L1,L2.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyPcDKFcTtyoxBB0UiPAaBhV",
      "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/Megha1230/ML/blob/main/L1%2CL2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0cQwgZIq-hzv"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x=np.array([1,2,3,4,5])\n",
        "y=np.array([2.1,3.8,6.5,9.2,11.3])"
      ],
      "metadata": {
        "id": "NzvcjyM1-soz"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x_b=np.c_[np.ones((x.shape[0],1)),x]\n",
        "x_b"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YLBPDqwu-slL",
        "outputId": "25a24d00-7b12-4cf6-ba4a-ef19dfd7831f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1., 1.],\n",
              "       [1., 2.],\n",
              "       [1., 3.],\n",
              "       [1., 4.],\n",
              "       [1., 5.]])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "alpha_ridge=1.0\n",
        "alpha_lasso=0.1\n",
        "num_iterations=1000\n",
        "learning_rate=0.01"
      ],
      "metadata": {
        "id": "ui1bBw0j-sZ5"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#can be minimized to 0\n",
        "def lasso_regression(x,y,alpha,num_iterations,learning_rate):\n",
        "  m,n=x.shape\n",
        "  theta=np.zeros(n)\n",
        "  for _ in range(n):\n",
        "    y_pred=x.dot(theta)\n",
        "    gradient=(x.T.dot(y_pred-y)-alpha*np.sign(theta))/m\n",
        "    theta-=learning_rate*gradient\n",
        "  return theta"
      ],
      "metadata": {
        "id": "g0cn4POY_-j9"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#cannot be minimized to 0\n",
        "def ridge_regression(x,y,alpha,num_iterations,learning_rate):\n",
        "  m,n=x.shape\n",
        "  theta=np.zeros(n)\n",
        "  for _ in range(n):\n",
        "    y_pred=x.dot(theta)\n",
        "    gradient=(x.T.dot(y_pred-y)+alpha*theta)/m\n",
        "    theta-=learning_rate*gradient\n",
        "  return theta"
      ],
      "metadata": {
        "id": "SSBCQGjZA-ZM"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "theta_ridge=ridge_regression(x_b,y,alpha_ridge,num_iterations,learning_rate)\n",
        "theta_lasso=lasso_regression(x_b,y,alpha_lasso,num_iterations,learning_rate)"
      ],
      "metadata": {
        "id": "vblLV486BWHJ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.scatter(x,y,label='Data')\n",
        "plt.plot(x,x_b.dot(theta_ridge),label='Ridge (L2) Regression',color='black')\n",
        "plt.plot(x,x_b.dot(theta_lasso),label='Lasso (L1) Regression',color='red')\n",
        "plt.xlabel('X')\n",
        "plt.ylabel('Y')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 449
        },
        "id": "zBo5zgJ2DuS9",
        "outputId": "c00aca2f-c142-41f5-bfc9-a8a2c0e0a8a9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}