Threshold.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Threshold.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyOFYlTl5r9npPtfRIa4ypnY"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "QMQ3e-0Tm0aR"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "R9VmqWlEkipF"
      },
      "source": [
        "from sklearn.datasets import load_boston"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WA4l8eSJmE4s"
      },
      "source": [
        "from sklearn.linear_model import LogisticRegression\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.pipeline import make_pipeline"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Zl9G_yLSmJDd"
      },
      "source": [
        "from sklearn.model_selection import train_test_split,cross_val_score\n",
        "from sklearn.metrics import roc_curve,plot_roc_curve, balanced_accuracy_score"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q--Hc4VumQQe"
      },
      "source": [
        "X,y = load_boston(return_X_y=True)\n",
        "\n",
        "\n",
        "y = (y > y.mean()).astype(int)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZMmrxRlImLSQ"
      },
      "source": [
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z43ZuZvtmPI6"
      },
      "source": [
        "model = make_pipeline(StandardScaler(),LogisticRegression())"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zzf0l6HzmXX3",
        "outputId": "f7800eb5-bd64-482a-8d7b-708b65221fef"
      },
      "source": [
        "model.fit(X_train,y_train)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Pipeline(memory=None,\n",
              "         steps=[('standardscaler',\n",
              "                 StandardScaler(copy=True, with_mean=True, with_std=True)),\n",
              "                ('logisticregression',\n",
              "                 LogisticRegression(C=1.0, class_weight=None, dual=False,\n",
              "                                    fit_intercept=True, intercept_scaling=1,\n",
              "                                    l1_ratio=None, max_iter=100,\n",
              "                                    multi_class='auto', n_jobs=None,\n",
              "                                    penalty='l2', random_state=None,\n",
              "                                    solver='lbfgs', tol=0.0001, verbose=0,\n",
              "                                    warm_start=False))],\n",
              "         verbose=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "epLsoevIxk_k",
        "outputId": "16bc8ad9-47b2-4aab-8b2c-5852aebd82ea"
      },
      "source": [
        "plot_roc_curve(model,X_train,y_train)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<sklearn.metrics._plot.roc_curve.RocCurveDisplay at 0x7f934a5c0850>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dbvF6TW3mYqc"
      },
      "source": [
        "threshold = []\n",
        "accuracy = []\n",
        "\n",
        "for p in np.unique(model.predict_proba(X_train)[:,1]):\n",
        "  threshold.append(p)\n",
        "  y_pred = (model.predict_proba(X_train)[:,1] >= p).astype(int)\n",
        "  accuracy.append(balanced_accuracy_score(y_train,y_pred))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "5OsZe4iTnHA-",
        "outputId": "aa0e241f-e636-427e-c71d-0276219546ed"
      },
      "source": [
        "plt.scatter(threshold,accuracy)\n",
        "plt.xlabel(\"Threshold\")\n",
        "plt.ylabel(\"Balanced accuracy\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jZGGUpLJzGDn",
        "outputId": "ac1265d2-4d28-455d-9087-a2d66c740cc4"
      },
      "source": [
        "threshold[np.argmax(accuracy)]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.5602892029098923"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "srGZ0zfSnOfF"
      },
      "source": [
        "fpr, tpr, thresholds = roc_curve(y_train,model.predict_proba(X_train)[:,1],drop_intermediate=False)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jd1zYR6KnzYf",
        "outputId": "fd562b47-f8a3-4fbd-e506-667f71e8142d"
      },
      "source": [
        "np.argmin(np.abs(fpr+tpr-1))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "154"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "A8_BOOpDyPQu",
        "outputId": "c9505de5-9ea0-4a95-fcab-636a3db811f2"
      },
      "source": [
        "plt.scatter(thresholds,np.abs(fpr+tpr-1))\n",
        "plt.xlabel(\"Threshold\")\n",
        "plt.ylabel(\"|FPR + TPR - 1|\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Av9NUfKsy5HQ",
        "outputId": "0a0b4fdb-4fdc-483a-ce1b-d1f82d8efcbe"
      },
      "source": [
        "thresholds[np.argmin(np.abs(fpr+tpr-1))]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.44625685602433796"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    }
  ]
}