Lasso_Regression.ipynb

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  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Lasso Regression.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "kmVVEI-YVJD2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#importing libraries\n",
        "\n",
        "import numpy as np \n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5sa9nJMqVUJs",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Generating Training data set\n",
        "No_of_observations = 50  \n",
        "No_of_Dimensions = 50\n",
        "\n",
        "X_input = (np.random.random((No_of_observations, No_of_Dimensions))-0.5)*10 #Generating 50x50 matrix forX with random values centered round 0.5      \n",
        "actual_weight =  np.array([1, 0.5, -0.5] + [0]*(No_of_Dimensions-3)) # Making first 3 features significant by setting w for them as non-zero and others zero\n",
        "Y_output = X_input@actual_weight + np.random.randn(No_of_observations)*0.5 #Setting Y = X.w + some random noise "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sH6wXkQLVbYm",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Initialising lambda(L1_coefficient) and alpha(learning_rate)\n",
        "losses = [] #Setting empty list for losses\n",
        "L1_coeff = 5    \n",
        "alpha = 0.001 "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NyGWBbsGXbZt",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#random initialisation of theta(weights)\n",
        "weight = np.random.randn(No_of_Dimensions)/np.sqrt(No_of_Dimensions) #Setting w to random values\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7NwgbD8yW1sU",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#implementing Hypothesis function\n",
        "def hypothesis(X, theta):\n",
        "  return X@theta"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "06Yhwn7pYkzb",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#implementing loss function (mean Square Error)\n",
        "def loss(theta, X, y):\n",
        "  return np.mean(np.square(hypothesis(X, theta) - y))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8lEt_mXuVppy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#implementing a training loop with 500 epochs\n",
        "for i in range(500):\n",
        "    delta = hypothesis(X_input,weight) - Y_output #the error between predicted output and actual output\n",
        "    weight = weight - alpha*(X_input.T@delta + L1_coeff*np.sign(weight)) #performing gradient descent for w\n",
        "    losses.append(loss(weight,X_input,Y_output)) #Appending mse for each iteration in losses list\n",
        "    "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2Laq8cp-lrED",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "f26b0346-a8ef-4b2f-a8a7-a45e4e6a4c97"
      },
      "source": [
        "losses[-1]"
      ],
      "execution_count": 103,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.1196436339716497"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 103
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pnXiB7EKV3v5",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "8bf59bec-f881-42e8-db28-9178bec2ad2e"
      },
      "source": [
        "# plot our weight vs true weight\n",
        "plt.plot(actual_weight, label='true weight')\n",
        "plt.plot(weight, label='weight determined by model')\n",
        "plt.legend()\n",
        "plt.show()\n"
      ],
      "execution_count": 104,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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RFst1lNba9j//8z9cd911FBUVtfofzhlnnMH111/PoEGD6Nu3L9OnT2987ZJLLmHcuHHk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\nG2OMS1jgG2OMS/x/wwr+pdZnE9AAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V7k1Aom4V6RD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}