62701_lasso_dependence_on_scale.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyMjAyPFRswUoB0BR7mU43QR",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/bmreiniger/datascience.stackexchange/blob/master/62701_lasso_dependence_on_scale.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "G-hjpv3WSzM4"
      },
      "outputs": [],
      "source": [
        "from sklearn.linear_model import Lasso, LinearRegression\n",
        "from sklearn.datasets import load_diabetes\n",
        "from sklearn.model_selection import train_test_split"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X, y = load_diabetes(return_X_y=True, as_frame=True)\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=42)\n",
        "\n",
        "X['age'].hist()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "pO6z61rGS521",
        "outputId": "b7457fda-e2a5-45b5-e9c2-e11c04c7bdb7"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<Axes: >"
            ]
          },
          "metadata": {},
          "execution_count": 16
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "reg = LinearRegression()\n",
        "reg.fit(X[['age']], y)\n",
        "print(reg.coef_)\n",
        "\n",
        "reg = Lasso()\n",
        "reg.fit(X[['age']], y)\n",
        "print(reg.coef_)\n",
        "\n",
        "reg.fit(1000 * X[['age']], y)\n",
        "print(reg.coef_)\n",
        "\n",
        "reg.fit(X[['age']] / X[['age']].std(), y)\n",
        "print(reg.coef_)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qSPT-Xb7TXTL",
        "outputId": "a0ce56a9-6e5f-4e9b-c48c-a121b1d09b1d"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[304.18307453]\n",
            "[0.]\n",
            "[0.30374107]\n",
            "[13.48264074]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "TuKYe8y1T90j"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}