logisticregression.ipynb

logisticregression.ipynb

{
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  "metadata": {
    "colab": {
      "name": "logisticregression.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyOVYWXo8T2P0ORoZdZvs/8K",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/maxkleiner/3dd1e5a7fd9fe1014f6dfd360aa8c288/logisticregression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MS7JmmTjexlp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "from sklearn.linear_model import LogisticRegression\n",
        "from sklearn.metrics import classification_report, confusion_matrix\n",
        "# https://realpython.com/logistic-regression-python/\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qm0fdjWKfJhM",
        "colab_type": "text"
      },
      "source": [
        "# For the purpose of this visual classification example, let’s just create arrays for the input (𝑥) and output (𝑦) values:\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8ySq6OeEfNI7",
        "colab_type": "code",
        "outputId": "79c7a8e1-631b-4718-e6eb-03ffc463012e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 203
        }
      },
      "source": [
        "X = np.arange(10).reshape(-1, 1)\n",
        "y = np.array([0, 0, 0, 0, 1, 1, 1, 1, 1, 1])\n",
        "#y = np.array([0, 1, 0,1, 1, 1, 1, 1, 0, 1])\n",
        "print(X)\n"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0]\n",
            " [1]\n",
            " [2]\n",
            " [3]\n",
            " [4]\n",
            " [5]\n",
            " [6]\n",
            " [7]\n",
            " [8]\n",
            " [9]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lMPVXyepfYoB",
        "colab_type": "text"
      },
      "source": [
        "# The array X is required to be two-dimensional as matrix. \n",
        "# Once you have the input and output prepared, you can create and define your classification model.\n",
        "# Other solver options are 'newton-cg', 'lbfgs', 'sag', and 'saga'.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pGBk1ps8ffk0",
        "colab_type": "code",
        "outputId": "f0152124-9ad9-4326-d961-91fabc7cf9f5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 110
        }
      },
      "source": [
        "model = LogisticRegression(solver='liblinear', random_state=0)\n",
        "model.fit(X, y)\n",
        "print(model)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
            "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
            "                   multi_class='auto', n_jobs=None, penalty='l2',\n",
            "                   random_state=0, solver='liblinear', tol=0.0001, verbose=0,\n",
            "                   warm_start=False)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LGjdypm8fyq6",
        "colab_type": "code",
        "outputId": "b4261b2e-ba68-49ad-88e7-7c2facea55c1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 314
        }
      },
      "source": [
        "model = LogisticRegression(solver='liblinear', C=1, random_state=0).fit(X, y)\n",
        "\n",
        "print(model.intercept_)\n",
        "#array([-1.04608067])\n",
        "print(model.coef_,'\\n')\n",
        "# The first column is the probability of the predicted output being zero, that is 1 - 𝑝(𝑥). \n",
        "# The second column is the probability that the output is one, or 𝑝(𝑥).\n",
        "print(model.predict_proba(X),'\\n')\n",
        "\n",
        "print('predict:',model.predict(X))\n",
        "print('score:  ',model.score(X, y))\n"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[-1.04608067]\n",
            "[[0.51491375]] \n",
            "\n",
            "[[0.74002157 0.25997843]\n",
            " [0.62975524 0.37024476]\n",
            " [0.5040632  0.4959368 ]\n",
            " [0.37785549 0.62214451]\n",
            " [0.26628093 0.73371907]\n",
            " [0.17821501 0.82178499]\n",
            " [0.11472079 0.88527921]\n",
            " [0.07186982 0.92813018]\n",
            " [0.04422513 0.95577487]\n",
            " [0.02690569 0.97309431]] \n",
            "\n",
            "predict: [0 0 0 1 1 1 1 1 1 1]\n",
            "score:   0.9\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BZH2sNCTzxNV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BqX52mfPfrFH",
        "colab_type": "text"
      },
      "source": [
        "# The first column is the probability of the predicted output being zero, that is 1 - 𝑝(𝑥). \n",
        "# The second column is the probability that the output is one, or 𝑝(𝑥).\n",
        "# You can use the fact that .fit() returns the model instance and chain the last two statements.\n",
        "\n",
        "# model = LogisticRegression(solver='lbfgs', C=1, random_state=0).fit(X, y)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c-uGPz0agB-h",
        "colab_type": "code",
        "outputId": "6ed27c6f-db9c-4715-dc1b-e1ea91d151b4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        }
      },
      "source": [
        "# One false positive prediction: The fourth observation is a zero that was wrongly predicted as one.\n",
        "\n",
        "print(confusion_matrix(y, model.predict(X)))"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[3 1]\n",
            " [0 6]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XS4_lgDcgHCP",
        "colab_type": "text"
      },
      "source": [
        "# It’s often useful to visualize the confusion matrix. \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lAs1g0Q1gLZh",
        "colab_type": "code",
        "outputId": "4cdbafd9-ff77-4849-8cbf-d1d769dc5988",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        }
      },
      "source": [
        "cm = confusion_matrix(y, model.predict(X))\n",
        "\n",
        "plt.rcParams.update({'font.size': 16})\n",
        "fig, ax = plt.subplots(figsize=(4, 4))\n",
        "ax.imshow(cm)\n",
        "ax.grid(False)\n",
        "ax.xaxis.set(ticks=(0, 1), ticklabels=('Predicted 0s', 'Predicted 1s'))\n",
        "ax.yaxis.set(ticks=(0, 1), ticklabels=('Actual 0s', 'Actual 1s'))\n",
        "ax.set_ylim(1.5, -0.5)\n",
        "for i in range(2):\n",
        "    for j in range(2):\n",
        "        ax.text(j, i, cm[i, j], ha='center', va='center', color='red')\n",
        "plt.show()\n"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NGTQ9gZvy4un",
        "colab_type": "code",
        "outputId": "0cb0aac0-0d38-489b-92df-bcfaf8495c7b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 184
        }
      },
      "source": [
        "print(classification_report(y, model.predict(X)))\n"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "              precision    recall  f1-score   support\n",
            "\n",
            "           0       1.00      0.75      0.86         4\n",
            "           1       0.86      1.00      0.92         6\n",
            "\n",
            "    accuracy                           0.90        10\n",
            "   macro avg       0.93      0.88      0.89        10\n",
            "weighted avg       0.91      0.90      0.90        10\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dcGPVrMny0AE",
        "colab_type": "text"
      },
      "source": [
        "# The code above creates a heatmap that represents the confusion matrix:\n",
        "# You can get a more comprehensive report on the classification with"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cEhwFRCwz1cV",
        "colab_type": "code",
        "outputId": "b59563bd-7f41-40b5-d55b-fa26dbfeb839",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 551
        }
      },
      "source": [
        "# from utilities2 import plot_classifier, plot_confusion_matrix\n",
        "import seaborn as sns\n",
        "\n",
        "def ap_log_regplot(ap_X, ap_y):\n",
        "    plt.figure(figsize=(10,5))\n",
        "    sns.regplot(ap_X, model.predict(X), logistic=True, color='green')\n",
        "    return None\n",
        "\n",
        "#ap_log_regplot(X, y)\n",
        "#plt.show()\n",
        "sns.set(style = 'whitegrid')\n",
        "sns.regplot(X, model.predict_proba(X)[:,1], logistic=True, \n",
        "                       scatter_kws={\"color\": \"red\"}, line_kws={\"color\": \"blue\"}) #label=model.predict(X))\n",
        "# sns.regplot(X, model.predict(X), logistic=True)\n",
        "plt.title('Logistic Probability Plot')\n",
        "plt.show()\n",
        "\n",
        "#df_confusion_matrix=pd.crosstab(y,model.predict(X)[:,1],rownames=['Actual'],colnames=['Predicted'], normalize=True)\n",
        "#plot_confusion_matrix(df_confusion_matrix, title='Cell Confusion matrix', cmap=plt.cm.Paired)\n",
        "sns.heatmap(cm,  annot=True)\n",
        "plt.title('heatmap confusion matrix')\n",
        "plt.show()"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lOr4XWiU0kSX",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "Now we improve our model with the exchange of the solver from liblinear to lbfgs:\n",
        "\n",
        "---\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TuVjHYwf0v9e",
        "colab_type": "code",
        "outputId": "6923a84e-f219-4943-8a5f-cc5af8ec7ed2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 551
        }
      },
      "source": [
        "model = LogisticRegression(solver='lbfgs', C=1, random_state=0).fit(X, y)\n",
        "sns.set(style = 'whitegrid')\n",
        "sns.regplot(X, model.predict_proba(X)[:,1], logistic=True, \n",
        "                       scatter_kws={\"color\": \"red\"}, line_kws={\"color\": \"blue\"}) #label=model.predict(X))\n",
        "# sns.regplot(X, model.predict(X), logistic=True)\n",
        "plt.title('Logistic Probability Plot')\n",
        "plt.show()\n",
        "\n",
        "#df_confusion_matrix=pd.crosstab(y,model.predict(X)[:,1],rownames=['Actual'],colnames=['Predicted'], normalize=True)\n",
        "#plot_confusion_matrix(df_confusion_matrix, title='Cell Confusion matrix', cmap=plt.cm.Paired)\n",
        "cm = confusion_matrix(y, model.predict(X))\n",
        "sns.heatmap(cm,  annot=True)\n",
        "plt.title('heatmap confusion matrix')\n",
        "plt.show()"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X7Rwblyo1yyW",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import statsmodels.api as sm"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x_3kqEkK1rr8",
        "colab_type": "text"
      },
      "source": [
        "# You can also implement AND study logistic regression in Python with the StatsModels package. \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mCj9Kk7w15Re",
        "colab_type": "code",
        "outputId": "ce965ee5-f9a8-4134-aa3c-97df6371c5a4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 982
        }
      },
      "source": [
        "y = np.array([0, 1, 0, 0, 1, 1, 1, 1, 1, 1])\n",
        "x = sm.add_constant(X)\n",
        "print(x, y)\n",
        "\n",
        "smodel = sm.Logit(y, x)\n",
        "\n",
        "result = smodel.fit(method='newton')\n",
        "print(result.params)\n",
        "print(result.predict(x))\n",
        "print((result.predict(x) >= 0.5).astype(int))\n",
        "print(result.pred_table())\n",
        "print(result.summary(),'\\n')\n",
        "\n",
        "# These are detailed reports with values that you can obtain with appropriate methods and attributes. \n",
        "\n",
        "print(result.summary2())\n",
        "\n",
        "# For more information, check out the official documentation related to LogitResults.\n",
        "# https://www.statsmodels.org/stable/generated/statsmodels.discrete.discrete_model.LogitResults.html\n"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[1. 0.]\n",
            " [1. 1.]\n",
            " [1. 2.]\n",
            " [1. 3.]\n",
            " [1. 4.]\n",
            " [1. 5.]\n",
            " [1. 6.]\n",
            " [1. 7.]\n",
            " [1. 8.]\n",
            " [1. 9.]] [0 1 0 0 1 1 1 1 1 1]\n",
            "Optimization terminated successfully.\n",
            "         Current function value: 0.350471\n",
            "         Iterations 7\n",
            "[-1.972805    0.82240094]\n",
            "[0.12208792 0.24041529 0.41872657 0.62114189 0.78864861 0.89465521\n",
            " 0.95080891 0.97777369 0.99011108 0.99563083]\n",
            "[0 0 0 1 1 1 1 1 1 1]\n",
            "[[2. 1.]\n",
            " [1. 6.]]\n",
            "                           Logit Regression Results                           \n",
            "==============================================================================\n",
            "Dep. Variable:                      y   No. Observations:                   10\n",
            "Model:                          Logit   Df Residuals:                        8\n",
            "Method:                           MLE   Df Model:                            1\n",
            "Date:                Thu, 16 Apr 2020   Pseudo R-squ.:                  0.4263\n",
            "Time:                        17:01:33   Log-Likelihood:                -3.5047\n",
            "converged:                       True   LL-Null:                       -6.1086\n",
            "Covariance Type:            nonrobust   LLR p-value:                   0.02248\n",
            "==============================================================================\n",
            "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
            "------------------------------------------------------------------------------\n",
            "const         -1.9728      1.737     -1.136      0.256      -5.377       1.431\n",
            "x1             0.8224      0.528      1.557      0.119      -0.213       1.858\n",
            "============================================================================== \n",
            "\n",
            "                        Results: Logit\n",
            "===============================================================\n",
            "Model:              Logit            Pseudo R-squared: 0.426   \n",
            "Dependent Variable: y                AIC:              11.0094 \n",
            "Date:               2020-04-16 17:01 BIC:              11.6146 \n",
            "No. Observations:   10               Log-Likelihood:   -3.5047 \n",
            "Df Model:           1                LL-Null:          -6.1086 \n",
            "Df Residuals:       8                LLR p-value:      0.022485\n",
            "Converged:          1.0000           Scale:            1.0000  \n",
            "No. Iterations:     7.0000                                     \n",
            "-----------------------------------------------------------------\n",
            "          Coef.    Std.Err.      z      P>|z|     [0.025   0.975]\n",
            "-----------------------------------------------------------------\n",
            "const    -1.9728     1.7366   -1.1360   0.2560   -5.3765   1.4309\n",
            "x1        0.8224     0.5281    1.5572   0.1194   -0.2127   1.8575\n",
            "===============================================================\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}