200010036_Lab_6_Regression_Part_2.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "09MzFpIPzTLT"
      },
      "source": [
        "# **LAB 7 : Regression Part 2**\n",
        "\n",
        "In this Lab we will look into the shortcomings of Linear Regression and see how those problems can be solved using Logistic Regression. We will also explore Polynomian Regression\n",
        "\n",
        "  1. Polynomial Regression\n",
        "  2. Linear Regression on a specific pattern of data to observe shortcomings\n",
        "  3. Logistic Regression to solve those problems"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "NtJiSQxW0I8O"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QIxEGua10LRu"
      },
      "source": [
        "# Polynomial Regression\n",
        "\n",
        "1. Generate data using relation $y=0.25x^{3}+1.25x^{2}-3x-3$\n",
        "2. Corrupt y by adding random noise (uniformly sampled)\n",
        "3. Fit the generated curve using different polynomial order. (Using matrix inversion and gradient descent)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "h68o2XKU0QTY"
      },
      "outputs": [],
      "source": [
        "# Use the Regression class defined in the previous lab\n",
        "\n",
        "class Regression:\n",
        "\t# Constructor\n",
        "\tdef __init__(self, name='reg'):\n",
        "\t\tself.name = name  # Create an instance variable\n",
        "\n",
        "\tdef grad_update(self,w_old,lr,y,x):\n",
        "\t\tw = w_old + 2 * lr / y.shape[0] * (x @ (y - x.T @ w_old))\n",
        "\t\treturn w\n",
        "\n",
        "\tdef error(self,w,y,x):\n",
        "\t\treturn np.mean((y - x.T @ w)**2)\n",
        "\n",
        "\tdef mat_inv(self,y,x_aug):\n",
        "\t\treturn np.linalg.inv(x_aug @ x_aug.T) @ x_aug @ y\n",
        "\t\n",
        "\t# By Gradien descent\n",
        "\n",
        "\tdef grad_descent(self,x,y,lr):\n",
        "\t\terr = []\n",
        "\t\tw_pred = np.random.uniform(-1, 1, (x.shape[0]))\n",
        "\n",
        "\t\tfor i in range(int(1e+20)):\n",
        "\t\t\tw_pred = self.grad_update(w_pred,lr,y,x)\n",
        "\t\t\terr.append(self.error(w_pred,y,x))\n",
        "\t\t\tif i > 1:\n",
        "\t\t\t\tdev = np.abs(err[-2] - err[-1])\n",
        "\t\t\telse:\n",
        "\t\t\t\tdev = 1\n",
        "\t\t\tif dev<=0.000001:\n",
        "\t\t\t\tbreak\n",
        "\n",
        "\t\treturn w_pred, err"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "W3OL0qEC00PG",
        "outputId": "fe36b6c7-3600-4142-b969-193dd263e41b"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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37D/MXQ8dGKnHyShnGG1dE9FyGbSgwt+n6Sou+KcRvmut9qmzaaupX+BRN5I18XMnbUGhMjl5mJ3ign/SAKz7yzmtOv2oxtlINu2f27v01Jqs6ph0QYXqKy74YbIAnPdfzklr88BYb4p1W1BIg7igYHaKDP5JLMIv57i1+Q3rAiI4emz4he9BF3EHtaBwtq86bLk8O8UH/6iz3WX75TzhDOZYAkkyuEQzaalLgnqTBzWn6OAfZ7YLy/XL2bvWn4i+6/v73eB63Iu4Lvssmxdx21d08I86211GvWcw8PyznkE3uB7nIq6tIOQKsPYVHfx1Z7vLrvcMZlj7hurmr1Eu4vY7Yxj2ZuFZwfJyBVj7ign+fkFSZ7ar4Te4rnMRd9AZw6A3C88KllO/HeWuAGtHEcE/LEjWmu1q+AXtOtc7Bp0xjHo3My2uQTvKwRVgbVjq4B+1vKDBJrmgPeyMocpbSS6vYW/my7RYYlEsbfCPWl5Qc8ZpeOdKj+Xgm/l8WtrgH7W8oGYNmtUNOiubtx3RGp1v5vNraYO/bnlB7al7VuYKn8Xim/n8W9rgX7YdtsuozlmZK3zmX+/ud0us829pgx+8aDTv6pyVucJnvvW+MV9z6WZLrAtgqYNf863OWVnvm8Omkzdyy337xtp3YcloegaVcxIssS6AyMy2x7CmlZWV3L17d9vDUEv63XR7lN5Kq89hyWg6+vW4Wi3n7HzHNsCNkPMiIvZk5krvcWf8mnurJbtb7ts3dm8lS0aT6zfLH1TO8b/tfDP4tTAm6a20CPdRmGfDVmBZzlk8Br8WxiS9lUZZ5eW1gOdzX8xyMfi1UCbprVRnlZebjvpzX8xyMfi11AbN3gcdt1d8vU62Jfx3WGYGv5ZCv7AatJJn2Aqf0nvFj9LJVovL4NfCG1SeGdSVtd8KH/jO9YKSe8W7+qkMBr8W3qDyzKCWAf02hS1zr/hRyl2ufiqDwa+FN6g8M2yNebVePWmv+DqrgNpaKTRquctafhlaCf6IuBL4CLAeuDUzb25jHFoO1bDqLc8MWn3SG+jjznLr7Ahuc9dw75vaXQ8dWPPmRNbyl9/Mgz8i1gO3AG8EDgAPRsSuzPzCrMei5VENq1HLM3Vnuf1m7XVq4oPCdxYz6t5Nb3fuOcDRY/U7Z7qnYTm1MeO/HNiXmY8BRMQngKsBg19TMc6Mda3vGTRrr1MTHxS+05j9rxXM1Te1J59+lo9/7vHam7Dsb7S82gj+84AnKo8PAN/f+0URcT1wPcCWLVtmMzJpgEEz+367iVe7h/a7plAN30lXzQzbbLY65tVxrNb173roQO1NWK7wWV5tBH/0Ofa8FqGZuQPYAZ3unE0PShpm2My+GqzDdv32C99qm+lRQ3XYaqZ+nUuHlbRc4VOWNoL/AHB+5fFm4MkWxiHVVuc6QJ1dv/0uRI9aSul3A/MTNpsN6Vzar6TlCp/ytBH8DwIXR8SFwJeBa4GfamEc0kiqobnWDHnYrt++baZrllIGnVVUVzON2rl00uWsWjwzD/7MPBoR7wT+mM5yzo9m5qOzHoc0rjoz5Dq7fscppfSGdPUG5tXVTKtfW2embkmnPK2s48/MTwOfbuNnS5OqO0Nea1npOKWUOtcaqo/rsKRTHnfuSiOqO0OuUyYZVD6C/jP2pkLakk5ZvOeuNIZpb2zqdx/b1VU53hNA4/Keu9IUTXuGfEL5qLIqp9R7AqhZ69oegKTvlI/WB5y0Pjip++91656/OkialDN+aQ702wFc6j0B1DyDX5oTg1blLMM9ATRfDH5pzrniRtNmjV+SCmPwS1JhDH5JKozBL0mFMfglqTAGvyQVZiF69UTEIWD/mN9+JvC1KQ6nTb6W+bMsrwN8LfNqktdyQWae1XtwIYJ/EhGxu1+TokXka5k/y/I6wNcyr5p4LZZ6JKkwBr8kFaaE4N/R9gCmyNcyf5bldYCvZV5N/bUsfY1fknSiEmb8kqQKg1+SClNM8EfEuyLibyPi0Yj4tbbHM6mI+LcRkRFxZttjGUdE/MeI+JuI+KuI+IOIOL3tMY0qIq7s/k7ti4ib2h7PuCLi/Ii4LyL2dv8+3t32mCYREesj4uGI+FTbY5lERJweEXd2/072RsRrp/XcRQR/RLwBuBp4VWa+Evj1loc0kYg4H3gj8HjbY5nAPcAlmfkq4H8D72t5PCOJiPXALcCPAa8A/nVEvKLdUY3tKPBLmflyYBtw4wK/FoB3A3vbHsQUfAT4o8z8HuD7mOJrKiL4gRuAmzPzWwCZ+VTL45nUbwLvARb2ynxmfiYzj3Yf3g9sbnM8Y7gc2JeZj2XmEeATdCYXCyczD2bmQ91/f5NOwJzX7qjGExGbgTcBt7Y9lklExGnA64HbADLzSGY+Pa3nLyX4vxv4wYh4ICL+LCJe0/aAxhURbwa+nJl/2fZYpujfAP+97UGM6DzgicrjAyxoWFZFxFbg1cADLQ9lXL9FZ1J0vOVxTOoi4BDwO92y1a0R8aJpPfnS3HoxIv4EeEmfT/0ynde5ic5p7GuAOyLiopzTtaxrvJb3Az862xGNZ9jryMy7u1/zy3RKDTtnObYpiD7H5vL3qa6IOAW4C/iFzPxG2+MZVURcBTyVmXsi4odaHs6kNgCXAu/KzAci4iPATcC/n9aTL4XM/JFBn4uIG4BPdoP+cxFxnE7jo0OzGt8oBr2WiPhe4ELgLyMCOuWRhyLi8sz8ygyHWMuw/ycAEbEduAq4Yl7fhIc4AJxfebwZeLKlsUwsIk6iE/o7M/OTbY9nTK8D3hwRPw68ADgtIj6Wmde1PK5xHAAOZObqmdeddIJ/Kkop9fwh8MMAEfHdwEYWsHNfZj6SmWdn5tbM3Ernl+PSeQz9tUTElcB7gTdn5jNtj2cMDwIXR8SFEbERuBbY1fKYxhKdWcRtwN7M/HDb4xlXZr4vMzd3/zauBT67oKFP92/6iYh4WffQFcAXpvX8SzPjX8NHgY9GxF8DR4DtCzjDXDb/Gfgu4J7u2cv9mflz7Q6pvsw8GhHvBP4YWA98NDMfbXlY43od8DPAIxHx+e6x92fmp9sbkoB3ATu7E4vHgLdN64lt2SBJhSml1CNJ6jL4JakwBr8kFcbgl6TCGPySVBiDX5IKY/BLUmEMfmkMEfGa7r0EXhARL+r2sb+k7XFJdbiBSxpTRPwHOj1hXkinr8qHWh6SVIvBL42pu5X+QeAfgR/IzGMtD0mqxVKPNL4zgFOAU+nM/KWF4IxfGlNE7KJz560LgXMz850tD0mqpZTunNJURcTPAkcz8/e699/9i4j44cz8bNtjk9bijF+SCmONX5IKY/BLUmEMfkkqjMEvSYUx+CWpMAa/JBXG4Jekwvx/mAu5wGfjlc8AAAAASUVORK5CYII=",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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aHtVjZlYxDn4zs4px8JuZVYyD38ysYhz8ZmYV4+A3M6sYB7+ZWcU4+M3MKsYTuMxs4Eysvjmx8Jpn6+7PwW9mAyW7Cue0IYHE2N7qrbk/GZd6zGyg7LcK595gT0XX3J+Me/xmNlCyq3AOpz3+vXurt+b+ZBz8ZjZQalfhBNf4azn4zWzg1K7C6cDfn2v8ZmYV4+A3M6sYB7+ZWcU4+M3MKsbBb2YDYXTjDpav2cDoxh1lN6XneVSPmfW97Gxdz9CdWmE9fknHSlojab2kdZI+kG4/TNJ9kp5Iv/r/jpm1Zb/Zup6hO6UiSz1jwIci4hRgCXC1pFOB64D7I+JE4P70sZlZyyZm6w4Lz9DNobBST0RsBbam378gaT0wH1gKvD592m3A14Bri2qHmQ2u7Cqc2dm6LvNMris1fkmLgdcCDwJHpgcFImKrpCMavOZK4EqAhQsXdqOZZtZH6tX1rz7vhLKb1RcKD35JhwB3Ah+MiOcl5XpdRKwAVgCMjIxEcS00s34y0cvfsnPXAXV99/TzKTT4JU0nCf2VEfG5dPOzko5Oe/tHA9uKbIOZDY7atfanDQ955c0WFBb8Srr2twLrI+JjmR/dDSwDbkq/3lVUG8xssGRH7+wdD95+zrHMP/Qg1/WbVGSP/1zgXcBjkr6VbvsISeCvkvRuYBPwtgLb0BOyF6Cyv5yNtptZfdm19qdPG+KSMxf4b6cFRY7q+TrQqKB/flHv22saTSyp3X7DRaex46XdLR8EfBCxKqhda9+/663xzN0Oqhe+9SaWnLVo7n7bd+8Z54a7vsN4REuzDj1r0aqkdq19a57X6umQifD903sf5523PPDKeiGNJpZktw8NifGIlmcdetaimTXDPf6cpiqlNOrZNzo1zW6fO2sGN35p3St1y+zohMned+Jnc2fN2K/u6dENZjYZB38OeUoptRedsuHb6NQ0u/3ko2bvd4/Q5Ws2vHJAqHcdAOjoNQIzqw4Hfw6NevNZ7V50mjgIZA8yQ9pXAqq9DnDJmQv2a9OOl3Z71qKZ5TLYwf/l6+CZx1p++Qsv7+H5XWP82rA4e8aLjAcMCU55fA48Nf2A55+V/sdTLb8lR+3cxV/qJUh3LyAyXyccsWEmS2e8PGWbJj7DnIOmMXvm9Cm353mtmXXRUWfAm27q6C4HO/jb8MLLe1i/9flXgnXRqw9mbG8UHoJzDprG0E4OeN9pw2Ljc/sOPvNmz2Te7JmTBvN+n2EnnHL0HGbPnN5we57XmpXBnZDOGuzgb+Mo+VdrNvCnGx9nPGBY8DtnnNxUKaXVSVuzgeGNO3g4fc6RmedszmyfnW6f3cRnePuRC5l/6EFs2bmLOzZu2vfZTj7wsx3w+es8x6xI2cEL2WtdHq7cvsEO/gbyTHaa7GLtVPvKO2mr0S9wnovBeWQ/w/CQWD26mbG9+dY4yfv5zYrQ6FqXF2PrjMoFfzPhO9XF2kb7yjNpq8hf4HprlG/ZuYs7HtqUe42TVi5We/awdUr2b4UIhoaECHdCOqRywd9M+E7Vw260r0a95W70ohutUT66cQd3PrK5qTVOmjnD6PQSFFZNjeam+PepsyoX/J0I36kmTuWZtFXUL3CzE8mKeN92l6CwanLnoXsqF/ztBmDeX85O1emb1cpEsk6/r1yTtRbUdlo8N6U4lQt+aC8Ae/2Xs93aPNDSQTHvEhRmjXhAQfdUMvjb0Q+/nK3W5qcNCSTG9k5+4bvRRdxGS1C4t295eMnl7ql88Dfb2x20X879zmD2BhAEjUs07Za6zCBf58GKU+ngb6W3C4P1y1k71h+p7vj+eje4bvUirod9Vpsv4pav0sHfbG93ENWewcCBZz2NbnDdykVc3zTGPAKsfJUO/ry93UFXewZT+4fX6AbXzVzErXfGMNnBwmcFg8sjwMpXmeCvFyR5ers2+Q2u81zEbXTG0Ohg4bOCwVRvRrlHgJWjEsE/WZBM1du1yS9o57ne0eiModm7mVn/ajSjHDwCrAwDHfzNlhessXYuaE92xpDlW0kOrskO5oM0WKJfDGzwN1tesOK0suCdR3oMBh/Me9PABn+z5QUrVqNeXaOzsl6bEW3N88G8dw1s8OctL1h58p6VeYRPf/HBvPcNbPAP2gzbQZTnrMwjfHpf7ex3l1h738AGP/iiUa/Lc1bmET69rfbAfMmZC1xi7QMDHfzW2/KcldUeHObOmsHyNRtamnfhklHnNCrnBLjE2gcUEWW3YUojIyOxdu3aspthJal30+1m1laa2IdLRp1Rb42riXLOyiuWAJ4I2SskjUbESO129/it502U7Jav2dDy2kouGbWvXi+/UTnH/7a9zcFvfaOdtZX64T4KvWyyEVgu5/QfB7/1jXbWVmpmlJevBRzI82IGi4Pf+ko7ayvlGeXlSUf1eV7MYHHw20Br1HtvtN1rxedbybYK/w6DzMFvA6FeWDUayTPZCJ+qrxXfzEq21r8c/Nb3GpVnGq3KWm+ED+y7XlDlteI9+qkaHPzW9xqVZxotGVBvUtggrxXfTLnLo5+qwcFvfa9ReWayMebZenW7a8XnGQVU1kihZstdruVXQynBL+lC4GZgGLglIm4qox02GLJhVVueaTT6pDbQW+3l5pkRXOas4dqD2p2PbJ7y5kSu5Q++rge/pGFgOXABsBl4WNLdEfHdbrfFBkc2rJotz+Tt5dbrteepiTcK3270qGsnva0e3czY3vwrZ3pOw2Aqo8d/DrAhIp4EkPQZYCng4LeOaKXHOtVrGvXa89TEG4VvJ3r/UwVz9qC2Zecu7nhoU+5JWF7faHCVEfzzgaczjzcDP1f7JElXAlcCLFy4sDstM2ugUc++3mziidVD611TyIZvu6NmJptsNtHmiXZM1PXvfGRz7klYHuEzuMoIftXZdsASoRGxAlgByeqcRTfKbDKT9eyzwTrZrN964ZtdZrrZUJ1sNFO9lUsnK2l5hE+1lBH8m4FjM48XAFtKaIdZbnmuA+SZ9VvvQnSzpZR6NzDfb7LZJCuX1itpeYRP9ZQR/A8DJ0o6DvgRcCnwjhLaYdaUbGhO1UOebNZv3WWmc5ZSGp1VZEczNbtyabvDWa3/dD34I2JM0nuBr5AM5/xURKzrdjvMWpWnh5xn1m8rpZTakM7ewDw7mmniuXl66i7pVE8p4/gj4h7gnjLe26xdeXvIUw0rbaWUkudaQ/ZxHi7pVI9n7po1KW8POU+ZpFH5COr32IsKaZd0qsX33DVrQacnNtW7j+3EqBzfE8Ba5XvumnVQp3vI+5WPMqNyqnpPACvWUNkNMLN95aNhwfRhMT39fmjowNFBZu1yj9+sB9SbAVzVewJY8Rz8Zj2i0aicQbgngPUWB79Zj/OIG+s01/jNzCrGwW9mVjEOfjOzinHwm5lVjIPfzKxiHPxmZhXTF2v1SNoObGzx5YcDP+5gc8rkz9J7BuVzgD9Lr2rnsyyKiHm1G/si+NshaW29RYr6kT9L7xmUzwH+LL2qiM/iUo+ZWcU4+M3MKqYKwb+i7AZ0kD9L7xmUzwH+LL2q459l4Gv8Zma2vyr0+M3MLMPBb2ZWMZUJfknvk/S4pHWS/qTs9rRL0u9KCkmHl92WVkj6n5K+J+mfJX1e0qFlt6lZki5Mf6c2SLqu7Pa0StKxktZIWp/+fXyg7Da1Q9KwpEclfanstrRD0qGSVqd/J+sl/Xyn9l2J4Jd0HrAU+NmIOA34aMlNaoukY4ELgE1lt6UN9wGnR8TPAt8HPlxye5oiaRhYDrwJOBX4D5JOLbdVLRsDPhQRpwBLgKv7+LMAfABYX3YjOuBm4O8j4meA19DBz1SJ4AeuAm6KiJcBImJbye1p158B1wB9e2U+Iu6NiLH04QPAgjLb04JzgA0R8WRE7AY+Q9K56DsRsTUiHkm/f4EkYOaX26rWSFoAvBm4pey2tEPSHOAXgVsBImJ3ROzs1P6rEvwnAb8g6UFJ/yjp7LIb1CpJFwM/iohvl92WDvpN4MtlN6JJ84GnM48306dhmSVpMfBa4MGSm9Kqj5N0isZLbke7jge2A59Oy1a3SDq4UzsfmFsvSvoH4Kg6P7qe5HPOJTmNPRtYJen46NGxrFN8lo8Ab+xui1oz2eeIiLvS51xPUmpY2c22dYDqbOvJ36e8JB0C3Al8MCKeL7s9zZJ0EbAtIkYlvb7k5rRrGnAm8L6IeFDSzcB1wO93aucDISLe0Ohnkq4CPpcG/UOSxkkWPtrerfY1o9FnkXQGcBzwbUmQlEcekXRORDzTxSbmMtn/EwBJy4CLgPN79SA8ic3AsZnHC4AtJbWlbZKmk4T+yoj4XNntadG5wMWSfhl4FTBH0u0RcVnJ7WrFZmBzREycea0mCf6OqEqp5wvALwFIOgmYQR+u3BcRj0XEERGxOCIWk/xynNmLoT8VSRcC1wIXR8RLZbenBQ8DJ0o6TtIM4FLg7pLb1BIlvYhbgfUR8bGy29OqiPhwRCxI/zYuBb7ap6FP+jf9tKST003nA9/t1P4Hpsc/hU8Bn5L0HWA3sKwPe5iD5n8DM4H70rOXByLit8ptUn4RMSbpvcBXgGHgUxGxruRmtepc4F3AY5K+lW77SETcU16TDHgfsDLtWDwJXN6pHXvJBjOziqlKqcfMzFIOfjOzinHwm5lVjIPfzKxiHPxmZhXj4DczqxgHv5lZxTj4zVog6ez0XgKvknRwuo796WW3yywPT+Aya5GkPyJZE+YgknVV/nvJTTLLxcFv1qJ0Kv3DwL8Cr4uIvSU3ySwXl3rMWncYcAgwm6Tnb9YX3OM3a5Gku0nuvHUccHREvLfkJpnlUpXVOc06StJvAGMR8Tfp/Xe/KemXIuKrZbfNbCru8ZuZVYxr/GZmFePgNzOrGAe/mVnFOPjNzCrGwW9mVjEOfjOzinHwm5lVzP8H0/LyS8m6YrAAAAAASUVORK5CYII=",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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fRORULH4RmneCrIv9jqTalPhFRGrr0C5YNxMG3ASBJL+jqTYlfhGR2lo2GULBBlXmASV+EZHaW/Qv6DQI2p/hdyQ1osQvIlIbO5bD9iUwqP6Ou18RJX4RkdpY/AIEkqHf9X5HUmNK/CIiNVVSDEtegl4joWlbv6OpMSV+EZGaWjsTDu2As27xO5JaUeIXEamphc9Bsw7Qa4TfkdSKEr+ISE0c3A5rZrC9+7VM+M8G8goK/Y6oxjQss4hITSx+AVwJX1vUmzXB1aQmB5h0Z06DGJWzlFr8IiLV5RwsfJ6tLQaxJtiRkIPiYIjc/D1+R1YjSvwiItW1MRf2rKNowFhSkwMkGaQkB8jJauN3ZDWiUo+ISDXt/nAiLZKaUph5BZN6pZGbv4ecrDYNqswDavGLiFTLwrUFpK19gylFw/jKs0sAuO+Sng0u6YMSv4hItRyYM4k0O86k4PAGWdePpMQvIlIV5xi2+zWWuSxWktUg6/qRVOMXEanKprk02bea5uf9mvtT+jTIun4kJX4RkarkPQOpzcm46DbuayDz6lZGpR4Rkcoc2QvLXvFm2YqDpA9K/CIilVv8IpQchyHj/Y4kapT4RUQq4pxX5jltKHTs73c0URPzxG9mSWa20MzeDD9ubWYzzWxt+HvDvUIiIvHtsw9g9xoYcrvfkURVXbT4vwOsjHj8EDDLOdcLmBV+LCJS/8z9G6S1gTOv8zuSqIpp4jez04ArgIkRi68Gng3//CxwTSxjEBGplX0bYfU0GDwOUhr7HU1UxbrF/wfgQSAUsayDc24bQPh7+/JWNLO7zWy+mc3ftWtXjMMUESlj3tMALOl0PRNmr2uQ4+5XJGb9+M1sDLDTOZdnZhfXdH3n3FPAUwBDhgxx0Y1ORKQSxUdhwT8p7DaCm17cRFEw1CDH3a9IlS1+M/tmLS/AngdcZWYbgBeBS83seWCHmXUKb7sTsLMW2xYRiZ1lr8DRvXzQ8hqKgqEGO+5+RapT6ukIzDOzl8xslJlZdTbsnHvYOXeacy4TuBl4zzl3CzAVGBd+2jjg9VrELSISG87B3P+DdqfTdfDIBj3ufkWqLPU4535sZo8CI4DxwF/M7CXgaefc+lrs83HgJTO7A9gI3FiLbYiIxMbGXNi2GK74HdmZrZl0Z06DHXe/ItWq8TvnnJltB7YDQSAdmGxmM51zD1Zj/feB98M/7wGG1zZgEZFYyCsoJDd/D1/d8AfSm6TDwK8AkJ2RHjcJv1SVid/Mvo1XktmN1y3zAedcsZkFgLV4vXZERBqsvIJCxk7MpUNwG/emzmDbwHvplNrU77Bipjot/rbAdc65gsiFzrlQuOeOiEiDlpu/h6JgiHFJMwgS4B/BEbSYvS6uyjuRqlPjf6yS362s6HciIg1FTlYbWicf46bA+0x35/DMkmMES1bHVRfOSBqkTUQSXnZGOq/mrKeZHWNzn/EES+KvC2ckJX4RkZIgXdf8EzLOJ+f84XHZhTOSZuASEVn+KuzfBKN/Q3ZGelx24YykxC8iic05+PiP0O506D0KiM8unJFU6hGRxLZuFuxYCud+GwKJkRIT4yhFRCry8R+gRRfonziDCCjxi0jCWjn/PdjwIZv6jIfkVL/DqTNK/CKSkPIKCtn0xq/Y79K4JrdHXI23XxUlfhFJGHkFhScmVVm1bD6XMZ9/loxgX7BRXPbXr4h69YhIQigdj6d0UpXpXSdxjFSeKxkZt/31K6LELyIJoXQ8npCDzsGtZGx9i139bmdc22Fx21+/Ikr8IpIQcrLakJocoDgY4hspUyEpmQ6jHuC+5h39Dq3OKfGLSEIovSN3+YqlXD/3Iyz7DkjApA9K/CKSQLIz0sle+qp3o9Z53/E7HN+oV4+IJI79W2Dh8zBoLLTs4nc0vlHiF5HE8eFvvbF5zv+e35H4SolfRBJD4QZY8BwMvg3SM/yOxldK/CKSGD74H7AAXPgDvyPxnRK/iMS/3etg8b9g6J3QorPf0fhOiV9E4t/7v4bkxglf2y+lxC8i8W3HClg2Bc7+OjRr53c09YISv4jEt3d/Co1awLnf8juSekM3cIlI3MkrKCQ3fw+Xpa2lz9oZcNlPIa2132HVG0r8IhJXPh+Fs4TzUx/jcJMOPHfscoYWFCbUQGyVUalHROJK6Sico2wOA209Pzt0Lb+ZVcDYibkJNdlKZZT4RSSu5GS1IS05xIPJ/2ZVqCuvlJxPyEFxMJRQk61URolfROJKdkY6085dT2ZgB9uHPkRycjJJRsJNtlIZ1fhFJL4c2Uu3JX+A7hdx8ZixTBqwj9z8PQk32UpllPhFJL68/zgc2w+jfg1m3lDMSvgnUalHROLHzlUwbyJkj4cOZ/odTb2lxC8i8cE5mPEIpDaDS37kdzT1mhK/iMSHte/A+llw8Q+hqS7iVkaJX0QavuKjMP1BaNMLht7ldzT1nhK/iDR8H/0BCjfwWpf7ydty2O9o6r2YJX4z62pms81spZktN7PvhJe3NrOZZrY2/F2X20Wk9vasJ/TRE7wZOpf757XUHbrVEMsWfxD4vnPuDCAHuM/M+gIPAbOcc72AWeHHIiI15xxMf5AgKfyieKzu0K2mmCV+59w259yC8M8HgZVAF+Bq4Nnw054FrolVDCIS39b/50VY9y5Le3+T/cltdIduNdXJDVxmlgmcBcwBOjjntoH34WBm7StY527gboBu3brVRZgi0oAsWrOBzu89zHKXwW3LBvDYmDMpPFKkO3SrIeaJ38yaAVOA7zrnDphZtdZzzj0FPAUwZMgQF7sIRaQhSpn9U9qwj9uLv88xjMIjRdx3SU+/w2oQYpr4zSwFL+lPcs69El68w8w6hVv7nYCdsYxBROJLXkEhGxfM4NptrzLRXclKslTeqaGYJX7zmvZPAyudc09E/GoqMA54PPz99VjFICLxJa+gkNsn/ofX7TEKrAPNRz3K/ceTVN6poVi2+M8DbgWWmtmi8LJH8BL+S2Z2B7ARuDGGMYhIHMnN38M33EtkJu3glqIfcc7xJJV3aiFmid859xFQUUF/eKz2Wx+Vzv9ZtlVS0fJo7kMkngxv+hm9k97ixZJLmJ/Un++pvFMrGpY5xj6f/zNEanKASXfmkJ2R/oXlp9IjoaJ9iMSV44c4/dMHON78NA4M/BmTenfT+7yWlPijqLxWd+n8n5E3lmRnpJ+0vKg4xGOvLyPkXK0Sd0X7EIkrMx+Dwg00+tpb3J050O9oGjQl/iipqNWdk9WG1OQAxcHQST0PIpebGSHnyk3clZVwSn+XnpZa7j5E4sa6WTD/aTjnm5B5nt/RNHhK/NVUVQ29olZ3dkY6k+7M+cK6kcvT01L5+ZvLTyTu9LRUJsxed2J5eeUgIGqlIpF67fBueO0b0LYPXPqo39HEBSX+aqhODb2ilj0lQbLTdpHdeT1sexdWFsCBrXBkD9mHd5N9bB8UH+HmlKMEkooACE0zSghwlEZcGmjE4ZTGFNKcvW+1ANeCD2e3pUtGbwaWGPmuI3uDrXTzisQn57ykf3Qv3DIZUhr7HVFcUOKvRGkrf+u+o1XW0LMz0pl0xzBWL1vAuY3Wk7noTZi+BHathpLjnz8xJQ1adIam7aBtT2jcClLSCKQ0gaRU5m3Yy6f5e0iihDSO09SKaMoRWttBMtjB4MAa2toB2AQ3pnqbPOiaEFjeGw70hw79oWN/6DQQGjWr8tgqO0NQTyHx3Zy/wtoZMPo33vtaokKJvwKRrfzkgJGcFKCkpJwa+sHtXv1x/Syy188m++heb3mTdOh8FnS/0Jv7s21vaJUBTdtCJcNWBAoK+d/Pck+cOTw25kw2HClif1oq499cTnFxiGbJQSbd2JXUQ5vYnr+M01N20P7YBlg9HRY+723IAtC+L7ta9mexnU6HAcPpf2b/LxxbRWcw6ikkvtu22Lug23s0eR1uJHf2OjVCokSJvwKRNfuSkOPLw7rSpVUT743X6jB8+gKseA02zfFWaNYBeo+EzPOhaw55h1qT+9neGvfdr+iaAECfjs1PLO+XkQ4Mpve5V3++snPeB9H2JbAlj/3rPiV19VQusxdg9U849GZnNrYcytrUwTQNduCYa1HhGYx6Comvju2Hl8dDWhsWZf+SsU/PUSMkipT4K1C2Zn/DgLYMPvIxfPAc5H8AOOjQny1nfZ8PA0Pp1f9ssjNbA+HW8tNV992v6A1celG4ustPMIMWnbyv3iN5nnU8kb+SXmwmJ7CSnNBKco68S197nZtSjSUuiw8YzCUtvwaux0lnIhVesxCJtXBd3xVu4NUB/0feiiNqhERZQib+6tSuS1veS1euYOThN+g0+V44Wggtu8FFP4QBN5F3qPXniXzunBOJvDp992P5Bo7s5pmSnMzaYDfWuQz+WTwSXIiBgXy+0W0j/Q/n8u2Dk7GpL8MHXeH0MdD3Kuh6dqVnHlXtV6fjcko+/iOsepPHQ7fyt7lpJAc2VVxqlVpJuMRf7dr1jhVkz3+C7OWvggvB6VfAkDug+0UQ8OavyV2yrtxEXp2++7F6A1d0R/DnXUZhZVJvWo++jY4Z6XBoJ6yZAavegvl/hzlPQtP2cOa1ZPe/geyLh1Z6TaKi/ep0XGpjde40er37M5a1vJS/7RxVfqlV76tTlnCJv8pW947l8MF/w4rXIbU5DLsHzr4b0jNPPKWqG6eq03c/Vm/gsscX2c0z8hrBiX03aw+Db/W+jh/0PgRWvAZ5/4C5/+ed4Qy4CQbeDG17VXu/UxZsVutfamTp8qV0nn4P+a4j43bfQnJS0olW/vWDT9P7KIoSLvFX2Orevxlm/QKWvOgl/AsfgJxvQFrrk9av7hg7ta7Tx+r4qrPvRs2h/w3e17ED3lnA0pfhoyfgw99Cl2wY9FXodwM0aVXhfpMCxuS8zQRL1PqXajp+kE7TvkYyQe4uvp8DNObLw05TKz9GzLn6P7nVkCFD3Pz586O2vZNq0Z1S4aPfwyd/9i4q5XwdzvvuFxJ+qQmz1/G7d1YTcpBkcP+IPvXuxqma1tqrfP7B7d4HwKIXYOdySG4MZ1wJg8d5vZjCpaDI+x5emLuxXr9GUo+ESuDFsbi173BH8Id8EOxHihoMUWFmec65IWWXJ1yLHyJavqunw4QHYP8m6Hc9DP8JpGdUum5D6O1Sk7OKap3BNO8I537LGydl2yJYOAmWvuR9GLTuAdnjYNAtZGe0OdF7acqCzfX6NZJ6ZNbPYM10bPT/cF/HG8lWiTDmErLFz4GtMO0BWPUmtDsDxvweMs6pdks5nnqvRJ7BBIBAwKocJTSvoJB5a7cw0ubQds0LNN8xj1AglcCZ18DQO6HrMPI27oub10hiaO7fYNoPYMjtcMUT1epIINWnFj94pZxlU+Ct+yFYBMN/woIuY/k0/yDp2zeeNCBaZaeZsa7T16WajhIaOXDcE4FOYN+ne2gjtyW/y82rppG09CXo2J/sYXeTff6NkNLE5yOU+iivoJCdc15m1IoH2d/1Mv6Vdg9nb9wXN/9X9V3itPiP7IU3v+f1WDltKFzzV/IOtzlR5ghEJL1Eq0uXTeqlJZrybjyLfJ1K22YO7zX74fCu3N1yHsybCDtXeOMQZY+DoXdBq65f2J/OBhJTXkEhv5v4D54J/JIVLpNxoR9zqCRFHQFiILFb/BvnwOTxXp/14Y/Bud+BpGRyl37eDx/nCAQMwyVcXTryDKa8Lp+RXTUjX6ekgIHZiS532b26QsYA77S94GNvgK1P/gyf/IXCjJG81+p6jnccys/fWqH+/gls3ZJPeDLwGza7ttxR9H0OkoJDd+XWpfhO/KEQfPpnePdnHG/WhdcHPUOPbueTneQddtkLtRrTvvwyVmWvE/DF1ruZ19sn83zYt5Ht7/6Fxkuf53qbxuJQD0aGRvOWG0ZxMLnCf3SdFcSfvIJCVi+dx3VL7mMvTRhf/BCHklqSEtF4SKQGl5/iu9Tzxnch7xkKM0Zzef6N7A02/kIrUwmmek7ldZowex3/+85irg18yO1Jb5MV2MZW14bn3ShG3PIgg3pnfmFfugs4vuQVFPLIxFd5LvAzAOZc9DwbrVPFjQeJioQs9azqeCU7e7ZlRtpV7A1uKveiZTxdqI2lU3mdcrLa8OfkNF4IXs6UwOU8mb2Xnuv/wYP7JsHk12HwbXD218k70KLa8x9Iw7Jy+SKeCfwXSZTw1eJHuco6nXQNTX/fuhW3iT+voJCxU4soCp5FcmCzBnnyUflDVdzqjbf+6QSY+xRuzl/ZUTKMmcErWGE99feKE155Zz7XLb2X4xRxa/HDFCR109/UZ3Gb+CsdT1+tizpX7hlDp4HkZf83S9PGkbX+eS7Y+SpfSs1lTuh0Vmd9jYPdhpPTo53+Xg1UXkEhP5/4b54O/JJDBJh3wT8ZHU76+pv6K24Tf9kLkhrkqf45eZazK2lql3EDsxif9DZnb3gIDvWGlt9kQXAEn248rITRQJReD0reModnAz/nMI25rfgRrkvqljBdpOu7uE38dTESppyasmdlo4f1plWrgWzL/CmdD34An/wJ3vg23VxLZpeM4L73RjDhzsv1t6xnIi/8A4ydmMuloVx+nzyBLbTla0UPsTO5g8o79Uh89+qReq20xV/2hrETnOO1V1+g1aK/cnFgMUddKmu7XMOAGx6G1ln+BS4nlO2Bdf3g00jNe4pHk55jkevJtP6/J71tJzW+fJKQvXqkfqvyrMyMrtmjGbswncyijdyZPI1rt72K+9PL7Os2gh397mLWoUxyerRVUqljkSOxlp61uWARV27+HTnJr/JOyRAe4Nv8fVg//W3qIbX4pd6LHFLiyTc/4stuBmOT3iXdDrEo1INnuYJbxn+b7O7tqrUdtT5PzcnXZry7t1uVFDIh9U8MtZVs73cPr7S+g7N7tNfr7LOKWvxK/NJgRI4kmsYxrk/6kNuTptE9sIODjTrQ/ML7vHsCmpR/J7BuCjs1Fc630O8wt218lKbBQgJXT4ABN/odqoSp1CMNXmRPrWCgCf+2kbxQPJzLkxfzm/T/wMzH4P3HYeBX4OyvQ7veJ9atq4nu41XZVn5yUoBQSZC7Ut7mG+texFp0gi/PgM5n+R2qVIMSvzQYZa8JQOmt/ufTPOPHsG2JNzDcwudg/tPQ41JvzuReI2o0gY5KQl9UtgfW7Wc1Y+z2x8nc+zH0GQNX/6XcMy2pn1TqkfhzaJc3Wfz8p+HgNkjPhCF3sKjtGD7eGqo0oVd3TuVEE9kDa0zyXH6b9k9Sgodg5K+8yXc0gUq9pBq/JJ6SYvI/fJHGC5+m8/6FkNQI+l0HQ24nr6QnuZ/t/UJCr82MZPGmojOexavWkjbrYXrtmumVdK55Etqf4WOkUhXV+CWulZes8jYfYuysthQFH6Bf8mYmnr6E9itfg8Uv0Mx1Y2fwEu4NXMCTd152Yp3qzkgWr8q9CN61Bcz/OwPf+wUUHYFLH4XzvgtJSh8Nlf5y0uBVVJ6J7GO+PHgaL3cYzn3XPs7sKU/SZtUL/CzlWR5x/6LgrUtZc9ZtzDzam5we7U5cRyg7I1ki3Hla9iJ4wcJ3yZ7+J9i+BLpfCF/6LbTr43eYcoqU+KXBi0xWRcUhHnt9GSHnTvQ+OWmUz0bNaXHeXdy0sj+9ivK5Ofl9btz7CakzZtDMtWHq+xdw/vXf5L5LhgLlz0jW0NTkYnXpGU/3kgIeTPk3lyxaAM07ww3PwJnXqpYfJ1TjlwYv8sKjlZk7+cvDupU7KmtkMpy3dgsrZ7/ANYEPuTCwhCRz0GkQ9L8BzrwOWnapcv9VJVa/egpVdv9CuTHtWM6eGf9N6/yplKQ2I/mC+72usalpdRazRE+9urhrZqOAPwJJwETn3OOVPV+JX6pS1YTxVa1b+sHROXk//8rZQtctb8HWhYBB17Oh79VwxpUnTRofuW5lN4b5efNY5MXqyA/C0tfJi8l4fUwSfdY/A2umQ0pTGHoHnP89SGtdJ3FKbNSbi7tmlgRMAC4HNgPzzGyqc25FXcci8aOqCeOrWjfy/oCuGenAA7BnPSybAitehxkPw4yH2dnsDII9R9L57Oug44Bq3RhW9jlTFmyus9Z/5MXqpIAxOW8zwZIQATPS3GFuCHzMrfYufaZv8vrhX/wIDLvrRMLXPQ3xqc5b/GZ2DvBT59zI8OOHAZxzv65oHbX4xW/LlixgxuSnuIg8BttaAuagWUd2dzyPX6/pzIfFfTmQnF5pi780+WJGsCQ6rf+alJm27jvK5Ln5XGiLuDrpEy4L5NHYilnmsmh2/j1kXnQrpDb9Qtwa5qLhqjctfqALsCni8Wbg7LJPMrO7gbsBunXrVjeRiVTggz0tmFB8JX92V9Le9vPrAdsZnryEtutn8bvAPmgER1v1psmyi+DgOXDaUGjZFcxOOqOIHOfmVLuIVnazGURMYN4mSHbhPAoLpvJw6mya2VH2uuZszLiexW2+RNagC+lXTgwa5iJ++ZH4y+sW8IXTDufcU8BT4LX4Yx2USGUiSyYHktNpde5oyEiHUIl3LeCz/9Bkw0eULJxE0ry/AVDUpD1b0s6gUddBZPcZRvbAvuTt78SUBZtPXINIT0tlwux1tSqllNebyVyQ3oFtnBnYwCBW0er9VWBbAUhv1pFdfa5hduo5dM4eTXb39pSOZlTemUNNhrmQhkWlHpFqqqqskldQyLiJH5FVsoHspPUMsrX05TOybKvXUwggqRFHm2eyNbkzxc268Ep+gC0l6RwItOShGy7gzB6ZkJLmfQUCJ++gJAjFh1mSv4WV69bTPnCAmXMX0yW0gwzbQYZto7dtoZEVA3DANSEv1IdGPS/g3Muv93oqldMds8Y9f6TBqE+lnnlALzPrDmwBbga+6kMcIjUSeQG5vISYm7+HI8EAS1wWS0NZwOU4oJkd46c5AW7oehB2r6HJ7rX02JtP8cZPeSRwzBsbAuDVMjtMSgUL/9KFoKQIgAHhL4BLAhAKJHE4rTOLD6fzXMmZrCKDFXRnbUknkpKTmXRxDnSuOGlXVtKJPGaJH3We+J1zQTP7JjADrzvn351zy+s6DpHaqqiFXLYHDWaUlIQIJqfRfVCOVxqKsGTDXu57+l3alOymfdIhHr20A1lNi6D4CBQf9b6fYJDalI8KjjBt9QF2uxbsoRVXn38Wt408l+ZJKTQpKOR4/h6+UrbGX82btlTSSRy6gUukhsr2jb9/RB/uu6Qn8MWJx6N9Y1eV8xTXkko68ale3cBVU0r8Up/4nXyVpKW6lPhFoijaybfaXTOV6KUG6tPFXZEGL9oXPSsbaC6aN3yJwOf9CUTER6UXWJPs88lfQg6KSxzFZXrciJwqtfhF6oHIu3sjB5qL7B2kHjcSLUr8IvVERQPNgWr8El1K/CL1UNlrCEr4Ek2q8YuIJBglfhGRBKPELyKSYJT4RUQSjBK/iEiCUeIXEUkwDWKsHjPbBRTUcvW2wO4ohuMnHUv9Ey/HATqW+upUjiXDOdeu7MIGkfhPhZnNL2+QooZIx1L/xMtxgI6lvorFsajUIyKSYJT4RUQSTCIk/qf8DiCKdCz1T7wcB+hY6quoH0vc1/hFRORkidDiFxGRCEr8IiIJJmESv5l9y8xWm9lyM/uN3/GcKjP7gZk5M2vrdyy1YWb/Y2arzGyJmb1qZq38jqmmzGxU+D21zswe8jue2jKzrmY228xWhv8/vuN3TKfCzJLMbKGZvel3LKfCzFqZ2eTw/8lKMzsnWttOiMRvZpcAVwMDnHNnAr/1OaRTYmZdgcuBjX7HcgpmAv2ccwOANcDDPsdTI2aWBEwARgN9ga+YWV9/o6q1IPB959wZQA5wXwM+FoDvACv9DiIK/gi87Zw7HRhIFI8pIRI/cC/wuHPuOIBzbqfP8Zyq3wMPAg32yrxz7h3nXDD8MBc4zc94amEYsM45l++cKwJexGtcNDjOuW3OuQXhnw/iJZgu/kZVO2Z2GnAFMNHvWE6FmbUALgSeBnDOFTnn9kVr+4mS+HsDF5jZHDP7wMyG+h1QbZnZVcAW59xiv2OJotuB6X4HUUNdgE0RjzfTQJNlJDPLBM4C5vgcSm39Aa9RFPI5jlOVBewCngmXrSaaWdNobTxupl40s3eBjuX86kd4x5mOdxo7FHjJzLJcPe3LWsWxPAKMqNuIaqey43DOvR5+zo/wSg2T6jK2KLByltXL91N1mVkzYArwXefcAb/jqSkzGwPsdM7lmdnFPodzqpKBwcC3nHNzzOyPwEPAo9HaeFxwzl1W0e/M7F7glXCin2tmIbyBj3bVVXw1UdGxmFl/oDuw2MzAK48sMLNhzrntdRhitVT2NwEws3HAGGB4ff0QrsRmoGvE49OArT7FcsrMLAUv6U9yzr3idzy1dB5wlZl9CWgMtDCz551zt/gcV21sBjY750rPvCbjJf6oSJRSz2vApQBm1htIpQGO3OecW+qca++cy3TOZeK9OQbXx6RfFTMbBfwQuMo5d8TveGphHtDLzLqbWSpwMzDV55hqxbxWxNPASufcE37HU1vOuYedc6eF/zduBt5roEmf8P/0JjPrE140HFgRre3HTYu/Cn8H/m5my4AiYFwDbGHGm78AjYCZ4bOXXOfc1/0Nqfqcc0Ez+yYwA0gC/u6cW+5zWLV1HnArsNTMFoWXPeKcm+ZfSAJ8C5gUbljkA+OjtWEN2SAikmASpdQjIiJhSvwiIglGiV9EJMEo8YuIJBglfhGRBKPELyKSYJT4RUQSjBK/SC2Y2dDwXAKNzaxpeBz7fn7HJVIduoFLpJbM7L/wxoRpgjeuyq99DkmkWpT4RWopfCv9POAYcK5zrsTnkESqRaUekdprDTQDmuO1/EUaBLX4RWrJzKbizbzVHejknPumzyGJVEuijM4pElVmdhsQdM79Kzz/7idmdqlz7j2/YxOpilr8IiIJRjV+EZEEo8QvIpJglPhFRBKMEr+ISIJR4hcRSTBK/CIiCUaJX0Qkwfw/a3xlGLk7nlkAAAAASUVORK5CYII=",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Data generation\n",
        "\n",
        "x=np.linspace(-6,6,100)\n",
        "x=x[np.newaxis,:]\n",
        "\n",
        "# Define Weights as per the given equation\n",
        "w = np.array([-3, -3, 1.25, 0.25]).T\t\t\t# w = [w0, w1, ..., wm]^T mx1\n",
        "\n",
        "## Function to transform the data into polynomial\n",
        "\n",
        "def data_transform(X,degree): \n",
        "\t# X = [x1, x2, ..., xn] 1xn\n",
        "\tX_new = np.array([np.squeeze(X)**i for i in range(degree+1)])\n",
        "\n",
        "\t# X_new = [[x0^0, x1^0, ..., xn^0], [x0^1, x1^1, ..., xn^1], ..., [x0^m, x1^m, ..., xn^m]] mxn\n",
        "\n",
        "\treturn X_new\n",
        "\n",
        "\n",
        "X = data_transform(x,3)\n",
        "\n",
        "y = X.T @ w \t\t# nx1\n",
        "\n",
        "y = y+5*np.random.uniform(0,1,y.shape)\n",
        "\n",
        "plt.plot(x.T,y,'.')\n",
        "plt.title('Data')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.show()\n",
        "\n",
        "reg=Regression()\n",
        "\n",
        "# By computation\n",
        "\n",
        "# Code for degree 0 polynomial fitting\n",
        "\n",
        "degree = 0\n",
        "X_1 = data_transform(x,degree)\n",
        "w_mat=reg.mat_inv(y,X_1)\n",
        "y_pred=X_1.T @ w_mat\n",
        "plt.figure()\n",
        "plt.plot(x.T,y,'.')\n",
        "plt.plot(x.T,y_pred)\n",
        "plt.title('0-Degree Polynoimal')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.show()\n",
        "\n",
        "def polyComputationFit(x,y,degree):\n",
        "\tX_1 = data_transform(x,degree)\n",
        "\tw_mat=reg.mat_inv(y,X_1)\n",
        "\ty_pred=X_1.T @ w_mat\n",
        "\tplt.figure()\n",
        "\tplt.plot(x.T,y,'.')\n",
        "\tplt.plot(x.T,y_pred)\n",
        "\tplt.title(str(degree)+'-Degree Polynoimal')\n",
        "\tplt.xlabel('x')\n",
        "\tplt.ylabel('y')\n",
        "\tplt.show()\n",
        "\n",
        "# Write the code for degree 1 polynomial fitting\n",
        "polyComputationFit(x,y,1)\n",
        "\n",
        "# Write the code for degree 2 polynomial fitting\n",
        "polyComputationFit(x,y,2)\n",
        "\n",
        "# Write the code for degree 3 polynomial fitting\n",
        "polyComputationFit(x,y,3)\n",
        "\n",
        "# Write the code for degree 4 polynomial fitting\n",
        "polyComputationFit(x,y,4)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "x7pFawen2JqQ"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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WgoY/vYPfzKzZXnwO+u9Ng/5ueGIF7NyaXHfgXDjij2HeEpizGKYfCz3NXWnv4Dcza7Rn+zOz+aXw1EMQg6AeOOwkWPDOZFY/dzHsf3jLh+fgNzOrx+Au2PCb4WWbZ9cm103aB2b3wsuvSEJ+di/stV++48XBb2Y2Pju2JqWa0mx+7T2w/bnkuv1mJjP5JZcl9fkZJ8KE9ovZ9huRmVk7eWHD8LLN+l/B4EBy3fTj4MQLkpCfuwgOnAdSvuOtgoPfzKwkAp7+7fCgf2ZNct3EvWHWQjjzQ0nQzzkdprTh0tAqOPjNrLgGtsO6+4bX57c9k1w39eAk4BdenHydeQpMnJzveBvEwW9mXae0+2Zp47Xd3brTI6nJ992dhPwTK2HX9uROB78EjnlNchB27uLk5w4o29TCwW9mXWVoF85dHNGzkYU9v+U0VrH/T38H6k9u1DMJDj8VzvjztGyzCPadnuu4W8nBb2bdIe2G3fqzH/AFfs7Cyb/lUG0B4LmYyorBo9n0R+ez+KzXJLX6SVPyHW+OHPxm1pkqdMO+DOjvmc4vB09gJcewIo7jkV0zmThxIje+YjG04149LebgN7PO8OwTySqbUtCP7IY97R3Jksq5S3hq8xSeWLOJ8488mPOhc3bkbBEHv5m1n8FdsGFVJuiXwbN9yXWT9oHZC0fthl24P8NC3oE/nIPfzPJX6oYtBf3ae2H7s8l1+x6WBPySDyRfZ5zUlt2wncT/embWeqVu2LXLkrLNHt2wb0pCfs4imDa/a5dV5sXBb2bNFQFP/25o7Xzf3UPdsBP2ynTDLobZp8PUg/IdbwE4+M2ssQa2w7r7M/X5pUPdsFMOSrth35Xpht0rz9EWkoPfzOqz9ZmkG7YU9Nlu2IP+KO2GXZScZOSQo5pWtsl26/pg7ugc/GZWvQjY/NjQBmZ9S2Hjw8l1PRNh5qlpN+ziJOhb1A071K07yOSJPdx4yWKH/yiaFvyS5gD/FzgMGASuiYgvSToI+CdgPvAY8JaI2NyscZhZHXbthCcfHB70pXPD7nUAzDkDTnpzEvSHL4DJU3MZ5tI1m9gxMMhgwM6BQZau2eTgH0UzZ/wDwEcjYqWk/YAVku4A3gXcGRFXSboSuBL4WBPHYWbVynbDrl0K/cv3PDdsaROz6cc1/dyw1Vp85MFMntjDzoFBJk3s2b05m5XXtOCPiPXA+vT75yWtAmYB5wNnpTe7HvgpDn6zfIzWDTvjxGHdsHmcG3Ys2br+jZcsdo2/Si2p8UuaD5wGLANmpG8KRMR6SYdWuM+lwKUAc+fObcUwzbrbsG7YZUnY7+6GnZqeG/avhpZVtsG5YUdTrq5/2StekvewOkLTg1/SvsAtwEci4jlVeUQ/Iq4BrgHo7e2N5o3QrEvt2ArrViYz+b5l6blhs92wi2Dx+5OgP+wkmDAp3/FWqTTLX7dlm+v6NWpq8EuaRBL6N0bEd9KLn5I0M53tzwQ2NHMMZoXxwsbha+fX35/phj0WTnzj0N7zHdoNm53lT+wREyf0sGuX6/rj1cxVPQKuA1ZFxOczV90GXARclX69tVljMOtapW7YbNA/82hy3YS9YNYCOPODSdB3UTdsdvXOrsHgT8+Yw6wDp7iuP07NnPG/FHgH8KCk+9PLPkES+DdJeg/QB7y5iWNoC5UaS9xwYlUb2J7sZ7O7bLMUtm5KrptyUFKuWfBOmHdmV3fDjly9c8GC2f7bqUEzV/X8O1Dps+TZzXredlOpsWTk5Z8+7wQ2b91R85uA30S6zLbNQ+eG7VuW7Fy5uxv2SDj63KEmqSZ2w7abhfOmefVOA7hzt4HKhW+lxpLs5Tt2DvLpW3/NYERNXYfuWuxwpW7Y0gZmfctg46rkuj26YRfBvmUXwhXGwnnT/PtdJwd/g1QK30qNJdnLJTEYUfPqBHctdphdA/DkA8OD/oUnk+t2d8NekMzmZy3MrRvWupeDv0pjlVIqhW+lj6bZy6dNncxnvv9Q2a7D0Z63dN20qZPdtdjOSt2wpaDvXwE7/5Bcd8BcOOJlaTfskrbqhrXu5eCvQjWllNFaxit9NM1efsxh++0OeICr71q9+w2h3HEAoKHHCKyBnluXzuTT1TZP/XpEN+zbkpLN3CVwwKy8R2sF5OCvQjWllHoPOpXeBLJvMj2ZEtDI4wAXLJg9bEybt+5w12IeBgeTenx2tc2WCt2ws3ph7/3zHa8ZDv5RjbeU0oiDTtk3GSLo6REi9jgOEFDVmOpZSuqVQmXs7oYtnRs22w07Iwn4RZ3XDWvF4uCvoNHLLas1smRUet6RxwEuWDCbCxbMHjWYq11KWq505ZVCqWq6YecsTrY/mHZEYZZVtponIY3l4K9gZHlnvKWUWmfao5WMsscBsgeJq30Nt6zsr3qPk0KuFIqATauHyjZ9d+/ZDbvk8nTbgzO6phu2XWU/cWePdRV2EtJAhQz+amYP1e7vXe6x6plpQ3UHg6uRfQ0TesTNK/oZ2FXdHieF2N+8mm7YhRclM/rDT+3abth2VOlYV2EmIU1WuOAfT/iOdbC20mNV07TVzF/gcnuUr9uyjW/e01f1Hie1HKxu+4/ju7th07LNupUw8GJyXakbds6iJPAPOdplmxxVOtbVtZOQFitc8I8nfMeaYVd6rGqatpr1C1xpj/IVj2/mlpX949rjZDyfMPI6JlJRBGx5fCjk+5aO6IY9BXrfM3Q2qYJ3w7aLSgsqcv996jKFC/5GhO9Yq32qadpq1i/weBvJmvG89W5BUZNdA/DUg5nVNsvg+fXJdXvt727YDtB2k4cuVrjgrzcAq/3lbFSdfrxqaSRr9PPWuwVFVbY/P3Ru2L7SuWEz3bDz/8PQJmaHHgc9Exr7/NZw9S6osOoVLvihvgBs91/OemvzQE1vitVuQVGz3eeGTVfbDOuGPSHTDbsYDphd//NZyxViQUGbKGTw16MTfjlrrc1P7BFIDOwa/cB3pYO4lbagGPeb7OAgbHx4+LYH5c4NO2dRcpIRd8N2BW+53DqFD/7xzna77Zdz2CeYXQEEQeUSTb2lrrJ2boMn0nPDrl2W/PfiiG7YDjw3rFVWzeTBmqfQwV/LbBe665dz5Fp/pLLr+8ud4LrWg7i/emQ1TzxwFwt4hMOevR/W3Q+DO5Mrpx8Lx78haZJyN2xX8kHc/BU6+Mc72+1GIz/BwJ6feiqd4Lqqg7i7u2GTks2La37JKc+t4RRgR0zkhRmnsu+Sy9wNWyC5rwCzYgd/tbPdbjfyE8xo2zdkm7/KHsQd2DHUDbt2WRL4W58G4MWJB/D7qSdy28AZ3LPrGH7DEVx+3EllD463fTOY1azlK8BsD4UJ/nJBUs1s10Y/wfXx0wbpf+CnLOx5hJk/+XJybthSN+y0I+CoV/HYvifzgZ9N4pHtM5iwbULyBkvlN1hvENedynWUN2UFmI2pEME/WpCMNdu1zBvko0/z8kO3cdKW2+GBZEZ/6obfcCrs2Q07ZxHsNwOAH9y1mocHHkna76vYLqKQG8R1uUod5VDnCjCrSVcHf7kDkg6Scdg1kKyX71vKwr67WTiyG3b26XDCm5KDsLN6K3bDjvaJIcunkuxeo72Zd9NiiU7RtcFf6YCkg2QU218Y6oZduxTW3pvphp0D8146dG7YcXTD1rLhnVd6dAe/mbenrg3+SgckHSQZz60b2tem72548tcQu4a6YU9969AmZnV2w1aa1VX6VNZuHdE2fn4zb19dG/zVlhcKY/e5YTNBnz037KyF8LKPJiHfom7Yaj+VeYVPZ/Gbefvr2uDvtg7bcSt1w67N7FZZ6obd59D03LDvS7thT86lG7aaT2Ve4dP+Rna/u8Ta/ro2+KFgB43+8PRQbb5v6fBu2EOOSbth07JNm3TDVvOpzCt82tvIN+YLFsx2ibUDdHXwd60I2PRo2iSVBv2m1cl1EybD4afBksuGllW2aTdsNZ/KRr45TJs6mavvWl1T34VLRo1TqZwT4BJrB1BE5D2GMfX29sby5cvzHkZ+St2wpZDPdMMyZVqy5/zcRclqm5mnwqS9cx1uo5U76fZ49lYqPYZLRo1Rbo+rUjnnxksWA26EbBeSVkRE78jLPeNvR9s2J0spS0FfphuWuYuSwD/kaOjpyXe8TVYq2V191+qa91Zyyah+5Wb5lco5/rdtbw7+vEUkq2uy9fkNq4BIumEPOxl63z10Nqm0G7aI6tlbqRPOo9DORluB5XJO53Hwt1qmG3Z30Je6YSfvl+xQubsbdiFM3iff8baRevZWGs8qLx8L2JP7YrqLg7/ZSt2wpbXz/cthxwvJdfvPhnlnpnvPL4ZDj/e5YcdQz95K1azyctNRee6L6S4O/kar1A2LYMaJcMqfDa22OXBO3qPtepVm75Uu917x1e1kW4R/h27m4K9H9tywo3bDls4Ne0C+4+1i5cKq0kqe0Vb4FH2v+PHsZGudy8E/HjtfhHXpuWH7liU1+uy5Yecsyr0btogqlWcq7cpaboUPDB0vKPJe8V79VAwO/tH8YdPwtfPr7mv7btgiqlSeqbRlQLmmsG7eK3485S6vfioGB39JBDyzJp3Nl7phf5dct7sb9gPJkso5i2Af/0G0i0rlmdHWmGfr1fXuFV/NKqC8VgqNt9zlWn4x5BL8ks4FvgRMAK6NiKtaPoiBHfDkA8ODflg37KJ0W+IlSeh3WTdsN8mG1cjyTKXVJyMDvdZZbjUdwXl2DY98U7tlZf+YJydyLb/7tTz4JU0ArgbOAfqBeyXdFhG/aeoTb9sCa+9JSzfL0m7Ybcl10+bDUecMNUkVoBu222TDarzlmWpnueVm7dXUxCuFbytm1COb3m5e0c/Arup3znRPQ3fKY8Z/BrA6ItYASPoWcD7Q+OBffSc8/P3h3bCaADNPhoXvgnlL0nPDHtbwp7b81DJjHes+lWbt1dTEK4VvI2b/YwVz9k1t3ZZtfPOevqqbsLy/UffKI/hnAWszP/cDi0beSNKlwKUAc+fOre2ZHv0JPPBtmHM6nPDGJORn97ob1sat0sy+XDdxaffQcscUsuFb76qZ0ZrNSmMujaNU179lZX/VTVhe4dO98gj+cktf9tgiNCKuAa6BZHfOmp7prCvhnM+4G9bqNtrMPhuso3X9lgvf7DbT4w3V0VYzldu5dLSSllf4FEsewd8PZFtWZwPrmvJMe+3XlIe14qnmOEA1Xb/lDkSPt5RS7gTmw5rNRtm5tFxJyyt8iieP4L8XOErSEcATwIXAW3MYh9m4ZENzrBnyaF2/ZbeZrrKUUulTRXY103h3Lq13Oat1npYHf0QMSLoc+DHJcs6vRcRDrR6HWa2qmSFX0/VbSyllZEhnT2CeXc1Uum01M3WXdIonl3X8EfFD4Id5PLdZvaqdIY+1rLSWUko1xxqyP1fDJZ3iceeu2ThVO0OupkxSqXwE5WfszQppl3SKxefcNatBoxubyp3HtrQqx+cEsFr5nLtmDdToGfKw8lFmVU5RzwlgzeV9CczaQKl8NEEwaYKYlH7f07Pn6iCzennGb9YGynUAF/WcANZ8Dn6zNlFpVU43nBPA2ouD36zNecWNNZpr/GZmBePgNzMrGAe/mVnBOPjNzArGwW9mVjAOfjOzgumIvXokbQQer/HuhwBPN3A4efJraT/d8jrAr6Vd1fNa5kXE9JEXdkTw10PS8nKbFHUiv5b20y2vA/xa2lUzXotLPWZmBePgNzMrmCIE/zV5D6CB/FraT7e8DvBraVcNfy1dX+M3M7PhijDjNzOzDAe/mVnBFCb4JX1Q0iOSHpL093mPp16S/lJSSDok77HUQtL/lPSwpAck/bOkA/Me03hJOjf9nVot6cq8x1MrSXMk3SVpVfr38eG8x1QPSRMk3Sfp+3mPpR6SDpR0c/p3skrSkkY9diGCX9IrgPOBkyPiBOBzOQ+pLpLmAOcAfXmPpQ53ACdGxMnAb4GP5zyecZE0AbgaeDVwPPBnko7Pd1Q1GwA+GhHHAYuByzr4tQB8GFiV9yAa4EvAv0TEscApNPA1FSL4gfcDV0XEdoCI2JDzeOr1BeAKoGOPzEfE7RExkP64FJid53hqcAawOiLWRMQO4Fskk4uOExHrI2Jl+v3zJAEzK99R1UbSbOC1wLV5j6UekvYHXg5cBxAROyJiS6MevyjBfzTwMknLJP2bpNPzHlCtJL0eeCIifpX3WBro3cCP8h7EOM0C1mZ+7qdDwzJL0nzgNGBZzkOp1RdJJkWDOY+jXkcCG4Gvp2WrayXt06gH75pTL0r6V+CwMld9kuR1TiP5GHs6cJOkI6NN17KO8Vo+AbyqtSOqzWivIyJuTW/zSZJSw42tHFsDqMxlbfn7VC1J+wK3AB+JiOfyHs94SToP2BARKySdlfNw6jURWAB8MCKWSfoScCXwXxr14F0hIl5Z6TpJ7we+kwb9PZIGSTY+2tiq8Y1Hpdci6STgCOBXkiApj6yUdEZEPNnCIVZltP8nAJIuAs4Dzm7XN+FR9ANzMj/PBtblNJa6SZpEEvo3RsR38h5PjV4KvF7Sa4C9gf0l3RARb895XLXoB/ojovTJ62aS4G+IopR6vgv8CYCko4HJdODOfRHxYEQcGhHzI2I+yS/HgnYM/bFIOhf4GPD6iNia93hqcC9wlKQjJE0GLgRuy3lMNVEyi7gOWBURn897PLWKiI9HxOz0b+NC4CcdGvqkf9NrJR2TXnQ28JtGPX7XzPjH8DXga5J+DewALurAGWa3+d/AXsAd6aeXpRHxvnyHVL2IGJB0OfBjYALwtYh4KOdh1eqlwDuAByXdn172iYj4YX5DMuCDwI3pxGINcHGjHthbNpiZFUxRSj1mZpZy8JuZFYyD38ysYBz8ZmYF4+A3MysYB7+ZWcE4+M3MCsbBb1YDSaen5xLYW9I+6T72J+Y9LrNquIHLrEaSPkuyJ8wUkn1V/nvOQzKrioPfrEZpK/29wIvAmRGxK+chmVXFpR6z2h0E7AvsRzLzN+sInvGb1UjSbSRn3joCmBkRl+c8JLOqFGV3TrOGkvROYCAivpGef/eXkv4kIn6S99jMxuIZv5lZwbjGb2ZWMA5+M7OCcfCbmRWMg9/MrGAc/GZmBePgNzMrGAe/mVnB/H8lZDEIomg1bwAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# By Gradient Descent\n",
        "\n",
        "def polyGradientFit(x, y, degree, lr):\n",
        "\tX_1 = data_transform(x, degree)\n",
        "\tw_pred, err = reg.grad_descent(X_1, y, lr)\n",
        "\ty_pred=X_1.T @ w_pred\n",
        "\tplt.figure()\n",
        "\tplt.plot(x.T,y,'.')\n",
        "\tplt.plot(x.T,y_pred)\n",
        "\tplt.title(str(degree)+'-Degree Polynoimal')\n",
        "\tplt.xlabel('x')\n",
        "\tplt.ylabel('y')\n",
        "\tplt.show()\n",
        "\n",
        "# Write the code for degree 0 polynomial fitting\n",
        "polyGradientFit(x,y,0,1e-3)\n",
        "\n",
        "# Write the code for degree 1 polynomial fitting\n",
        "polyGradientFit(x,y,1,1e-3)\n",
        "\n",
        "# Write the code for degree 2 polynomial fitting\n",
        "polyGradientFit(x,y,2,1e-3)\n",
        "\n",
        "# Write the code for degree 3 polynomial fitting\n",
        "polyGradientFit(x,y,3,1e-4)\n",
        "\n",
        "# Write the code for degree 4 polynomial fitting\n",
        "polyGradientFit(x,y,4,1e-6)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nEX1qGqs2S16"
      },
      "source": [
        "# Linear Regression\n",
        "\n",
        "  Generate the data as shown in the figure below\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "id": "QE1KLlB22VBi",
        "outputId": "6bce72aa-f256-48ca-e9f8-b5fd61779058"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "x1 = np.linspace(0, 0.6, 100)\n",
        "x2 = np.linspace(0.8, 1.3, 100)\n",
        "x = np.concatenate((x1, x2))\n",
        "y = np.concatenate((np.zeros(100), np.ones(100)))\n",
        "\n",
        "plt.plot(x, y, '.')\n",
        "plt.title('Data')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NtR9XmbE2kgS"
      },
      "source": [
        "  Use the Regression class defined in the previous lab to fit the curve"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "1CzcCV9A2hls"
      },
      "outputs": [],
      "source": [
        "class Regression:\n",
        "\t# Constructor\n",
        "\tdef __init__(self, name='reg'):\n",
        "\t\tself.name = name  # Create an instance variable\n",
        "\n",
        "\tdef grad_update(self,w_old,lr,y,x):\n",
        "\t\tw = w_old + 2 * lr / y.shape[0] * (x @ (y - x.T @ w_old))\n",
        "\t\treturn w\n",
        "\n",
        "\tdef error(self,w,y,x):\n",
        "\t\treturn np.mean((y - x.T @ w)**2)\n",
        "\n",
        "\tdef mat_inv(self,y,x_aug):\n",
        "\t\treturn np.linalg.inv(x_aug @ x_aug.T) @ x_aug @ y\n",
        "\t\n",
        "\t# By Gradien descent\n",
        "\n",
        "\tdef grad_descent(self,x,y,lr):\n",
        "\t\terr = []\n",
        "\t\tw_pred = np.random.uniform(-1, 1, (x.shape[0]))\n",
        "\n",
        "\t\tfor i in range(int(1e+10)):\n",
        "\t\t\tw_pred = self.grad_update(w_pred,lr,y,x)\n",
        "\t\t\terr.append(self.error(w_pred,y,x))\n",
        "\t\t\tif i > 1:\n",
        "\t\t\t\tdev = np.abs(err[-2] - err[-1])\n",
        "\t\t\telse:\n",
        "\t\t\t\tdev = 1\n",
        "\t\t\tif dev<=0.000001:\n",
        "\t\t\t\tbreak\n",
        "\n",
        "\t\treturn w_pred, err"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "woxTUEqQ3HoH"
      },
      "source": [
        "  Augment the Data and generate optimal weights"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ExZLoNSg3G_H",
        "outputId": "635c93a9-24ef-40f8-9c3f-ff2b97400745"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Shape of x: (1, 200)\n",
            "Shape of x_aug: (2, 200)\n"
          ]
        }
      ],
      "source": [
        "# Augment the data\n",
        "_x = x[np.newaxis,:]\n",
        "print(f\"Shape of x: {_x.shape}\")\n",
        "\n",
        "x_aug = np.vstack((np.ones((1,_x.shape[1])), _x))\n",
        "print(f\"Shape of x_aug: {x_aug.shape}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Optimal weights: [-0.24220603  1.08598856]\n"
          ]
        },
        {
          "data": {
            "image/png": 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+Y60sf053thSRi09BfxFMryzhlhkj+NHztew5pDtbisjFpaC/SP77TZPp6HT+8bdbwi5FRDKMgv4iGTWkkM/NG8vDa+rYvOdI2OWISAZR0F9Edy+cQFFeNt/8zcawSxGRDKKgv4gGF+Vy98IJrNrcyKpNDWGXIyIZQkF/kX1hfhXjyor4i19v0A3PROSiUNBfZLnZWfzvW6axY/9xfvyCHjkoIv1PQR+CBZPKef/UoXzv6Rqdbiki/U5BH5L/9aGptHc6f7NSB2ZFpH8p6EMyurSQJQvG8+ibu3hh676wyxGRCFPQh+gPrhtPVVkRf/rIek606sCsiPQPBX2I8nNi/M1HL+PdA8f5zlO6YlZE+oeCPmTzxpdy25Wj+NHztby181DY5YhIBCnoU8CfLLqE0gF5fP1X62jv6Ay7HBGJGAV9ChhUmMNf3jKNDbsOs+zZbWGXIyIRo6BPEYsuG86Hpw/nO09t1RCOiPQpBX0K+etbL6V0QC5f+eVaPWNWRPqMgj6FlBTm8u1PzKCm4SjfenxT2OWISEQo6FPM+yaWc+e8Mfz0xR26kEpE+oSCPgXdu+gSxpUX8UcPr2Xf0ZawyxGRNKegT0EFuTH+3+1XcPB4G1/95Vo6Oj3skkQkjSnoU9S0EYP4849M4/mt+1i6qibsckQkjSnoU9jtc0Zx6+Uj+M5TW3hpm8brReT8KOhTmJnxfz56GVVlRdzzi7U0HNa960Wk9xT0Ka4oL5vv3zGL463t3PUva3R+vYj0moI+DUweVsw/fHIGa+ua+NMV63HXwVkRSV5SQW9mN5vZZjOrMbN7e1g+xcxeNrMWM/vj3mwrybn50uF89cZJrHhjJ8ufqw27HBFJI+cMejOLAUuBRcBU4HYzm9pttQPAPcC3z2NbSdI9N0zgQ5cN55uPb+LpTXvDLkdE0kQye/RzgBp3r3X3VuBBYHHiCu7e4O6rgbbebivJMzO+/YkZTB0+kLt//gbr6pvCLklE0kAyQT8SqEuYrw/akpH0tmZ2l5lVm1l1Y2Njkh+feQpyY/z081cyuDCXL96/mnf2Hwu7JBFJcckEvfXQluzRwKS3dffl7j7b3WeXl5cn+fGZqWJgPg98aQ7tnc7nfvKabpMgImeVTNDXA6MS5iuBXUl+/oVsK2cxvnwAP77zSvYebuaL96/maEt72CWJSIpKJuhXAxPNrMrMcoHbgEeT/PwL2VbOYdaYwXzv9pls2HWYL96/muOtCnsRea9zBr27twN3A08AG4GH3H2DmS0xsyUAZjbMzOqBrwH/08zqzWzgmbbtr85kohunDuU7n7qc6h0H+PI/V+uCKhF5D0vFi29mz57t1dXVYZeRVla8Xs8fPfwm75tYzvLPziI/JxZ2SSJyEZnZGnef3dMyXRkbER+bWck3P3YZz21pZMnP1nCiVXv2IhKnoI+QT105mv/7sct4dksjd/70NY40d7+sQUQykYI+Ym6fM5rv3nYFr79zkDvue5UDx1rDLklEQqagj6BbZoxg+edmsXnPET71w5fZfehE2CWJSIgU9BF1/ZSh3P+FOew+1MxHl77Ehl2Hwi5JREKioI+weeNLeXjJPMzgE8te5ncbdSM0kUykoI+4S4YP5N//cD7jyov4Lw9Uc/+L23U/e5EMo6DPAEMH5vPQ78/j+ilD+fNfv83Xf7VOF1aJZBAFfYYozM3mh5+dxT3XT+Ch6np+b9lL1B04HnZZInIRKOgzSCzL+NoHJvPjO2fzzv7jfOR7L/DM5oawyxKRfqagz0A3XDKUx/7rNQwbmM/nf7qav1m5kZZ2DeWIRJWCPkONKS3ikT+Yz2euGs3y52r56NKXqGk4EnZZItIPFPQZrCA3xl/fehn3fW42ew4386F/eoEHXt5BZ6fOyhGJEgW9cOPUoTz+lfdx1bhSvvEfG7j9R69Q23g07LJEpI8o6AWAiuJ87v/Clfztx6ezcfdhbv7u8yxdVUNbR2fYpYnIBVLQy0lmxievHMVTX1vADVMq+LsnNnPL915k9Y4DYZcmIhdAQS/vUTEwnx98ZhY//OwsDh5r5RPLXuaeX7zBribdHE0kHSno5YxumjaMp/94AfdcP4EnNuzh+r9/hu8+tVUPNRFJMwp6OavC3Gy+9oHJ/O6PFnDDJUP5x6e2cO3freKBl3fQ2q7xe5F0oKCXpFQOLmTpp2fy8JJ5VJUW8Y3/2MD1f/8MD1fX0a4DtiIpTQ8Hl15zd57buo9vP7GZ9TsPMa6siN9fMI5brxhJXrYeSi4ShrM9HFxBL+fN3Xliwx6+t6qGt3YeZujAPL44v4pPzx1NcX5O2OWJZBQFvfQrd+eFmn0se3YbL9bspzg/m9vnjOaOuaMZU1oUdnkiGUFBLxfNuvomfvhsLY9v2ENHp7NgUjmfvWoMC6dUEMuysMsTiSwFvVx0ew418+Dqd/nFa++y93ALI0sK+OTsUXz0ipGMLi0MuzyRyFHQS2jaOjp56u29/OzVd3hp237c4cqxg/nYzEo+eNlwBhVoLF+kLyjoJSXsbDrBv7+xkxWv17Ot8Ri52VksnFzOokuHc/0lFQzUAVyR86agl5Ti7qzfeYgVr+9k5frdNBxpISdmzJ9Qxs3ThvH+qUMpHZAXdpkiaUVBLymrs9N5o66JJzbs4Tdv7abuwAmyDKZXlrBgUjkLJpczo7JEB3JFzuGCg97Mbga+C8SA+9z9m92WW7D8g8Bx4PPu/nqwbAdwBOgA2s9USCIFfWZyd97efZgnN+zlua2NrK1rwh0GFeRwzcQyrp1YxtyqUsaUFhL/JyciXc4W9NlJbBwDlgLvB+qB1Wb2qLu/nbDaImBi8JoL/CB477LQ3fedZ/2SIcyMaSMGMW3EIL76/kkcPNbKCzX7eG5LI89uaeQ/1+0GoKI4jzlVQ5hbNYQ5VaVMrBhAlvb4Rc7onEEPzAFq3L0WwMweBBYDiUG/GHjA478evGJmJWY23N1393nFkjEGF+XykRkj+MiMEbg72xqP8dr2A7y6fT+v1h7gsSD4BxXkML1yENMrBzGjsoQZo0oYOjA/5OpFUkcyQT8SqEuYr+f0vfUzrTMS2A048KSZOfBDd19+/uVKpjIzJlQMYELFAD49dzTuTv3BE7y6/QDVOw7wZv0hlj1bS0fwvNuhA/OYXlnCpSMGMXlYMVOGFTN6SKH2/CUjJRP0Pf1kdB/YP9s68919l5lVAL81s03u/tx7/hCzu4C7AEaPHp1EWZLJzIxRQwoZNaSQ35tVCcCJ1g7e3n2IN+sOsa6+iXX1h3hq4166DkMV5MSYNHQAk4cVM2loMZOHFTO2tIgRJQU62CuRlkzQ1wOjEuYrgV3JruPuXe8NZvYI8aGg9wR9sKe/HOIHY5OsX+SkgtwYs8YMYdaYISfbjre2s2XvUTbvOczmPUfZvPcwT29q4KHq+pPr5GZnMWZIIWPLiqgqK2JsaRFjywoZW1rE0IH5+hKQtJdM0K8GJppZFbATuA34dLd1HgXuDsbv5wKH3H23mRUBWe5+JJj+APCXfVe+yNkV5mZz+agSLh9Vclr7vqMtbN17lB37j7Fj3zFq98Xfn93SeNoDVWJZxrCB+YwsKWDk4AJGlOQzsqQweC9g6KB8ivOydRaQpLRzBr27t5vZ3cATxE+v/Im7bzCzJcHyZcBK4qdW1hA/vfILweZDgUeCH4Js4Ofu/nif90Kkl8oG5FE2II9540tPa+/odHYfOsH2fcd498BxdjWdYFdTMzsPnuC17QfYc7j55HGALvk5WZQX51E+II+K4vz4dHEeFcF7eXEegwtzKSnMYYC+FCQEumBKpBc6Op29h5vZ1XSCnU0naDjcQsORZhqPtNBwpIXGIy00Hm2h6Xhbj9vnxIxBBbkMLsxhcFHwXphLSWF8uqQwh+L8+BfCgPxsBuZnMyAvhwH52RTmxHQwWc7ogs6jF5FTYlnGiJICRpQUcLYr/1raO9h3tJWGw/EvgabjbRw83srB4200HW89Ob193zHeON5E0/E2Ws/xSEYzGJCXTXHwJTAgL5vi/ByK8mLk58QozI1RkBO8crMpyMmiILdrWXbQnnXafG52VvwVyyInZvptI6IU9CL9IC87Fh/XLylIan1353hrB00n2jja3M6R5jaOtLRztLmdoy3x+aPN7SfbjgTtTcdb2dXUwYm2Dk60Bu9tHZzvL+q52VnkxbLICcI/8YugazovYT7n5LsRyzKys7LIzjJiMSO723xOVlZ8nWDdxPnsrunu8zEjy+JnWWWZETPDjPh01qllXdNZwfL4fDAdbJtlhmWdmk9cr+tzokpBL5ICzIyivGyK8i78R9LdaWnvPC34T04H781tHRxv7aC1vTP+6uikpWu6vZPWjtOXtbafWn60pf20ZW3tnbR3evzV0UlH13Snv+d4Rirr+gLpCn0L2ozT2zCCZRYsP/UFA6faura17uv31B58bllRHg8tmdfnfVPQi0SMmZGfEx+yGRxyLe5+evB3OG2dCV8GHZ0nvxDaO5z2zlPzbR2ddHZCp/up12nz8emOTsedU22dp5Z3uOPudHY6HR6v5+SyzmBZ9+lgHeL/4d71+eD4yd+W3D1YHm/vdIJl8XU8Yf2T653cJnHbU/MD8/snkhX0ItJvzIKhmFjYlWS2rLALEBGR/qWgFxGJOAW9iEjEKehFRCJOQS8iEnEKehGRiFPQi4hEnIJeRCTiUvLulWbWCLxznpuXAen+IPIo9AGi0Y8o9AGi0Y8o9AH6rx9j3L28pwUpGfQXwsyqz3SrznQRhT5ANPoRhT5ANPoRhT5AOP3Q0I2ISMQp6EVEIi6KQb887AL6QBT6ANHoRxT6ANHoRxT6ACH0I3Jj9CIicroo7tGLiEgCBb2ISMRFJujN7GYz22xmNWZ2b9j1nI2ZjTKzVWa20cw2mNl/C9qHmNlvzWxr8D44YZs/Cfq22cxuCq/605lZzMzeMLPHgvl07EOJmf2bmW0K/k7mpVs/zOyrwb+lt8zsF2aWnw59MLOfmFmDmb2V0Nbrus1slpmtD5b9k13EB8CeoQ9/F/x7Wmdmj5hZSah98OBRW+n8AmLANmAckAu8CUwNu66z1DscmBlMFwNbgKnA3wL3Bu33At8KpqcGfcoDqoK+xsLuR1Db14CfA48F8+nYh38GvhxM5wIl6dQPYCSwHSgI5h8CPp8OfQCuBWYCbyW09bpu4DVgHvHHsP4GWBRyHz4AZAfT3wq7D1HZo58D1Lh7rbu3Ag8Ci0Ou6Yzcfbe7vx5MHwE2Ev9hXUw8dAjebw2mFwMPunuLu28Haoj3OVRmVgl8CLgvoTnd+jCQ+A/qjwHcvdXdm0izfhB/LGiBmWUDhcAu0qAP7v4ccKBbc6/qNrPhwEB3f9njiflAwjb9rqc+uPuT7t4ezL4CVAbTofQhKkE/EqhLmK8P2lKemY0FrgBeBYa6+26IfxkAFcFqqdq/7wD/A+hMaEu3PowDGoGfBkNQ95lZEWnUD3ffCXwbeBfYDRxy9ydJoz5009u6RwbT3dtTxReJ76FDSH2IStD3NJaV8ueNmtkA4FfAV9z98NlW7aEt1P6Z2YeBBndfk+wmPbSlwt9RNvFfu3/g7lcAx4gPF5xJyvUjGMNeTHwoYARQZGafOdsmPbSlwt/FuZyp7pTtj5n9GdAO/GtXUw+r9XsfohL09cCohPlK4r+6piwzyyEe8v/q7iuC5r3Br3AE7w1Beyr2bz5wi5ntID5Udr2Z/Yz06gPE66p391eD+X8jHvzp1I8bge3u3ujubcAK4GrSqw+Jelt3PaeGRhLbQ2VmdwIfBu4IhmMgpD5EJehXAxPNrMrMcoHbgEdDrumMgqPpPwY2uvs/JCx6FLgzmL4T+I+E9tvMLM/MqoCJxA/chMbd/8TdK919LPH/30+7+2dIoz4AuPseoM7MJgdNNwBvk179eBe4yswKg39bNxA/7pNOfUjUq7qD4Z0jZnZV0P/PJWwTCjO7Gfg6cIu7H09YFE4fLtaR6f5+AR8kfvbKNuDPwq7nHLVeQ/zXsnXA2uD1QaAU+B2wNXgfkrDNnwV928xFPKMgyf5cx6mzbtKuD8DlQHXw9/HvwOB06wfwF8Am4C3gX4if1ZHyfQB+Qfy4QhvxvdovnU/dwOyg79uA7xFc9R9iH2qIj8V3/XwvC7MPugWCiEjERWXoRkREzkBBLyIScQp6EZGIU9CLiEScgl5EJOIU9CIiEaegFxGJuP8P6ermzeQECvkAAAAASUVORK5CYII=",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Generate optimal weights using gradient descent\n",
        "reg = Regression()\n",
        "w_pred, err = reg.grad_descent(x_aug, y, 1e-3)\n",
        "print(f\"Optimal weights: {w_pred}\")\n",
        "\n",
        "# Plot the error\n",
        "plt.plot(err)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k7SoRLJ83Ri2"
      },
      "source": [
        "Using the optimal weights, fit the curve"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 630
        },
        "id": "YEsVt0MG3L09",
        "outputId": "fe5b2a39-3b56-41da-e4c9-98e850a6bfaf"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Plot the data, predictions and the optimal line\n",
        "plt.plot(x, y, '.')\n",
        "y_pred = w_pred[0] + w_pred[1] * x\n",
        "plt.plot(x,  y_pred, '-')\n",
        "pred_zero = np.where(y_pred < 0.5)\n",
        "pred_one = np.where(y_pred >= 0.5)\n",
        "plt.plot(x[pred_zero], np.zeros(x[pred_zero].shape[0]), 'oy')\n",
        "plt.plot(x[pred_one], np.ones(x[pred_one].shape[0]), 'or')\n",
        "plt.title('Predictions')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vg_f56OL3wGj"
      },
      "source": [
        "# Drawback of Linear regression based Classificaton\n",
        "\n",
        "  Generate the Data as shown in the figure and follow the same steps as above to fit a curve using regression class "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "rKOgF7-t3-uh",
        "outputId": "a37a0fcf-1ee7-4aa8-88fd-713bf628709c"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "x1 = np.linspace(0, 0.6, 100)\n",
        "x2 = np.linspace(0.8, 1.3, 100)\n",
        "x3 = np.linspace(3.5, 3.8, 100)\n",
        "x = np.concatenate((x1, x2, x3))\n",
        "y = np.concatenate((np.zeros(100), np.ones(100), np.ones(100)))\n",
        "\n",
        "plt.plot(x, y, '.')\n",
        "plt.title('Data')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 582
        },
        "id": "Jwx2zhf23_Yj",
        "outputId": "9a6cb643-5a1c-45b6-9bfc-d67e75557f34"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Shape of x: (1, 300)\n",
            "Shape of x_aug: (2, 300)\n",
            "Optimal weights: [0.34069199 0.20446734]\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Augment the data\n",
        "_x = x[np.newaxis,:]\n",
        "print(f\"Shape of x: {_x.shape}\")\n",
        "\n",
        "x_aug = np.vstack((np.ones((1,_x.shape[1])), _x))\n",
        "print(f\"Shape of x_aug: {x_aug.shape}\")\n",
        "\n",
        "# Generate optimal weights using gradient descent\n",
        "reg = Regression()\n",
        "w_pred, err = reg.grad_descent(x_aug, y, 1e-3)\n",
        "print(f\"Optimal weights: {w_pred}\")\n",
        "\n",
        "# Plot the error\n",
        "plt.plot(err)\n",
        "plt.xlabel('Iteration')\n",
        "plt.ylabel('Error')\n",
        "plt.show()\n",
        "\n",
        "# Plot the data and the optimal line\n",
        "plt.plot(x, y, '.')\n",
        "y_pred = w_pred[0] + w_pred[1] * x\n",
        "plt.plot(x,  y_pred, '-')\n",
        "pred_zero = np.where(y_pred < 0.5)\n",
        "pred_one = np.where(y_pred >= 0.5)\n",
        "plt.plot(x[pred_zero], np.zeros(x[pred_zero].shape[0]), 'oy')\n",
        "plt.plot(x[pred_one], np.ones(x[pred_one].shape[0]), 'or')\n",
        "plt.title('Predictions')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "praLrLBjM2EW"
      },
      "source": [
        "# Logistic regression\n",
        "\n",
        "  Error Surface (Comparison between Logistic Loss and Mean Squared Error)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "cU3DV5bkDX8c",
        "outputId": "9c63b0d4-ca6b-4b4b-bd9e-0389ef40723b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f204f121270>]"
            ]
          },
          "execution_count": 12,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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C",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "x=np.linspace(-5,5,25)\n",
        "y=np.zeros(x.shape)\n",
        "y[np.where(x>0.7314)]=1\n",
        "\n",
        "plt.plot(x,y,'.')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tIdvMRuDLOGM"
      },
      "source": [
        "1. MSE=$\\frac{1}{2N}\\sum_{i=1}^{N}(y^{p}_{i}-y_{i})^2$, where $y^{p}=\\frac{1}{1+e^{-w^{T}x}}$\n",
        "2. Logistic loss=$-\\frac{1}{N}\\sum_{i=1}^{N}y_{i}log(y^{p}_{i})+(1-y_{i})log(1-y_{i}^{p})$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "JDzS5KMHGIlK"
      },
      "outputs": [],
      "source": [
        "# search space (only w1 is searched, where as w0 is fixed)\n",
        "w1_in=10/(x[1]-x[0])\n",
        "w0=-w1_in*0.7314\n",
        "w1=np.linspace(-w1_in,4*w1_in,100)\n",
        "\n",
        "\n",
        "cost_fn_mse=[]\n",
        "cost_fn_logis=[]\n",
        "for i in range(w1.shape[0]):\n",
        "\n",
        "\t# Compute Mean square error and logistic loss using cost function\n",
        "\ty_pred = (1 + np.exp(-w0 - w1[i] * x))**(-1)\n",
        "\tcost_fn_mse.append(np.mean((y - y_pred)**2)/2)\n",
        "\tcost_fn_logis.append(-np.mean(y * np.log(y_pred+1e-20) + (1 - y) * np.log(1 - y_pred+1e-20)))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "1QdaVsP1Js_x",
        "outputId": "4f1ca4ff-6f4b-4775-f40b-df3f2f91da82"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Ploting of error surface\n",
        "plt.figure()\n",
        "plt.plot(w1,np.log(cost_fn_mse),label='MSE Loss')\n",
        "plt.plot(w1,np.log(cost_fn_logis),label = 'Logistic Loss')\n",
        "plt.legend()\n",
        "plt.xlabel('w1')\n",
        "plt.ylabel('Loss')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lzRAXAYsiuhp"
      },
      "source": [
        "**Solving the Outlier Issue**\n",
        "\n",
        "  Generate the Data as shown in the figure"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "_CGKgXFTh5B-",
        "outputId": "27dbecdd-63f0-4747-84b7-129fe1f0ba9f"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "x1 = np.linspace(0, 0.6, 100)\n",
        "x2 = np.linspace(0.8, 1.3, 100)\n",
        "x3 = np.linspace(3.5, 3.8, 100)\n",
        "x = np.concatenate((x1, x2, x3))\n",
        "y = np.concatenate((np.zeros(100), np.ones(100), np.ones(100)))\n",
        "\n",
        "plt.plot(x, y, '.')\n",
        "plt.title('Data')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3L7SJMRx56yF"
      },
      "source": [
        "Define a Logistic Regression class"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "id": "PE5x893HD4Km"
      },
      "outputs": [],
      "source": [
        "class logis_regression:\n",
        "\t# Constructor\n",
        "\tdef __init__(self, name='reg'):\n",
        "\t\tself.name = name  # Create an instance variable\n",
        "\n",
        "\tdef logis(self,x,w_old):\n",
        "\t\top = 1/(1+np.exp(-x.T@w_old))\n",
        "\t\treturn op\n",
        "\n",
        "\tdef grad_update(self,w_old,lr,y,x):\n",
        "\t\tw = w_old + lr / y.shape[0] * (x @ (y - self.logis(x,w_old)))\n",
        "\t\treturn w\n",
        "\n",
        "\tdef error(self,w,y,x):\n",
        "\t\ty_pred = self.logis(x,w)\n",
        "\t\treturn -np.mean(y * np.log(y_pred+1e-40) + (1 - y) * np.log(1 - y_pred+1e-40))\n",
        "\t\n",
        "\tdef grad_descent(self,x,y,lr):\n",
        "\t\terr = []\n",
        "\t\tw_pred = np.random.uniform(-1, 1, (x.shape[0]))\n",
        "\n",
        "\t\tfor i in range(int(1e+10)):\n",
        "\t\t\tw_pred = self.grad_update(w_pred,lr,y,x)\n",
        "\t\t\terr.append(self.error(w_pred,y,x))\n",
        "\t\t\tif i > 1:\n",
        "\t\t\t\tdev = np.abs(err[-2] - err[-1])\n",
        "\t\t\telse:\n",
        "\t\t\t\tdev = 1\n",
        "\t\t\tif dev<=0.000001:\n",
        "\t\t\t\tbreak\n",
        "\n",
        "\t\treturn w_pred, err"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Vr5q2R036CLf"
      },
      "source": [
        "Augment the data and fit the curve by obtaining optimal weights (Using Gradient Descent)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 580
        },
        "id": "8pRanc1ejLWO",
        "outputId": "4611d6c0-c1be-4945-b104-c8248899066b"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Shape of x: (1, 300)\n",
            "Shape of x_aug: (2, 300)\n",
            "Shape of y: (300,)\n",
            "Optimal weights: [-2.63830307  4.15241269]\n"
          ]
        },
        {
          "data": {
            "image/png": 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0kZBg/OCTw/j2JUN4cu56bnyonLq9euiQiJyceI5BjAUq3H21u+8HZgBTozdw911Rs8N2JXLaqln7SmxmxtcuGsxPPzOCdyo2c+W97+rxpSJyUpobEDcQOYqYTeQeiDlA+XH2KQTWRS1XBW2HMbNPm9ly4Dk+Huto1r7B/tOC01PltbW1zfgoncNVY/ry4JfGsn7bHi6/+20Wr98Rdkki0s40KyBijD80Zwwi1gjpEZfXuPtT7l4CXA78+ET2Dfa/z91L3b00Ly/vOCV1LucM7sETt0wgOTGBz/7uXV5bpqk5RKT5jhkQZnZ71Osrm6w73p3UVUBR1HIf4Kh3c7n7bGCgmfU40X3l6IYUZPDUrRMYlN+Nr/yhnP+ZvVqXwYpIsxzvCOLqqNffa7JuynH2LQMGm1l/M0sJ3mtm9AZmNsjMLHg9GkgBtjRnX2m+/Iw0Zkwbx+RhPfl/zy/jtscWsPdAQ9hliUgbd7z7IOwor2MtH8bd681sOvASkAg84O5LzOymYP29wGeA683sALAHuCoYtI65b3M/lBwpPSWJe64dzd2vV/DLV1eyqqaO332+lMLsLmGXJiJtlB3rdIOZzXX30U1fx1puC0pLS728/Hhj5/Lq0mq++ef5pCYFDyIakBt2SSISEjOb4+6lsdYd7xTTSDPbaWZ1wBnB64PLI1q8UmkVFw8r4OlbJ5LVJZlr73+fh96p1LiEiBzhmAHh7onununuGe6eFLw+uJzcWkVKyxuU342np0/k/CF5/GDmEqY/Ok831YnIYU7kgUHSwWSmJfM/15fy3SklvLh4E5+6622WbtgZdlki0kYoIDq5hATj5gsG8uhXxrF7fz2X3/M2j/59rU45iYgCQiLG9s/hua+fy9n9c/jek4v41p/ns2tffdhliUiIFBBySI9uqTz4pbHcdskQZi7YwCfufJN5a7eFXZaIhEQBIYdJTDC+ftFgHv3KOOobnCvufZc7X1tFvaYOF+l0FBAS09kDcnn+G+fyiRG9+OUrK7n6vvdYt3V32GWJSCtSQMhRZXVJ5s5rzuTXV41ixaY6Lv3Nmzw5t0oD2CKdhAJCjuvyMwt5/hvnUtIzg9seW8DNf5pLbd2+sMsSkThTQEizFOWkM2PaOG6fMpRZy2uY/Ku/8dcFG3Q0IdKBKSCk2ZISE7jlgkE89/Vz6JuTztcenaejCZEOTAEhJ2xwQQZP3DyB704pOXQ0MVNHEyIdjgJCTkpSYgI3XzAwcjSR25WvPzqPr/xhjp5/LdKBKCDklAwuyOCJm8bzfy4r4a2KWi7+5d/437c+1H0TIh2AAkJOWVJiAtPOG8gr3zqfs/vn8ONnl3L5PW+zqGpH2KWJyClQQEiLKcpJ54EvjuGea0dTs3MfU+9+ix/9dYnmdBJppxQQ0qLMjMtG9OLVb5/PdeP68eA7lVz8C10SK9IeKSAkLjLTkvm3qafz5M0TyO2WwtcencfV973Hso163oRIe6GAkLg6s293Zk4/h//49AhWVtfxiTvf5F+fWcz23fvDLk1EjkMBIXGXmGB87uy+vP6dC/j8uH786b01XPDzN/jTe2toaNRpJ5G2SgEhrSY7PYUfTT2d575+LkMLMviXpxfzyd++xTsVm8MuTURiiGtAmNkUM1thZhVmdkeM9dea2cLg6x0zGxm1rtLMFpnZfDMrj2ed0rpO65XJjGnjuOtzZ7JjzwE+d//7fOn3f2dldV3YpYlIFIvXlSVmlgisBC4BqoAy4Bp3Xxq1zQRgmbtvM7NLgR+6+9nBukqg1N2b/edlaWmpl5crS9qTvQcaeOidSu56vYKP9tXz2dIibrtkCPmZaWGXJtIpmNkcdy+NtS6eRxBjgQp3X+3u+4EZwNToDdz9HXc/+EzL94A+caxH2qC05ES+ev5AZv/zJL4woZgn5lZx/s/e4FevrOQj3T8hEqp4BkQhsC5quSpoO5obgReilh142czmmNm0o+1kZtPMrNzMymtra0+pYAlP964p/OCTw3n1tvO5sCSf37y2igt+/gZ/fG8N++s1bYdIGOIZEBajLeb5LDObRCQgvhvVPNHdRwOXArea2Xmx9nX3+9y91N1L8/LyTrVmCVm/3K7cfe1onrxlAsW56fzfpxdz4S/e4C/l6zS/k0gri2dAVAFFUct9gA1NNzKzM4D7ganuvuVgu7tvCL7XAE8ROWUlncTovt157KvjefBLY+iensI/P76Qyb+ezbMLN9CoS2NFWkU8A6IMGGxm/c0sBbgamBm9gZn1BZ4EPu/uK6Pau5pZxsHXwGRgcRxrlTbIzLhgaD4zp0/k3utGk2jG9Efm8YnfvsVry6o1dYdInCXF643dvd7MpgMvAYnAA+6+xMxuCtbfC/wrkAvcY2YA9cFoegHwVNCWBDzi7i/Gq1Zp28yMKaf34pJhPfnrgg386tWV3PhQOaOKsvnGxYO5YEgewb8VEWlBcbvMNQy6zLVzONDQyBNzqvjtrArWb9/DiMIspl84iEtOKyAhQUEhciKOdZmrAkLarf31jTw9bz13v1HBmi27KemZwa2TBnHZiF4kKihEmkUBIR1afUMjf124gbtmVfBB7UcMyOvKrRcMYuqo3iQlajYZkWNRQEin0NDovLh4E7+dtYrlm+ooyunCV84dwJVnFdElJTHs8kTaJAWEdCqNjc5ry2u4+/UK5q/bTvf0ZK4fX8z14/uR2y017PJE2hQFhHRK7k5Z5Tbum/0Bry6rITUpgStL+/DlcwZQ3KNr2OWJtAnHCoi4XeYqEjYzY2z/HMb2z6Gipo7/mf0hj5VV8fD7a7n09J5MO28go4qywy5TpM3SEYR0KjU79/LgO5X86b017Nxbz5ji7nxxQn8mDy8gWQPa0gnpFJNIE7v21fPnsnU89E4la7fupldWGteN68c1Y/uS0zUl7PJEWo0CQuQoGhqdN1bU8OA7lby5ajMpSQlMHdmbL04sZnjvrLDLE4k7jUGIHEVignHRaQVcdFoBq6rreOjdSp6Ys56/zKlibHEOX5xYzCXDdPpJOicdQYg0sWP3Af4yZx0PvVvJuq17yM9I5eoxRVw1ti+F2V3CLk+kRekUk8hJaGh0Zi2v4ZH31/DGyloMuGBoPp8b25dJJfmazkM6BAWEyCmq2rabP5etY0bZOmrr9tE7K42rxvTlqjFF9MzS87Ol/VJAiLSQAw2NvLasmoffX8ubqzaTmGBcWJLPNWOLOG9wnuZ+knZHg9QiLSQ5MYEpp/diyum9WLtlN4+WreUv5et4ZWk1+RmpfHp0IVeeVcSg/G5hlypyynQEIXKK9tc38vqKGh6fU8Xry2uob3TO7JvNFWf14ZMje5OZlhx2iSJHpVNMIq2ktm4fz8xfz1/Kq1hRXUdqUgJTTu/JFWf1YeLAHnqgkbQ5CgiRVubuLFq/g7+UV/HM/PXs3FtP76w0pp5ZyNRRvSnpmRl2iSKAAkIkVHsPNPDqsmqemFPF7FWbaWh0SnpmMHVUIZ8a1Vv3VkioFBAibcSWXft4btFGnp63nrlrtwMwtjiHqWf25rLTe9Fd80BJK1NAiLRBa7fs5pn563l6/no+qP2I5ETj/CF5TB1VyEWn5ZOeoosMJf4UECJtmLuzZMNOnpm/npkLNlC9cx9pyQlcWJLPZSN6cWGJwkLiJ7SAMLMpwG+AROB+d/9Jk/XXAt8NFncBN7v7gubsG4sCQtq7hkbn/Q+38Pyijby4eBObd+0nLTmBSUM/DouuqQoLaTmhBISZJQIrgUuAKqAMuMbdl0ZtMwFY5u7bzOxS4IfufnZz9o1FASEdSUOj8/cPt/L8oo28sHgTm3ftIzUpCIszenGRwkJaQFh3Uo8FKtx9dVDEDGAqcOiXvLu/E7X9e0Cf5u4r0tElJhjjB+YyfmAuP/zUcMoqPw6LF5dsIjUpgfOH5DF5eE8uKsnXALe0uHgGRCGwLmq5Cjj7GNvfCLxwovua2TRgGkDfvn1PtlaRNi0xwRg3IJdxA3L5wSeHUx6ExUtLqnl5aTUJBmOKc5g8vCeThxVQlJMedsnSAcQzIGLdMhrzfJaZTSISEOec6L7ufh9wH0ROMZ14mSLtS2KCcfaAXM4eEDmyWLR+B68sreblJdX8+Nml/PjZpZT0zGDysAImD+/J8N6ZmOkObjlx8QyIKqAoarkPsKHpRmZ2BnA/cKm7bzmRfUU6OzPjjD7ZnNEnm29PHsqaLR9FwmJpNXe9XsGdsyronZXGxcMKuGRYAWP755CalBh22dJOxHOQOonIQPNFwHoiA82fc/clUdv0BWYB10ePRzRn31g0SC3ysS279jFreQ0vL63mzVW17D3QSNeURCYO6sGkknwmDc3XsywknEFqd683s+nAS0QuVX3A3ZeY2U3B+nuBfwVygXuCQ+B6dy892r7xqlWkI8rtlsqVpUVcWVrEnv0NvF2xmddX1PB6EBoAp/XK5MKSPCYNzWdUUbaeZyGH0Y1yIp2Mu7Oyehevr6hh1vIa5qzZRkOjk9UlmfOH5DGpJI/zh+STo6uiOgXdSS0iR7VjzwHeWrWZWctr+NvKGjbv2o8ZnNEnm3MH9eDcwT04s293UpJ0dNERKSBEpFkaGyPTlL++oobZK2tZULWDhkYnPSWR8QNyOXdwD84ZnMfAvK66MqqDUECIyEnZsecA736whbcqanlr1WYqt+wGoHdWGucM7sG5g/OYOKiHTke1YwoIEWkR67bu5s1Vm3lzVS1vV2xm5956zOD03llMHNSD8QNzGVPcXZMLtiMKCBFpcQ2NzsKq7by1ajNvrtrM3LXbqG90khKMkUXZjA/u/D6rX3e6pOjei7ZKASEicbd7fz3lldt4d/UW3lu9hYXB+EVKYgKjirIZNzCX8QNyObNvNmnJCoy2QgEhIq1u1756yiq38t4HW3h39RYWr99Bo0NKUgKj+2YzfkAPzh6Qw6giBUaYFBAiErqdew9Q9uFW3g0CY+nGnbhDcmJkupDS4u6MLc7hrH7dyU7XoHdrUUCISJuzffd+yiu3UbZmK2UfbmXR+h0caIj8PhpakBEJjP45lBbnUJjdJeRqOy4FhIi0eXsPNDB/3XbKK7dSVrmNOWu2sWtfPQCF2V0oLe7OmOIcxhTnMDi/GwkJug+jJYT1wCARkWZLS0489MwLiFwltXzTTso+3ErZmm28+8EWnpkfmdQ5IzWJkUXZjO6bzZl9uzOqKFsPTIoDHUGISLvg7qzbuoeyyq3MW7eNuWu2s3zTThqDX2EDenRlVBAYo/tmM7QgQ5MPNoNOMYlIh/TRvnoWVu1g3rptzFu7nXlrt7F5134AuiQnckafrEOBcWbf7uRlpIZccdujU0wi0iF1TU069NxuiBxlVG3bw9y1HwfG/W+upj44zCjM7sKIwizOKMrijMJsRhRmkZWeHOZHaNMUECLSYZgZRTnpFOWkM3VUIRAZ/F68fgfz1m5n4fodLKzazotLNh3apzg3nRF9shnZJ4sRhVkML8yiW6p+NYICQkQ6uLTkREqLI5fLHrR9934Wrd/BwqpIYMyp3MpfF0QGwM1gUF43RvTJYmSfbEb0yWJYr8xOeTOfAkJEOp3s9BTOHZzHuYPzDrXV1u1j0frtQWjsYPbKWp6cux6ApARjUH43hvXOZFivTIb3zmJY70yyunTs01MapBYRicHd2bRzLwvW7WDR+u0s2bCTJRt2Ulu379A2RTldDgXG8N6ZDOudSc/MtHb1rAwNUouInCAzo1dWF3pldWHK6T0PtdfU7WVpEBZLN+5k6YadvLSk+tD6nK4pkbDoFQmM4b2z6N+jK4nt8MY+BYSIyAnIz0gjf2gaFwzNP9S2a189y4KwWLJhB0s37uT3b1eyv6ERiFxyO6SgG0N7ZjC0Zyan9cxgaM8Mcru17ctuFRAiIqeoW2rSoWlADtpf30hFzS6WboyExopNdby6rIbHyqsObdOjWyolPTMoCQKjpGcmgwu6tZkB8biOQZjZFOA3QCJwv7v/pMn6EuD3wGjg++7+86h1lUAd0ADUH+0cWTSNQYhIW+bu1O7ax4pNdazYVMfy4PvK6jr21UeONhIMinO7UtIrg6EFmUFwZNA3Jz0u80+FMgZhZonA3cAlQBVQZmYz3X1p1GZbga8Dlx/lbSa5++Z41Sgi0prMLHKKKiPtsCuoGhqdyi0fHQqN5RsjYxwvLN7Ewb/huyQnMii/G4MLujGkIIMhBd0YnJ9BYXaXuE1cGM9TTGOBCndfDWBmM4CpwKGAcPcaoMbMPhHHOkRE2rTEBGNgXjcG5nXjshG9DrXv3l/PyupdLN+4kxXVdayq3sVbqzYfuvwWID0lkeG9M3nsq+Nb/OqpeAZEIbAuarkKOPsE9nfgZTNz4Hfufl+sjcxsGjANoG/fvidZqohI25OeksSoomxGFWUf1r5j9wFW1kQCY2V1HXsPNMTl0tp4BkSsak9kwGOiu28ws3zgFTNb7u6zj3jDSHDcB5ExiJMrVUSk/chKTz5iUDwe4jkXbhVQFLXcB9jQ3J3dfUPwvQZ4isgpKxERaSXxDIgyYLCZ9TezFOBqYGZzdjSzrmaWcfA1MBlYHLdKRUTkCHE7xeTu9WY2HXiJyGWuD7j7EjO7KVh/r5n1BMqBTKDRzL4JDAN6AE8F59SSgEfc/cV41SoiIkeK641y7v488HyTtnujXm8icuqpqZ3AyHjWJiIix6bn8YmISEwKCBERiUkBISIiMSkgREQkpg71wCAzqwXWnOTuPQDN+3R86qfmUT81n/qqeeLVT/3cPS/Wig4VEKfCzMqbM2NsZ6d+ah71U/Opr5onjH7SKSYREYlJASEiIjEpID4Wc7ZYOYL6qXnUT82nvmqeVu8njUGIiEhMOoIQEZGYFBAiIhJTpw8IM5tiZivMrMLM7gi7ntZgZkVm9rqZLTOzJWb2jaA9x8xeMbNVwffuUft8L+ijFWb2D1HtZ5nZomDdnRZMwWtmqWb256D9fTMrbvUP2kLMLNHM5pnZs8Gy+qkJM8s2s8fNbHnw72q8+ulIZvat4P+5xWb2qJmltel+cvdO+0VkGvIPgAFACrAAGBZ2Xa3wuXsBo4PXGcBKItOs/xdwR9B+B/DT4PWwoG9Sgf5BnyUG6/4OjCfyBMEXgEuD9luAe4PXVwN/Dvtzn0J/3QY8AjwbLKufjuyjh4AvB69TgGz10xF9VAh8CHQJlh8DvtiW+yn0Tgv5P9h44KWo5e8B3wu7rhD64RngEmAF0Cto6wWsiNUvRJ7xMT7YZnlU+zVEnh9+aJvgdRKRO0At7M96En3TB3gNuDAqINRPh/dRZvCLz5q0q58O749CYB2QE3yGZ4k8DK3N9lNnP8V08D/YQVVBW6cRHIKeCbwPFLj7RoDge36w2dH6qTB43bT9sH3cvR7YAeTG5UPE16+B24HGqDb10+EGALXA74NTcfcHT4JUP0Vx9/XAz4G1wEZgh7u/TBvup84eEBajrdNc92tm3YAngG+6+85jbRqjzY/Rfqx92g0z+0egxt3nNHeXGG0dvp+I/KU6Gvhvdz8T+IjIqZKj6ZT9FIwtTCVyuqg30NXMrjvWLjHaWrWfOntAVAFFUct9gA0h1dKqzCyZSDg87O5PBs3VZtYrWN8LqAnaj9ZPVRz+RMDo/ju0j5klAVnA1pb/JHE1EfiUmVUCM4ALzexPqJ+aqgKq3P39YPlxIoGhfjrcxcCH7l7r7geAJ4EJtOF+6uwBUQYMNrP+ZpZCZFBnZsg1xV1wxcP/Asvc/ZdRq2YCXwhef4HI2MTB9quDKyT6A4OBvweHw3VmNi54z+ub7HPwva4AZnlwYrS9cPfvuXsfdy8m8m9jlrtfh/rpMB55dPA6MxsaNF0ELEX91NRaYJyZpQef7yJgGW25n8IeuAn7C7iMyFU8HwDfD7ueVvrM5xA57FwIzA++LiNyrvI1YFXwPSdqn+8HfbSC4IqJoL0UWBysu4uP785PA/4CVBC54mJA2J/7FPvsAj4epFY/Hdk/o4Dy4N/U00B39VPMfvoRsDz4jH8kcoVSm+0nTbUhIiIxdfZTTCIichQKCBERiUkBISIiMSkgREQkJgWEiIjEpIAQicHMdgXfi83scy383v+nyfI7Lfn+Ii1FASFybMXACQWEmSUeZ5PDAsLdJ5xgTSKtQgEhcmw/Ac41s/nBXP6JZvYzMyszs4Vm9lUAM7vAIs/YeARYFLQ9bWZzgvn/pwVtPwG6BO/3cNB28GjFgvdeHMz1f1XUe79hHz9v4eGD8/+LxFNS2AWItHF3AN9x938ECH7R73D3MWaWCrxtZi8H244FTnf3D4PlG9x9q5l1AcrM7Al3v8PMprv7qBg/65+I3JE8EugR7DM7WHcmMJzInDtvE5kn6q2W/rAi0XQEIXJiJgPXm9l8IlOk5xKZIwci8+R8GLXt181sAfAekQnUBnNs5wCPunuDu1cDfwPGRL13lbs3EpkapbgFPovIMekIQuTEGPA1d3/psEazC4hMcx29fDGRh7fsNrM3iMyTc7z3Ppp9Ua8b0P+70gp0BCFybHVEHst60EvAzcF06ZjZkODhOE1lAduCcCgBxkWtO3Bw/yZmA1cF4xx5wHlEJlwTCYX+ChE5toVAfXCq6EHgN0RO78wNBoprgctj7PcicJOZLSQyE+d7UevuAxaa2Vx3vzaq/Skij5RcQGS23dvdfVMQMCKtTrO5iohITDrFJCIiMSkgREQkJgWEiIjEpIAQEZGYFBAiIhKTAkJERGJSQIiISEz/H90p6c/oaekDAAAAAElFTkSuQmCC",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Augment the data\n",
        "_x = x[np.newaxis,:]\n",
        "print(f\"Shape of x: {_x.shape}\")\n",
        "\n",
        "x_aug = np.vstack((np.ones((1,_x.shape[1])), _x))\n",
        "print(f\"Shape of x_aug: {x_aug.shape}\")\n",
        "\n",
        "print(f\"Shape of y: {y.shape}\")\n",
        "\n",
        "# Generate optimal weights using gradient descent\n",
        "reg = logis_regression()\n",
        "w_pred, err = reg.grad_descent(x_aug, y, 1e-3)\n",
        "print(f\"Optimal weights: {w_pred}\")\n",
        "\n",
        "# Plot the error\n",
        "plt.plot(err)\n",
        "plt.xlabel('Iteration')\n",
        "plt.ylabel('Error')\n",
        "plt.show()\n",
        "\n",
        "# Plot the data and the optimal line\n",
        "plt.plot(x, y, '.')\n",
        "y_pred = reg.logis(x_aug,w_pred)\n",
        "plt.plot(x,  y_pred)\n",
        "pred_zero = np.where(y_pred < 0.5)\n",
        "pred_one = np.where(y_pred >= 0.5)\n",
        "plt.plot(x[pred_zero], np.zeros(x[pred_zero].shape[0]), 'oy')\n",
        "plt.plot(x[pred_one], np.ones(x[pred_one].shape[0]), 'or')\n",
        "plt.title('Predictions')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Tu72LaBk68W1"
      },
      "source": [
        "# Classification of circularly separated data using logistic regression\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 601
        },
        "id": "BB9LN7-QZ9Lb",
        "outputId": "e51fef3d-f7a1-479c-8cdc-743540d097e1"
      },
      "outputs": [
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAEWCAYAAABv+EDhAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAAsTAAALEwEAmpwYAAATmElEQVR4nO3df7DldV3H8deLZRFGIFJuiSzLikOm7RDGijiammHtqImaluSvUmdHy7SmGkqm/FFMOhSjNc3YjjD5A3UsdGJQE8wf5OgKu4QI4o+N3GHTiStCgr9w3Vd/3Mu4P85399675+znc877+ZjZgXv3Pu95nwH2zTn3fL7HSQQAqOeI1gMAANpgAQBAUSwAACiKBQAARbEAAKAoFgAAFMUCAICiWADAPmx/zfb3bN9j+27bn7H9CtsH/e/F9jrbsX3k4ZgVOBQsAGC0X0tynKRTJb1J0gWSLm07EjBeLADgAJL8X5IrJf2mpJfYXm/76bb/0/a3bd9u+/V7JNcu/vVu2/fafpzth9v+uO07bX/T9uW2Tzjc9wXYFwsAWIIk10naKekXJX1H0oslnSDp6ZJeaftZi1/6xMW/npDk2CSflWRJfy3poZIeKekUSa8/XLMDQ1gAwNJ9XdKDknwyyReS7E5yk6T3SnrSUJRke5JrkvwgybykSw709cDhwg+qgKU7WdK3bD9WCz8XWC/pKEkPkPTPQ5Htn5L0d1p49HCcFv7H666JTwscBI8AgCWw/RgtLIBPS3qPpCslnZLkJyS9TQtP80jSqMvr/vXi589IcrykF+7x9UAzLADgAGwfb/sZkt4n6d1JvqCF/4v/VpLv2z5b0m/tkcxL2i3ptD0+d5yke7Xwg+GTJf3J4ZkeODDzfgDA3mx/TdJPS9qlhT/Mvyjp3ZLeluRHtp8r6W8lPUjSpyR9TQs/9H3hYv9GSa+UtFrSRkn3SHqnpEdI2i7pXZL+MMmaw3evgP2xAACgKJ4CAoCiWAAAUBQLAACKYgEAQFFTdRDsxBNPzLp161qPAQBTZdu2bd9MMrfv56dqAaxbt05bt25tPQYATBXbO0Z9nqeAAKAoFgAAFMUCAICiWAAAUBQLAACKarYAbB9t+zrbn7d9i+03tJoFACpq+QjgB5KekuTnJZ0paaPtcyZxQ9t23KV/+MR2bduxsvfgoKenp19p38sMozQ7B5CFy5Deu/jh6sVfY7806bYdd+kFb9+i+3bt1lFHHqHLX36Ozjr1J+np6ekn3vcyw5CmPwOwvcr2jZLukHRNks+N+JpNtrfa3jo/P7/s29hy2526b9du7Y70w127teW2O+np6ekPS9/LDEOaLoAkP0pypqQ1ks62vX7E12xOsiHJhrm5/U4yH9Q5pz1YRx15hFZZWn3kETrntAfT09PTH5a+lxmGdPOGMLZfJ+k7Sf5m6Gs2bNiQlVwKYtuOu7Tltjt1zmkPXtFDJ3p6evqV9j3MYHtbkg37fb7VArA9J+mHSe62fYykqyW9OclVQ81KFwAAVDa0AFpeDO4kSe+wvUoLT0W9/0B/+AMAxqvlq4BukvToVrcPANVxEhgAimIBAEBRLAAAKKrEAmh9DJuenr5u38sMo0zVW0KuROtj2PT09HX7XmYYMvOPAFofw6anp6/b9zLDkJlfAK2PYdPT09fte5lhSDeXglgKLgVBT08/bX0PM3R3KYiV4FIQALB8Qwtg5p8CAgCMxgIAgKJYAABQFAsAAIoqsQBan8Kjp6ev2/cywyicBKanp6efUN/LDENm/hFA61N49PT0dfteZhgy8wug9Sk8enr6un0vMwwpcRCs9Sk8enr6un0PM3ASGACK4iQwAGAvLAAAKIoFAABFsQAAoKgSC6D1KTx6evq6fS8zjNLsJLDtUyS9U9JDJO2WtDnJW8d9O61P4dHT09fte5lhSMtHALsk/VGSR0o6R9Lv2X7UuG+k9Sk8enr6un0vMwxptgCSfCPJDYt/f4+kWyWdPO7baX0Kj56evm7fywxDujgIZnudpGslrU/y7X1+b5OkTZK0du3as3bs2LHs79/6FB49PX3dvocZuj0JbPtYSZ+SdFGSDxzoazkJDADL1+VJYNurJV0h6fKD/eEPABivZgvAtiVdKunWJJe0mgMAqmr5CODxkl4k6Sm2b1z89bSG8wBAKc3OAST5tCS3un0AqK7ESWAAwP5KLIDWx7Dp6enr9r3MMApvCk9PT08/ob6XGYbM/COA1sew6enp6/a9zDBk5hdA62PY9PT0dfteZhjS/CTwcvCm8PT09NPW9zBDt5eCWA4uBQEAy9flpSAAAO2wAACgKBYAABTFAgCAokosgNan8Ojp6ev2vcwwCieB6enp6SfU9zLDkJl/BND6FB49PX3dvpcZhsz8Amh9Co+enr5u38sMQ0ocBGt9Co+enr5u38MMnAQGgKI4CQwA2AsLAACKYgEAQFEsAAAoigUAAEWVWACtj2HT09PX7XuZYRQuBUFPT08/ob6XGYY0fQRg+zLbd9i+eVK30foYNj09fd2+lxmGtH4K6J8kbZzkDbQ+hk1PT1+372WGIc1PAtteJ+mqJOsP9rVcCoKenn7a+h5m6PZSEAdbALY3SdokSWvXrj1rx44dh3E6AJh+U3spiCSbk2xIsmFubq71OAAwM7pfAACAyWABAEBRrV8G+l5Jn5X0CNs7bb+s5TwAUEnTBZDk/CQnJVmdZE2SSydxO61P4dHT09fte5lhFE4C09PT00+o72WGITP/M4DWp/Do6enr9r3MMGTmF0DrU3j09PR1+15mGNL8INhycBKYnp5+2voeZuj2JPBy8KbwALB8U3sSGAAwGSwAACiKBQAARbEAAKCoEgug9Sk8enr6un0vM4zCSWB6enr6CfW9zDBk5h8BtD6FR09PX7fvZYYhM78AWp/Co6enr9v3MsOQEgfBWp/Co6enr9v3MAMngQGgKE4CAwD2wgIAgKJYAABQFAsAAIpiAQBAUSUWQOtj2PT09HX7XmYYhUtB0NPT00+o72WGITP/CKD1MWx6evq6fS8zDJn5BdD6GDY9PX3dvpcZhhzwJLDt4yXNJfmvfT5/RpKbDvnG7Y2S3ipplaS3J3nTgb6eS0HQ09NPW9/DDMu+FITt35D0Fkl3SFot6beTXL/4ezck+YVlT7H3918l6SuSnippp6TrJZ2f5ItDDZeCAIDlW8mlIF4r6awkZ0r6HUnvsv2c+7/fGGY6W9L2JLcluU/S+ySdN4bvCwBYggO9CmhVkm9IUpLrbP+SpKtsr5E0jivInSzp9j0+3inpsft+ke1NkjZJ0tq1a8dwswAA6cCPAO6x/fD7P1hcBk/Wwv+l/9wYbnvUo4j9FkuSzUk2JNkwNzc3hpsFAEgHXgCvlHSE7Ufd/4kk90jaKOnlY7jtnZJO2ePjNZK+PobvCwBYgsEFkOTzSb4q6f22L/CCYyRdIul3x3Db10s63fbDbB8l6fmSrhzD991P61N49PT0dfteZhhlKSeBHyvpzZI+I+k4SZdLevyh3nCSXbZfJemjWngZ6GVJbjnU77uv1qfw6Onp6/a9zDBkKQfBfijpe5KOkXS0pP9OsnscN57kw0l+JsnDk1w0ju+5r9an8Ojp6ev2vcwwZCkL4HotLIDHSHqCpPNt/8vYJpiw1qfw6Onp6/a9zDDkoO8JbHtDkq37fO5FSd41timWiJPA9PT009b3MANvCg8ARfGm8ACAvbAAAKAoFgAAFMUCAICiWAAAUFSJBdD6GDY9PX3dvpcZRuFN4enp6ekn1Pcyw5CZfwTQ+hg2PT193b6XGYbM/AJofQybnp6+bt/LDENKnARufQybnp6+bt/DDFwKAgCK4lIQAIC9sAAAoCgWAAAUxQIAgKJKLIDWp/Do6enr9r3MMAongenp6ekn1Pcyw5CZfwTQ+hQePT193b6XGYbM/AJofQqPnp6+bt/LDENKHARrfQqPnp6+bt/DDJwEBoCiujoJbPt5tm+xvdv2fkMBACav1c8Abpb0HEnXNrp9ACivyctAk9wqSbZb3DwAQFPwKiDbm2xvtb11fn6+9TgAMDMmtgBsf8z2zSN+nbec75Nkc5INSTbMzc2taJbWp/Do6enr9r3MMMrEngJKcu6kvvdytD6FR09PX7fvZYYh3T8FdKhan8Kjp6ev2/cyw5BWLwN9tu2dkh4n6UO2Pzqp22p9Co+enr5u38sMQ0ocBGt9Co+enr5u38MMnAQGgKK6OgkMAGiPBQAARbEAAKAoFgAAFMUCAICiSiyA1sew6enp6/a9zDAKbwpPT09PP6G+lxmGzPwjgNbHsOnp6ev2vcwwZOYXQOtj2PT09HX7XmYYUuIkcOtj2PT09HX7HmbgUhAAUBSXggAA7IUFAABFsQAAoCgWAAAUVWIBtD6FR09PX7fvZYZROAlMT09PP6G+lxmGzPwjgNan8Ojp6ev2vcwwZOYXQOtTePT09HX7XmYYUuIgWOtTePT09HX7HmbgJDAAFMVJYADAXlgAAFBUkwVg+2LbX7J9k+0P2j6hxRwAUFmrRwDXSFqf5AxJX5H0Z43mAICymiyAJFcn2bX44RZJa1rMAQCV9fAzgJdK+sjQb9reZHur7a3z8/MruoHWx7Dp6enr9r3MMMrELgVh+2OSHjLity5M8q+LX3OhpF2SLh/6Pkk2S9osLbwMdLlztD6GTU9PX7fvZYYhE3sEkOTcJOtH/Lr/D/+XSHqGpBdkgocRWh/Dpqenr9v3MsOQVq8C2ijpAknPTPLdSd5W62PY9PT0dfteZhjS5CSw7e2SHiDp/lW2JckrDtZxKQh6evpp63uYgUtBAEBRXAoCALAXFgAAFMUCAICiWAAAUFSJBdD6FB49PX3dvpcZRuFN4enp6ekn1Pcyw5CZfwTQ+hQePT193b6XGYbM/AJofQqPnp6+bt/LDENKHARrfQqPnp6+bt/DDJwEBoCiOAkMANgLCwAAimIBAEBRLAAAKIoFAABFlVgArY9h09PT1+17mWEULgVBT09PP6G+lxmGzPwjgNbHsOnp6ev2vcwwZOYXQOtj2PT09HX7XmYYUuIkcOtj2PT09HX7HmbgUhAAUBSXggAA7IUFAABFsQAAoKgmC8D2X9q+yfaNtq+2/dAWcwBAZa0eAVyc5IwkZ0q6StJfTPLGWp/Co6enr9v3MsMoTU4CJ/n2Hh8+UNLEXorU+hQePT193b6XGYY0+xmA7Yts3y7pBTrAIwDbm2xvtb11fn5+2bfT+hQePT193b6XGYZMbAHY/pjtm0f8Ok+SklyY5BRJl0t61dD3SbI5yYYkG+bm5pY9R+tTePT09HX7XmYY0vwgmO1TJX0oyfqDfS0ngenp6aet72GGrk4C2z49yVcX//73JT0pyXMP1nESGACWb2gBtLoc9JtsP0LSbkk7JL2i0RwAUFarVwH9eovbBQD8GCeBAaAoFgAAFMUCAICiWAAAUFTzcwDLYXteC68aWokTJX1zjOO0xH3pz6zcD4n70qtDuS+nJtnvJO1ULYBDYXvrqNfBTiPuS39m5X5I3JdeTeK+8BQQABTFAgCAoiotgM2tBxgj7kt/ZuV+SNyXXo39vpT5GQAAYG+VHgEAAPbAAgCAokotgFl6M3rbF9v+0uL9+aDtE1rPtBK2n2f7Ftu7bU/ly/Vsb7T9Zdvbbf9p63lWyvZltu+wfXPrWQ6F7VNsf8L2rYv/br2m9UwrZfto29fZ/vzifXnDWL9/pZ8B2D7+/vcjtv1qSY9KMpWXorb9K5I+nmSX7TdLUpILGo+1bLYfqYXLgv+jpD9OMlVv+GB7laSvSHqqpJ2Srpd0fpIvNh1sBWw/UdK9kt65lDdo6pXtkySdlOQG28dJ2ibpWVP6z8SSHpjkXturJX1a0muSbBnH9y/1COBwvhn9pCW5OsmuxQ+3SFrTcp6VSnJrki+3nuMQnC1pe5Lbktwn6X2Szms804okuVbSt1rPcaiSfCPJDYt/f4+kWyWd3HaqlcmCexc/XL34a2x/bpVaANLS34x+yrxU0kdaD1HUyZJu3+PjnZrSP2xmke11kh4t6XONR1kx26ts3yjpDknXJBnbfZm5BTCuN6PvwcHuy+LXXChplxbuT5eWcj+mmEd8bmofWc4S28dKukLSH+zz6H+qJPlRkjO18Cj/bNtje3qu1VtCTkySc5f4pe+R9CFJr5vgOIfkYPfF9kskPUPSL6fjH+Ys45/JNNop6ZQ9Pl4j6euNZsGixefLr5B0eZIPtJ5nHJLcbfuTkjZKGssP6mfuEcCB2D59jw+fKelLrWY5VLY3SrpA0jOTfLf1PIVdL+l02w+zfZSk50u6svFMpS3+4PRSSbcmuaT1PIfC9tz9r/CzfYykczXGP7eqvQroCkl7vRl9kv9pO9XK2N4u6QGS7lz81JZpfEWT7WdL+ntJc5LulnRjkl9tOtQy2X6apLdIWiXpsiQXtZ1oZWy/V9KTtXDZ4f+V9LoklzYdagVsP0HSf0j6ghb+W5ek1yb5cLupVsb2GZLeoYV/t46Q9P4kbxzb96+0AAAAP1bqKSAAwI+xAACgKBYAABTFAgCAolgAAFAUCwAYE9v/Zvtu21e1ngVYChYAMD4XS3pR6yGApWIBAMtk+zGL78NwtO0HLl6nfX2Sf5d0T+v5gKWauWsBAZOW5HrbV0r6K0nHSHp3kql+ExXUxAIAVuaNWrgO0PclvbrxLMCK8BQQsDIPknSspOMkHd14FmBFWADAymyW9OdaeB+GNzeeBVgRngIClsn2iyXtSvKexfcE/oztp0h6g6SflXSs7Z2SXpbkoy1nBQ6Eq4ECQFE8BQQARbEAAKAoFgAAFMUCAICiWAAAUBQLAACKYgEAQFH/D4gGhuFkbYGjAAAAAElFTkSuQmCC",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "x1=np.linspace(-3,3,20)\n",
        "x2=np.linspace(-3,3,20)\n",
        "\n",
        "x11,x22=np.meshgrid(x1,x2)\n",
        "plt.plot(np.reshape(x11,(-1,1)),np.reshape(x22,(-1,1)),'.')\n",
        "plt.title('Data')\n",
        "plt.xlabel('x1')\n",
        "plt.ylabel('x2')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UH3gwRKNbf34"
      },
      "source": [
        "  Using the above data generate circular data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "EP4mon7Rc80v",
        "outputId": "4aadc914-9f1f-4d77-931f-7f3f32e7f120"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "x = np.hstack((x11.reshape(-1,1),x22.reshape(-1,1)))\n",
        "in_points = np.where((x[:,0]**2+x[:,1]**2)<=1)\n",
        "out_points = np.where((x[:,0]**2+x[:,1]**2)>=2.1)\n",
        "in_points = x[in_points]\n",
        "out_points = x[out_points]\n",
        "points = np.concatenate((in_points,out_points))\n",
        "\n",
        "plt.plot(points[:,0],points[:,1],'.')\n",
        "plt.title('Data')\n",
        "plt.xlabel('x1')\n",
        "plt.ylabel('x2')\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZBZR6c0JcnDm"
      },
      "source": [
        "As in case of circularly separated data, the boundary is nonlinear, so squared feature is taken."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OvI2_KIfhKsS",
        "outputId": "cb4c749c-b53f-4620-b355-96a477c0f9a4"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Shape of x: (3, 364)\n",
            "Shape of y: (364,)\n",
            "Optimal weights: [ 4.77630224 -3.28668146 -3.28679952]\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# perform logistic regression\n",
        "reg = logis_regression()\n",
        "\n",
        "x = np.hstack((np.ones((points.shape[0],1)),points**2)).T\n",
        "print(f\"Shape of x: {x.shape}\")\n",
        "y = np.concatenate((np.ones(in_points.shape[0]),np.zeros(out_points.shape[0])))\n",
        "print(f\"Shape of y: {y.shape}\")\n",
        "\n",
        "w_pred, err = reg.grad_descent(x, y, 1e-1)\n",
        "print(f\"Optimal weights: {w_pred}\")\n",
        "\n",
        "# Plot the error\n",
        "plt.plot(err)\n",
        "plt.xlabel('Iteration')\n",
        "plt.ylabel('Error')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aPZH3-2FdCMB"
      },
      "source": [
        "Plot classification using 0.5 as threshold"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3b65To6rtIGN",
        "outputId": "bb3539a3-3e77-42b1-cfc6-a4f1529180f3"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Plot the classification using 0.5 threshold\n",
        "y_pred = reg.logis(x,w_pred)\n",
        "pred_zero = np.where(y_pred < 0.5)\n",
        "pred_one = np.where(y_pred >= 0.5)\n",
        "plt.plot(points[pred_zero,0], points[pred_zero,1], 'or')\n",
        "plt.plot(points[pred_one,0], points[pred_one,1], 'xy')\n",
        "plt.title('Predictions')\n",
        "plt.xlabel('x1')\n",
        "plt.ylabel('x2')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Lb-RLgsnC23C"
      },
      "source": [
        "# Multiclass logistic regression\n",
        "\n",
        "1. Generate 1D data with 3 classes\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GgonBFE8I2IL"
      },
      "source": [
        "### One vs rest classification\n",
        "\n",
        "1. Lets take a polynomial of order 2 (by seeing the data distribution)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "id": "AcyM3i2N673z",
        "outputId": "c8a055b6-2c67-4073-a959-0090d5e46b02"
      },
      "outputs": [
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "## Write your code here\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "x1=np.linspace(0,0.6,100)\n",
        "x2=np.linspace(1.1,2.7,100)\n",
        "x3=np.linspace(3.5,3.8,100)\n",
        "\n",
        "x=np.concatenate((x1,x2,x3))\n",
        "\n",
        "y1=np.zeros(x1.shape)\n",
        "y2=np.ones(x2.shape)\n",
        "y3=np.tile([2],x3.shape)\n",
        "\n",
        "y=np.concatenate((y1,y2,y3))\n",
        "\n",
        "plt.figure()\n",
        "plt.plot(x,y,'.')\n",
        "plt.title('Data')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "id": "wBzA2n2eI1Oe"
      },
      "outputs": [],
      "source": [
        "# def data_transform(X,degree): \n",
        "#   X_new=[]      \n",
        "#   for i in range(degree +1):\n",
        "#     # write code here to generate a polynomial\n",
        "\n",
        "def data_transform(X,degree): \n",
        "  X_new=[]      \n",
        "  for i in range(degree +1):\n",
        "    X_new.append(X**i)              \n",
        "  X_new = np.concatenate(X_new)  \n",
        "  return X_new\n",
        "\n",
        "x_aug=data_transform(x[np.newaxis,:],2)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "id": "bPupnA3L9H98"
      },
      "outputs": [],
      "source": [
        "# plot for classification\n",
        "def plot_op(x,y_pred):\n",
        "\n",
        "  ind0=np.where(y_pred<0.5)\n",
        "  ind1=np.where(y_pred>=0.5)\n",
        "  x0=x[ind0]\n",
        "  x1=x[ind1]\n",
        "  plt.plot(x0,np.zeros((x0).shape),'o',color='y')\n",
        "  plt.plot(x1,np.ones((x1).shape),'x',color='r')\n",
        "  "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lqYEZP5G9O58"
      },
      "source": [
        "Using the above function for plotting, plot the curve using different configurations"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 563
        },
        "id": "sRzwjLWIRIk_",
        "outputId": "dd2b9c1b-3980-427f-bec7-03fc76b338c3"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Optimal weights: [-5.76344227  1.8439777   4.72853547]\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# take class 0 as '0' and other to '1'\n",
        "zeros = np.where(y==0)\n",
        "ones = np.where(y!=0)\n",
        "\n",
        "ys = np.zeros(y.shape)\n",
        "ys[ones] = 1\n",
        "\n",
        "# perform logistic regression\n",
        "reg = logis_regression()\n",
        "\n",
        "w_pred, err = reg.grad_descent(x_aug, ys, 1e-1)\n",
        "print(f\"Optimal weights: {w_pred}\")\n",
        "\n",
        "# Plot the error\n",
        "plt.plot(err)\n",
        "plt.xlabel('Iteration')\n",
        "plt.ylabel('Error')\n",
        "plt.show()\n",
        "\n",
        "# Plot the classification using 0.5 threshold\n",
        "y_pred1 = reg.logis(x_aug,w_pred)\n",
        "plt.plot(x,y_pred1)\n",
        "plot_op(x,y_pred1)\n",
        "plt.title('Predictions')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 563
        },
        "id": "Cs1SQW-RRTed",
        "outputId": "e6923c6e-792c-4b98-a5a4-4550f5f8a9f9"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Optimal weights: [  9.25100732 -14.44348674   3.68771526]\n"
          ]
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# take class 1 as '0' and other to '1'\n",
        "zeros = np.where(y==1)\n",
        "ones = np.where(y!=1)\n",
        "\n",
        "ys = np.zeros(y.shape)\n",
        "ys[ones] = 1\n",
        "\n",
        "# perform logistic regression\n",
        "reg = logis_regression()\n",
        "\n",
        "w_pred, err = reg.grad_descent(x_aug, ys, 1e-1)\n",
        "print(f\"Optimal weights: {w_pred}\")\n",
        "\n",
        "# Plot the error\n",
        "plt.plot(err)\n",
        "plt.xlabel('Iteration')\n",
        "plt.ylabel('Error')\n",
        "plt.show()\n",
        "\n",
        "# Plot the classification using 0.5 threshold\n",
        "y_pred2 = reg.logis(x_aug,w_pred)\n",
        "plt.plot(x,y_pred2)\n",
        "plot_op(x,y_pred2)\n",
        "plt.title('Predictions')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 27,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 563
        },
        "id": "0JmvDrlzRWUX",
        "outputId": "a7100e66-4815-49f1-c5ca-c3e21be82501"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Optimal weights: [ 5.58158324  4.25724647 -2.0110733 ]\n"
          ]
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Take class 2 as '0' and other to '1'\n",
        "zeros = np.where(y==2)\n",
        "ones = np.where(y!=2)\n",
        "\n",
        "ys = np.zeros(y.shape)\n",
        "ys[ones] = 1\n",
        "\n",
        "# perform logistic regression\n",
        "reg = logis_regression()\n",
        "\n",
        "w_pred, err = reg.grad_descent(x_aug, ys, 1e-1)\n",
        "print(f\"Optimal weights: {w_pred}\")\n",
        "\n",
        "# Plot the error\n",
        "plt.plot(err)\n",
        "plt.xlabel('Iteration')\n",
        "plt.ylabel('Error')\n",
        "plt.show()\n",
        "\n",
        "# Plot the classification using 0.5 threshold\n",
        "y_pred3 = reg.logis(x_aug,w_pred)\n",
        "plt.plot(x,y_pred3)\n",
        "plot_op(x,y_pred3)\n",
        "plt.title('Predictions')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "lables = []\n",
        "for i, _ in enumerate(x):\n",
        "  label = np.argmin([y_pred1[i], y_pred2[i], y_pred3[i]])\n",
        "  lables.append(label)\n",
        "\n",
        "plt.scatter(x, lables, c=lables)\n",
        "plt.title('Predictions')\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "plt.show()"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [
        "lzRAXAYsiuhp",
        "9poZ8N56Z94R",
        "Lb-RLgsnC23C",
        "GgonBFE8I2IL",
        "dOe8btABKSBO",
        "p8Zk66RiWuS5",
        "lzZC16m_2Dw5",
        "wfA70l6m2Rgl",
        "09Xcn_ng2KXr"
      ],
      "name": "Classification_V2.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3.10.5 64-bit",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.10.7"
    },
    "vscode": {
      "interpreter": {
        "hash": "767d51c1340bd893661ea55ea3124f6de3c7a262a8b4abca0554b478b1e2ff90"
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}