ModelEvaluation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/yueliyl/comp551-notebooks/blob/master/ModelEvaluation.ipynb)\n",
    "\n",
    "# Model Evaluation and Selection\n",
    "\n",
    "We are going to work a simulated dataset using the following function, which simulates 90 \"normal\" samples and 90 \"cancer\" samples from a two-dimensional Gaussian distributions.\n",
    "\n",
    "Note that the normal samples are sampled from 3 different Gaussian distributions with different means and covariances whereas the cancer samples are sampled from 2 different Gaussian distributions."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.model_selection import train_test_split\n",
    "np.random.seed(1234)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/jp/b2sr0gz54vj1pmbj1cxq4p5r0000gn/T/ipykernel_14805/2813543773.py:36: RuntimeWarning: covariance is not positive-semidefinite.\n",
      "  cancer1 = np.random.multivariate_normal(means,cov, npoints)\n",
      "/var/folders/jp/b2sr0gz54vj1pmbj1cxq4p5r0000gn/T/ipykernel_14805/2813543773.py:44: RuntimeWarning: covariance is not positive-semidefinite.\n",
      "  cancer2 = np.random.multivariate_normal(means,cov, npoints)\n"
     ]
    }
   ],
   "source": [
    "def simulate_prostate_cancer_data():\n",
    "    # simulate normal samples\n",
    "    npoints = 30\n",
    "    means=[70,70]\n",
    "    #cov = [[90,40],[40,50]]\n",
    "    cov = [[120,60],[60,50]]\n",
    "    np.random.seed(3)\n",
    "\n",
    "    normal1 = np.random.multivariate_normal(means,cov, npoints)\n",
    "    labels_normal1 = np.zeros((npoints, 1))\n",
    "    npoints = 30\n",
    "    means=[140,60]\n",
    "    #cov = [[90,40],[40,50]]\n",
    "    cov = [[160,30],[30,50]]\n",
    "\n",
    "    normal2 = np.random.multivariate_normal(means,cov, npoints)\n",
    "    labels_normal2 = np.zeros((npoints, 1))\n",
    "\n",
    "    npoints = 30\n",
    "    means=[250,110]\n",
    "    #cov = [[90,40],[40,50]]\n",
    "    cov = [[300,30],[30,30]]\n",
    "\n",
    "    normal3 = np.random.multivariate_normal(means,cov, npoints)\n",
    "    labels_normal3 = np.zeros((npoints, 1))\n",
    "\n",
    "    normal=np.concatenate((normal1,normal2,normal3))\n",
    "    labels_normal=np.concatenate((labels_normal1,labels_normal2,labels_normal3))\n",
    "\n",
    "    # simulate cancer samples\n",
    "    npoints = 50\n",
    "    means=[155,80]\n",
    "    #cov = [[150,50],[50,50]]\n",
    "    cov = [[4000,-600],[-600,50]]\n",
    "\n",
    "    cancer1 = np.random.multivariate_normal(means,cov, npoints)\n",
    "    labels_cancer1 = np.ones((npoints, 1))\n",
    "\n",
    "    npoints = 40\n",
    "    means=[50,80]\n",
    "    #cov = [[150,50],[50,50]]\n",
    "    cov = [[40,-60],[-60,50]]\n",
    "\n",
    "    cancer2 = np.random.multivariate_normal(means,cov, npoints)\n",
    "    labels_cancer2 = np.ones((npoints, 1))\n",
    "\n",
    "    cancer=np.concatenate((cancer1,cancer2))\n",
    "    labels_cancer=np.concatenate((labels_cancer1,labels_cancer2))\n",
    "\n",
    "    X= np.concatenate((normal,cancer), axis=0)\n",
    "    y = np.concatenate((labels_normal,labels_cancer), axis=0).squeeze() # to (N,)\n",
    "\n",
    "    return X, y\n",
    "\n",
    "X,y = simulate_prostate_cancer_data()"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state=1, shuffle=True)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can visualize the simulated data points as follows."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.clf()\n",
    "positive_train = y_train==1\n",
    "negative_train = y_train==0\n",
    "\n",
    "positive_test = y_test==1\n",
    "negative_test = y_test==0\n",
    "\n",
    "plt.plot(X_train[positive_train,0],X_train[positive_train,1],\"or\",label=\"Positive training examples\")\n",
    "plt.plot(X_train[negative_train,0],X_train[negative_train,1],\"ob\",label=\"Negative training examples\")\n",
    "\n",
    "plt.plot(X_test[positive_test,0],X_test[positive_test,1],\"xr\",label=\"Positive testing examples\")\n",
    "plt.plot(X_test[negative_test,0],X_test[negative_test,1],\"xb\",label=\"Negative testing examples\")\n",
    "\n",
    "plt.xlabel(\"CBC\")\n",
    "plt.ylabel(\"PSA\")\n",
    "plt.legend(loc='best')\n",
    "plt.savefig(\"train_test_scatterplot.png\", bbox_inches='tight', dpi=300)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Instead of importing our implementation of `KNN`, to keep things simple, let's use `scikit-learn`'s `KNN` implementation."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "knn = KNeighborsClassifier() # n_neighbors=5 (default)\n",
    "fit = knn.fit(X_train, y_train)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Evaluate the prediction accuracy on training and testing as follows"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9305555555555556\n",
      "0.9722222222222222\n"
     ]
    }
   ],
   "source": [
    "y_train_pred = fit.predict(X_train)\n",
    "y_test_pred = fit.predict(X_test)\n",
    "\n",
    "acc_train = np.sum(y_train_pred==y_train)/len(y_train)\n",
    "acc_test = np.sum(y_test_pred==y_test)/len(y_test)\n",
    "\n",
    "print(acc_train)\n",
    "print(acc_test)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Generalization error\n",
    "What we really care about is the performance of the model on new data.\n",
    "In other words, we want to see how our model **generalizes** to unseen data.\n",
    "An assumption that justifies deployment of our model on unseen data is the fact that our training and deployment data come from the *same* distribution. In fact very often we assume that there exists some distribution $p(x,y)$ over our features and labels, such that our training data is composed of independent samples from this distribution -- that is $x^{(n)}, y^{(n)} \\sim p(x, y)$ for all $x^{(n)}, y^{(n)} \\in \\mathcal{D}$. We assume that unseen data are also samples from the same distribution.\n",
    "\n",
    "**Generalization error** is the *expected error* of our model $f: x \\mapsto y$ under this distribution:\n",
    "$$\n",
    "Err(f) = \\mathbb{E}_{x,y \\sim p}[\\ell(f(x), y)].\n",
    "$$\n",
    "Here $\\ell$ is some *loss function* such as classification error $\\ell(y, \\hat{y}) = \\mathbb{I}(y \\neq \\hat{y})$ or square loss $\\ell(y, \\hat{y}) = (y - \\hat{y})^2$ that we often use in regression.\n",
    "\n",
    "## Test set\n",
    "Unfortunately, we don't have access to the true data distribution, we only have samples from this dataset. We can estimate the generalization error by setting aside a portion of our dataset that **we do not using in any way in learning or selecting the model**. This part of the dataset is called the **test set**. Let's use $\\mathcal{D}_{\\text{train}}$ and $\\mathcal{D}_{\\text{test}}$ to this partitioning of our original dataset $\\mathcal{D}$. The **test error** is\n",
    "$$\n",
    "\\widehat{Err}(f) = \\mathbb{E}_{x, y \\sim \\mathcal{D}_{\\text{test}}}[\\ell(f(x), y)] = \\frac{1}{|\\mathcal{D}_{\\text{test}}|} \\sum_{x,y \\in \\mathcal{D}_{\\text{test}}} \\ell(f(x), y).\n",
    "$$"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Model selection using validation data"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can split the data twice:\n",
    "\t1. first split the entire data into training and testing set\n",
    "\t2. then split the training data into training and validation set\n"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = \\\n",
    "    train_test_split(X, y, test_size=0.2, random_state=11)\n",
    "\n",
    "X_train, X_valid, y_train, y_valid = \\\n",
    "    train_test_split(X_train, y_train, test_size=0.2, random_state=11)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Use validation data to choose K in the range from 1 to 10"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9444444444444444\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_choices=[]\n",
    "valid_acc = []\n",
    "\n",
    "n_valid = y_valid.shape[0]\n",
    "\n",
    "for k in range(1,11):\n",
    "    knn = KNeighborsClassifier(n_neighbors=k) # create a KNN object (OOP)\n",
    "    knn.fit(X_train, y_train)\n",
    "    y_valid_pred = knn.predict(X_valid)\n",
    "    accuracy = np.sum(y_valid_pred == y_valid)/n_valid\n",
    "    model_choices.append(k)\n",
    "    valid_acc.append(accuracy)\n",
    "\n",
    "# use the best K to predict test data\n",
    "best_valid_K = model_choices[valid_acc.index(max(valid_acc))]\n",
    "knn = KNeighborsClassifier(n_neighbors=best_valid_K)\n",
    "knn.fit(X_train, y_train)\n",
    "y_test_pred = knn.predict(X_test)\n",
    "test_accuracy = np.sum(y_test_pred == y_test)/y_test.shape[0]\n",
    "print(test_accuracy)\n",
    "\n",
    "plt.clf()\n",
    "plt.plot(model_choices, valid_acc, marker='o', color='blue', label='validation')\n",
    "plt.plot(best_valid_K, test_accuracy, marker='*', color='red', label='testing')\n",
    "plt.xlabel(\"K\")\n",
    "plt.ylabel(\"Accuracy\")\n",
    "plt.legend(loc='best')\n",
    "\n",
    "# plt.show()\n",
    "plt.savefig(\"training_validation_testing.png\",bbox_inches='tight', dpi=300)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## True/false positive rates\n",
    "\n",
    "True negative (TN)\n",
    "* Negative example that is predicted to be negative\n",
    "* A person who is predicted to be healthy and in fact is healthy\n",
    "\n",
    "False positive (FP)\n",
    "* Negative example that is predicted to be positive\n",
    "* A person who is predicted to have cancer but in fact is healthy\n",
    "\n",
    "False negative (FN)\n",
    "* Positive example that is predicted to be negative\n",
    "* A person who is predicted to be healthy but in fact has cancer\n",
    "\n",
    "True positive (TP)\n",
    "* Positive example that is predicted to be positive\n",
    "* A person who is predicted to have cancer and in fact has cancer"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can compute a confusion matrix that contains TN, FP, FN, and TP as follows."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 Predicted Negative  Predicted Positive\n",
      "Actual Negative                  22                   0\n",
      "Actual Positive                   2                  12\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "### confusion matrix ###\n",
    "from sklearn.metrics import confusion_matrix\n",
    "\n",
    "cm = confusion_matrix(y_test, y_test_pred)\n",
    "\n",
    "cm_df = pd.DataFrame(cm, index=['Actual Negative','Actual Positive'],\n",
    "                     columns=['Predicted Negative', 'Predicted Positive'])\n",
    "print(cm_df)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## True/false positive rates\n",
    "\n",
    "True negative (TN)\n",
    "* Negative example that is predicted to be negative\n",
    "* A person who is predicted to be healthy and in fact is healthy\n",
    "\n",
    "False positive (FP)\n",
    "* Negative example that is predicted to be positive\n",
    "* A person who is predicted to have cancer but in fact is healthy\n",
    "\n",
    "False negative (FN)\n",
    "* Positive example that is predicted to be negative\n",
    "* A person who is predicted to be healthy but in fact has cancer\n",
    "\n",
    "True positive (TP)\n",
    "* Positive example that is predicted to be positive\n",
    "* A person who is predicted to have cancer and in fact has cancer"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can compute a confusion matrix that contains TN, FP, FN, and TP as follows."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 Predicted Negative  Predicted Positive\n",
      "Actual Negative                  22                   0\n",
      "Actual Positive                   2                  12\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "### confusion matrix ###\n",
    "from sklearn.metrics import confusion_matrix\n",
    "\n",
    "cm = confusion_matrix(y_test, y_test_pred)\n",
    "\n",
    "cm_df = pd.DataFrame(cm, index=['Actual Negative','Actual Positive'],\n",
    "                     columns=['Predicted Negative', 'Predicted Positive'])\n",
    "print(cm_df)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Receiver Operating Characteristic (ROC) Curve\n",
    "\n",
    "Instead of setting an arbitrary threhold on the probabilities score we can evalaute the method based on *all thresholds* and compute the ROC using the resulting True Postiive Rates (y-axis) and False Positive Rates (x-axis) as follows."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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Ky2cCKiLsE8Hp07BsGUREOGMTG2NCz5EjR0hLSyM6Opph7m1/lgQCF9TbR0VkkIh8JSJZIvJMMcsTRCRdRDaJyDYRmRTMeIqTng55eXDPPWA1SGNCi6oC8OWXX9KzZ08mTpxIY2vfLbeg1QhEJBJ4GRgAZAMbRCRNVbf7FfsesF1Vh4lIU+ArEXlHVS8HK66irFnImNCUnZ1Neno6Dz/8MH379vU6nJAWzKah24AsVd0FICLvASMA/0SgQH1x6nDxwAkgP4gxXeXMGViyxJkeObK69mqMqYy8vDxWrlzJ1q1buf/++8Oim+hgC2YiaAHs95vPBm4vUuYlIA04CNQHxqqqr+iGRGQKMAWgdevWVRbgokVw6RLcdRfccEOVbdYYEyR5eXmoKqpKamoqcdZXfJUI5jWC4q7UaJH5+4EM4AagB/CSiFzTCbiqvqaqKaqa0rRp0yoLsLBvIWsWMqZmu3jxImlpacyePZvo6GgGDRpkSaAKBTMRZAOt/OZb4pz5+5sEzFFHFrAb6BTEmK44fx4WLnSmH3qoOvZojKmIrKwsXnnlFSIjI3nI/lmDIphNQxuAZBFJAg4A44BHipTZB/QHPhKR64GOwK4gxnTF0qVOMrjtNqjC1iZjTBU5d+4csbGxVxJA27ZtvQ6p1gpaIlDVfBH5PrAUiATeVNVtIjLVXf4q8J/ADBHZgtOU9LSqHg9WTP4K7xayLqeNqVlUlS1btvDhhx8yevRokpKSvA6p1pPC+3BDRUpKin7++eeV2salS9C0qXPXUFYWtG9fRcEZYyolPz+f999/n9zcXIYPH84NdhdHlRGRjaqaUtyysHyyeNkyJwnccoslAWNqAlXl6NGjXH/99fTo0YOOHTtaJ3HVKCwHprFmIWNqjpycHGbMmMHSpUtRVbp06WJJoJqFXY3g8mWYP9+ZtttGjfHWl19+SVpaGvfccw+33Xab9Q/kkbBLBKtWwalTcNNNEObjVRvjmcOHDxMbG0vLli357ne/S6NGjbwOKayFXdOQ9S1kjHfy8/NZuXIlb7/9NsePHyc+Pt6SQA0QVjWC/HxnbGKwRGBMdVNVZsyYQf369Zk6dSr169f3OiTjCqtEsHYtHD8ON97oNA0ZY4Lv8uXLbNmyhZ49ezJ69GgSEhLsWkANE1ZNQ/59C9nfoTHBt3PnTqZNm8b+/fspKCigYcOGlgRqoLCpERQUwJw5zrTdNmpM8O3atYv09HSGDh1Khw4dvA7HlCJsEsG6dXD4MCQlOQ+SGWOCIzMzk8jISJKTk0lNTaVu3bpeh2TKEHDTkIjUC2YgwbZokfPzoYesWciYYDh79izvv/8+K1asIDY2FhGxJBAiykwEInKniGwHMt357iLyStAjq2K5uc5P67/KmOBIT0+ncePGTJ06lVatWpW9gqkxAmka+h+cAWTSAFR1k4jcE9SojDEh4dSpU6xatYrBgwczduxYIiLC6v6TWiOgawSqur/Ilf6C4IRjjAkFqsqGDRtYvXo1vXv3JioqypJACAskEewXkTsBFZFo4Ie4zUTGmPB0/Phxtm/fzuOPP06TJk28DsdUUiCJYCrwZ5zB6LOBD4GnghmUMabmKSgoYN26dVy6dIn77ruPxx57zOuQTBUJJBF0VNVv+78hIncBnwQnJGNMTXPo0CHS0tKoV68eQ4cO9TocU8UCSQR/AXoG8J4xppbx+XxERETw9ddfc/vtt9O9e3d7MrgWKjERiEhv4E6gqYj8h9+iBjhjEBtjarF9+/aRnp7O2LFjueceu1GwNiutRhANxLtl/LsJzAWs705jaqnLly+zfPlyMjMzGTJkiF0MDgMlJgJVXQOsEZEZqrq3GmMyxnjk8uXLANSpU4ennnqK2NhYjyMy1SGQawTnReQPwE1ATOGbqvqtoEVljKlW58+f58MPP+TChQuMHz+egQMHeh2SqUaBPAHyDvAlkAT8H2APsCGIMRljqtGOHTuYNm0adevWZZR1zRuWAqkRJKrqdBH5N7/mojXBDswYE1xnz54lLi6O6OhoxowZY/0DhbFAEkGe+/OQiDwAHARaBi8kY0wwqSoZGRksX76cMWPG0LZtW69DMh4LJBE8JyIJwI9xnh9oAPwomEEZY4IjPz+fWbNmceHCBSZMmECzZs28DsnUAGUmAlVd4E6eBu6FK08WG2NChM/n48iRIzRv3pxevXpx4403Widx5ooS/xJEJFJExovIT0Skq/veUBFZB7xUbREaYyrl2LFjvPXWW6xYsQJVpVOnTpYEzFVKqxFMB1oBnwEvisheoDfwjKrOq4bYjDGVlJmZyYIFC+jXrx8pKSnWPYQpVmmJIAXopqo+EYkBjgMdVPVw9YRmjKmogwcPEhcXR6tWrZgyZQoJCQleh2RqsNLqh5dV1QegqheBHeVNAiIySES+EpEsEXmmhDL9RCRDRLbZbanGVE5eXh7Lli3j3Xff5cSJE8THx1sSMGUqrUbQSUQ2u9MCtHfnBVBV7VbahkUkEngZGIAzjsEGEUlT1e1+ZRoCrwCDVHWfiFxX8UMxJrypKjNmzKBRo0akpqZSr149r0MyIaK0RNC5ktu+DchS1V0AIvIeMALY7lfmEWCOqu4DUNWjldynMWHn0qVLbN68mZSUFMaMGWM1AFNupXU6V9mO5loA+/3ms4Hbi5S5EYgSkdU4PZz+WVX/WnRDIjIFmALQunXrSoZlTO3x9ddfs2DBAtq3b4/P57MkYCokoMHrK6i42xO0mP3fCvQHYoF/ish6Vd1x1UqqrwGvAaSkpBTdhjFhaefOnSxatIgRI0bQrl07r8MxISyYiSAb5/bTQi1xuqcoWua4qp4DzonIWqA7sANjzDVUlW3bthEVFcWNN95Iamoq0dHRXodlQlxAT5WISKyIdCzntjcAySKSJCLRwDggrUiZ+cDdIlJHROJwmo4yy7kfY8JCbm4uf//731m7di3x8fGIiCUBUyXKrBGIyDDgBZwRy5JEpAfwG1UdXtp6qpovIt8HluIMbfmmqm4Tkanu8ldVNVNElgCbAR/whqpurdQRGVNLLVy4kGbNmjF69Gjq1AlmZd6Em0D+mn6NcwfQagBVzRCRtoFsXFUXAYuKvPdqkfk/AH8IZHvGhJsTJ06watUqHnjgAcaOHWtdQ5igCCQR5KvqaXs03Zjq4/P5+PTTT/noo4/o06cP0dHRlgRM0ASSCLaKyCNApIgkAz8E1gU3LGPC24kTJ8jKyuKJJ56gcePGXodjarlATjF+gDNe8SXgXZzuqH8UxJiMCUsFBQWsXr2aZcuW0aRJEyZMmGBJwFSLQGoEHVX1F8Avgh2MMeHqwIEDpKWl0bBhQx544AGvwzFhJpBE8EcRaQ78A3hPVbcFOSZjwobP5yMiIoLdu3fTp08funbtal1Fm2pXZtOQqt4L9AOOAa+JyBYR+WWwAzOmttu9ezcvv/wyOTk59OnTh5tvvtmSgPFEQLchqOphVX0RmApkAL8KZlDG1GaXLl0iPT2defPmMXDgQBITE70OyYS5QB4o6wyMBUYDOcB7OAPZG2PK6dKlS0RERBAXF0dqaioxMTFeh2RMQNcI3gJmAQNVtWhfQcaYAJw7d44lS5aQl5fHuHHj6N+/v9chGXNFmYlAVe+ojkCMqa2++uor0tPT6datG/fee6/X4RhzjRITgYi8r6pjRGQLV3cfHdAIZcaEu9zcXOrVq0dMTAzjx4+nRYsWXodkTLFKqxH8m/tzaHUEYkxtoaps3LiRVatWMXbsWNq0aeN1SMaUqrQRyg65k0+p6tP+y0Tkd8DT165lTHjLz8/nnXfeIS8vj0cffZTrrrNhuE3NF8jtowOKeW9wVQdiTCjz+XwcOHCAOnXqcOedd/L4449bEjAho7RrBKnAU0A7Ednst6g+8EmwAzMmVBw5coS0tDTi4+MZN24cycnJXodkTLmUdo3gXWAx8N/AM37vn1HVE0GNypgQsX37dhYuXEj//v255ZZb7MlgE5JKSwSqqntE5HtFF4hIY0sGJpxlZ2dTr1492rRpw9SpU6lfv77XIRlTYWXVCIYCG3FuH/U/1VGgXRDjMqZGunz5MitXrmTbtm089NBDJCUleR2SMZVW2l1DQ92f9pduDM5toTNmzKBp06akpqYSFxfndUjGVIky7xoSkbtEpJ47/R0R+aOItA5+aMbUDBcvXmT9+vUAjB8/npEjR1oSMLVKILePTgPOi0h34GfAXuDtoEZlTA3x5Zdf8sorr5CTk4PP57NrAaZWCnTwehWREcCfVXW6iDwa7MCM8VpWVhbLli1j1KhR9nSwqdUCSQRnROR/AROAu0UkEogKbljGeENV2bx5M9HR0XTq1ImpU6cSFWV/7qZ2C6RpaCzOwPWPq+phoAXwh6BGZYwHTp8+zbvvvss///lPEhISEBFLAiYsBNIN9WEReQfoJSJDgc9U9a/BD82Y6rV48WJatWrFXXfdRWRkpNfhGFNtArlraAzwGfAwMAb4VERGBzswY6pDTk4O77//PhcvXmTs2LHcc889lgRM2AnkGsEvgF6qehRARJoCy4HZwQzMmGDy+XysW7eOdevW0bdvX6Kjo617CBO2AkkEEYVJwJVDgIPeG1MTqSonTpxg3759TJkyhYYNG3odkjGeCiQRLBGRpTjjFoNz8XhR8EIyJjjy8/NZs2YNBQUFDBw4kEceecTrkIypEQK5WPxTEXkI6IPT39Brqjo36JEZU4X2799PWloaTZo0YciQIV6HY0yNUtp4BMnAC0B7YAvwE1U9UF2BGVMVCgoKiIyMZP/+/dx777106dLF65CMqXFKa+t/E1gAjMLpgfQv5d24iAwSka9EJEtEnimlXC8RKbC7kUxV2rlzJy+99BI5OTnceeedlgSMKUFpTUP1VfV1d/orEfmiPBt2n0B+GWeoy2xgg4ikqer2Ysr9Dlhanu0bU5JLly6xZMkSdu/ezdChQ0lMTPQ6JGNqtNISQYyI3MI34xDE+s+ralmJ4TYgS1V3AYjIe8AIYHuRcj8APgB6lTN2Y65x8eJFIiMjSUhIIDU1lbp163odkjE1XmmJ4BDwR7/5w37zCnyrjG23APb7zWcDt/sXEJEWwEh3WyUmAhGZAkwBaN3aesA21zp79iyLFi1CVRk7diz9+vXzOiRjQkZpA9PcW8ltF/d0jhaZ/xPwtKoWlPYwj6q+BrwGkJKSUnQbJsxlZmayYMECevbsSd++fb0Ox5iQE8hzBBWVDbTym28JHCxSJgV4z00CTYAhIpKvqvOCGJepJU6fPk18fDzx8fF85zvfoXnz5l6HZExICmYi2AAki0gScAAYB1z1BI//MJgiMgNYYEnAlEVV+eyzz1izZg3jxo2z5kJjKiloiUBV80Xk+zh3A0UCb6rqNhGZ6i5/NVj7NrVXXl4eb7/tDJD3+OOP06RJE48jMib0lZkIxGm3+TbQTlV/445X3ExVPytrXVVdRJHuKEpKAKr6WEARm7BUUFDAwYMHadWqFX379qVdu3bWSZwxVSSQzuNeAXoD4935MzjPBxhTLQ4dOsTrr7/OunXrUFXat29vScCYKhRI09DtqtpTRP4FoKonRSQ6yHEZA8DWrVtZvHgxAwcOpFu3bpYAjAmCQBJBnvv0r8KV8Qh8QY3KhL29e/fSoEED2rVrR2pqKvHx8V6HZEytFUjT0IvAXOA6Efkt8DHwX0GNyoStS5cusXDhQj744ANyc3OJi4uzJGBMkAXSDfU7IrIR6I/zkNiDqpoZ9MhM2FFVZsyYQbNmzUhNTSU2NtbrkIwJC4HcNdQaOA+k+7+nqvuCGZgJH+fPnycjI4PevXvzne98h3r16nkdkjFhJZBrBAtxrg8IEAMkAV8BNwUxLhMGVJXt27ezZMkSbrrpJnw+nyUBYzwQSNPQzf7zItITeDJoEZmwsXPnTlavXs2YMWNo1apV2SsYY4Ki3E8Wq+oXImJdRpsKUVUyMjKoW7cunTt35sknn6ROnWD2dGKMKUsg1wj+w282AugJHAtaRKbWOnnyJOnp6Vy8eJHhw4cjIpYEjKkBAvkvrO83nY9zzeCD4IRjarMPP/yQ9u3b07t3byIiArlz2RhTHUpNBO6DZPGq+tNqisfUMseOHWPFihWMGDGCMWPG2JPBxtRAJSYCEanj9iDaszoDMrVDQUEBH3/8MZ999hn33nsvMTExlgSMqaFKqxF8hnM9IENE0oB/AOcKF6rqnCDHZkKUqnLy5EkOHTrElClTSEhI8DokY0wpArlG0BjIwRlXuPB5AgUsEZir5OXlsXr1anw+H/fffz/jxo3zOiRjTABKSwTXuXcMbeWbBFDIxg02V9mzZw/p6ek0b96cwYMHex2OMaYcSksEkUA8gQ1Cb8JUQUEBkZGRHD58mAEDBtCpUyevQzLGlFNpieCQqv6m2iIxIWfHjh0sWrSICRMmcMcdd3gdjjGmgkpLBHaLhynWxYsXWbRoEdnZ2YwYMYLExESvQzLGVEJpiaB/tUVhQoKqcuHCBaKiomjSpAlDhw4lOtoGqzMm1JWYCFT1RHUGYmq23NxcFi5cSGRkJGPGjOGee+7xOiRjTBWxjl5MmbZt28aiRYvo1asXffr08TocY0wVs0RgSnTy5EkaNGhAQkICEydO5Prrr/c6JGNMEFgiMNfw+XysX7+ejz/+mPHjx9tYAcbUcpYIzFXy8vKYOXMmUVFRPPHEEzRu3NjrkIwxQWaJwADOg2HZ2dm0adOG/v3707ZtW+skzpgwYYnAcODAAebPn0/Tpk1p3bo1SUlJXodkjKlGlgjC3JYtW1i6dCn3338/Xbt2tVqAMWHIEkGY2r17NwkJCbRv357U1FTq1avndUjGGI/YeIFh5uLFi6SnpzNv3jzOnj1LXFycJQFjwlxQE4GIDBKRr0QkS0SeKWb5t0Vks/taJyLdgxlPuFNVZsyYgYiQmppK69atvQ7JGFMDBK1pyB3v+GVgAJANbBCRNFXd7ldsN9BXVU+KyGDgNeD2YMUUrs6dO8cXX3xBnz59mDhxInFxcV6HZIypQYJZI7gNyFLVXap6GXgPGOFfQFXXqepJd3Y90DKI8YQdVWXz5s1MmzaNixcv4vP5LAkYY64RzIvFLYD9fvPZlH62PxlYXNwCEZkCTAGsOaMcsrKy+OSTT3jkkUe44YYbvA7HGFNDBTMRBDyymYjci5MIiu3RTFVfw2k2IiUlxUZHK4WqsnHjRmJjY+nSpQvt2rUjMjLS67CMMTVYMBNBNuDfSU1L4GDRQiLSDXgDGKyqOUGMp9bLyckhPT2d/Px8hg8fjohYEjDGlCmYiWADkCwiScABYBzwiH8BEWkNzAEmqOqOIMYSFlasWEGnTp247bbbiIiwO4ONMYEJWiJQ1XwR+T6wFIgE3lTVbSIy1V3+KvArIBF4xX2iNV9VU4IVU210+PBhVqxYwUMPPcTDDz9sTwYbY8otqE8Wq+oiYFGR9171m34CeCKYMdRW+fn5rF27lo0bN3LfffcRExNjScAYUyHWxUQIUlVOnTpFTk4OU6dOpX79+l6HZIwJYZYIQsjly5dZuXIlAIMGDeLhhx/2OCJjTG1gVxRDxK5du5g2bRoXLlywgeONMVXKagQ1XH5+PnXq1OHYsWMMGTKE5ORkr0MyxtQyViOowTIzM3nxxRc5ceIEt99+uyUBY0xQWI2gBrpw4QILFizg8OHDjBo1ysYNNsYElSWCGkRVOX/+PHXr1uWGG27gwQcfJCoqyuuwjDG1nCWCGuLUqVMsWLCAunXr8vDDD3PXXXd5HZIxJkxYIqgBtmzZwuLFi+nduzd33nmn1+EYY8KMJQIP5eTkkJCQQOPGjZk0aRJNmzb1OiRjTBiyu4Y8UFBQwMcff8z06dM5fPgwLVq0sCRgjPGM1QiqWV5eHm+99RaxsbFMmTKFhg0beh2SMSbMWSKoJvn5+WRnZ9O2bVsGDRpEq1atrJM4Y0yNYImgGuzbt4+0tDSaN29OmzZtbLhNY0yNYokgyDZv3syyZcsYPHgwXbp08TocY4y5hiWCIMnKyqJRo0YkJyeTnJxMbGys1yEZY0yx7K6hKnbhwgXmzZvHggULOH/+PLGxsZYEjDE1miWCKqSqzJgxg7p16/LUU0/RqlUrr0MyxpgyWdNQFTh79iwbN27knnvuYdKkScTExHgdkjHGBMxqBJWgqmRkZDBt2jTy8/Px+XyWBIwxIcdqBJWQlZXFp59+yoQJE2jWrJnX4RhjTIVYIignn8/Hhg0biIuLo2vXrrRv356ICKtYmdorLy+P7OxsLl686HUoJgAxMTG0bNmyXF3YWyIoh2PHjpGeno6IMGzYMETEng42tV52djb169enbdu29vdew6kqOTk5ZGdnk5SUFPB6lgjKYfXq1dx8882kpKTYP4QJGxcvXrQkECJEhMTERI4dO1au9SwRlOHQoUMsX76c0aNHM3r0aPtnMGHJ/u5DR0V+V5YISpCXl8eaNWvIyMhgwIABxMTE2D+DMaZWsqucxVBVcnNzyc3NZerUqXTv3t2SgDEemzt3LiLCl19+eeW91atXM3To0KvKPfbYY8yePRuAfv360bFjR7p3706vXr3IyMi4Uu706dNMnDiR9u3b0759eyZOnMjp06evLN+xYwdDhgyhQ4cOdO7cmTFjxnDkyJFKHcOJEycYMGAAycnJDBgwgJMnTxZb7s9//jNdu3blpptu4k9/+tOV93/961/TokULevToQY8ePVi0aFGl4ilkicDPpUuXWLhwIUuXLiUxMZGHHnqI+Ph4r8MyxgCzZs2iT58+vPfee+Va75133mHTpk089dRT/PSnP73y/uTJk2nXrh07d+5k586dJCUl8cQTTwDOdZEHHniA1NRUsrKyyMzMJDU1tdxt70U9//zz9O/fn6+//pr+/fvz/PPPX1Nm69atvP7663z22Wds2rSJBQsW8PXXX19Z/u///u9kZGSQkZHBkCFDKhVPIUsErqysLKZNm0ZBQQF9+/b1OhxjaiSR4LzKcvbsWT755BOmT59e7kRQqHfv3hw4cABw/t83btzIs88+e2X5r371Kz7//HN27tzJu+++S+/evRk2bNiV5ffeey9du3at0L4LzZ8/n0cffRSARx99lHnz5l1TJjMzkzvuuIO4uDjq1KlD3759mTt3bqX2W5awTwR5eXkAnDx5kuHDhzN8+HDrJM6YGmbevHkMGjSIG2+8kcaNG/PFF1+UextLlizhwQcfBGD79u306NGDyMjIK8sjIyPp0aMH27ZtY+vWrdx6661lbvPMmTNXmmmKvrZv335N+SNHjtC8eXMAmjdvztGjR68p07VrV9auXUtOTg7nz59n0aJF7N+//8ryl156iW7duvH444+X2LRUXmF7sVhV2b59O0uWLGHSpEn06tXL65CMqfFUvdnvrFmz+NGPfgTAuHHjmDVrFj179izx2p3/+9/+9rc5d+4cBQUFVxKIqha7bknvl6R+/fpXXXeoCp07d+bpp59mwIABxMfH0717d+rUcb6qU1NTefbZZxERnn32WX784x/z5ptvVnqfQU0EIjII+DMQCbyhqs8XWS7u8iHAeeAxVS1/qi+nCxcuMH/+fHJychgzZgyNGzcO9i6NMRWUk5PDypUr2bp1KyJCQUEBIsLvf/97EhMTrzkrPnHiBE2aNLky/84779C9e3eeeeYZvve97zFnzhxuuukm/vWvf+Hz+a70DODz+di0aROdO3fm6NGjrFmzpszYzpw5w913313ssnffffeawaiuv/56Dh06RPPmzTl06BDXXXddsetOnjyZyZMnA/Dzn/+cli1bXlm/0He/+91rLpRXVNCahkQkEngZGAx0AcaLSNEhugYDye5rCjAtWPE4FJ/vLFFRUbRp04Ynn3zSuoo2poabPXs2EydOZO/evezZs4f9+/eTlJTExx9/THJyMgcPHiQzMxOAvXv3smnTJnr06HHVNqKionjuuedYv349mZmZdOjQgVtuuYXnnnvuSpnnnnuOnj170qFDBx555BHWrVvHwoULryxfsmQJW7ZsuWq7hTWC4l7FjUg4fPhwZs6cCcDMmTMZMWJEscdc2GS0b98+5syZw/jx4wHnuaZCc+fOrfQ1i0LBvEZwG5ClqrtU9TLwHlD0qEcAf1XHeqChiDQPRjARESeZOPFtzp5dSp06dejdu/eV6pYxpuaaNWsWI0eOvOq9UaNG8e6771K3bl3+9re/MWnSJHr06MHo0aN54403SEhIuGY7sbGx/PjHP+aFF14AYPr06ezYsYMOHTrQvn17duzYwfTp06+UXbBgAX/5y19ITk6mS5cuzJgxo8Qz+EA988wzLFu2jOTkZJYtW8YzzzwDwMGDB6+6A2jUqFF06dKFYcOG8fLLL9OoUSMAfvazn3HzzTfTrVs3Vq1axf/8z/9UKp5CokFq9BOR0cAgVX3CnZ8A3K6q3/crswB4XlU/dudXAE+r6udFtjUFp8ZA69atb927d2+5Ytm0aRNz5y5l3bq7GDOmN088EfbXyI0JWGZmJp07d/Y6DFMOxf3ORGSjqqYUVz6Yp8TFXXEpmnUCKYOqvga8BpCSkhJw5jp+/DgNGzakadOm/OAHk/n1rxMDXdUYY8JGME+NswH/BviWwMEKlCm3goIC1qxZw1tvvcWRI0e44YYbSEy0JGCMMcUJZiLYACSLSJKIRAPjgLQiZdKAieK4AzitqoeKbqg88vLyeP311zlw4ABTpkyhRYsWldmcMQbntkoTGiryuwpa05Cq5ovI94GlOLePvqmq20Rkqrv8VWARzq2jWTi3j06q6P7y8vLYv38/7dq1Y+jQobRo0cL6BzKmCsTExJCTk0NiYqL9T9VwheMRlHfI3KDeNqOqi3C+7P3fe9VvWoHvVXY/e/bsIT09nVatWpGUlHTlnltjTOW1bNmS7OzsSvezY6pH4Qhl5RHy909u2rSJFStW8MADD9CxY0evwzGm1omKiirXaFcm9IRsItixYweNGzemY8eOdOzYsdxVIWOMMY6Qu6He5/MxZ84clixZwqVLl4iJibEkYIwxlRByNYKcnBzq1atHamoqUVFRXodjjDEhL2hPFgeLiBwDyvdo8TeaAMerMJxQYMccHuyYw0NljrmNqjYtbkHIJYLKEJHPS3rEurayYw4PdszhIVjHHHLXCIwxxlQtSwTGGBPmwi0RvOZ1AB6wYw4PdszhISjHHFbXCIwxxlwr3GoExhhjirBEYIwxYa5WJgIRGSQiX4lIlog8U8xyEZEX3eWbRaSnF3FWpQCO+dvusW4WkXUi0t2LOKtSWcfsV66XiBS4o+aFtECOWUT6iUiGiGwTkbJHYK/hAvjbThCRdBHZ5B5zhXsxrglE5E0ROSoiW0tYXvXfX6paq144XV7vBNoB0cAmoEuRMkOAxTgjpN0BfOp13NVwzHcCjdzpweFwzH7lVuL0gjva67ir4ffcENgOtHbnr/M67mo45p8Dv3OnmwIngGivY6/EMd8D9AS2lrC8yr+/amON4DYgS1V3qepl4D1gRJEyI4C/qmM90FBEmld3oFWozGNW1XWqetKdXY8zGlwoC+T3DPAD4APgaHUGFySBHPMjwBxV3QegqqF+3IEcswL1xRksIR4nEeRXb5hVR1XX4hxDSar8+6s2JoIWwH6/+Wz3vfKWCSXlPZ7JOGcUoazMYxaRFsBI4FVqh0B+zzcCjURktYhsFJGJ1RZdcARyzC8BnXGGud0C/Juq+qonPE9U+fdXyHU6F4DihlAqeo9sIGVCScDHIyL34iSCPkGNKPgCOeY/AU+rakEtGVkrkGOuA9wK9AdigX+KyHpV3RHs4IIkkGO+H8gAvgW0B5aJyEeqmhvk2LxS5d9ftTERZAOt/OZb4pwplLdMKAnoeESkG/AGMFhVc6optmAJ5JhTgPfcJNAEGCIi+ao6r1oirHqB/m0fV9VzwDkRWQt0B0I1EQRyzJOA59VpQM8Skd1AJ+Cz6gmx2lX591dtbBraACSLSJKIRAPjgLQiZdKAie7V9zuA06p6qLoDrUJlHrOItAbmABNC+OzQX5nHrKpJqtpWVdsCs4GnQjgJQGB/2/OBu0WkjojEAbcDmdUcZ1UK5Jj34dSAEJHrgY7ArmqNsnpV+fdXrasRqGq+iHwfWIpzx8GbqrpNRKa6y1/FuYNkCJAFnMc5owhZAR7zr4BE4BX3DDlfQ7jnxgCPuVYJ5JhVNVNElgCbAR/whqoWextiKAjw9/yfwAwR2YLTbPK0qoZs99QiMgvoBzQRkWzgfwNRELzvL+tiwhhjwlxtbBoyxhhTDpYIjDEmzFkiMMaYMGeJwBhjwpwlAmOMCXOWCEyN5PYWmuH3altK2bNVsL8ZIrLb3dcXItK7Att4Q0S6uNM/L7JsXWVjdLdT+LlsdXvcbFhG+R4iMqQq9m1qL7t91NRIInJWVeOrumwp25gBLFDV2SIyEHhBVbtVYnuVjqms7YrITGCHqv62lPKPASmq+v2qjsXUHlYjMCFBROJFZIV7tr5FRK7paVREmovIWr8z5rvd9weKyD/ddf8hImV9Qa8FOrjr/oe7ra0i8iP3vXoistDt/36riIx1318tIiki8jwQ68bxjrvsrPvz7/5n6G5NZJSIRIrIH0Rkgzh9zD8ZwMfyT9zOxkTkNnHGmfiX+7Oj+yTub4Cxbixj3djfdPfzr+I+RxOGvO572172Ku4FFOB0JJYBzMV5Cr6Bu6wJzlOVhTXas+7PHwO/cKcjgfpu2bVAPff9p4FfFbO/GbjjFQAPA5/idN62BaiH073xNuAWYBTwut+6Ce7P1Thn31di8itTGONIYKY7HY3Ti2QsMAX4pft+XeBzIKmYOM/6Hd8/gEHufAOgjjt9H/CBO/0Y8JLf+v8FfMedbojTB1E9r3/f9vL2Veu6mDC1xgVV7VE4IyJRwH+JyD04XSe0AK4HDvutswF40y07T1UzRKQv0AX4xO1aIxrnTLo4fxCRXwLHcHpo7Q/MVacDN0RkDnA3sAR4QUR+h9Oc9FE5jmsx8KKI1AUGAWtV9YLbHNVNvhlFLQFIBnYXWT9WRDKAtsBGYJlf+ZkikozTE2VUCfsfCAwXkZ+48zFAa0K7PyJTSZYITKj4Ns7oU7eqap6I7MH5ErtCVde6ieIB4G0R+QNwElimquMD2MdPVXV24YyI3FdcIVXdISK34vT38t8i8qGq/iaQg1DViyKyGqfr5LHArMLdAT9Q1aVlbOKCqvYQkQRgAfA94EWc/nZWqepI98L66hLWF2CUqn4VSLwmPNg1AhMqEoCjbhK4F2hTtICItHHLvA5Mxxnubz1wl4gUtvnHiciNAe5zLfCgu049nGadj0TkBuC8qv4NeMHdT1F5bs2kOO/hdBR2N05narg/UwvXEZEb3X0WS1VPAz8EfuKukwAccBc/5lf0DE4TWaGlwA/ErR6JyC0l7cOED0sEJlS8A6SIyOc4tYMviynTD8gQkX/htOP/WVWP4XwxzhKRzTiJoVMgO1TVL3CuHXyGc83gDVX9F3Az8JnbRPML4LliVn8N2Fx4sbiID3HGpV2uzvCL4IwTsR34QpxBy/8fZdTY3Vg24XTN/Huc2sknONcPCq0CuhReLMapOUS5sW11502Ys9tHjTEmzFmNwBhjwpwlAmOMCXOWCIwxJsxZIjDGmDBnicAYY8KcJQJjjAlzlgiMMSbM/X9zBnzNpVuubQAAAABJRU5ErkJggg==\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import roc_curve, roc_auc_score\n",
    "\n",
    "knn = KNeighborsClassifier() # create a KNN object (OOP)\n",
    "knn.fit(X_train, y_train)\n",
    "# column 0 is healthy\n",
    "# column 1 is cancer\n",
    "y_test_prob = knn.predict_proba(X_test)[:,1]\n",
    "fpr, tpr, thresholds = roc_curve(y_test, y_test_prob)\n",
    "roc_auc = roc_auc_score(y_test, y_test_prob)\n",
    "\n",
    "plt.clf()\n",
    "plt.plot(fpr, tpr, \"b-\", lw=2, label=\"AUROC = %0.2f\"%roc_auc)\n",
    "plt.axline((0, 0), (1, 1), linestyle=\"--\", lw=1, color='gray')\n",
    "plt.xlabel('False Positive Rate')\n",
    "plt.ylabel('True Positive Rate')\n",
    "plt.title('ROC in predicting cancer')\n",
    "plt.legend(loc=\"best\")\n",
    "plt.savefig(\"roc_curve.png\",bbox_inches='tight', dpi=300)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Cross validation\n",
    "\n",
    "In our above example, we split the data into training and testing set. This is quite wasteful because we sacrifice half of the data. To evaluate the data on *every data point*, we can perform K-fold cross-validation.\n",
    "\n",
    "<img src=\"kfold_cv/cross_validation.png\" width=1200>\n",
    "\n",
    "<img src=\"kfold_cv/cross_validation_2.png\" width=1000>"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.model_selection import KFold\n",
    "\n",
    "def cross_validate(model, X_input, Y_output):\n",
    "    kf = KFold(n_splits=5, random_state=1, shuffle=True)\n",
    "    y = np.array([0] * X_input.shape[0])\n",
    "    yh = np.array([0.0] * X_input.shape[0])\n",
    "    for train_index, test_index in kf.split(X_input):\n",
    "        model.fit(X_input[train_index], Y_output[train_index])\n",
    "        y[test_index] = Y_output[test_index]\n",
    "        yh[test_index] = model.predict_proba(X_input[test_index])[:,1]\n",
    "    return y, yh\n",
    "\n",
    "knn = KNeighborsClassifier()\n",
    "\n",
    "true_labels,pred_scores = cross_validate(knn, X, y)\n",
    "\n",
    "fpr, tpr, _ = roc_curve(true_labels, pred_scores)\n",
    "auc = roc_auc_score(true_labels, pred_scores)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "# plot the roc curve for the model\n",
    "plt.plot(fpr, tpr, marker='.')\n",
    "plt.axline((0, 0), (1, 1), linestyle=\"--\", lw=1, color='gray')\n",
    "plt.text(0.7, 0.3, 'AUC: '+str(round(auc,2)))\n",
    "\n",
    "plt.xlabel(\"False Positive Rate\")\n",
    "plt.ylabel(\"True Positive Rate\")\n",
    "plt.savefig('prostate_cancer_knn_crossvalid_roc.eps')"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Method comparison\n",
    "\n",
    "* There are many machine learning methods implemented in scikit-learn\n",
    "* How do we know which one performs the test on our data set?\n",
    "* To get the answer, we will need to compare these methods using cross validation\n",
    "* Let's compare three machine learning methods namely\n",
    "    * K-nearest neighbours (KNN)\n",
    "    * Decision tree classifier (DT)  (Lec 4)\n",
    "    * Logistic regression (LR) (Lec 6)\n",
    "* Note: for each method (or class), we create an *object* of the method using their initializer method defined under that class\n",
    "* Training and prediction follows the *generic* syntax"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LogisticRegression\n",
      "KNeighborsClassifier\n",
      "DecisionTreeClassifier\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "\n",
    "models = [LogisticRegression(),\n",
    "          KNeighborsClassifier(),\n",
    "          DecisionTreeClassifier()]\n",
    "\n",
    "perf = {}\n",
    "\n",
    "for model in models:\n",
    "    model_name = type(model).__name__\n",
    "    print(model_name)\n",
    "    label,pred = cross_validate(model, X, y)\n",
    "    fpr, tpr, _ = roc_curve(label, pred)\n",
    "    auc = roc_auc_score(label, pred)\n",
    "    perf[model_name] = {'fpr':fpr,'tpr':tpr,'auc':auc}\n",
    "\n",
    "\n",
    "fig = plt.figure()\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "i = 0\n",
    "for model_name, model_perf in perf.items():\n",
    "    plt.plot(model_perf['fpr'], model_perf['tpr'],\n",
    "             label=model_name)\n",
    "    plt.text(0.4, i, model_name + ': AUC = '+\n",
    "             str(round(model_perf['auc'],2)))\n",
    "    i += 0.1\n",
    "\n",
    "plt.axline((0, 0), (1, 1), linestyle=\"--\", lw=1, color='gray')\n",
    "plt.legend(loc='upper center', bbox_to_anchor=(0.75, 0.6))\n",
    "plt.xlabel(\"False Positive Rate\")\n",
    "plt.ylabel(\"True Positive Rate\")\n",
    "\n",
    "plt.savefig('roc_multimethods.png', bbox_inches='tight', dpi=300)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Precision-recall\n",
    "\n",
    "To be updated soon"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}