Linear_Regression_from_Scratch.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "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/SrivinaySridhar/MLT_workshop/blob/main/Linear_Regression_from_Scratch.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "3RQLKkM58BiF"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import random"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Data\n",
        "\n",
        "$\\mathbf{X}$ is a feature matrix corresponding to $n$ training examples, each represented with $d$ features and has shape $d \\times n$.  \n",
        "\\begin{equation}\n",
        "  \\mathbf{X}_{d \\times n} = \\begin{bmatrix}\n",
        "       | & | &\\dots & |\\\\\n",
        "       \\mathbf{x}_{1}&  \n",
        "       \\mathbf{x}_{2} &\n",
        "      \\dots &\n",
        "       \\mathbf{x}_{n}  \\\\\n",
        "        | & | &\\dots & |\\\\\n",
        "    \\end{bmatrix}\n",
        "\\end{equation}\n",
        "\n",
        "* here each $\\mathbf{x}_i \\in \\mathbb{R}^d$\n",
        "\n",
        "*  $\\mathbf{y}$ is a label vector of shape $n \\times 1$.  \n",
        "\\begin{equation}\n",
        "    \\mathbf{y} = \\begin{bmatrix}\n",
        "        y_{1}  \\\\\n",
        "        y_{2} \\\\\n",
        "        \\vdots  \\\\\n",
        "        y_{n} \\\\\n",
        "      \\end{bmatrix}\n",
        "\\end{equation}\n",
        "\n",
        "*  The $i$-th entry in this vector, $\\mathbf{y}[i]$ gives label for $i$-th example, which is denoted by $y_{i} \\in \\mathbb{R}$."
      ],
      "metadata": {
        "id": "FAlr8M-Z8Zor"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Training data\n",
        "\n",
        "Generated from a deterministic distribution with Noise ~ Normal(0, 1)\n",
        "\n",
        "$$y_{train} = 2X^3 + 3X^2 + 4 + Noise$$"
      ],
      "metadata": {
        "id": "5xKGE4b6hTq5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "rng = np.random.default_rng(seed = 101)\n",
        "\n",
        "X_train = (np.arange(-2, 2, 0.01).reshape(1, -1))\n",
        "\n",
        "y_train = (2 * (X_train)**3 + 3 * (X_train)**2 + 4 + rng.normal(0, 1, X_train.shape[1]).reshape(1, -1)).T"
      ],
      "metadata": {
        "id": "GbDDcyLKiGsq"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "X_train.shape, y_train.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "W5D5VxgK_A6o",
        "outputId": "4bb0b53a-544d-495f-82a7-59062565794e"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((1, 400), (400, 1))"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.scatter(X_train, y_train);"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "OUqra1H_A_vb",
        "outputId": "352ebb52-e42b-420b-a87c-e396976ce520"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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Ul6YXJES+B8CcDyIiooDZ7ALKaxtwrqkNvTI7114RAwg5Qyg/viUPU4bH79Radww+iIiIAlBaVYeSTdUuQysGnQazx/ZF/5wM5GRoYNBpUW9pg+DlGCoAv581Ct8d2TssbY4WDD6IiIhkKq2qw7zVFV2CCpPFiuVbjjn+n5WeAgGdQYanAGTlfaMwZXhiBR4Acz6IiIhkEWexeOvNcNbY0rl2S4bG9be+Ua/FW3NGJ2TgATD4ICIikkXuLBYAuGS97Ph3hiYJP7j+akzMNyjdtJjB4IOIiEiGYAuBNVtteH3rcYz55WaUVtUp1KrYwuCDiIhIBqUKgTW2dGDe6oqEDEAYfBAREckwNi8bRr0WSlTkEACUbKqGzS4lgyR+MPggIiKSIUmtwtJp+QCgSABSZ25DeW2DAkeKHQw+iIiIZCouMOLNOaNh0CszBJMoC8qJWOeDiIgoAMUFRkzMN6C8tgEmcyuWbDzsMqtFjkRZUE7E4IOIiChASWoVCgf2AACkpSZ5LDzmiwqAQa9NmAXlRBx2ISIiUsDEfAOeLLoGGalJsvZbOi0/YRaUE7Hng4iIKEie1nnxJys9Bb+eUQB9Wio2Vp7psjBdPGPwQUREFARv67z481Bhf7z04RGXgMWo12LptHwUF8T3CrccdiEiIgqQnHVeRCp09nq8sfVYl54Sk7ktIQqPMfggIiIKkNx1XpxXt/UUsIi3xXvhMQYfREREAZJbn8Og12Jh0WDHareeCIj/wmPM+SAiIgqQ1PocC24fhPGDcjA2LxsfHDwraZ94LjzG4IOIiChAF5utfrcx6rVYOPEaxywWqQFLPBce47ALERFRAGx2AS99eMTvdsVDO6ugijkc/hamU6EzYInnwmMMPoiIiAIgNdl01acnMPvtvbj5lW0orarzuTCd+P94LzzG4IOIiCgAcnMynKfReluYzqDX4s05o+O+zgdzPoiIiAJw4nyzrO0FdPZslGyqxsR8g8vCdOea2hKqwqmsno9ly5bhhhtuQGZmJnr16oUZM2bg6NGjLtu0tbVh/vz56NGjB7p164Z77rkH9fX1ijaaiIgokmx2AWvLT8nez30arbgw3fSRV6FwYI+ECDwAmcHHzp07MX/+fOzduxebN29GR0cH7rzzTjQ3fxv9LVy4EJs2bcL69euxc+dOnD17FjNnzlS84URERJFSXtsAk8X/TBdv4nkarRSyhl1KS0td/v/OO++gV69e2L9/P2655RaYzWb85S9/wZo1azBhwgQAwKpVq3Dddddh7969uPHGG5VrORERUYQEGzzE8zRaKYJKODWbzQCA7OzO6UD79+9HR0cHioqKHNtce+216Nu3L8rKyjwew2q1wmKxuPwRERFFs0CDh0SYRitFwMGH3W7Hk08+ifHjx6OgoAAAYDKZkJqaiqysLJdtc3NzYTKZPB5n2bJl0Ov1jr8+ffoE2iQiIqKw8Ferw5NEmUYrRcDBx/z581FVVYV169YF1YDFixfDbDY7/r7++uugjkdERBRqUmp1ZKWnuNyeKNNopQhoqu2CBQvwwQcfYNeuXbj66qsdtxsMBrS3t6OxsdGl96O+vh4Gg8HjsTQaDTQaTSDNICIiihixVkfJpmqXYmMGvRZLp+Un7DRaKWQFH4Ig4PHHH8eGDRuwY8cO5OXludw/ZswYpKSkYOvWrbjnnnsAAEePHsWpU6dQWFioXKuJiIgiwGYXXAKKifkGn0FG4cAeEW5xdJIVfMyfPx9r1qzBxo0bkZmZ6cjj0Ov1SEtLg16vx9y5c7Fo0SJkZ2dDp9Ph8ccfR2FhIWe6EBFRzLLZBazYdhyr9tSisbXDcbvxSi8Hh1LkUQmCIEjeWOW5u2jVqlV46KGHAHQWGXvqqaewdu1aWK1WTJo0CX/4wx+8Dru4s1gs0Ov1MJvN0Ol0UptGRESkGOcejhPnW7oEHSLxqshcDnnXb1nBRzgw+CAiokgqrarrksfhiwqdeR67n5mQ0Dkdcq7fXFiOiIjoitKqOsxbXSE58AC6lkwn/xh8EBERoXOopWRTNQIdDkj0kulyMPggIiJC53otcno83CV6yXQ5GHwQEREhuJ4LlkyXh8EHERERgJxugRe8ZMl0eRh8EBFRwiutqsNT/6wMaF99WjIm5ksrJ0GdGHwQEVFCE2e4mCzWgPY3t17Gim3HFW5VfGPwQURECSvYGS6i5Vu+QmlVnSJtSgQMPoiIKGEFO8PFWcmmatjsUVW3M2ox+CAiooSlZG0OFhqTjsEHERElLKVrc7DQmDQMPoiIKGGNzcuGUa+FUpNkT5xvUehI8Y3BBxERJRybXUBZzQV8cPAsZt3QFwAUCUBeZ+KpJMmRbgAREVE4eVq1NistGZftwCXr5aCPX7KpGhPzDSw65gN7PoiIKGF4W7W2sfWyS+CRqU0K6Phc4VYaBh9ERJQQ5NT0aGqzBfVYTDz1jcEHERElBCVrevjDFW59Y84HERElhHD0RqgAGLjCrV/s+SAiooQQ6t4IMb2UK9z6x+CDiIgSgtI1PbLSUlz+b9Br8eac0SguMCr0CPGLwy5ERJQQktQqLJ2Wj3mrK6ACgl5MbuV9o6FWq3CuqQ29MjuHWtjjIQ2DDyIiShjFBUa8OWd0lzofcoh5HTcO7MFgI0AMPoiIKKEUFxgxMd+A8toGnGtqw4nzLVhbfgomi1PRsfQUNLZ0dOkhYV6HMhh8EBFRXLHZBUdg4W04JEmtwti8bEcxsP+9dwSgAs5fsjr22Vxt6tJDYtBrsXRaPvM6gsTgg4iI4oan0ulGDwGD5xLrKXh4fH98d3hvJKlVXXpImNehHJUgCMHm3CjKYrFAr9fDbDZDp9NFujlERBQjxNLp7hc1MVQQZ6J4206UlZ6Cl2cOY++GTHKu35xqS0REMc9X6XThyt+z/z6E/3z1DV5833eJ9caWDsxbXcHVaUOIwQcREcU8KaXTG1s78MBfy10SS70R0Lk6rc0eVYMDcYPBBxERxbxQlE7n6rShw+CDiIhiXqhKp3N12tBg8EFERDFP6dLpopwMjcJHJIDBBxERxQGxdDoARQOQp9Z/wcTTEGDwQUREcUEsnW7QKzcEU29p48yXEGDwQUREcaO4wIglU/P9bqcCkJWWjG4a37U2xbkunPmiLAYfREQUN2x2Ac+9d8jvdgKAxtbLuGS9LGlbznxRFoMPIiKKGyu2HUNjS4ff7fz1eHjCmS/KYfBBRERxwWYXsGrPCUnbSunxcBeq6byJiAvLERFRXCivbUBjq/9eD7lU6FzNdmxetuLHTlTs+SAiophmswsoq7mAjyXOSMlIlX7pE6ftLp2Wz9VsFSQ7+Ni1axemTZuG3r17Q6VS4b333nO5/6GHHoJKpXL5Ky4uVqq9RESU4MRgY2PlGbyx5RjGv7wNs9/ei7+VnZR4BOlBhEGvdayGS8qRPezS3NyMESNG4Ec/+hFmzpzpcZvi4mKsWrXK8X+NhhXiiIgoeKVVdSjZVO13ETlfmtttfreZO74/ivINGJuXzR6PEJAdfEyePBmTJ0/2uY1Go4HBYAi4UURERO5Kq+owb3UFQlltw6jXYum0fPZ0hFhIcj527NiBXr16YciQIZg3bx4uXLjgdVur1QqLxeLyR0RE5MxmF1CyqTrgwCMjNUnSdq99bwQDjzBQPPgoLi7G3/72N2zduhWvvPIKdu7cicmTJ8Nm89zNtWzZMuj1esdfnz59lG4SERHFuPLahoCGWtKvBB1ShloA4HyzVfZjkHyKT7WdNWuW49/Dhg3D8OHDMXDgQOzYsQN33HFHl+0XL16MRYsWOf5vsVgYgBARkYtAC3y1SAw6RKzlER4hn2o7YMAA5OTk4Pjx4x7v12g00Ol0Ln9ERETOQh0UqNCZ78FaHuER8uDj9OnTuHDhAoxGjqEREVFgxuZlw6jXypgkKx1reYSf7ODj0qVLqKysRGVlJQCgtrYWlZWVOHXqFC5duoSnn34ae/fuxYkTJ7B161ZMnz4dgwYNwqRJk5RuOxERJYgktQpLp3WuVqt0eMBaHuEnO/j4/PPPMWrUKIwaNQoAsGjRIowaNQovvPACkpKScPDgQdx111245pprMHfuXIwZMwb/+c9/WOuDiIiCUlxgxJtzRsOgdx2CyUoLLn3x+9f3YeARZipBEEI5ZVo2i8UCvV4Ps9nM/A8iIurCZhdQXtuAc01tyMnQ4Kn1X8BkCbzoWFZ6CvY/P5FDLkGSc/3m2i5ERBRTktQqFA7sgekjr4JarQoq8ACAxpYOlNc2KNQ6koKr2hIRUdRz7u3olal1lD0PNvAQBTqVlwLD4IOIiKKap/VcjHot7hphxPr9pxV5DNb3CC8GH0REFLW8redSZ27DH3fVSjqGSgV4y25UoXO2C+t7hBdzPoiIKCoFu56L6srfo9/J8zg9l/U9Ioc9H0REFJUCXc9FlKFJxmv3DkdxgRGj+nbvMnRj4Aq2EcPgg4iIoo7NLuBvZSeCOsYl62XHv4sLjJiYb/CYtErhx+CDiIiiSmlVHZ599xAaWzqCPlbJpmpMzDcgSa1yTNGlyGPOBxERRY3Sqjo8trpCkcAD6ExMZQ2P6MPgg4iIooKYYKo01vCIPgw+iIgoKuz974WgEky9YQ2P6MOcDyIiirjSqjo8++9Dih6TNTyiF4MPIiIKG09l0jdXmzwWEgsGa3hENwYfREQUFp7KpBt0GrRdtisaeACs4RHtGHwQEVHIeSuTbrJYZR0nIzUJze02r/ffcW1P/M93BrKGR5Rj8EFERCEVbJl0AEhPTcKPbxmABRMGY3O1qUsPSnZGCn45vQBThvcOvsEUcgw+iIgopIItkw4Abz9wPcYPzgHAaqXxgMEHERGFVDB1NsQZKze6VSZltdLYxjofREQUUoHW2eCMlfjF4IOIiEJqbF42jHqtx2XtfTHotXhzzmjOWIlDDD6IiCikktQqLJ2WL2ufJVOvw86nb4c+LRUbK8+grOYCbHalJ+RSpDDng4iIQq64wIg354zGi+8f9jm9VszxMOrTcOtvtrskqhpZuyNusOeDiIjCYmK+Af9770hMLsj1eL84LHPXCCPmr6noMkPGZG7DvNUVKK2qC3FLKdTY80FERLJ4KpHuLyHUU3VTtQpwHkkx6LVYMvU6vPThEY81QcTbXnz/MCbmG5iEGsMYfBARkWSegghPwyE2u4C9NRdQ9t/zqPmmGR9XmbocSww85o7vj6J8A8bmZUuqCWKyWLFi23E8UTRYmZOisGPwQUREkngtkX5lOEScmVJaVYdn3z2ExpYOv8dUAfioyoTnpnZOp91S3TVI8WT5lq8wxNCN+R8xisEHERH55atEuoDOIKJkUzXsduAnayokH1cAUGduQ3ltA8yt7fjLnhOS9y3ZVM3hlxjFhFMiIvLL33CIGET8/L1DAR3/w0Nn8dyGKln7iEELxR72fBARkV9SS6RflDDU4snqvacC2i+Y0u0UOez5ICIivwItkR5q0dou8o3BBxER+eWvRLoKncvah4sKnbNsxuZlh+0xSTkMPoiIyC/nEunuAYj4/19OL4BBpwl5W7jgXOxj8EFERJKIJdINetehDnEBuCnDe+PFu4b6Pc5t1+QE1Q4uOBf7VIIgRNVKPRaLBXq9HmazGTqdLtLNISIiN/4qnHqr89E9PQXLZg6DPi0Vs9/eK/nxDDoNZo/ti/45GZIrqlL4ybl+c7YLERHJkqRWoXBgD6/3FxcYMTHf4KhwCnRuf+OAHkhSq2CzCzDqtX4rmT58U3/cOdTAYCMOseeDiIjC7oPKs1iw7oDPbYx6LXY/M4GBR4xgzwcREUUN92Gai83teGGT/4JideY27K25gPGDg8sRoejD4IOIiBTlHGycON+CteWnYLIEVgxs/poKvHzPMCaXxhkGH0REpBhPq94Go7G1w2XROooPsqfa7tq1C9OmTUPv3r2hUqnw3nvvudwvCAJeeOEFGI1GpKWloaioCMeOHVOqvUREFKXEVW+VCjyclWyqhs0eVSmKFATZwUdzczNGjBiBlStXerz/1Vdfxe9+9zu89dZb2LdvHzIyMjBp0iS0tbH+PhFRvLLZBbz4vudVb4PlvPItxQfZwy6TJ0/G5MmTPd4nCAJef/11PP/885g+fToA4G9/+xtyc3Px3nvvYdasWcG1loiIotKKbccCzuuQiovIxQ9FK5zW1tbCZDKhqKjIcZter8e4ceNQVlbmcR+r1QqLxeLyR0REsaO0qg7Lt4R+eJ2LyMUPRRNOTSYTACA3N9fl9tzcXMd97pYtW4aSkhIlm0FERAoTZ7CYzK1oaG5HdjcNDDotRvbJwnMb/E+bDYYKnSXVuYhc/Ij4bJfFixdj0aJFjv9bLBb06dMngi0iIoo//kqi++JrBosKCEmeh/PxAS4iF28UDT4MBgMAoL6+Hkbjt1Oi6uvrMXLkSI/7aDQaaDShXwWRiChReQoejHotlk7L9zt9VZzB4i3AUDLwyEpPgTY5ySV3xCCxnRRbFA0+8vLyYDAYsHXrVkewYbFYsG/fPsybN0/JhyIiIgm8BQ8mc5vH+hnOPSQ5GZqQzWBxJvZnvDxzGCbmGwLuoaHYITv4uHTpEo4fP+74f21tLSorK5GdnY2+ffviySefxC9/+UsMHjwYeXl5WLJkCXr37o0ZM2Yo2W4iIvLDZhdQsslz8CCg86JfsqkaE/MNSFKrFC8QJpV774avResoPsgOPj7//HPcfvvtjv+L+RoPPvgg3nnnHfzsZz9Dc3MzHn30UTQ2NuLmm29GaWkptFpmKRMRhVN5bYPPQMK5foa5td3n8IrSsjNSsOS7Q2HQsXcjEckOPm677Tb4WghXpVLhF7/4BX7xi18E1TAiIgqO1LoYJnMrXv3kaNgCDwBoaO6AQadlL0eCUrTOBxERRQ+pdTEamtvDPtQCsGhYImPwQUQUp8bmZcOo18LbgIYKnbNeTl9sVewx5QyesGhY4mLwQUQUp5LUKiydlg+ga1Ag/v+uEUas+vSEYo+pT0vBE3cMgkHnP+hh0bDExeCDiCiOFRcY8eac0TDoXXsZDHotVt43Cu9/UafI43TTJAEAGls78MbW42i7bHPMqHHGomEEREGFUyIiCq3iAqPH+hn+ZsPIcclqc/m/uaUDAKBPT0HjlX8DLBpGnRh8EBElgCS1yhFwnGvqnF4bylVoxV4PbbIaf/+fcTh/ycqiYeTA4IOIKAF4KiCWnZES0scUAJgsVqhVKkwfeVVIH4tiC3M+iIjinFhi3X2IpaG5w8seytpc7XlVc0pcDD6IiOKYrxLrwZLac/LXPSdQWqVMYivFBwYfRERxTMmkUlFWWgr+/j/jsHdxEYx6/7U6xDVkbPZw1lClaMbgg4gojoWiimhjawfUKhVSk9WOOiK+OK8hQwQw+CAiimuhqiIqBjXFBUbMHd9f1j5EnO1CRBQHbHahSx0PcXqtUa+FydymaN5HToYGZTUXcK6pDb2z0iTtw3LqJGLwQUQU5bwFFiJP02iNTsW8lk7Lx7zVFVABigQgWekpeGr9Fy51QtQqwFtKhwqdxcVYTp1EDD6IiKKYv8BCnEbrft03mdswb3UF3pwz2lFi/cX3D8NksQbdps6Kpa7TdH0FHgDLqZMr5nwQEUUpb/U56sxteGx1BZZvPooX3/c8jVa8rWRTNdov26FPS8U9o68OeZvd4wuDXusIgIhEKkEQomruk8VigV6vh9lshk6ni3RziIgiwmYXcPMr2xSZJpudkYqG5nYFWiXNkqnXISdTw3LqCUbO9ZvDLkREUUjJ+hzhDDwA4ExjK+Z+Z0BYH5NiC4MPiln+kvCIYon7+zmUi74FQk6y6sbKs/j5VOZ4kHcMPijslAga/CXhEcWSSCz6JpdBr8WSqdfh+Y1VfteEudDcjvLaBhQO7BGm1lGsYfBBYaVE0CA1u58oFnh7P4dr0TcpsjNSsPPp25GarMb+kxfxlz0n/O7DgmLkC2e7UNh4y9wXgwYpC0/5WiTLObufa0hQLAjlom8ZqUmKHauhuQP7T14EABTlGyTtw4Ji5At7Pigs/AUN4sJTE/MNPodg/CXhOa8hMTYv2zG8k5OhAVTA+UvWgId6mGNCSpOaVNo9PQUXW7z3hKgA5Oo0mHVDX7zz6Qk0tnagud2mYEu/7cnwVzGVBcVICgYfFBZyggZf48RSu3I3V5uw6J+VXh8zkKEe5piQ0qS+n2eM7I31+8/gkvVyl/vE8Hf6yN54Y+uxkPSiAN/2ZCSpVV4rprKgGEnFYRcKC6lfsv62k9qV+9c9J3wGO3KGepQYLoomNruAspoL2Fh5BmU1FzhEFUFS38+rPj3pMfAAOkudr7xvFP7x+emQBB4qdAbazj0ZYsVUg961/SwoRlKx54PCQuqXrL/tpCyS5WuNCZHUoR6lhouiBXtwoosS72dNshpf1V+6UvJcWb56MooLjJiYb+BQJAWEPR9xJtp+1YrtMZlbkZ2RCm9fS55+XXkidvmK+7gfA/AfeIich3q8kTNcFO3irQcnHijxfjZZrFi547jibQP892QkqVUoHNgD00dehcKBPRh4kGTs+Ygj4fhVKyfp0lN7PJE7Tix2+bof26DXYkqBQdI0QGe+hnqUGi6KtHjrwYknSryfO2zK/chYcPtADM7NZE8GhRSDjygn9WIf6toXNruAFduOY9WeWjS2ftu96y248dYeTwx+AiRPz4G3Lt/y2gbZwUdOhsbrfcEMF0l57cI1g0aphF8KDSXfz8EaP6gn3wMUcgw+opjUnoxQ/6otrarDs+8e8jim7Cm4kVK7ICM1CQ+N74+bBubgxgHeu2v9PQfuX5JSxtDdPbX+C7x4l+fgJ9BphVJeu3DmX0jtmdlz/Bv+2o0QcQgD+DYoNZlbkalNRlOb52RTJXGKLIUTcz6ilJzx+VDmJZRW1eGx1RVek9k8FfaSUrugud2Gldtr8NP1X2BztcnrY8vNUfA1hu5NvSWw43kbLpLS7kDOLZh8Hqk9OCu21+DmV7ZFTf5HtOUwhUNpVR1ufmUbZr+9Fwv/+UXYAg+AU2QpfNjzEYXk9mQEk5fgq9tfbIc/7l32cvIfvA0LBdOb420M3Vf73Y/n/rysvG80Xvqw65i8p16oF9/33e4X3z8MQCXr3ILtJZHTIxQtZerDPTPH3xCYt/uVHDqTM1wZCBUAfXoKtMlJLgvX+Rv6JFIag48oJHd8PtC8BH9f7nKX9D7X1AabXcD5JqvkfbxdbOU+B+4XgIn5Bpcx9HMWK3710RFJxzO3tnt8XpZMvQ7dMzQ+Lz7/+eq8z9VIBXTOTvD3nDifm7cLUp25DY+trsBbEoIEX4WhPD1+pBNQw71+j7/Pgrf77xphxPtf1AUVIDkPsbz04ZGQBh4A8PLMYZwiSxHH4CMKye3JCCQvQcqXu/WyXVa7//PVN1i68bBLQqoU4sX2nT21yMnUyFpO/FxTm6RfyBsrz0g63uZqE1btOeHxeZm/5gDenDMa00de5bhd6oyeQIjBnL/8mWffPSQpSJDTIxTJBNRwz8zxF9w98p08/Pk/tR7v/+Ou2i7HkxMUhvL9o1IBglOj3Xs3mFRKkcTgIwrJ7clIUquwZGo+frKmoss2nsZypX65v3bvCMltVgH4V4W0C7w3L334bc+E1OXET5xvwetbvvL7C1nqc7p+v+cqkZ4ueqHuIu+VqZXU+9TY0oEV247jiaLBfo8pzqpYvvkrrNjuvzZEJKYQBzozJ5DhDynB3dv/6RpgSOEvKAz1+2fl7FEee+qIogETTqOQ2JMhtSBXaVUdXvrQc26GpyJBUr/cIcBnO9z3UZK/5cRVAAw6DdaWn/IaLAjozK+w2QW/z6nIV3Kf80UvlKuROr++Ui/+qz6tlZyMmaRWYfygHEnbHqu/FHSip9yk0UBymJyTNJ9YV4nZb++VlDgrd2hRDjEo9MRXbpA/3xt9FbLSvAfn3dNT8Nac0ZgyvDcLgFHUYs9HFJKzcJO/X09Lpl7XpetX6pf7+War3zwB967dUPD2HMwe2xfLtxzzua/JYnX0CkjNefDnXFNbyC5a7q/vifPNkvZrbOnwOkTiqUdAagLqiu3HsWL7cb95DN56HQJJGpXb8xdMfkioe3ZWfVqLBRMGdbnwr9h2TPLQojOjXotXvtfZIynmiZy/ZEVjawdU6Jyq62vqOlG0YPARpbyNz+vTUvDw+P6YmG/w++tbhc6hjEkFRpcvIzlf7oUDe3hsR1ZaCoqu6yV7qCWQC383tzoH4ti11JyU5Vu+whBDN9mzYLw5cb4l4H39cR6Xt9kFrC0/JXnfPce/kXXxlxOMiXkMC4sGY8GEzuEdMdg4cb4Fa8tPuVxMxWTMP+3qmivhLyiQk8MUbH6I1M9CoBpbOvDOnlo8UNgf+09edDxf/oJmb2bd0NdxHszZoFimEoRQ/26Vx2KxQK/Xw2w2Q6fTRbo5EWezC/j91mP48+7/4pLV5rjdqNdi1g19JH2JrX3kxi5j4ze/ss3vl/vuZyY4ZnPsrbmAsv+eB5x+XX1w8CyeWFcp+Vy6aZKRnKQKaAGsDE0SZl3fB0X5Bozp1x37T17EnuPfYMX2Gkn7G93OR/zV+ML7h2XXUTDqtXjt3hG4/8/7ZJ+HJ0umXudItHUely+ruYDZb+8N6Ji+Lv7iJfjNOaMBQHYwlpGaBKCzVkug3N9j7sTeDMBzr5cYuEh9jtw/AyLxsxCqoReRlMUOpXhj1kiXhGeiaCLn+q14z8eLL76IkpISl9uGDBmCL7/8UumHSgivlh7xmlEv9deTe9ey3GEd94vTvytOY+m0fNm/GputlyEAWFg0GP1zMnC+yeqSZOp7Xxv+sucEkpNUWPTPStkXC+cERbGSZFnNhYAKONWZ2/B/y07I3s+T7IwUPFDYH6nJXdOvghkS8DYTA3DtEdj9zATHtEupwVwwQYdzG3zNpvG13onzkI3U58hkbvV4u69kbSUpVRvtfJMVNrvAYRWKeSEZdhk6dCi2bNny7YMkc3QnEB8dPOv1AiJHr0ytxzoYK+8bjec3VqGhud2xrfOwjr+x9JX3jZJVylzcZm35Kez62QR8VtuArLQUWVNzg3k+3C9UW7xUVpWi9HB9wPs6a2juwK2/2e4xByKUQwLuF3+5xeGU4usxPa13IvZ6baw8g16ZWuR0874uj7OXPjyCtNQkj2sQeUvWjkYvfXgEf95d67G4na9igazpQdEmJFFBcnIyDAZDKA6dMGx2Ac9vrArqGGLX9sXm9i5dy1npndny7kMgja0dWL7lGNaWn0LbZbvPsfSXPjyCJVPzMX+NvCROk8WK0S9txiVr6MtGO3O+mJdW1YV9wS5v3HMgnIeFsjNScbG5PWTTMZ0v/qHOf/DkP1+ddzy2v4qiF5vbcetvtrvlQCVLSnq+2NzeJc/ko4N1Ie/xCAX394uvvB6g67BaKKvEEkkVkuDj2LFj6N27N7RaLQoLC7Fs2TL07dvX47ZWqxVW67cVHy0WSyiaFHPKaxv8Tjf1RwAwpl93zF/TtffCX96F1Cqc3TNS8eac0Xjx/cN+93EW7sAjKy0FdkFwTPOUUjY+XJyHQex2dCnjHko5GRqU1VzAuaY25GRoYNBpUW+RvihfsP5VcRr/qjgNwH9FUU/MrdLeR+7Jp59U1WHB2gNBtj4y3N8vnj7fpisJwp5ES/l8SmyKJ5x+/PHHuHTpEoYMGYK6ujqUlJTgzJkzqKqqQmZmZpftPeWIAEiohFNP3aJykzkjRUyA23P8vGIJmKEkJ1FXSdkZKUEHk0rytsZHVnpKQAnBSrUJAB69Jc9joqxSFhZdg+VbvgrR0cMrOyPVZdhUKn8Jv0SBkJNwGvLZLo2NjejXrx9++9vfYu7cuV3u99Tz0adPn4QJPrx1mUbiAhkIcabGsfpLkipmhlqyWoXLEV75VAUgV6fB/35/JM5fsjrKxS/8R2VQx83OSMHPp+TjxU3yZuh4Sir2NT1bQOdwhtReBV80yWrZZfqVmhnijdw8o0hIS1GjtUPe8xYIb7OAiAIR0dku7rKysnDNNdfg+HHPFyaNRgONRlrSWLzxldC5fMuxiP4KlUKlguTZKuESDYEHALx411CXKqJlNReCPnZDcwcaW9olBx4qdPYiuC98lqvToO2y3eN7S+zST0tJwoOF/fE7LxU6pZIbeAChDTwARH3gASAsgQcQmfL5REAYgo9Lly6hpqYGDzzwQKgfKqq5D62M6dfdb3EkILCiXOESqj6zQH4tR4us9BQsmzmsy1j62LxsGHQaWXkxnpxskFbgLCM1Cf/7/REoLjDiZ8XXubz37ILgc4hMXHlX76OEt7tofp/Gqqy0FJhbO7zW4umuwFBeJJKMiYAQrO3y05/+FDt37sSJEyfw6aef4u6770ZSUhJmz56t9EPFDE/rTty4bIvf9VUaWzpwz+irYNC5fkF0T0+GPi0+py+rVcCPvzMg0s0I2EUvPVVJahVmj/WcdC1Hv+x0Sdv96YHrHQGQWNdEXOPj/CVpAZDUQGds/+4MPELg4fF5Hm8Xf5j8cnqB5LWXPB3DeX0oonBT/Ap2+vRpzJ49GxcuXEDPnj1x8803Y+/evejZs6fSDxUTvA2tSP3F8q+KMzDoNI7CXGJC6uZqk9ds9lhmF4DfbT+OrPQUmFs8/+qLds9tOITWDjsMOtfpo/1zMgI+ppgg+EBhf/x5d63P2ipGvRY3+hjHl/prV2qgMzavB8pPXJS0LfknvtaDe3WD3sPQq3Pvmlqt8losUPDwb/H/gOtK10ThpnjPx7p163D27FlYrVacPn0a69atw8CBA5V+mJgQzMqVzuotVry+5Rg0yWpHhc7iAiPemjPaUa8j2iy4fSDemDUSC4uu6dJzI9Zm8Ebl5d+RNmNkb0nbNTR3YOE/uq6sGkwXt4DOi0VqstpRv8H9uVFd+fN3UZG6avIDhf39/rLOSk9hwmII3DXCiPlrKjzm5Tj3romVYA161/eWQa/FW3NG4y0v93GaLUUa13YJoTe2fKXYjBVvU+Oc110pr22Iml+gzln07vku/nIORAuLrsG6z06FreaFN+Jz/7Pia2XPWHFei2RivsHnmjq+/Gh8f7wwbajj/4GsFutM6toppVV1fnvY/nDfKLz04ZGAzive6LTJsARQsl/UIyMVL00fipc+POL1fe/pu4AVTikaRNVsl0RVWlWn6FRZb2thJKlVGD84B+MH58BmFzDml5sjPkOmmybJUdArSa1y5ByINlZKWwm3w2bDzqdvx/6TF/GnXTXYfvSbUDUZ6alJaL2yZon7BVQAMKXAgAaJuRLu+zoXtxLX1JFrYr5rxWDn0uMmcysamtuR3U0DfVqq17U/3C9CK+8b3aWgWa5Og9lj+8J62Y6ymguYcG2u31lXv/igGi98d6jHSrfi/2N5GE2Opd/Nx2ubvwooYM7OSEHZ4juw/+RFv/lg7t8F7p8xZ77uI4oUBh8hIC7zLZWcQkG+psYlqVV4eeawiOeCXLLacP+f93n9JS51+GHF9hr8u+IMCq7ShTTwAIAf3zIQQwzduvQmiDUnxFLsgczqEC8W//v/jqJHRipuu7Yntn8p/Xx6ZKR6TAxMUqtgbm3Hq58c9dsD4q2nZMnU69A9Q+NY6n1t+SmXoLm7hOneJosVx85d8rgQXPeMFPxyegHUalXI35dZHoqmhVvv7ulYMvU6/GSN9OqpYpj467uHITVZLXn6K6fJUixTPOeDOkujS/3lY9RrsXfxHVgy9TpJ258473sGwsR8Q9TMhBHLOIs5DyJ/OQfO6sxt2Fx9zuc23nqQM1KTUDw0F9kZqX7zFhZMGITiAiN2PzMBax+5ET8a3x9A15oTwfxy/8OOGrz04RFZgQcAFFylQ3ltg6M0vEgcOnF/r4nP+0cHz6Ks5gJ+sekwHvOwXZ25DT9ZcwDm1nZoktV4fctXXS7c3mbvuBMrhi6Zmo/sjFTH7Q3NHY5aMAuLBks74QD9ekYB9jzb+fp5yzcKFefZI90z5NUtcs/BkBqcc5osxbLouErFGH9jqHJ+kYhJhCaL5yW/3a377BQWTBjkdcy2vLZBkcqUSnAfchDbnKRWBTz84Ild6Ky0KvYgZXfTuMw0ES/S3notXp45zKVt4no40WLnV+ex86vzLj0aYu+atzoxADB/zQFJwdIz/z6ItJTkoIdEnn33kMehlbor64zMvRLQhcpLHx6B+koytmjBhEEun9VtX9bj7f/IXxnZV9VV99kjUj//Pyzsh8kFxi7fH2Jw7i2HRsz54DRZimUMPmSSkugn9RdJRmoSjpqasPe/F/DOpycl7eMp78NZtHXFestVKS4w4tFb8vDHXfIvBJ7kZGowfeRVHu8TZwRISdAsrarDcxsORdU6LCLnBcH0aal+e9ekBhPm1suKBKz+hmdW75P2Hg+UpwXTnPMdbHYBi/5ZKfu4C24fiP9zxzXYf/IiNleb8F7lWZdhUkOAn//JBUaPn2Pn4JzTZCleMfiQwVc5dOcvPX+/XETN7baAklJ9BRjR2hV7rqnNpccoJ0ODjZV1/neUyN95OydoOleZ3X/yIjZWnnEs2e5phdBo4dyT9LPiayPdHNmsl0P7zLr3tAHoMssqkETQ8YN6IvXKNPfCgT3w86n5Pns+lei58BYwuwc6RLGKwYdE/rq53YcXlBxWcOfrQqtUGW+gMxeiw2ZHs9UW9LFOnG/Bza9sC8m0WW8Jme6cfwWXVtXh1t9s75JcGq2Bh0jsSQpk5k08mDGyN96rPOv1fvH5eeZfX2DLkXMu67hkySgXD3gPEvzNHlGq58JTwMxpshQvmHAqkb8kUvFLb/nmr1BWcwET8w1Yed9oZGqVje/8lUROUqvw4l1Dvd4vxQ8L+2HtIzdi//MTcWDJnS4JhJ6oVd6LganQGcS8viWw6YdSvDS9QNYXsrdEzQivSSdLdkZqwKW1Y9nV3aVVXf1XxZkuC8jJWVAu2OENb8W/umek4Efj+zumRPvjXhqfgQfFCwYfEknNpVix/Thmv70XY176f/jZvw/KWvrcHxU6EyvLaxuwsfIMymouePwCE6ufpqcmBfQ44lh0klqF1GQ1fn13gaN6pnt7VAAe+U6e4//u94utC9V1/ce35GHKcOld0L56sCLNqNdKnhFyqqHVUek0URj12rDVq1CiCqj77KnOhOgO/GXPiS7Vb4kSDYddJJKbS9Go8IyT7ukp+P71V3epfJidkYK7R16FonyDS5fsxHwDdNpqtLRLHzLx1s0sZfx5VN/uHu+fdUMfRYqtuddCyb5SP2LKcGklz0VypkEHw9fsCHdzx/d3vH4AsLb8lN9hs3WfncLuZyZg5X2jJM9qiXVLpubjxgE9JOVTBf9Y1/kMPKRWDRVrsazac8JvrhhRImHwIZHUJNJQmDbcgMkFvT0mQ4q/pP6y54TL7I3y2gZZxZb8dTP7G3/2dv8HB72Pz8uxZOp1MOjTgh77DmY2UDdNkiP/xVMVT3Hxv/NNVkdtC196ZKTiV3cXdLnw3NC/OzYdNPncV5xB1D1DE9b3o1iYrLquCSu2Hw/jIwPdM1JDnk8FdL6eL314BJMKjB7fY3JK28vNFSNKFAw+JPKVRBYq4q/7SQVG3PzKNr+P6fxLynrZLuuxpGTRe0q08/cLUKnZNwZ9miJd7oG0Rzyb1+4dAQB+ZyBILR//vIdf16VVdX4DD1E4p1VPLjDgh4X9Ha/vsXNfBXwsOb1CzsTzVXqatjtv08MB6TPeRFJzxXxNnyeKRww+ZPA2/KA05274JLUKZTUXJD2e8y8p8ULpz4LbB2H8oJyAehKk/AKU0mPkr4CTkgWVAmmPe3DhbwaC1ADHoE9z+b/csvznm6y42CKtLH+wSqtMmD6yt6NoW6BDaSoAK2aPQvcMjceaGb6Iz6vNLuD9L0KfK+Ee3AXSi8FS6USeMfiAvFUfnYcX9hz/Biu21wT0mN8bfRV2H7/gMjTiretWzheT+EsKAiTVGlg48ZqAunu9/QIUq1m+deUXoJRph498Jw9/uvIrNtQFlXx124uPIF4cvb0f/E21DLTOg5x8FLUKkoZ2lFSyqRoTrs2VHCB10yTjkvXb3CcxP6l7hgZj87IdNTN+t/UYfrf1mNdg0P35ClfejnsQGUgvBkulE3mW8MFHIEuTixefsXnZ+HfFGdl5ID0yUvHK9zp7JvbWXEDZf88D6DzmjQO6XtQC+WI632wNWZVEKTNGnn33kOMXYDAJq6EqqKT3sGBaVnoKls0cFvTjBVrnQU6QGe5pweKF9f+WnZB04V9YdI2jtLlzD4d7fhIAn4GHyPn52lItbVgqUN6Cw0B6MVgqncizhA4+5I7fuhMvMnJX6xTrUrgHPiu2H/cY+ASS7Nors3NaYiiqJEr55dnY0oEV247jiStTRwNNWFU6Cc/baw5IX0RNikAqVIbi129WWjJuHtwTu4+dd6lzYdRr8fPJ1+KFTdWShz0A4GSD74UNRf1z0v3O9HhsdQWy0lN8vqfVKmDF7G8/h6VVdY4VhkPBV3AYSC8GS6UTeZawwYeUhbme23AIrR12l0XK3E3MNyBLwrLjIrEuhZzAR26Gv3MhslBc1KX+Alz1aa3LInhSKkOGMunOX4+N0jMP5D73Ss2omjGyN67unu7oSUtSq7wOLSYnq70GY570y5ZW5KtXplbSZ8zf58YudM5yAeTlxGRnpODnU/Kx9P3DLkM//vgKDgPtxWCpdKKuEjb4kPLrvaG5Awv/UQnA+1BMeW2DpMBDBeD3s0bhuyN7S05cm3BtLvafvOi4YPx+1ij8n38c8NvlvmRqvqwcBbmk/gJsbOmIqiz+SMw8kPPcKzWj6vZre3VZZM9bO8QL44vvH/ZZW0S8sD5Q2B9/3l0r6QKsVG6GGOzKOd6v7+4cPsvQJEkKrtyTvD0JpheDpdKJXCVs8CE3u9zbUIzUWhoCgB6ZGgDSL4I3LtvapbCWlLH+7n7KoQdrbF42stJSJJWrjqYs/liYeSA1GPBF7vCNeGFcse04lm/pOoXW+cKamqz2GSAJAKYUGGTXmfFFPB+pr8uPxvd3fEb9zVDzl9/lLphejFD37BHFkoQNPuR+QXuaSldaVYeXPjgs+Rjil6fUhDn3sXipy7yH+uKZpFbh4fH9JU23jKYs/liZeVBcYESmNgX3/3mfrP2CSV5MUqvwRNFgDDF083th9XYBFqcoi0ml2RnyFnLzdz5SXxdxRVuRc6+DydyKhuZ2ZHfT+BxO9YW9GETBS9jgI5DxdedueXNru6yxcqDzyzPUCXPi44TaggmDserTE16HnKIxiz+WZh6cl7lqrVLJi1IvrM7bba424a97TnTplfMXLKvQOevIfOU95G8YI5jXT+leB/ZiEAUnYReWE8dvAxlX/8+xc3j234dk7WvUazGmX3dZRaQC4W/VW6UkqVV4eeYwj6uqerpw2OwCymou+FwQL9TE19y5jaJom3kgN4BUYiE0kdSVVJPUKozNy8bHVf578rw93y/PHOZx9VdP5xNLrx8R+ZawPR+A/Jkqoj/s+K+s7VXo/FLcf/JiyIsjzbqhb9i+fKWOfwdSSyXSbY40KT1z2RkpWPLdoQEPHyhBahJod7eFAeVWjRXFyutHRL4ldPAhdaZKMJwvslLX/AhG/xxpUyGV4q+bPthaKpFoczSQMrNCnNERSVLzi/wtDChnGCMWXj8i8i2hg49QJ2YumXodHhqf5/hSlNqVnp2RiovN7QENCUUiWdLbhSOaV/SMhTH7WPiVL2cdG+ZcEJEooYOPUF2oxcQ358ADAC42+08i7FyyPB/z18ir9RBNyZIirugZvGj/lR9LSbxEFD0SMuFUTH40mVuRoUlS/PgCuia+2ewCnnuvyu++S6bmY8pwo8ckvKz0zqmLsZJsFwt1NWKB1ATQSGASKBEFIuF6PjwlPyrNuciRaMW2Y5LyS8QCYd5+8W6uNkV1N7yzWKmrQcGJheEhIoouCRV8+FpUTEl3XJuLspoLjqBhTL/uWCWxtodzL4Cnce1o74Z3xi75xBFL70siiryECT6kLAMfLLFo0lPrv3ApLZ2dIa0UOSCtFyBWku24omdiiZX3JRFFXsLkfCi1yJUvAjoXU3Nf00JqWfSs9JS46wUQu+SlFJEiIqLEkDA9H1LXUxFlapPQ1GaTtY9KBQhBdK08fFNeXPYCsEueiIicJUTwYbML2CCzwJfcwAMILvDISk/BggmDAj9AlGOXPBERiRJi2KW8tkHy0EekvDxzGHsCiIgoISRE8BFoHYnu6cEtCe5J9pWptCKjXou3mPtAREQJJCGGXQKpI5GdkYLpI6+SPEXWH3Fa6c6nb8f+kxeZ+0BERAkrIYIPKSuEumto7nAEHnLKnHviPK00NVnN3AciIkpoCTHs4qsEtBRi4DGlIBc/uW0gsjNSfR7HvSOD00qJiIi+FbLgY+XKlejfvz+0Wi3GjRuH8vLyUD2UJGK9CX2AeRwqAAe+NuOpO4fg13cXOG5z30YFYMXsUVj7yI14Y9ZIrH3kRux+ZgIDDyIioitCEnz84x//wKJFi7B06VJUVFRgxIgRmDRpEs6dOxeKh5NsYr4B2uTAFpITV2B9Z08trJfteLLoGuTqPBfOmjK8d9QuBEZERBRpKkEIpjqFZ+PGjcMNN9yAFStWAADsdjv69OmDxx9/HM8++6zPfS0WC/R6PcxmM3Q6naLtKqu5gNlv71XseAadBrPH9kX/nAwmjxIRUUKTc/1WvOejvb0d+/fvR1FR0bcPolajqKgIZWVlXba3Wq2wWCwuf6Gi9NLt9RYrXt9yDJorSaQMPIiIiPxTPPg4f/48bDYbcnNzXW7Pzc2FydS1xPmyZcug1+sdf3369FG6SQ5KL90udhmVbKqGzR7qtXKJiIjiQ8RnuyxevBhms9nx9/XXX4fsscQpt0r2T4i5IOW1DQoelYiIKH4pHnzk5OQgKSkJ9fX1LrfX19fDYDB02V6j0UCn07n8hYqvKbfiTJVHvtO/y1RZKZQe0iEiIopXigcfqampGDNmDLZu3eq4zW63Y+vWrSgsLFT64SSz2QWU1VzwO1NlwrUGBDKCovSQDhERUbwKSYXTRYsW4cEHH8T111+PsWPH4vXXX0dzczMefvjhUDycX6VVdSjZVI0687e9EwadBguLBneZqbJR5uq3Ytn0sXnZCreaiIgoPoUk+PjBD36Ab775Bi+88AJMJhNGjhyJ0tLSLkmo4VBaVYd5qyu6lEcXZ6q8OWe0S7lzOT0YzmXTOdOFiIhImpDU+QiGknU+bHYBN7+yzaXHw5nYa7H7mQmO4EHcR8o6MEa9Fkun5bN6KRERJTw51++4XliuvLbBa+ABuM5UEXs/xKTUeasrvC4oN3d8fxTlG1hUjIiIKAARn2obSlJnoLhvJ64DY9C7DsEY9Vq8NWc0lkwbyqJiREREAYrrng+p+RuetisuMGJivgHltQ0419TG8ulEREQKievgQywq5i1/w99MlSS1yiUZlYiIiIIX18Mu/oqKAZypQkREFG5xHXwA3vM3xKJinKlCREQUXnE97CJi/gYREVH0iPueD1GSWoWxednolanFuabO6bVciZaIiCj8EqLnA/BcYp1FwoiIiMIvIXo+xBLr7gXHTOY2zFtdgdKqugi1jIiIKPHEffBhswso2VTtcaqteFvJpmoOwRAREYVJ3AcfckqsExERUejFffARaIl1IiIiCo24Dz6CKbFOREREyov74EMsse6toocKnbNevJVYJyIiImXFffDBEutERETRJe6DD4Al1omIiKJJwhQZY4l1IiKi6JAwwQfQOQRTOLBHpJtBRESU0BJi2IWIiIiiB4MPIiIiCisGH0RERBRWDD6IiIgorBh8EBERUVgx+CAiIqKwYvBBREREYcXgg4iIiMKKwQcRERGFVdRVOBUEAQBgsVgi3BIiIiKSSrxui9dxX6Iu+GhqagIA9OnTJ8ItISIiIrmampqg1+t9bqMSpIQoYWS323H27FlkZmZCpVJ20TeLxYI+ffrg66+/hk6nU/TY0SDezw+I/3OM9/MD4v8c4/38gPg/x3g/PyA05ygIApqamtC7d2+o1b6zOqKu50OtVuPqq68O6WPodLq4fUMB8X9+QPyfY7yfHxD/5xjv5wfE/znG+/kByp+jvx4PERNOiYiIKKwYfBAREVFYJVTwodFosHTpUmg0mkg3JSTi/fyA+D/HeD8/IP7PMd7PD4j/c4z38wMif45Rl3BKRERE8S2hej6IiIgo8hh8EBERUVgx+CAiIqKwYvBBREREYRXXwceJEycwd+5c5OXlIS0tDQMHDsTSpUvR3t7uc7+2tjbMnz8fPXr0QLdu3XDPPfegvr4+TK2W51e/+hVuuukmpKenIysrS9I+Dz30EFQqlctfcXFxaBsahEDOURAEvPDCCzAajUhLS0NRURGOHTsW2oYGqKGhAffffz90Oh2ysrIwd+5cXLp0yec+t912W5fX8LHHHgtTi/1buXIl+vfvD61Wi3HjxqG8vNzn9uvXr8e1114LrVaLYcOG4aOPPgpTSwMj5/zeeeedLq+VVqsNY2vl2bVrF6ZNm4bevXtDpVLhvffe87vPjh07MHr0aGg0GgwaNAjvvPNOyNsZDLnnuGPHji6voUqlgslkCk+DZVq2bBluuOEGZGZmolevXpgxYwaOHj3qd79wfg7jOvj48ssvYbfb8cc//hGHDx/G8uXL8dZbb+G5557zud/ChQuxadMmrF+/Hjt37sTZs2cxc+bMMLVanvb2dtx7772YN2+erP2Ki4tRV1fn+Fu7dm2IWhi8QM7x1Vdfxe9+9zu89dZb2LdvHzIyMjBp0iS0tbWFsKWBuf/++3H48GFs3rwZH3zwAXbt2oVHH33U736PPPKIy2v46quvhqG1/v3jH//AokWLsHTpUlRUVGDEiBGYNGkSzp0753H7Tz/9FLNnz8bcuXNx4MABzJgxAzNmzEBVVVWYWy6N3PMDOqtIOr9WJ0+eDGOL5WlubsaIESOwcuVKSdvX1tZi6tSpuP3221FZWYknn3wS//M//4NPPvkkxC0NnNxzFB09etTldezVq1eIWhicnTt3Yv78+di7dy82b96Mjo4O3HnnnWhubva6T9g/h0KCefXVV4W8vDyv9zc2NgopKSnC+vXrHbcdOXJEACCUlZWFo4kBWbVqlaDX6yVt++CDDwrTp08PaXtCQeo52u12wWAwCL/5zW8ctzU2NgoajUZYu3ZtCFsoX3V1tQBA+Oyzzxy3ffzxx4JKpRLOnDnjdb9bb71VeOKJJ8LQQvnGjh0rzJ8/3/F/m80m9O7dW1i2bJnH7b///e8LU6dOdblt3Lhxwo9//OOQtjNQcs9Pzmcz2gAQNmzY4HObn/3sZ8LQoUNdbvvBD34gTJo0KYQtU46Uc9y+fbsAQLh48WJY2qS0c+fOCQCEnTt3et0m3J/DuO758MRsNiM7O9vr/fv370dHRweKiooct1177bXo27cvysrKwtHEsNixYwd69eqFIUOGYN68ebhw4UKkm6SY2tpamEwml9dQr9dj3LhxUfcalpWVISsrC9dff73jtqKiIqjVauzbt8/nvn//+9+Rk5ODgoICLF68GC0tLaFurl/t7e3Yv3+/y3OvVqtRVFTk9bkvKytz2R4AJk2aFHWvFRDY+QHApUuX0K9fP/Tp0wfTp0/H4cOHw9HcsIil1y9YI0eOhNFoxMSJE7Fnz55IN0cys9kMAD6vfeF+HaNuYblQOn78OH7/+9/jtdde87qNyWRCampql9yC3NzcqB3fk6u4uBgzZ85EXl4eampq8Nxzz2Hy5MkoKytDUlJSpJsXNPF1ys3Ndbk9Gl9Dk8nUpes2OTkZ2dnZPtt63333oV+/fujduzcOHjyIZ555BkePHsW7774b6ib7dP78edhsNo/P/ZdffulxH5PJFBOvFRDY+Q0ZMgR//etfMXz4cJjNZrz22mu46aabcPjw4ZAvohkO3l4/i8WC1tZWpKWlRahlyjEajXjrrbdw/fXXw2q14s9//jNuu+027Nu3D6NHj45083yy2+148sknMX78eBQUFHjdLtyfw5js+Xj22Wc9Jv84/7l/EZw5cwbFxcW499578cgjj0So5dIEcn5yzJo1C3fddReGDRuGGTNm4IMPPsBnn32GHTt2KHcSfoT6HCMt1Of36KOPYtKkSRg2bBjuv/9+/O1vf8OGDRtQU1Oj4FmQEgoLC/HDH/4QI0eOxK233op3330XPXv2xB//+MdIN40kGjJkCH784x9jzJgxuOmmm/DXv/4VN910E5YvXx7ppvk1f/58VFVVYd26dZFuiouY7Pl46qmn8NBDD/ncZsCAAY5/nz17Frfffjtuuukm/OlPf/K5n8FgQHt7OxobG116P+rr62EwGIJptmRyzy9YAwYMQE5ODo4fP4477rhDseP6EspzFF+n+vp6GI1Gx+319fUYOXJkQMeUS+r5GQyGLomKly9fRkNDg6z327hx4wB09u4NHDhQdnuVkpOTg6SkpC6zw3x9fgwGg6ztIymQ83OXkpKCUaNG4fjx46FoYth5e/10Ol1c9Hp4M3bsWOzevTvSzfBpwYIFjiR2f71s4f4cxmTw0bNnT/Ts2VPStmfOnMHtt9+OMWPGYNWqVVCrfXf2jBkzBikpKdi6dSvuueceAJ0ZzqdOnUJhYWHQbZdCzvkp4fTp07hw4YLLhTrUQnmOeXl5MBgM2Lp1qyPYsFgs2Ldvn+xZQYGSen6FhYVobGzE/v37MWbMGADAtm3bYLfbHQGFFJWVlQAQ1tfQk9TUVIwZMwZbt27FjBkzAHR2+27duhULFizwuE9hYSG2bt2KJ5980nHb5s2bw/Z5kyOQ83Nns9lw6NAhTJkyJYQtDZ/CwsIuUzKj9fVTUmVlZcQ/b94IgoDHH38cGzZswI4dO5CXl+d3n7B/DkOSxholTp8+LQwaNEi44447hNOnTwt1dXWOP+dthgwZIuzbt89x22OPPSb07dtX2LZtm/D5558LhYWFQmFhYSROwa+TJ08KBw4cEEpKSoRu3boJBw4cEA4cOCA0NTU5thkyZIjw7rvvCoIgCE1NTcJPf/pToaysTKitrRW2bNkijB49Whg8eLDQ1tYWqdPwSe45CoIgvPzyy0JWVpawceNG4eDBg8L06dOFvLw8obW1NRKn4FNxcbEwatQoYd++fcLu3buFwYMHC7Nnz3bc7/4ePX78uPCLX/xC+Pzzz4Xa2lph48aNwoABA4RbbrklUqfgYt26dYJGoxHeeecdobq6Wnj00UeFrKwswWQyCYIgCA888IDw7LPPOrbfs2ePkJycLLz22mvCkSNHhKVLlwopKSnCoUOHInUKPsk9v5KSEuGTTz4RampqhP379wuzZs0StFqtcPjw4Uidgk9NTU2OzxgA4be//a1w4MAB4eTJk4IgCMKzzz4rPPDAA47t//vf/wrp6enC008/LRw5ckRYuXKlkJSUJJSWlkbqFPySe47Lly8X3nvvPeHYsWPCoUOHhCeeeEJQq9XCli1bInUKPs2bN0/Q6/XCjh07XK57LS0tjm0i/TmM6+Bj1apVAgCPf6La2loBgLB9+3bHba2trcJPfvIToXv37kJ6erpw9913uwQs0eTBBx/0eH7O5wNAWLVqlSAIgtDS0iLceeedQs+ePYWUlBShX79+wiOPPOL44oxGcs9REDqn2y5ZskTIzc0VNBqNcMcddwhHjx4Nf+MluHDhgjB79myhW7dugk6nEx5++GGXwMr9PXrq1CnhlltuEbKzswWNRiMMGjRIePrppwWz2RyhM+jq97//vdC3b18hNTVVGDt2rLB3717Hfbfeeqvw4IMPumz/z3/+U7jmmmuE1NRUYejQocKHH34Y5hbLI+f8nnzySce2ubm5wpQpU4SKiooItFoacVqp+594Tg8++KBw6623dtln5MiRQmpqqjBgwACXz2I0knuOr7zyijBw4EBBq9UK2dnZwm233SZs27YtMo2XwNt1z/l1ifTnUHWloURERERhEZOzXYiIiCh2MfggIiKisGLwQURERGHF4IOIiIjCisEHERERhRWDDyIiIgorBh9EREQUVgw+iIiIKKwYfBAREVFYMfggIiKisGLwQURERGHF4IOIiIjC6v8DxB/lL2H02PsAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Test data\n",
        "\n",
        "Generated from a deterministic distribution with Noise ~ Normal(0, 2)\n",
        "\n",
        "$$y_{test} = 2X^3 + 3X^2 + 4 + Noise$$"
      ],
      "metadata": {
        "id": "ffSQPM_4BQya"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "rng = np.random.default_rng(seed = 102)\n",
        "\n",
        "X_test = np.arange(-2, 2, 0.02).reshape(1, -1)\n",
        "\n",
        "y_test = (2 * (X_test)**3 + 3 * (X_test)**2 + 4 + rng.normal(0, 2, X_test.shape[1]).reshape(1, -1)).T"
      ],
      "metadata": {
        "id": "kACpsUAh8Xpx"
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "X_test.shape, y_test.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7qbkXfUKwmF3",
        "outputId": "147c7020-57e5-4f7a-d897-394b77f6a8e6"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((1, 200), (200, 1))"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Model\n",
        "\n",
        "Linear regression model for the dataset ${\\mathbb{x}, y}$ is given as\n",
        "$$h_w(\\mathbb{x}) = w_1x^{1}+w_2x^{2}+...+w_dx^{d} =  \\mathbf{x}^Tw\n",
        "$$\n",
        "\n",
        "where $x^{i}$ is the $i^{th}$ feature of the data point $\\mathbf{x}$ and $w = [w_1, w_2, ...w_d]^T$ is the weight vector.\n",
        "\n",
        "\n",
        "Notice that above model always pass through the origin but for a given dataset, best fit model need not pass through the origin. To tackle this issue, we add an intercept $w_0$ in the model and set the corresponding featrue $x^{0}$ to $1$. That is\n",
        "\n",
        "$$h_w(\\mathbb{x}) =w_0x^{0}+ w_1x^{1}+w_2x^{2}+...+w_dx^{n} =  \\mathbf{x}^Tw\n",
        "$$\n",
        "\n",
        "We call $x^{0}$ the dummy feature and set its value to 1 for each examples. Now $w$ is of shape $(d+1, 1)$ and $\\mathbf{X}$ is of shape $(d+1, n)$ where the first row of $\\mathbf{X}$ has entries as 1.\n"
      ],
      "metadata": {
        "id": "EmK77bhCkKI-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Add dummy feature"
      ],
      "metadata": {
        "id": "A156drNBk37x"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "dummy_feature = np.ones(X_train.shape[1])\n",
        "X = np.row_stack((dummy_feature, X_train))"
      ],
      "metadata": {
        "id": "h1SiEEmyCgCx"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "X.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jFzjXIybC6Ij",
        "outputId": "ab89aa05-3933-4ffc-dbf5-29041fde42d7"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2, 400)"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Test data"
      ],
      "metadata": {
        "id": "ivJZNL_aC8_Q"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "dummy_feature_t = np.ones(X_test.shape[1])\n",
        "X_t = np.row_stack((dummy_feature_t, X_test))"
      ],
      "metadata": {
        "id": "vIZA0Ls6DA-3"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "X_t.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BhLm2D8iDXpn",
        "outputId": "92b9fa7e-21a5-4236-b7b7-db235c854423"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2, 200)"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Loss function\n",
        "\n",
        "The total loss is the sum of square of errors between actual and predicted labels for each training point.  \n",
        "\n",
        "The error for $i$-th training point is calculated as follows:\n",
        "\\begin{eqnarray}\n",
        "e^{(i)} &=& (\\mathrm{{actual\\ label} - {predicted\\ label}})^2 \\\\\n",
        "        &=& \\left ({y_{i}} -\n",
        "        {h_{\\mathbf{w}}(\\mathbf{x}_{i})} \\right)^2 \\\\\n",
        "        &=& \\left ({y_{i}} -\n",
        "        {\\mathbf{w}^T \\mathbf{x}_{i}} \\right)^2\n",
        "\\end{eqnarray}\n",
        "\n",
        "\n",
        "\n",
        "The total loss $L(\\mathbf{w})$ is sum of errors at each training point:\n",
        "\\begin{equation}\n",
        "L(\\mathbf{w}) = \\sum_{i=1}^{n} e^{(i)}\n",
        "\\end{equation}\n",
        "\n",
        "We divide this by $\\frac{1}{2}$ for mathematical convenience in later use:\n",
        "\n",
        "\n",
        "\\begin{eqnarray}\n",
        "  L(\\mathbf{w}) &=& \\frac{1}{2} \\sum_{i=1}^{n} e^{(i)} \\\\ &=&  \\frac{1}{2} \\left({{\\mathbf{X}^T \\mathbf{w}}} - \\mathbf{y} \\right)^T \\left({{\\mathbf{X}^T \\mathbf{w}}} - \\mathbf{y} \\right))\n",
        "\\end{eqnarray}\n"
      ],
      "metadata": {
        "id": "Wp1v00V9lBMd"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Optimization\n",
        "\n"
      ],
      "metadata": {
        "id": "MQtN8F2j9r42"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 1. Normal equation\n",
        "\n",
        "Let's set $\\dfrac{\\partial L(\\mathbf{w})}{\\partial \\mathbf{w}}$ to 0 and solve for $\\mathbf{w}$:\n",
        "\\begin{eqnarray}\n",
        "\\frac{\\partial L(\\mathbf{w})}{\\partial \\mathbf{w}} &=& \\mathbf{X} \\mathbf{X}^T \\mathbf{w} - \\mathbf{X} \\mathbf{y} = 0 \\\\\n",
        "\\mathbf{X}^T \\mathbf{X} \\mathbf{w} &=& \\mathbf{X}^T \\mathbf{Y} \\\\\n",
        "\\mathbf{w} &=& \\left( \\mathbf{X} \\mathbf{X}^T \\right)^{-1} \\mathbf{X} \\mathbf{y}\n",
        "\\end{eqnarray}\n",
        "\n"
      ],
      "metadata": {
        "id": "GvxZvoJO-OIn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Find weight vector and prediction for training and test dataset"
      ],
      "metadata": {
        "id": "gwcJYj2Ml71z"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "### weight\n",
        "def weights(X, y):\n",
        "    return np.linalg.pinv(X@(X.T))@X@y"
      ],
      "metadata": {
        "id": "UiO64nmAeSkz"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "w = weights(X, y_train)\n",
        "w"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IUswb7ATD1l4",
        "outputId": "a73662af-167e-46c0-c5ed-229b8266ad9e"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[7.93982825],\n",
              "       [4.79910241]])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "### Prediction\n",
        "def pred(X, w):\n",
        "    return (X.T)@w"
      ],
      "metadata": {
        "id": "b_KErNi9eXTm"
      },
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Store the train predictions in y_hat\n",
        "y_hat = pred(X, w)"
      ],
      "metadata": {
        "id": "TulEVIf2EE_0"
      },
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Store the test predictions in y_test_hat\n",
        "y_test_hat = pred(X_t, w)"
      ],
      "metadata": {
        "id": "AKrxHgM8wSKd"
      },
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Plot weight vector"
      ],
      "metadata": {
        "id": "ohC5eG-GETPq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "### Plot weight vector\n",
        "plt.scatter(X_train, y_train)\n",
        "axes = plt.gca() #Gets coordinate axis\n",
        "\n",
        "x_values = np.array(axes.get_xlim())\n",
        "y_values = w[0] + w[1]*x_values\n",
        "\n",
        "plt.plot(x_values, y_values, 'r-');"
      ],
      "metadata": {
        "id": "PEUE5Fhvea3Q",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "outputId": "64ca162c-65f8-4486-be75-ed165fe1c293"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Evaluation\n",
        "\n",
        "##### RMSE $$ \\sqrt{\\dfrac{1}{n}\\sum\\limits_{i=1}^{n} (y_i- \\hat{y}_i)^2}\n",
        "$$\n",
        "\n"
      ],
      "metadata": {
        "id": "Sk1KvxpCn1Xr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "### Loss function\n",
        "def loss(y, y_hat):\n",
        "    return np.sqrt(np.mean((y - y_hat)**2))"
      ],
      "metadata": {
        "id": "zVMo6BF_ediw"
      },
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Training error\n",
        "loss(y_train, y_hat)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1vbazha1F34d",
        "outputId": "7a8774af-9223-4834-e670-ee0b6ae974a6"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "4.477002001803876"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Test error\n",
        "loss(y_test, y_test_hat)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uZvR-fkYR8DV",
        "outputId": "cef12c05-573e-48df-c3c4-c9065c7f4e0a"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "4.718639896481515"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### 2. Gradient Descent"
      ],
      "metadata": {
        "id": "r8MYjq1qHnM1"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "Gradient of a function $f$ at a point $x$ gives the direction of maximum change in $f$ at the point $x$.\n",
        "\n",
        "---\n",
        "\n",
        "We start at a random point $\\mathbf{w}$ at the loss function $L(\\mathbf{w})$.\n",
        "\n",
        "\n",
        "We basically need an update rule in gradient descent, which is as follows:\n",
        "\n",
        "\\begin{eqnarray}\n",
        "\\mathbf{w}_{k+1} &:=& \\mathbf{w}_k - \\alpha{\\frac{\\partial L(\\mathbf{w})}{\\partial \\mathbf{w}}} \\\\\n",
        "   &:=& \\mathbf{w}_k - \\alpha{\\left(\\mathbf{X} \\mathbf{X}^T \\mathbf{w}_{k} - \\mathbf{X} \\mathbf{y}\\right)} \\\\\n",
        "\\end{eqnarray}\n",
        "\n",
        "Note that this is the vectorized implementation.  It will make sure that all the parameters are updated in one go through this.\n"
      ],
      "metadata": {
        "id": "SxdpExPLHw5L"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Gradient calculation\n",
        "def gradient(X, w, y):\n",
        "    return (X@X.T)@w - (X@y)"
      ],
      "metadata": {
        "id": "aJ08wiSLeiMx"
      },
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Gradient descent\n",
        "def grad_desc(X, y, eta, n_iter):\n",
        "    w_0 = np.zeros(X.shape[0]).reshape((2,-1))\n",
        "\n",
        "    for i in range(n_iter):\n",
        "        w_0 = w_0 - eta * gradient(X, w_0, y)\n",
        "\n",
        "    return w_0"
      ],
      "metadata": {
        "id": "29qM5zSLGefi"
      },
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "grad_desc(X, y_train, 0.001, 1000)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5-1PnCfMHmnM",
        "outputId": "edd1a275-f57d-47ee-e3f9-4684d9cb7c4c"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[7.93982825],\n",
              "       [4.79910241]])"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Gradient descent output is close to optimum w\n",
        "w"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ACVMDjpcH32o",
        "outputId": "a2df7124-6fbe-46df-fb87-30c8cb01aa4b"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[7.93982825],\n",
              "       [4.79910241]])"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Number of iterations vs loss (for fixed alpha)"
      ],
      "metadata": {
        "id": "kQmmqovFoKkx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Plot nunber of iterations vs loss\n",
        "n_iter_list = [10, 20, 50, 100, 250]\n",
        "loss_list = []\n",
        "for n_iter in n_iter_list:\n",
        "    w = grad_desc(X, y_train, 0.0001, n_iter)\n",
        "    y_hat = pred(X, w)\n",
        "    loss_iter = loss(y_train, y_hat)\n",
        "    loss_list.append(loss_iter)"
      ],
      "metadata": {
        "id": "5rGjFal8ekdg"
      },
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(n_iter_list, loss_list)\n",
        "plt.title(\"Number of iterations vs Loss\");"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 452
        },
        "id": "trqok0rCJ6jG",
        "outputId": "77f24786-b2c7-4aa9-8b04-fc34e607b0b4"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###SGD:\n",
        "\n"
      ],
      "metadata": {
        "id": "PDmCReoUofgs"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Implementation 1"
      ],
      "metadata": {
        "id": "NyPKXKxD1chB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def SGD_1(X, y, eta, n_iter):\n",
        "    w_0_list = []\n",
        "    w_0 = np.zeros(X.shape[0]).reshape((2,-1))\n",
        "    batches = np.arange(0, X.shape[1], 20)\n",
        "\n",
        "    for i in range(n_iter):\n",
        "        indices = np.arange(batches[i%20], batches[i%20] + 20)\n",
        "\n",
        "        X_batch = X[:, indices]\n",
        "        y_batch = y[indices]\n",
        "\n",
        "        w_0 = w_0 - eta*(gradient(X_batch, w_0, y_batch))\n",
        "        w_0_list.append(w_0[1])\n",
        "\n",
        "    return w_0, w_0_list"
      ],
      "metadata": {
        "id": "BTz4yLWuwwb7"
      },
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "w_star, w_list = SGD_1(X, y_train, 0.001, 100)"
      ],
      "metadata": {
        "id": "A0n4GN79FyV8"
      },
      "execution_count": 27,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(w_star, '\\n')\n",
        "print(f\"Optimum: \\n {w}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4d41c77a-50b4-4444-eb05-7f658feaa13e",
        "id": "38KDEO9IF2ec"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[7.1102333 ]\n",
            " [4.98889206]] \n",
            "\n",
            "Optimum: \n",
            " [[7.939532  ]\n",
            " [4.79909273]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.scatter([i for i in range(len(w_list))], w_list);"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "outputId": "1f8673d0-77c4-4b01-9dba-f527715c311a",
        "id": "bF7agj9JF2ee"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Implementation 2"
      ],
      "metadata": {
        "id": "jPpspPvm1k1m"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def SGD_2(X, y, eta, n_iter, batch_size):\n",
        "    w_0_list = []\n",
        "    w_0 = np.zeros(X.shape[0]).reshape((2,-1))\n",
        "\n",
        "    for i in range(n_iter):\n",
        "        indices = random.sample(range(0, X.shape[1]), batch_size)\n",
        "\n",
        "        X_batch = X[:, indices]\n",
        "        y_batch = y[indices]\n",
        "\n",
        "        w_0 = w_0 - eta*(gradient(X_batch, w_0, y_batch))\n",
        "        w_0_list.append(w_0[1])\n",
        "\n",
        "    return w_0, w_0_list"
      ],
      "metadata": {
        "id": "36zVkHXuFtye"
      },
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "w_star, w_list = SGD_2(X, y_train, 0.001, 1000, 20)"
      ],
      "metadata": {
        "id": "NxONb5vnwvp6"
      },
      "execution_count": 31,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(w_star, '\\n')\n",
        "print(f\"Optimum: \\n {w}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LFlfIVAJDEMQ",
        "outputId": "d60f9df0-3e73-4bec-ab79-5c642f3e773d"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[7.82459257]\n",
            " [4.67107434]] \n",
            "\n",
            "Optimum: \n",
            " [[7.939532  ]\n",
            " [4.79909273]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.scatter([i for i in range(len(w_list))], w_list);"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "MXc2z1ADC84g",
        "outputId": "a0fdeb3c-edd2-4a2f-bfa4-da3f4f79f930"
      },
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}