Logistic Regression for Banknote Authentication.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression for Banknote Authentication \n",
    "<hr>\n",
    "### Overview"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- [Choosing a classification algorithm](#Choosing-a-classification-algorithm)\n",
    "- [First steps with scikit-learn](#First-steps-with-scikit-learn)\n",
    "- [Loading the Dataset](#Dataset)\n",
    "    \n",
    "- [Logistic regression](#Logistic-regression:)\n",
    "    - [Training a logistic regression model with scikit-learn](#Training-a-logistic-regression-model-with-scikit-learn)\n",
    "    - [Measuring our classifier using Binary classification performance metrics](#Measuring-our-classifier-using-Binary-classification-performance-metrics)\n",
    "        - [Confusion Matrix](#Confusion-Matrix)\n",
    "        - [Precision and Recall](#Precision-and-Recall:)        \n",
    "        - [Calculating the F1 measure](#Calculating-the-F1-measure)\n",
    "        - [ROC-AUC](#ROC-AUC)\n",
    "    - [Finding the most Important Features](#Finding-the-most-important-features-with-forests-of-trees)\n",
    "    - [Plotting our model decison regions](#Plotting-our-model-decison-regions)\n",
    "    - [Tackling overfitting via regularization](#Tackling-overfitting-via-regularization)\n",
    "- [Summary](#Summary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Choosing a classification algorithm\n",
    "\n",
    "In the subsequent chapters, we will take a tour through a selection of popular and powerful machine learning algorithms that are commonly used in academia as well as in the industry. While learning about the differences between several supervised learning algorithms for classification, we will also develop an intuitive appreciation of their individual strengths and weaknesses by tackling real-word classification problems. We will take our first steps with the scikit-learn library, which offers a user-friendly interface for using those algorithms efficiently and productively. \n",
    "\n",
    "Choosing an appropriate classification algorithm for a particular problem task requires practice: each algorithm has its own quirks and is based on certain assumptions. The \"No Free Lunch\" theorem: no single classifier works best across all possible scenarios. In practice, it is always recommended that you compare the performance of at least a handful of different learning algorithms to select the best model for the particular problem; these may differ in the number of features or samples, the amount of noise in a dataset, and whether the classes are linearly separable or not.\n",
    "\n",
    "Eventually, the performance of a classifier, computational power as well as predictive power, depends heavily on the underlying data that are available for learning. The five main steps that are involved in training a machine learning algorithm can be summarized as follows:\n",
    "\n",
    "1. Selection of features.\n",
    "2. Choosing a performance metric.\n",
    "3. Choosing a classifier and optimization algorithm.\n",
    "4. Evaluating the performance of the model.\n",
    "5. Tuning the algorithm.\n",
    "\n",
    "Since the approach of this section is to build machine learning knowledge step by step, we will mainly focus on the principal concepts of the different algorithms in this chapter and revisit topics such as feature selection and preprocessing, performance metrics, and hyperparameter tuning for more detailed discussions later in the section."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## First steps with scikit-learn\n",
    "\n",
    "In this example we are going to use Logistic Regression algorithm to classify banknotes as authentic or not. Since we have two outputs (Authentic or Not Authentic) this type of classification is called Binary Classification. Classification task consisting cases where we have to classify into one or more classes is called Multi-Class Classifation. \n",
    "\n",
    "### Dataset\n",
    "\n",
    "You can get the Banknote Authentication dataset from here: http://archive.ics.uci.edu/ml/datasets/banknote+authentication. [UCI Machine Learning Repository](http://archive.ics.uci.edu/ml/index.html) is one of the most widely used resource for datasets. As you'll see, we use multiple datasets from this repository to tackle different Machine Learning tasks. \n",
    "\n",
    "The Banknote Authentication data was extracted from images that were taken from genuine and forged banknote-like specimens. For digitization, an industrial camera usually used for print inspection was used. The final images have 400x 400 pixels. Due to the object lens and distance to the investigated object gray-scale pictures with a resolution of about 660 dpi were gained. Wavelet Transform tool were used to extract features from images. The dataset contains the following attributes:\n",
    "\n",
    "1. variance of Wavelet Transformed image (continuous) \n",
    "2. skewness of Wavelet Transformed image (continuous) \n",
    "3. curtosis of Wavelet Transformed image (continuous) \n",
    "4. entropy of image (continuous) \n",
    "5. class (integer 0 for fake and 1 for authentic bank notes) \n",
    "\n",
    "Save the downloaded `data_banknote_authentication.txt` in the same directory as of your code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "# read .csv from provided dataset\n",
    "csv_filename=\"data_banknote_authentication.txt\"\n",
    "\n",
    "# We assign the collumn names ourselves and load the data in a Pandas Dataframe\n",
    "df=pd.read_csv(csv_filename,names=[\"Variance\",\"Skewness\",\"Curtosis\",\"Entropy\",\"Class\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll take a look at our data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Variance</th>\n",
       "      <th>Skewness</th>\n",
       "      <th>Curtosis</th>\n",
       "      <th>Entropy</th>\n",
       "      <th>Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3.62160</td>\n",
       "      <td>8.6661</td>\n",
       "      <td>-2.8073</td>\n",
       "      <td>-0.44699</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.54590</td>\n",
       "      <td>8.1674</td>\n",
       "      <td>-2.4586</td>\n",
       "      <td>-1.46210</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.86600</td>\n",
       "      <td>-2.6383</td>\n",
       "      <td>1.9242</td>\n",
       "      <td>0.10645</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.45660</td>\n",
       "      <td>9.5228</td>\n",
       "      <td>-4.0112</td>\n",
       "      <td>-3.59440</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.32924</td>\n",
       "      <td>-4.4552</td>\n",
       "      <td>4.5718</td>\n",
       "      <td>-0.98880</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Variance  Skewness  Curtosis  Entropy  Class\n",
       "0   3.62160    8.6661   -2.8073 -0.44699      0\n",
       "1   4.54590    8.1674   -2.4586 -1.46210      0\n",
       "2   3.86600   -2.6383    1.9242  0.10645      0\n",
       "3   3.45660    9.5228   -4.0112 -3.59440      0\n",
       "4   0.32924   -4.4552    4.5718 -0.98880      0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Apparently, the first 5 instances of our datasets are all fake (Class is 0)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No of Fake bank notes = 762\n"
     ]
    }
   ],
   "source": [
    "print(\"No of Fake bank notes = \" + str(len(df[df['Class'] == 0])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No of Authentic bank notes = 610\n"
     ]
    }
   ],
   "source": [
    "print(\"No of Authentic bank notes = \" + str(len(df[df['Class'] == 1])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shows we have 762 total instances of Fake banknotes and 610 total instances of Authentic banknotes in our dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Our features :\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "['Variance', 'Skewness', 'Curtosis', 'Entropy']"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features=list(df.columns[:-1])\n",
    "print(\"Our features :\"  )\n",
    "features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = df[features]\n",
    "y = df['Class']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Class labels: [0 1]\n"
     ]
    }
   ],
   "source": [
    "print('Class labels:', np.unique(y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To evaluate how well a trained model performs on unseen data, we will further split the dataset into separate training and test datasets. Splitting data into 70% training and 30% test data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.cross_validation import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "         X, y, test_size=0.3, random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many machine learning and optimization algorithms also require feature scaling\n",
    "for optimal performance. Here, we will standardize the features using the StandardScaler class from scikit-learn's preprocessing module:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Standardizing the features:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "sc = StandardScaler()\n",
    "sc.fit(X_train)\n",
    "X_train_std = sc.transform(X_train)\n",
    "X_test_std = sc.transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the preceding code, we loaded the StandardScaler class from the preprocessing module and initialized a new StandardScaler object that we assigned to the variable sc. Using the fit method, StandardScaler estimated the parameters μ (sample mean) and \u001f (standard deviation) for each feature dimension from the training data. By calling the transform method, we then standardized the training data using those estimated parameters μ and \u001f. Note that we used the same scaling parameters to standardize the test set so that both the values in the training and test dataset are comparable to each other."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Logistic regression:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logistic regression is a classification model that is very easy to implement but performs very well on linearly separable classes. It is one of the most widely used algorithms for classification in industry. The logistic regression model is a linear model for binary classification that can be extended to multiclass classification via the OvR technique."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The sigmoid function used in the Logistic Regression:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/mzuNpLbgiJIkLaNRo+CZZ+CRRxxNkqqVI0qStAzmz4eBA+F730sjSpKqkyNKkrQMbr8d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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8b50da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "def sigmoid(z):\n",
    "    return 1.0 / (1.0 + np.exp(-z))\n",
    "\n",
    "z = np.arange(-7, 7, 0.1)\n",
    "phi_z = sigmoid(z)\n",
    "\n",
    "plt.plot(z, phi_z)\n",
    "plt.axvline(0.0, color='k')\n",
    "plt.ylim(-0.1, 1.1)\n",
    "plt.xlabel('z')\n",
    "plt.ylabel('$\\phi (z)$')\n",
    "\n",
    "# y axis ticks and gridline\n",
    "plt.yticks([0.0, 0.5, 1.0])\n",
    "ax = plt.gca()\n",
    "ax.yaxis.grid(True)\n",
    "\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/sigmoid.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Learning the weights of the logistic cost function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VFUVQUFDWuVKlSlGrVq0c77uU86cN27VrR3x8PJZlceONNxIfH8/YsWMv+b39+/fnhx9+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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9f60cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def cost_1(z):\n",
    "    return - np.log(sigmoid(z))\n",
    "\n",
    "\n",
    "def cost_0(z):\n",
    "    return - np.log(1 - sigmoid(z))\n",
    "\n",
    "z = np.arange(-10, 10, 0.1)\n",
    "phi_z = sigmoid(z)\n",
    "\n",
    "c1 = [cost_1(x) for x in z]\n",
    "plt.plot(phi_z, c1, label='J(w) if y=1')\n",
    "\n",
    "c0 = [cost_0(x) for x in z]\n",
    "plt.plot(phi_z, c0, linestyle='--', label='J(w) if y=0')\n",
    "\n",
    "plt.ylim(0.0, 5.1)\n",
    "plt.xlim([0, 1])\n",
    "plt.xlabel('$\\phi$(z)')\n",
    "plt.ylabel('J(w)')\n",
    "plt.legend(loc='best')\n",
    "plt.tight_layout()\n",
    "# plt.savefig('./figures/log_cost.png', dpi=300)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training a logistic regression model with scikit-learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scikit-learn implements a highly optimized version of logistic regression that also supports multiclass settings off-the-shelf, we will skip the implementation and use the `sklearn.linear_model.LogisticRegression` class as well as the familiar fit method to train the model on the standardized flower training dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1000.0, class_weight=None, dual=False,\n",
       "          fit_intercept=True, intercept_scaling=1, max_iter=100,\n",
       "          multi_class='ovr', n_jobs=1, penalty='l2', random_state=0,\n",
       "          solver='liblinear', tol=0.0001, verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "lr = LogisticRegression(C=1000.0, random_state=0)\n",
    "\n",
    "lr.fit(X_train_std, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(412,)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Having trained a model in scikit-learn, we can make predictions via the predict method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Misclassified samples: 5\n"
     ]
    }
   ],
   "source": [
    "y_pred = lr.predict(X_test_std)\n",
    "print('Misclassified samples: %d' % (y_test != y_pred).sum())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On executing the preceding code, we see that the perceptron misclassifies 5 out of the 412 note samples. Thus, the misclassification error on the test dataset is 0.012 or 1.2 percent (5/412 = 0.012\u001d",
    ")."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measuring our classifier using Binary classification performance metrics\n",
    "A variety of metrics exist to evaluate the performance of binary classifiers against\n",
    "trusted labels. The most common metrics are accuracy, precision, recall, F1 measure,\n",
    "and ROC AUC score. All of these measures depend on the concepts of true positives,\n",
    "true negatives, false positives, and false negatives. Positive and negative refer to the\n",
    "classes. True and false denote whether the predicted class is the same as the true class.\n",
    "\n",
    "For our Banknote classifier, a true positive prediction is when the classifier correctly\n",
    "predicts that a note is authentic. A true negative prediction is when the classifier\n",
    "correctly predicts that a note is fake. A prediction that a fake note is authentic\n",
    "is a false positive prediction, and an authentic note is incorrectly classified as fake is a\n",
    "false negative prediction. \n",
    "\n",
    "### Confusion Matrix\n",
    "\n",
    "A confusion matrix, or contingency table, can be used to\n",
    "visualize true and false positives and negatives. The rows of the matrix are the true\n",
    "classes of the instances, and the columns are the predicted classes of the instances:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[227   5]\n",
      " [  0 180]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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aTtySvgUcExFDtbTNzHpC1R+kUCTSSaS1t83Melrx6e7FW+jdVCRxewEpM7Me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\nm5mVzP8H4yTQJXWS3RsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa525d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "confusion_matrix = confusion_matrix(y_test, y_pred)\n",
    "print(confusion_matrix)\n",
    "plt.matshow(confusion_matrix)\n",
    "plt.title('Confusion matrix')\n",
    "plt.colorbar()\n",
    "plt.ylabel('True label')\n",
    "plt.xlabel('Predicted label')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The confusion matrix indicates that there were 227 true negative predictions, 180\n",
    "true positive predictions, 0 false negative predictions, and 5 false positive\n",
    "prediction."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scikit-learn also implements a large variety of different performance metrics that are available via the metrics module. For example, we can calculate the classification accuracy of the perceptron on the test set as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.99\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "print('Accuracy: %.2f' % accuracy_score(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, y_test are the true class labels and y_pred are the class labels that we predicted previously.\n",
    "\n",
    "\n",
    "Furthermore, we can predict the class-membership probability of the samples via\n",
    "the predict_proba method. For example, we can predict the probabilities of the\n",
    "first banknote sample:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  3.97356229e-06,   9.99996026e-01]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.predict_proba(X_test_std[0,:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The preceding array tells us that the model predicts a chance of 99.96 percent that the sample is an autentic banknote (y = 1) class, and 0.003 percent chance that the sample is a fake note (y = 0)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "While accuracy measures the overall correctness of the classifier, it does not distinguish between false positive errors and false negative errors. Some applications may be more sensitive to false negatives than false positives, or vice\n",
    "versa. Furthermore, accuracy is not an informative metric if the proportions of the classes are skewed in the population. For example, a classifier that predicts whether or not credit card transactions are fraudulent may be more sensitive to\n",
    "false negatives than to false positives.\n",
    "\n",
    "A classifier that always predicts that transactions are legitimate could have a high accuracy score, but would not be useful. For these reasons, classifiers are often evaluated using two additional measures called precision and recall.\n",
    "\n",
    "## Precision and Recall:\n",
    "\n",
    "**Precision is the fraction of positive predictions that are correct.** For instance, in our Banknote Authentication\n",
    "classifier, precision is the fraction of notes classified as authentic that are actually\n",
    "authentic. \n",
    "\n",
    "Precision is given by the following ratio:\n",
    "####                                                     P = TP / (TP + FP) \n",
    "\n",
    "Sometimes called sensitivity in medical domains, recall is the fraction of the truly\n",
    "positive instances that the classifier recognizes. A recall score of one indicates\n",
    "that the classifier did not make any false negative predictions. For our Banknote Authentication\n",
    "classifier, **recall is the fraction of authentic notes that were truly classified as authentic.**\n",
    "\n",
    "Recall is calculated with the following ratio:\n",
    "#### R = TP / (TP + FN)\n",
    "\n",
    "Individually, precision and recall are seldom informative; they are both incomplete\n",
    "views of a classifier's performance. Both precision and recall can fail to distinguish\n",
    "classifiers that perform well from certain types of classifiers that perform poorly. A\n",
    "trivial classifier could easily achieve a perfect recall score by predicting positive for\n",
    "every instance. For example, assume that a test set contains ten positive examples\n",
    "and ten negative examples. \n",
    "\n",
    "A classifier that predicts positive for every example will\n",
    "achieve a recall of one, as follows:\n",
    "#### R = 10 / (10 + 0) = 1\n",
    "\n",
    "A classifier that predicts negative for every example, or that makes only false positive\n",
    "and true negative predictions, will achieve a recall score of zero. Similarly, a classifier\n",
    "that predicts that only a single instance is positive and happens to be correct will\n",
    "achieve perfect precision.\n",
    "\n",
    "Scikit-learn provides a function to calculate the precision and recall for a classifier\n",
    "from a set of predictions and the corresponding set of trusted labels. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Calculating our Banknote Authentication classifier's precision and recall:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Precision 0.988712972421 [ 0.96629213  1.          0.97727273  1.          1.        ]\n",
      "Recalls 0.988372093023 [ 1.          0.95348837  1.          1.          0.98837209]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.cross_validation import cross_val_score\n",
    "\n",
    "precisions = cross_val_score(lr, X_train_std, y_train, cv=5,scoring='precision')\n",
    "print('Precision', np.mean(precisions), precisions)\n",
    "\n",
    "recalls = cross_val_score(lr, X_train_std, y_train, cv=5,scoring='recall')\n",
    "print('Recalls', np.mean(recalls), recalls)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our classifier's precision is 0.988; almost all of the notes that it predicted as\n",
    "authentic were actually authentic. Its recall is also high, indicating that it correctly classified\n",
    "approximately 98 percent of the authentic messages as authentic."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculating the F1 measure\n",
    "\n",
    "The F1 measure is the harmonic mean, or weighted average, of the precision and\n",
    "recall scores. Also called the f-measure or the f-score, the F1 score is calculated using\n",
    "the following formula:\n",
    "\n",
    "#### F1 = 2PR / (P + R)\n",
    "\n",
    "The F1 measure penalizes classifiers with imbalanced precision and recall scores,\n",
    "like the trivial classifier that always predicts the positive class. A model with perfect\n",
    "precision and recall scores will achieve an F1 score of one. A model with a perfect\n",
    "precision score and a recall score of zero will achieve an F1 score of zero. As for\n",
    "precision and recall, scikit-learn provides a function to calculate the F1 score for\n",
    "a set of predictions. Let's compute our classifier's F1 score."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F1 0.988341082592 [ 0.98285714  0.97619048  0.98850575  1.          0.99415205]\n"
     ]
    }
   ],
   "source": [
    "f1s = cross_val_score(lr, X_train_std, y_train, cv=5, scoring='f1')\n",
    "print('F1', np.mean(f1s), f1s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The arithmetic mean of our classifier's precision and recall scores is 0.98. As the\n",
    "difference between the classifier's precision and recall is small, the F1 measure's\n",
    "penalty is small. Models are sometimes evaluated using the F0.5 and F2 scores,\n",
    "which favor precision over recall and recall over precision, respectively."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ROC AUC\n",
    "A Receiver Operating Characteristic, or ROC curve, visualizes a classifier's performance. Unlike accuracy, the ROC curve is insensitive to data sets with unbalanced class proportions; unlike precision and recall, the ROC curve illustrates the classifier's performance for all values of the discrimination threshold. ROC curves plot the classifier's recall against its fall-out. Fall-out, or the false positive rate, is the number of false positives divided by the total number of negatives. It is\n",
    "calculated using the following formula:\n",
    "\n",
    "#### F = FP / (TN + FP)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.98922413793103448"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import roc_auc_score, roc_curve, auc\n",
    "roc_auc_score(y_test,lr.predict(X_test_std))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Plotting the ROC curve for our SMS spam classifier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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q1CWZW3Mq8Ia7nx3df9nM9gfOIAwsE6lFtXQ+9UnCF48LCIMz5xPGc1yWZFAikr+yGwNi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\nYvf/Aa9se5H0FaXwAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9ff92e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "y_pred = lr.predict_proba(X_test_std)\n",
    "\n",
    "false_positive_rate, recall, thresholds = roc_curve(y_test, y_pred[:, 1])\n",
    "roc_auc = auc(false_positive_rate, recall)\n",
    "plt.title('Receiver Operating Characteristic')\n",
    "plt.plot(false_positive_rate, recall, 'b', label='AUC = %0.2f' % roc_auc)\n",
    "plt.legend(loc='lower right')\n",
    "\n",
    "plt.plot([0, 1], [0, 1], 'r--')\n",
    "plt.xlim([0.0, 1.0])\n",
    "plt.ylim([0.0, 1.0])\n",
    "plt.ylabel('Recall')\n",
    "plt.xlabel('Fall-out')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the ROC AUC plot, it is apparent that our classifier outperforms random\n",
    "guessing and does a very good job in classifying; almost all of the plot area lies under its curve.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Finding the most important features with forests of trees\n",
    "This examples shows the use of forests of trees to evaluate the importance of features on an artificial classification task. The red bars are the feature importances of the forest, along with their inter-trees variability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Feature ranking:\n",
      "1. feature 0 - Variance (0.502450) \n",
      "2. feature 1 - Skewness (0.280639) \n",
      "3. feature 2 - Curtosis (0.153946) \n",
      "4. feature 3 - Entropy (0.062965) \n"
     ]
    },
    {
     "data": {
      "image/png": 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3fP/995cvv/zy8qBBg8oDBgwoNzQ0lJ944ok99l+8eHH5pJNOKh9++OHlY445pnzFFVeU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\nYoFvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa9b5ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.ensemble import ExtraTreesClassifier\n",
    "\n",
    "# Build a classification task using 3 informative features\n",
    "# Build a forest and compute the feature importances\n",
    "forest = ExtraTreesClassifier(n_estimators=250,\n",
    "                              random_state=0)\n",
    "\n",
    "forest.fit(X, y)\n",
    "importances = forest.feature_importances_\n",
    "std = np.std([tree.feature_importances_ for tree in forest.estimators_],\n",
    "             axis=0)\n",
    "indices = np.argsort(importances)[::-1]\n",
    "\n",
    "# Print the feature ranking\n",
    "print(\"Feature ranking:\")\n",
    "\n",
    "for f in range(X.shape[1]):\n",
    "    print(\"%d. feature %d - %s (%f) \" % (f + 1, indices[f], features[indices[f]], importances[indices[f]]))\n",
    "\n",
    "# Plot the feature importances of the forest\n",
    "plt.figure(num=None, figsize=(10, 6), dpi=80, facecolor='w', edgecolor='k')\n",
    "plt.title(\"Feature importances\")\n",
    "plt.bar(range(X.shape[1]), importances[indices],\n",
    "       color=\"r\", yerr=std[indices], align=\"center\")\n",
    "plt.xticks(range(X.shape[1]), indices)\n",
    "plt.xlim([-1, X.shape[1]])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll cover the details of the code later. For now it can be evidently seen that our most important features that are helping us to correctly classify are: Variance and Skewness.\n",
    "We'll use these two features to plot our graph.    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting our model decison regions\n",
    "Finally, we can plot the decision regions of our newly trained perceptron model and visualize how well it separates the different samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "         X[['Variance','Skewness']], y, test_size=0.3, random_state=0)\n",
    "sc = StandardScaler()\n",
    "sc.fit(X_train)\n",
    "X_train_std = sc.transform(X_train)\n",
    "X_test_std = sc.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from matplotlib.colors import ListedColormap\n",
    "import matplotlib.pyplot as plt\n",
    "import warnings\n",
    "\n",
    "\n",
    "def versiontuple(v):\n",
    "    return tuple(map(int, (v.split(\".\"))))\n",
    "\n",
    "\n",
    "def plot_decision_regions(X, y, classifier, test_idx=None, resolution=0.02):\n",
    "\n",
    "    # setup marker generator and color map\n",
    "    markers = ('s', 'x', 'o', '^', 'v')\n",
    "    colors = ('red', 'blue', 'lightgreen', 'gray', 'cyan')\n",
    "    cmap = ListedColormap(colors[:len(np.unique(y))])\n",
    "\n",
    "    # plot the decision surface\n",
    "    x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n",
    "    x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n",
    "    xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, resolution),\n",
    "                           np.arange(x2_min, x2_max, resolution))\n",
    "    Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T)\n",
    "    Z = Z.reshape(xx1.shape)\n",
    "    plt.contourf(xx1, xx2, Z, alpha=0.4, cmap=cmap)\n",
    "    plt.xlim(xx1.min(), xx1.max())\n",
    "    plt.ylim(xx2.min(), xx2.max())\n",
    "\n",
    "    for idx, cl in enumerate(np.unique(y)):\n",
    "        plt.scatter(x=X[y == cl, 0], y=X[y == cl, 1],\n",
    "                    alpha=0.8, c=cmap(idx),\n",
    "                    marker=markers[idx], label=cl)\n",
    "\n",
    "    # highlight test samples\n",
    "    if test_idx:\n",
    "        # plot all samples\n",
    "        if not versiontuple(np.__version__) >= versiontuple('1.9.0'):\n",
    "            X_test, y_test = X[list(test_idx), :], y[list(test_idx)]\n",
    "            warnings.warn('Please update to NumPy 1.9.0 or newer')\n",
    "        else:\n",
    "            X_test, y_test = X[test_idx, :], y[test_idx]\n",
    "\n",
    "        plt.scatter(X_test[:, 0],\n",
    "                    X_test[:, 1],\n",
    "                    c='',\n",
    "                    alpha=1.0,\n",
    "                    linewidths=1,\n",
    "                    marker='o',\n",
    "                    s=55, label='test set')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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C5VISBo5HRRA6oBaVCGrB3u2coxhYb1mkxGJ8FonUMlXDvv8r/auCAtJ8Pk4/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\nD/C9bXMvcH9dHYYQNAC3TZ+OJ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gaU8c/YCXi0iWmH0AQJqHe5t/QnvNZxFM/GfsT/Av8g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\nqd5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      "text/plain": [
       "<matplotlib.figure.Figure at 0xac5af28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "lr = LogisticRegression(C=1000.0, random_state=0)\n",
    "lr.fit(X_train_std, y_train)\n",
    "\n",
    "plot_decision_regions(X_combined_std, y_combined,\n",
    "                      classifier=lr, test_idx=range(105, 150))\n",
    "plt.xlabel('Variance')\n",
    "plt.ylabel('Skewness')\n",
    "plt.legend(loc='upper left')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see in the resulting plot, the banknote classes have been seperated by a abstract line generated by the Logistic Regression Classifier. We could plot this 2D plot using the features Skewness and Variance.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tackling overfitting via regularization\n",
    "\n",
    "Overfitting is a common problem in machine learning, where a model performs well on training data but does not generalize well to unseen data (test data). If a model suffers from overfitting, we also say that the model has a high variance, which can be caused by having too many parameters that lead to a model that is too complex given the underlying data. Similarly, our model can also suffer from underfitting (high bias), which means that our model is not complex enough to capture the pattern in the training data well and therefore also suffers from low performance\n",
    "on unseen data.\n",
    "\n",
    "The problem of overfitting and underfitting can be best illustrated by using a more complex, nonlinear decision boundary as shown in the following figure:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "<img src=\"images/overfitting.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One way of finding a good bias-variance tradeoff is to tune the complexity of the model via regularization. Regularization is a very useful method to handle collinearity (high correlation among features), filter out noise from data, and eventually prevent overfitting. The concept behind regularization is to introduce additional information (bias) to penalize extreme parameter weights. The most common form of regularization is the so-called L2 regularization (sometimes also called L2 shrinkage or weight decay). \n",
    "\n",
    "The parameter C that is implemented for the LogisticRegression class in\n",
    "scikit-learn comes from a convention in support vector machines, which will be\n",
    "the topic of the next section. C is directly related to the regularization parameter, which is its inverse.\n",
    "\n",
    "Consequently, decreasing the value of the inverse regularization parameter C means that we are increasing the regularization strength.\n",
    "_____\n",
    "## Summary\n",
    "In this chapter, we learned that Logistic regression is not only a useful model for online learning via stochastic gradient descent, but also allows us to predict the probability of a particular event. Feel free to try out different datasets to better understand the cases where Logistic Regression works best.\n",
    "<hr>"
   ]
  }
 ],
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