Troy_Bradley_Copy_of_AUC_Coding_Challenge.ipynb

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      "name": "Troy Bradley Copy of AUC Coding Challenge.ipynb",
      "version": "0.3.2",
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "[View in Colaboratory](https://colab.research.google.com/github/bitcointroy/MLcodechallenges/blob/master/Troy_Bradley_Copy_of_AUC_Coding_Challenge.ipynb)"
      ]
    },
    {
      "metadata": {
        "id": "aD8Yb0P8D04e",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# Area-Under-Curve Measurement\n",
        "\n",
        "Objectives:\n",
        "* Compute true positive, true negative, false positive, and false negative classification rate\n",
        "* Adjust classification threshold to control above rates\n",
        "* Plot AUC  to demonstrate accuracy\n",
        "* Calculate AUC as a single value\n",
        "\n",
        "### Background\n",
        "\n",
        "You want to be familiar with ROC and AUC.\n",
        "\n",
        "#### Receiver Operating Characteristic Curve (ROC)\n",
        "\n",
        "[wikipedia](https://en.wikipedia.org/wiki/Receiver_operating_characteristic)\n",
        "[Precision and Recall](https://en.wikipedia.org/wiki/Precision_and_recall) [sklearn](http://scikit-learn.org/stable/auto_examples/model_selection/plot_roc.html)\n",
        "\n",
        "#### Area Under Curve (AUC)\n",
        "\n",
        "[sklearn](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.auc.html)\n",
        "\n",
        "The ROC curve provides a visualization of the performance of a classifier, with false-positive rates along the $x$ axis and true-positive rates along the $y$ axis. A perfect classifier produces no false positives (100% specificity) and no false negatives (100% sensitivity). In reality, classifiers are not so discerning.\n",
        "\n",
        "### Do:\n",
        "\n",
        "Correct the bugs in the following code blocks in order to work through the mechanics of building an AUC. \n",
        "\n",
        "Once you've calculated `FPR` and `TPR` for the Logistic Regression classifier on its Sprint Challenge dataset and visualized the results, modify it to compute the same data using the _test_ data, instead of the _train_ data."
      ]
    },
    {
      "metadata": {
        "id": "9JrCk2HEPwoI",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### 1. Compute Linear Regression Model\n",
        "\n",
        "Create a training set and train a Logistic Regression model with it"
      ]
    },
    {
      "metadata": {
        "id": "5UeD3N5_PwCF",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        },
        "outputId": "2fe14568-916d-481c-9127-1972d500d5ae"
      },
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "#import necessary libraries\n",
        "import pandas as pd\n",
        "from sklearn.linear_model import LogisticRegression\n",
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "data = pd.read_csv('https://www.dropbox.com/s/bnwfu81bjpf22hp/logistic_regression.csv?raw=1')\n",
        "# Use train_test_split to create a training set\n",
        "train_x, test_x, train_y, test_y = train_test_split(data[['x1','x2']],data['y'])\n",
        "\n",
        "# Create and train(fit) the model\n",
        "regr = LogisticRegression()\n",
        "regr.fit(train_x, train_y)"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
              "          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
              "          penalty='l2', random_state=None, solver='liblinear', tol=0.0001,\n",
              "          verbose=0, warm_start=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 2
        }
      ]
    },
    {
      "metadata": {
        "id": "jSfpHHfJFPc5",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### 2. Predict values for $\\hat{y}$ for the test set"
      ]
    },
    {
      "metadata": {
        "id": "x3K306_pFUQc",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "ac0fe099-ec31-4f51-ea4d-83f3b1e3dde0"
      },
      "cell_type": "code",
      "source": [
        "# Predict y_hat for the test set created previously\n",
        "\n",
        "y_hat = regr.predict(train_x)\n",
        "print(y_hat)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1. 1. 1. 1. 1. 0. 1. 1. 1. 0. 0. 0. 0. 1. 0. 0. 1. 0. 1. 0. 0. 1. 1. 0.\n",
            " 1. 1. 0. 0. 0. 1.]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "xS6VlmpYTzPx",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Observe precision"
      ]
    },
    {
      "metadata": {
        "id": "Fv_8vZvrT44v",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1071
        },
        "outputId": "ecd23856-0fc0-4b98-8d9b-0da11d110ac6"
      },
      "cell_type": "code",
      "source": [
        "# True positive: if the prediction is 1, and the original data is 1, their sum is 2\n",
        "true_positives = (y_hat+train_y)==2\n",
        "# False positive: if the prediction is 1, but the original data is 0, their sum is 1\n",
        "false_positives = (y_hat-train_y)==1\n",
        "print(true_positives.T)\n",
        "print(false_positives.T)"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "31     True\n",
            "26     True\n",
            "27     True\n",
            "1     False\n",
            "21     True\n",
            "13    False\n",
            "25     True\n",
            "22     True\n",
            "29     True\n",
            "5     False\n",
            "4     False\n",
            "30    False\n",
            "28    False\n",
            "33     True\n",
            "0     False\n",
            "6     False\n",
            "32     True\n",
            "8     False\n",
            "38     True\n",
            "15    False\n",
            "16    False\n",
            "37     True\n",
            "19    False\n",
            "11    False\n",
            "35     True\n",
            "39     True\n",
            "7     False\n",
            "17    False\n",
            "2     False\n",
            "36     True\n",
            "Name: y, dtype: bool\n",
            "31    False\n",
            "26    False\n",
            "27    False\n",
            "1      True\n",
            "21    False\n",
            "13    False\n",
            "25    False\n",
            "22    False\n",
            "29    False\n",
            "5     False\n",
            "4     False\n",
            "30    False\n",
            "28    False\n",
            "33    False\n",
            "0     False\n",
            "6     False\n",
            "32    False\n",
            "8     False\n",
            "38    False\n",
            "15    False\n",
            "16    False\n",
            "37    False\n",
            "19     True\n",
            "11    False\n",
            "35    False\n",
            "39    False\n",
            "7     False\n",
            "17    False\n",
            "2     False\n",
            "36    False\n",
            "Name: y, dtype: bool\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "Yybc_0TTTo6s",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 612
        },
        "outputId": "94400aeb-8100-45aa-c70b-54e3e9a7353a"
      },
      "cell_type": "code",
      "source": [
        "# The probabilities computed by Logistic Regression:\n",
        "# The columns correspond with class 0 or 1\n",
        "proba = regr.predict_proba(train_x)\n",
        "print(proba)\n",
        "\n",
        "# The decision function computed by Logistic Regression - this is simply\n",
        "# \\sum w_i x_i + b, before the logit function has been applied\n",
        "dec = regr.decision_function(train_x)\n",
        "print(dec)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0.18997529 0.81002471]\n",
            " [0.00758194 0.99241806]\n",
            " [0.03203427 0.96796573]\n",
            " [0.49809953 0.50190047]\n",
            " [0.04427393 0.95572607]\n",
            " [0.91546865 0.08453135]\n",
            " [0.00453142 0.99546858]\n",
            " [0.04553849 0.95446151]\n",
            " [0.02186341 0.97813659]\n",
            " [0.96157723 0.03842277]\n",
            " [0.69085626 0.30914374]\n",
            " [0.56579569 0.43420431]\n",
            " [0.58521427 0.41478573]\n",
            " [0.12439685 0.87560315]\n",
            " [0.82795754 0.17204246]\n",
            " [0.79662282 0.20337718]\n",
            " [0.01003417 0.98996583]\n",
            " [0.74772494 0.25227506]\n",
            " [0.01467767 0.98532233]\n",
            " [0.77338042 0.22661958]\n",
            " [0.90661936 0.09338064]\n",
            " [0.00488259 0.99511741]\n",
            " [0.45319989 0.54680011]\n",
            " [0.54224806 0.45775194]\n",
            " [0.03375722 0.96624278]\n",
            " [0.22353276 0.77646724]\n",
            " [0.86436865 0.13563135]\n",
            " [0.75886788 0.24113212]\n",
            " [0.79447703 0.20552297]\n",
            " [0.20032944 0.79967056]]\n",
            "[ 1.45017076  4.87437579  3.40839049  0.00760191  3.07207539 -2.38231364\n",
            "  5.39217801  3.04258932  3.80083497 -3.21992471 -0.80412542 -0.26471785\n",
            " -0.34421599  1.95143613 -1.57122057 -1.36531903  4.59167443 -1.08651517\n",
            "  4.20664134 -1.22749833 -2.27303865  5.31718593  0.18775002 -0.16939615\n",
            "  3.35422094  1.2451965  -1.85205878 -1.14648272 -1.35212628  1.3842366 ]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "PYmuA8VwJ4_y",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### 2.1 Build ROC curves"
      ]
    },
    {
      "metadata": {
        "id": "Jcyi6Z16OGuM",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 544
        },
        "outputId": "0dccc668-b40a-4fc7-e4d3-f3369113dbdc"
      },
      "cell_type": "code",
      "source": [
        "thresholds = np.linspace(0.0,1.0,11)\n",
        "predictions = pd.DataFrame()\n",
        "\n",
        "for decision_threshold in thresholds:\n",
        "    decision_threshold = np.round(decision_threshold,2)\n",
        "    true_false_array = (proba[::,1:2:] > decision_threshold).T[0]\n",
        "    predictions[str(decision_threshold)] = true_false_array.astype(int)\n",
        "        \n",
        "print(predictions)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "    0.0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1.0\n",
            "0     1    1    1    1    1    1    1    1    1    0    0\n",
            "1     1    1    1    1    1    1    1    1    1    1    0\n",
            "2     1    1    1    1    1    1    1    1    1    1    0\n",
            "3     1    1    1    1    1    1    0    0    0    0    0\n",
            "4     1    1    1    1    1    1    1    1    1    1    0\n",
            "5     1    0    0    0    0    0    0    0    0    0    0\n",
            "6     1    1    1    1    1    1    1    1    1    1    0\n",
            "7     1    1    1    1    1    1    1    1    1    1    0\n",
            "8     1    1    1    1    1    1    1    1    1    1    0\n",
            "9     1    0    0    0    0    0    0    0    0    0    0\n",
            "10    1    1    1    1    0    0    0    0    0    0    0\n",
            "11    1    1    1    1    1    0    0    0    0    0    0\n",
            "12    1    1    1    1    1    0    0    0    0    0    0\n",
            "13    1    1    1    1    1    1    1    1    1    0    0\n",
            "14    1    1    0    0    0    0    0    0    0    0    0\n",
            "15    1    1    1    0    0    0    0    0    0    0    0\n",
            "16    1    1    1    1    1    1    1    1    1    1    0\n",
            "17    1    1    1    0    0    0    0    0    0    0    0\n",
            "18    1    1    1    1    1    1    1    1    1    1    0\n",
            "19    1    1    1    0    0    0    0    0    0    0    0\n",
            "20    1    0    0    0    0    0    0    0    0    0    0\n",
            "21    1    1    1    1    1    1    1    1    1    1    0\n",
            "22    1    1    1    1    1    1    0    0    0    0    0\n",
            "23    1    1    1    1    1    0    0    0    0    0    0\n",
            "24    1    1    1    1    1    1    1    1    1    1    0\n",
            "25    1    1    1    1    1    1    1    1    0    0    0\n",
            "26    1    1    0    0    0    0    0    0    0    0    0\n",
            "27    1    1    1    0    0    0    0    0    0    0    0\n",
            "28    1    1    1    0    0    0    0    0    0    0    0\n",
            "29    1    1    1    1    1    1    1    1    0    0    0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "nDEdBrtYFjEr",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### 3. Calculate TP and FP at each discrimination level"
      ]
    },
    {
      "metadata": {
        "id": "B73O-XcrF9Wd",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 835
        },
        "outputId": "756ed4f0-ca78-4bd7-f8c0-4f84662050d2"
      },
      "cell_type": "code",
      "source": [
        "# Base case:\n",
        "false_positives = np.sum(predictions['0.1']-train_y.values>1)\n",
        "true_positives = np.sum(predictions['0.1']+train_y.values==2)\n",
        "print('False positive rate at threshold 0.1: ',false_positives/np.sum(train_y==0))\n",
        "print('True positive rate at threshold 0.1: ',true_positives/np.sum(train_y==1))\n",
        "\n",
        "# Now automate the base case across the set of all decision thresholds\n",
        "fp = pd.DataFrame()\n",
        "tp = pd.DataFrame()\n",
        "for threshold in predictions.columns:\n",
        "    fp[threshold] = [np.sum(predictions[threshold]-train_y.values==1)/np.sum(train_y==0)]\n",
        "    tp[threshold] = [np.sum(predictions[threshold]+train_y.values==2)/np.sum(train_y==1)]\n",
        "\n",
        "# The false positives and true positive rated, based on the sliding decision threshold\n",
        "print(fp.T)\n",
        "print(tp.T)\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "plt.plot(fp.T,tp.T);\n",
        "plt.plot([0, 1], [0, 1], 'k--', lw=2)\n",
        "plt.xlabel('False Positive Rate')\n",
        "plt.ylabel('True Positive Rate')\n",
        "plt.title('Receiver operating characteristic example')\n",
        "    "
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "False positive rate at threshold 0.1:  0.0\n",
            "True positive rate at threshold 0.1:  1.0\n",
            "            0\n",
            "0.0  1.000000\n",
            "0.1  0.785714\n",
            "0.2  0.642857\n",
            "0.3  0.285714\n",
            "0.4  0.214286\n",
            "0.5  0.142857\n",
            "0.6  0.000000\n",
            "0.7  0.000000\n",
            "0.8  0.000000\n",
            "0.9  0.000000\n",
            "1.0  0.000000\n",
            "         0\n",
            "0.0  1.000\n",
            "0.1  1.000\n",
            "0.2  1.000\n",
            "0.3  1.000\n",
            "0.4  1.000\n",
            "0.5  0.875\n",
            "0.6  0.875\n",
            "0.7  0.875\n",
            "0.8  0.750\n",
            "0.9  0.625\n",
            "1.0  0.000\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5,1,'Receiver operating characteristic example')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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pY6soIiJ53ldfbWbUqGGEh4fh6lqQ8eMn07dvPxwcdK4ue2TTfd4jR45MtfzX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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f2b062a3be0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "Jhg7EM4YQ6nG",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### 4. Example using sklearn"
      ]
    },
    {
      "metadata": {
        "id": "t2xGVuYcQfAo",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "from sklearn import metrics"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "O1_hD-raG2s2",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 415
        },
        "outputId": "b67c5d93-28ef-4957-a75b-62738bebd719"
      },
      "cell_type": "code",
      "source": [
        "# The Area-Under-The-Curve Score\n",
        "print(metrics.auc(fp.T,tp.T))\n",
        "print(metrics.roc_auc_score(train_y.values,proba[::,1:2:]))\n",
        "\n",
        "# Producing the same false/true positive data via a library and plotting it\n",
        "fpr, tpr, _ = metrics.roc_curve(train_y.values,proba[::,1:2:])\n",
        "print(fpr)\n",
        "print(tpr)\n",
        "plt.plot(fpr,tpr);"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.9776785714285714\n",
            "0.9732142857142857\n",
            "[0.         0.         0.21428571 0.21428571 1.        ]\n",
            "[0.0625 0.875  0.875  1.     1.    ]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f2b06ca7940>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "QS0KgX-_QbX6",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## Do\n",
        "\n",
        "### 5. Compute the ROC and AUC using the _testset_ instead of the _trainset_\n"
      ]
    },
    {
      "metadata": {
        "id": "CVtzXgERHI4B",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# Compute and plot"
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}