Lasso4RandomData.ipynb

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  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# **Lasso Regression for Random Data**\n",
        "\n",
        "This Jupyter Notebook generates a random linear dataset with Gaussian noise added to the following equation: y = 5 + 2X<sub>1</sub>. It employs the [numpy.random.rand()](https://numpy.org/doc/stable/reference/random/generated/numpy.random.rand.html) function from the [NumPy](https://numpy.org/) library to generate random noise. Then, this code uses the [Lasso](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Lasso.html) class from the\n",
        " [Scikit-Learn](https://scikit-learn.org/stable/) library\n",
        "([Pedregosa et al., 2011](https://doi.org/10.48550/arXiv.1201.0490)) to\n",
        "build a regression model for this toy dataset. The following code is similar to Jupyter Notebooks discussed by\n",
        "[Géron, 2023](https://www.isbns.net/isbn/9781098125974/).\n",
        "<br> </br>\n",
        "<img src=\"https://drive.usercontent.google.com/download?id=1A_dBySZp5D0JPTeK9p-ggP1wfTSzCTaC&export=view&authuser=0\" height=200 alt=\"Dice\">\n",
        "<br><i>This image shows a pair of dice as an analogy of random data. Image source: Pixabay: https://pixabay.com/pt/vectors/dados-jogos-jogatina-cubos-n%C3%BAmeros-160005/</i></br>\n",
        "<br> </br>\n",
        "**References**\n",
        "<br> </br>\n",
        "Géron, A. Hands-on Machine Learning with Scikit-Learn, Keras, and TensorFlow 3e: Concepts, Tools, and Techniques to Build Intelligent Systems, 3rd ed.; O’Reilly Media: Sebastopol, CA, 2023.\n",
        "[ISBN: 978-1-098-12597-4](https://www.isbns.net/isbn/9781098125974/)\n",
        "<br> </br>\n",
        "Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, Prettenhofer P, Weiss R, Dubourg V, Verplas J, Passos A, Cournapeau D, Brucher M, Perrot M, Duchesnay E. Scikitlearn: Machine Learning in Python. J Mach Learn Res., 2011; 12:2825–2830.\n",
        "[DOI: 10.48550/arXiv.1201.0490](https://doi.org/10.48550/arXiv.1201.0490)\n",
        "<br> </br>\n",
        "It follows the complete Python code."
      ],
      "metadata": {
        "id": "Ow35NMeKjlR8"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Fv6CVTbijE1v",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 716
        },
        "outputId": "17db7581-3f26-4ae4-fad5-c4c9a893f3bf"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Generating and plotting random linear data......done!\n",
            "\n",
            "Generating Lasso regression models and plotting them......\n",
            "\n",
            "Model 1: [5.57707549 1.93915383] MSE: 0.0882\n",
            "\n",
            "\n",
            "Model 2: [6.21476457 1.62170981] MSE: 0.2627\n",
            "\n",
            "\n",
            "Model 3: [9.04893826 0.21084751] MSE: 4.4953\n",
            "done!\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "#!/usr/bin/env python3\n",
        "#\n",
        "################################################################################\n",
        "# Dr. Walter F. de Azevedo, Jr.                                                #\n",
        "# [Scopus](https://www.scopus.com/authid/detail.uri?authorId=7006435557)       #\n",
        "# [GitHub](https://github.com/azevedolab)                                      #\n",
        "# July 20, 2024                                                                #\n",
        "################################################################################\n",
        "#\n",
        "################################################################################\n",
        "# Import section                                                               #\n",
        "################################################################################\n",
        "import numpy as np\n",
        "from sklearn.linear_model import Lasso\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.metrics import mean_squared_error\n",
        "\n",
        "################################################################################\n",
        "# Randomly generated linear dataset                                            #\n",
        "################################################################################\n",
        "msg_out = \"\\nGenerating and plotting random linear data...\"\n",
        "print(msg_out,end=\"...\")\n",
        "np.random.seed(1123581321)          # Set up a random seed\n",
        "X = 4*np.random.rand(100,1)\n",
        "y = 5 + np.random.rand(100,1) + 2*X\n",
        "X_b = np.c_[np.ones((100,1)), X]    # Add x0 = 1 to each instance\n",
        "\n",
        "# Plotting randomly generated linear dataset\n",
        "plt.title(\"Randomly Generated Linear Dataset (y = 5 + 2*X$_1$)\")\n",
        "plt.plot(X,y,\".\", color = \"black\")\n",
        "plt.xlabel(\"X$_{1}$\")\n",
        "plt.ylabel(\"y\")\n",
        "plt.axis([0,4,0,15])\n",
        "plt.grid()\n",
        "plt.savefig(\"random_data.pdf\",dpi=1500)\n",
        "plt.close()\n",
        "print(\"done!\")\n",
        "\n",
        "################################################################################\n",
        "# Generate a Lasso regression model                                            #\n",
        "################################################################################\n",
        "msg_out = \"\\nGenerating Lasso regression models and plotting them...\"\n",
        "print(msg_out,end=\"...\")\n",
        "\n",
        "# Initial plotting\n",
        "plt.title(\"Lasso Regression Models for a Random Dataset (y = 5 + 2*X$_1$)\")\n",
        "plt.plot(X,y,\".\", color = \"black\")\n",
        "plt.xlabel(\"X$_{1}$\")\n",
        "plt.ylabel(\"y\")\n",
        "plt.axis([0,4,0,15])\n",
        "plt.grid()\n",
        "\n",
        "# Generate regression models and plot them\n",
        "# Set up an new array for predictions\n",
        "X_in = np.array([[0],[4]])\n",
        "X_in_b = np.c_[np.ones((2,1)), X_in] # Add x0 = 1 to each instance\n",
        "\n",
        "# Set up string and lists for regression models\n",
        "alpha_lst = [0.05,0.5,2.5]\n",
        "color_lst = [\"red\",\"green\",\"blue\"]\n",
        "\n",
        "# Looping through regression models\n",
        "for i,a in enumerate(alpha_lst):\n",
        "\n",
        "    # Regresion\n",
        "    lin_reg = Lasso(alpha = a)\n",
        "    lin_reg.fit(X,y)\n",
        "\n",
        "    # Prediction\n",
        "    theta_vector = np.array([lin_reg.intercept_[0],lin_reg.coef_[0]])\n",
        "    y_predict = X_in_b.dot(theta_vector)\n",
        "\n",
        "    # Plotting\n",
        "    plt.plot(X_in,y_predict, \"-\", color = color_lst[i],\n",
        "                    label = \"Model \"+str(i+1)+\" ($\\\\alpha$ = \"+str(a)+\")\")\n",
        "    plt.legend()\n",
        "\n",
        "    # Prediction for metrics\n",
        "    y_predict = X_b.dot(theta_vector)\n",
        "\n",
        "    # Calculate MSE\n",
        "    print(\"\\n\\nModel \"+str(i+1)+\":\",theta_vector, end = \" \")\n",
        "    print(\"MSE: {:.4f}\".format(mean_squared_error(y, y_predict)))\n",
        "\n",
        "# Save plot\n",
        "plt.savefig(\"lasso_regression_5_plus_2x.pdf\",dpi=1500)\n",
        "print(\"done!\")\n",
        "###############################################################################"
      ]
    }
  ]
}