\n",
    "Let us assume a set of _cases_ or _objects_ taken from a universe $\\Omega$. Let us further assume that each object is described by a set of _measurements_ and let us arrange these measurements in some pre-assigned order, i.e., take the input values to be $x_1, x_2, ..., x_p$, where $x_j \\in {\\cal X}_j$ (for $j=1, ..., p$) corresponds to the value of the input variable $X_j$. Together, the input values $(x_1, ..., x_p)$ form a $p$-dimensional input vector ${\\bf x}$ taking its values in ${\\cal X}_1 \\times ... \\times {\\cal X}_p = {\\cal X}$, where ${\\cal X}$ is defined as the input space. Similarly, let us define as $y \\in {\\cal Y}$ the value of the output variable $Y$, where ${\\cal Y}$ is defined as the output space. By definition, both the input and the output spaces are assumed to respectively contain all possible input vectors and all possible output values. \n",
    "\n",
    "_Note._ Input variables are also known as _features_ or _descriptors_, input vectors as _instances_, or _samples_ and the output variable as _target_ or _response_.\n",
    "\n",
    "_Note._ In High Energy Physics _samples_ are referred to as _events_, and _features_ as _variables_. We will use these terms interchangeably in this notebook."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Supervised learning\n",
    "\n",
    "Let us assume a learning set ${\\cal L}$ composed of $N$ pairs of input vectors and output values $({\\bf x}_1, y_1), ..., ({\\bf x}_N, y_N)$, where ${\\bf x}_i \\in {\\cal X}$ and $y_i \\in {\\cal Y}$. In this framework, the supervised learning task can be stated as learning a function (or _model_) $\\varphi : {\\cal X} \\mapsto {\\cal Y}$ from ${\\cal L}$. In particular, the objective is to find a model such that its predictions $\\varphi({\\bf x})$, also denoted by the variable $\\hat{Y}$, are as good as possible.\n",
    "\n",
    "The innput and output variables $X_1, ..., X_p$ and $Y$ are _random variables_ taking their joint values from ${\\cal X} \\times {\\cal Y}$ with respect to the joint probability distribution $P(X, Y)$, where $X$ denotes the random vector $(X_1, ..., X_p)$. That is, $P(X={\\bf x}, Y=y)$ is the probability that random variables $X$ and $Y$ take values ${\\bf x}$ and $y$ from ${\\cal X}$ and ${\\cal Y}$ when drawing an object uniformly at random from the universe $\\Omega$. Accordingly, trying to learn a model $\\varphi_{\\cal L}$ whose predictions are as good as possible can be stated as finding a model which minimizes or maximizes some scoring function in expectation over $X,Y$ (e.g., minimizing the expected prediction error or maximizing the expected ROC AUC).\n",
    "\n",
    "In practice, simplifying assumptions are made to solve supervised learning. In particular, one often assumes that the very best model, or at least a good approximation of it, lives in a family ${\\cal H}$ of candidate models, also known as _hypotheses_, of restricted structure (e.g., the family of linear models or the family of decision trees). In this sense, learning amounts to constructing or finding a model in ${\\cal H}$ for which the scoring function is as low (resp. high) as possible."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Classification of events in high energy physics\n",
    "\n",
    "In high energy physics, experimentalists build detectors for the observation and discovery of a phenomenon predicted by some theoretical model (e.g., the discovery of the Higgs boson as predicted by the Standard Model). To achieve this, classifiers are often built on simulated data and then used to evaluate real data as observed and recorded through the detector. Provided a classifier trained on simulated data transfers to real data, the goal is then to assess whether the predicted phenomenon exists with high level of confidence.\n",
    "\n",
    "In machine learning terms, let us assume a universe of objects, or _events_, each described by a vector of physical input values ${\\bf x} = (x_1, ..., x_p)$. Let us further assume that some of these events correspond to _signal_ ($y=s$), the phenomenon of interest, while others correspond to _background_ ($y=b$), a known and verified physical process.\n",
    "\n",
    "In this setting, given a learning set ${\\cal L}$ of (i) simulated signal and (ii) real data background, supervised learning algorithms can be used to find a model $\\varphi : {\\cal X} \\mapsto {\\cal Y}$, where ${\\cal Y} = \\{s, b\\}$, capable of distinguishing signal from background events given physical input values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Control channel\n",
    "\n",
    "The simulation is not be exempt of inaccuracies, often discriminative patterns exist between simulated and real data events. Therefore caution should be taken when learning a classifier $\\varphi$.  It should not exploit simulation artefacts to indirectly separate signal from background. Exploiting these imperfections in the simulation would lead to a model whose  performance on simulated events (separating simulated signal from simulated background) might significantly differ from its actual performance on data (separating real signal from real background), therefore making it far less reliable in an actual experiment pipeline. \n",
    "\n",
    "To prevent this, the learned classifier is required to not have a large discrepancy when applied to simulated and real data. In practice, this can be verified by evaluating whether the classifier behaves differently on simulated signal and real data signal from a _control channel_. A phenomenon with a topology similar to the phenomenon under study, but with a well-known and well-observed behavior. \n",
    "\n",
    "More formally, let us assume control channel events, comprising both simulated signal and real data signal from a phenomenon similar to the one we wish to observ, and respectively denoted as ${\\cal C}^\\text{sim} = \\{  {\\bf x}_1, ..., {\\bf x}_{N_\\text{sim}} \\}$ and ${\\cal C}^\\text{data} = \\{ {\\bf x}_1, ..., {\\bf x}_{N_\\text{data}}\\}$. We want to find a model $\\varphi$ which is as good as possible, while ensuring that the distributions of $\\varphi({\\bf x})$ are not significantly different for ${\\bf x} \\in {\\cal C}^\\text{sim}$ and for ${\\bf x} \\in {\\cal C}^\\text{data}$. \n",
    "\n",
    "_Example._ A _control channel test_ consists in requiring the Kolmogorov-Smirnov test statistic between the two samples $\\{ \\varphi({\\bf x}) | {\\bf x} \\in {\\cal C}^\\text{sim} \\}$ and $\\{ \\varphi({\\bf x}) | {\\bf x} \\in {\\cal C}^\\text{data} \\}$ to be strictly smaller than some pre-defined threshold $t$.\n",
    "\n",
    "Equivalently, this can be stated as restricting the family ${\\cal H}$ of candidate models to the family $\\bar{{\\cal H}} \\subseteq {\\cal H}$ for which the control channel test is satisfied. The open problem is then to adapt supervised learning algorithms to best navigate this restricted space of models. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Negative result: Control channel tests can be bypassed, even by chance\n",
    "\n",
    "_Proposition._ Assuming that\n",
    "1. control data can be distinguished from training data with high confidence,\n",
    "2. simulated features are more discriminative than they are in real data,\n",
    "\n",
    "Then, even by chance, a learning procedure exploring $\\bar{{\\cal H}}$ might capture and exploit differences between control and training data to pass the control channel test and overfit with respect to real data.\n",
    "\n",
    "_Corollary._ Even if the control channel test passes, the true performance of the classifier on real data may be significantly different (typically lower) than expected.\n",
    "\n",
    "_Corollary._ The choice of the control channel matters. The closer the distribution of the control signal to the distribution of the signal under study, the less likely the classifier is to exploit the defects, and is therefore more reliable for real data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Toy example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "As an illustrative example, let us consider an artificial classification problem between signal and background events, along with some close control channel data ${\\cal C}^\\text{sim}$ and ${\\cal C}^\\text{data}$. Let us assume an input space defined on three input variables $X_1, X_2, X_3$,\n",
    "such that \n",
    "\n",
    "- $X_1$ is irrelevant for discrimination between real data signal and real data background but, because of simulation imperfections, has discriminative power between simulated events and real data events ;\n",
    "- $X_2$ is discriminative between signal and background events ;\n",
    "- $X_3$ is discriminative between events from the original problem and the control channel, but has otherwise no discriminative power between signal and background events."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "np.random.seed(1)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams[\"figure.figsize\"] = 8, 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Generate data\n",
    "from scipy.stats import norm\n",
    "\n",
    "parameters = {\n",
    "    \"signal-data\":      [(0, 1),     (2, 1),     (0, 1)],\n",
    "    \"signal-sim\":       [(3, 1),     (2.2, 1),   (0, 1)],\n",
    "    \"background-data\":  [(0, 1),     (-1, 1),    (0, 1)],\n",
    "    \"control-data\":     [(0.3, 1.2), (2.3, 1.2), (3, 1)],\n",
    "    \"control-sim\":      [(3.3, 1.2), (2.5, 1.2), (3, 1)],\n",
    "}\n",
    "\n",
    "def build(label, n_samples=10000): \n",
    "    p = parameters[label]\n",
    "    \n",
    "    X = np.empty((n_samples, 3))\n",
    "    X[:, 0] = norm(*p[0]).rvs(n_samples)\n",
    "    X[:, 1] = norm(*p[1]).rvs(n_samples)\n",
    "    X[:, 2] = norm(*p[2]).rvs(n_samples)\n",
    "    \n",
    "    return X\n",
    "\n",
    "X_signal_data = build(\"signal-data\")\n",
    "X_signal_sim = build(\"signal-sim\")\n",
    "X_background_data = build(\"background-data\")\n",
    "X_control_data = build(\"control-data\")\n",
    "X_control_sim = build(\"control-sim\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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8MTGRDRs2sH///oK27Oxs4uPjqVevHgsXLuTVV1/VHeYVxT0L9w24bxjLzd9/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\neuUbOaU5b6dVpO0EKEsv61aeXt71qplX/Xx159WbC8OFucQ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      "text/plain": [
       "<matplotlib.figure.Figure at 0x112b56f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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FixYxePDgctuHGjp0KOPGjWPTpk2sWbOGxx9/vGTb1q1bMTNSU1PZt28fzzzz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\nqi8k6oUYkwEmOuo8EnYSJnSnSKkcFIhN1xL9Io5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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110ddd810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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N5/M5Pbf3SnW/BhdLRGoKFWiRA1tiaawA/uFS3axXbMjVbVjzUNCh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\nLSIikoJUoEVERFKQCrSIiEgK+v8mYxeytCvwkAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113128f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the distributions\n",
    "for i in range(3):\n",
    "    plt.hist(X_signal_data[:, i], normed=1, bins=50, histtype=\"step\", label=\"signal data\")\n",
    "    plt.hist(X_signal_sim[:, i], normed=1, bins=50, histtype=\"step\", label=\"signal sim\")\n",
    "    plt.hist(X_background_data[:, i], normed=1, bins=50, histtype=\"step\", label=\"background data\")\n",
    "    plt.hist(X_control_data[:, i], normed=1, bins=50, histtype=\"step\", label=\"control data\")\n",
    "    plt.hist(X_control_sim[:, i], normed=1, bins=50, histtype=\"step\", label=\"control sim\")\n",
    "    plt.legend(loc=\"best\")\n",
    "    plt.title(\"X%d\" % (i+1))\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now build a random forest on simulated signal versus real data background:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ROC AUC (simulated signal vs. data background) = 0.998003674128\n",
      "ROC AUC (data signal vs. data background) = 0.943449695\n"
     ]
    }
   ],
   "source": [
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.metrics import roc_auc_score\n",
    "from sklearn.cross_validation import train_test_split\n",
    "\n",
    "X = np.vstack((X_background_data, X_signal_sim))\n",
    "y = np.concatenate((np.zeros(len(X_background_data)), np.ones(len(X_signal_sim))))\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y,test_size=0.5, random_state=1)\n",
    "X_data = np.vstack((X_background_data, X_signal_data))\n",
    "y_data = np.concatenate((np.zeros(len(X_background_data)), np.ones(len(X_signal_data))))\n",
    "\n",
    "rf = RandomForestClassifier(n_estimators=100, random_state=1)\n",
    "rf.fit(X_train, y_train)\n",
    "\n",
    "print \"ROC AUC (simulated signal vs. data background) =\", roc_auc_score(y_test, rf.predict_proba(X_test)[:, 1])\n",
    "print \"ROC AUC (data signal vs. data background) =\", roc_auc_score(y_data, rf.predict_proba(X_data)[:, 1])  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the results show, the true performance on real data signal and real data background events is significantly lower that the expected performance of the forest, as estimated on simulated signal and real data background events."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Kolmogorov-Smirnov statistic on simulated signal and data signal events from the control channel is indeed quite large, suggesting that the random forest has picked discriminative features between simulated and real data events rather than discriminative features between signal and background events."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KS statistic = 0.6563\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import roc_curve\n",
    "\n",
    "def ks_statistic(pred_sim, pred_data):\n",
    "    y = np.concatenate((np.ones(len(pred_sim)), np.zeros(len(pred_data))))\n",
    "    pred = np.concatenate((pred_sim, pred_data))\n",
    "    fpr, tpr, _ = roc_curve(y, pred)\n",
    "    return np.max(np.abs(fpr - tpr))\n",
    "\n",
    "print \"KS statistic =\", ks_statistic(rf.predict_proba(X_control_sim)[:, 1],\n",
    "                                     rf.predict_proba(X_control_data)[:, 1]) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed, as the variable importances of the forest show, $X_1$ is used as discriminative variable, while it has in fact no power on real data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.46063437,  0.52114898,  0.01821664])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rf.feature_importances_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To prevent the classifier from using imperfections in the simulation as discriminative features we restrict our family of models to those for which the KS statistic is lower than `t=0.09`.\n",
    "\n",
    "The open problem is now how to best navigate $\\bar{{\\cal H}}$? For lack of a better procedure, we randomly explore a small fraction of the family of totally randomized trees:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ROC AUC (simulated signal vs. data background) = 0.986357983199\n",
      "ROC AUC (data signal vs. data background) = 0.90973817\n",
      "KS statistic = 0.0578\n"
     ]
    }
   ],
   "source": [
    "from sklearn.ensemble import ExtraTreesClassifier\n",
    "\n",
    "def find_best_tree(threshold, X_train, y_train, \n",
    "                              X_test, y_test, \n",
    "                              X_data, y_data, \n",
    "                              X_control_sim, X_control_data, n_trials=2000):\n",
    "    best_auc_test = 0\n",
    "    best_auc_data = 0\n",
    "    best_ks = 0\n",
    "    best_tree = None\n",
    "\n",
    "    for seed in range(n_trials):\n",
    "        clf = ExtraTreesClassifier(n_estimators=1, max_features=1,\n",
    "                                   max_leaf_nodes=5, random_state=seed)\n",
    "        clf.fit(X_train, y_train)\n",
    "\n",
    "        auc_test = roc_auc_score(y_test, clf.predict_proba(X_test)[:, 1])   \n",
    "        auc_data = roc_auc_score(y_data, clf.predict_proba(X_data)[:, 1])\n",
    "        ks = ks_statistic(clf.predict_proba(X_control_sim)[:, 1],\n",
    "                          clf.predict_proba(X_control_data)[:, 1])\n",
    "\n",
    "        if auc_test > best_auc_test and ks < threshold:\n",
    "            best_auc_test = auc_test\n",
    "            best_auc_data = auc_data\n",
    "            best_ks = ks\n",
    "            best_tree = clf\n",
    "    \n",
    "    return best_auc_test, best_auc_data, best_ks, best_tree\n",
    "\n",
    "auc_test, auc_data, ks, tree = find_best_tree(0.09, X_train, y_train, \n",
    "                                                    X_test, y_test, \n",
    "                                                    X_data, y_data, \n",
    "                                                    X_control_sim, X_control_data)\n",
    "\n",
    "print \"ROC AUC (simulated signal vs. data background) =\", auc_test\n",
    "print \"ROC AUC (data signal vs. data background) =\", auc_data\n",
    "print \"KS statistic =\", ks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What just happened? By chance, we have found a classifier that\n",
    "\n",
    "1. has seemingly good test performance (AUC=0.986 on simulated signal versus real data background); and\n",
    "2. passes the control channel test that we have defined.\n",
    "\n",
    "This classifier appears to be exactly the one we were seeking. It has very good performance on simulated signal versus real data background and it passes the KS test. This might lead us to believe that the classifier has not used the simulation artefacts of $X_1$. Therefore it should perform equally well on real data signal vs. real data background.\n",
    "\n",
    "Wrong. The expected ROC AUC of 0.91 on real data signal and real data background is significantly lower than our first estimate, suggesting that there is still something wrong. Indeed, inspecting the variable importances of the classifier reveals that $X_1$ is still used to discriminate between signal and background:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.60000595e-01,   8.39935498e-01,   6.39069727e-05])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tree.feature_importances_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now look at the tree we found:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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QevHiRUJCgr+/P+cQBCG54mVxMTExSUlJ4XsSRU1NTVVVlTMlJCRk1qxZ5ubmfKsCvQ66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\nQmCC\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.tree import export_graphviz\n",
    "from IPython.display import Image  \n",
    "with open(\"tree.dot\", 'w') as f:\n",
    "    f = export_graphviz(tree.estimators_[0], out_file=f, feature_names=[\"X1\", \"X2\", \"X3\"])\n",
    "!dot -Tpng tree.dot -o tree.png\n",
    "Image(\"tree.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, $X_3$ appears at the top of tree. By chance, we have found that splitting on this variable allows us to pass the control channel test (since it separates control data from the rest) thereby giving the other child nodes the freedom to exploit simulation artefacts to separate signal from background. This is illustrated by the later splits on $X_1$ in the left half of the tree. In other words, we managed to accidentally exploit differences between control and training data to circumvent the control channel test.\n",
    "\n",
    "Note that we never explicitly told the model to separate control data from training data. We merely explored the space of valid models at random and kept the best one which also passes the test. Unfortunately the obtained model is not as reliable nor as useful for an actual experiment pipeline as we would expect from a model that passes the control channel test.\n",
    "\n",
    "For this reason, we argue that any procedure exploring $\\bar{{\\cal H}}$ in some way or another (e.g., by random exploration, by repeatedly tuning hyper-parameters, by malicious intent, or by regularization injected in the learning procedure with respect to the KS statistic) will  suffer from the same problem, making the obtained models useless for real data. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Proof of concept: Finding τ → μμμ Kaggle challenge\n",
    "\n",
    "In light of the previous example, we illustrate a more efficient/malicious procedure than random exploration to obtain similar models in the context of the [Flavours of physics](https://www.kaggle.com/c/flavours-of-physics/) Kaggle challenge:\n",
    "\n",
    "1. learn to distinguish between training and control data,\n",
    "2. build a classifier on training data, with all the freedom to exploit simulation artefacts,\n",
    "3. assign predictions to samples predicted as control data, so that the test is passed (e.g., random predictions in the case of the KS statistic), otherwise predict using the classifier found in the previous step.\n",
    "\n",
    "This is an efficient method, as currently showed by our [1st place ranking](https://www.kaggle.com/c/flavours-of-physics/leaderboard)  (August 3rd, LB score=0.990873) on the leaderboard."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Control channel tests prevent some models to exploit simulation imperfections that are discriminative between simulation and real data, rather than between signal and background. However, as we have shown control channel tests do not exclude all such models. If control data can be distinguished from the training data, these differences may be exploited to put control data aside and then exploit simulation artefacts. Caution should therefore be taken: the obtained classifier might not perform as well as expected on real data, even if control channel tests pass.\n",
    "\n",
    "Unfortunately, without real signal data, it is difficult to know whether control channel tests are successful because the classifier truely does not exploit simulation imperfections or because control data has been distinguished from training data.\n",
    "\n",
    "For this reason, we stress that the choice of the control matters. The closer the distribution of the control channel signal to the distribution of the signal under study, the less likely it is that the classifier will manage to exploit the defects, and therefore it will be more reliable for real data. At the limit, the best control channel would be to use simulated signal and real data signal events from the _same_ phenomenon as the one under study. Unfortunately, this is a chicken and egg problem: we cannot collect real data signal events since establishing whether they exist or not is the original task."
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    "---\n",
    "\n",
    "_Suggestions, comments, ideas for a better test? Let's discuss! (Gilles Louppe -- [@glouppe](https://twitter.com/glouppe), Tim Head -- [@betatim](https://twitter.com/betatim))_"
   ]
  }
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