Ds_che_210477_assign2.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "dZIUN8NgDy_D",
        "outputId": "d7491883-c5ba-46e2-fb85-e86dae6c7ecc"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[7.71320643 0.20751949 6.33648235 7.48803883 4.98507012 2.24796646\n",
            " 1.98062865 7.60530712 1.69110837 0.88339814 6.85359818 9.53393346\n",
            " 0.03948266 5.12192263 8.12620962 6.12526067 7.21755317 2.91876068\n",
            " 9.17774123 7.14575783 5.42544368 1.42170048 3.7334076  6.74133615\n",
            " 4.41833174 4.34013993 6.17766978 5.13138243 6.50397182 6.01038953\n",
            " 8.05223197 5.21647152 9.08648881 3.19236089 0.90459349 3.00700057\n",
            " 1.13984362 8.28681326 0.46896319 6.26287148 5.47586156 8.19286996\n",
            " 1.9894754  8.56850302 3.51652639 7.54647692 2.95961707 8.8393648\n",
            " 3.25511638 1.65015898]\n",
            "[ 9.62182172 -4.79765865  7.33382445 10.28824759  5.53529292 -0.65148735\n",
            " -1.06464804 10.49970845 -2.15766234 -2.5250437   9.54942111 14.27144772\n",
            " -2.52633101  6.16130421 11.14014676  6.88834089  9.20292409  0.33579246\n",
            " 14.4842676   8.59370564  5.76976518 -2.68589513  3.51299806  7.06411627\n",
            "  3.47416431  3.55837418  7.67469599  5.72366775  7.79215375  8.00985153\n",
            " 11.41921772  7.9005941  11.66465613  2.00532244 -4.23594555  0.21599232\n",
            " -0.73522817 13.31844067 -5.91825909  7.30296927  5.88587527  9.2540278\n",
            " -1.06987972 12.53034727  2.25031793  8.09856006  2.02694237 12.92327357\n",
            "  1.44832073 -2.45357501]\n",
            "50\n",
            "[-1.11976455]\n",
            "[0.22664606]\n",
            "no of iterations: 0\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "no of iterations: 10000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "no of iterations: 20000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "no of iterations: 30000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "no of iterations: 40000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([0.8893091]), array([2.23571972]))"
            ]
          },
          "metadata": {},
          "execution_count": 2
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "\n",
        "#a) |x - x̂|³ , Linear Regression\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "%matplotlib inline\n",
        "\n",
        "rng = np.random.RandomState(10)\n",
        "x = 10 * rng.rand(50)\n",
        "y = 2 * x - 5 + rng.randn(50)\n",
        "#plt.scatter(x, y);\n",
        "\n",
        "#print(x)\n",
        "\n",
        "#print(rng)\n",
        "\n",
        "#print(y)\n",
        "\n",
        "#xlen = len(x)\n",
        "#print(xlen)\n",
        "\n",
        "#ylen = len(y)\n",
        "#print(ylen)\n",
        "\n",
        "print(x)\n",
        "print(y)\n",
        "\n",
        "def loss(y_hat, y):\n",
        "    l = (y_hat - y)**3\n",
        "    return l.mean()\n",
        "\n",
        "def forward_pass(x,m,c):\n",
        "    return m*x+c\n",
        "\n",
        "learningrate = 0.01\n",
        "numiter = 50000\n",
        "\n",
        "L=[]\n",
        "N=x.shape[0]\n",
        "print(N)\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "m1 = np.random.randn(1)\n",
        "c1 = np.random.randn(1)\n",
        "\n",
        "print(m1)\n",
        "print(c1)\n",
        "\n",
        "\n",
        "learningrate = 0.01\n",
        "numiter = 50000\n",
        "\n",
        "for i in range(numiter):\n",
        "    \n",
        "    y_hat=forward_pass(x,m1,c1)\n",
        "    \n",
        "   \n",
        "    \n",
        "    dm = (3.0/N) *  -np.sum(np.multiply(x,(y - (m1*x +c1))))\n",
        "   \n",
        "    dc = (3.0/N) * -np.sum(y - (m1*x + c1))\n",
        "    \n",
        "    m1 = m1 -learningrate * dm\n",
        "    c1 = c1 - learningrate * dm\n",
        "    if i%10000==0:\n",
        "        L.append(loss(y_hat,y))\n",
        "        print (\"no of iterations:\",i )\n",
        "        plt.plot(x,y,'go')\n",
        "        plt.plot(x,y_hat,'r*')\n",
        "    #plt.plot(x,m1*x+c1,'r*')\n",
        "        plt.ylabel('Data')\n",
        "        plt.show()\n",
        "        \n",
        "        \n",
        "        \n",
        "        \n",
        "plt.plot(L)\n",
        "\n",
        "m1,c1\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#b) |x - x̂| , Linear Regression"
      ],
      "metadata": {
        "id": "bSF1GiOsEMMB"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "rng = np.random.RandomState(10)\n",
        "x = 10 * rng.rand(50)\n",
        "y = 2 * x - 5 + rng.randn(50)\n",
        "\n",
        "def loss(y_hat, y):\n",
        "    l = (y_hat - y)\n",
        "    return l.mean()\n",
        "\n",
        "def forward_pass(x,m,c):\n",
        "    return m*x+c\n",
        "\n",
        "learningrate = 0.01\n",
        "numiter = 50000\n",
        "\n",
        "L=[]\n",
        "N=x.shape[0]\n",
        "print(N)\n",
        "\n",
        "\n",
        "m1 = np.random.randn(1)\n",
        "c1 = np.random.randn(1)\n",
        "\n",
        "print(m1)\n",
        "print(c1)\n",
        "\n",
        "\n",
        "learningrate = 0.01\n",
        "numiter = 50000\n",
        "\n",
        "for i in range(numiter):\n",
        "    \n",
        "    y_hat=forward_pass(x,m1,c1)\n",
        "    \n",
        "   \n",
        "    \n",
        "    dm = (1.0/N) *  -np.sum(np.multiply(x,(y - (m1*x +c1))))\n",
        "   \n",
        "    dc = (1.0/N) * -np.sum(y - (m1*x + c1))\n",
        "    \n",
        "    m1 = m1 -learningrate * dm\n",
        "    c1 = c1 - learningrate * dm\n",
        "    if i%10000==0:\n",
        "        L.append(loss(y_hat,y))\n",
        "        print (\"no of iterations:\",i )\n",
        "        plt.plot(x,y,'go')\n",
        "        plt.plot(x,y_hat,'r*')\n",
        "    #plt.plot(x,m1*x+c1,'r*')\n",
        "        plt.ylabel('Data')\n",
        "        plt.show()\n",
        "        \n",
        "        \n",
        "plt.plot(L)  \n",
        "\n",
        "m1,c1"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "DZgnfPFFEPtd",
        "outputId": "e8b1851b-aeed-44f3-b7fc-88162025e94c"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "50\n",
            "[-0.77172556]\n",
            "[0.79351433]\n",
            "no of iterations: 0\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "no of iterations: 10000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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/F+u+KjZgrlXijS3VAOLuL7v7FHcfzjp2q7vfGj7+mruf7O5z3f10d/9Veq0ViUl2hmEW3DaHc0U2bx5dJuSNbzxUHqQl/F94yZJgMHyMpUGiMgaAVmvFMKZMnMKUiVNKnhWWxFoWSY9KmYikLTvDeOwxeN/7IHsWoRm4BxnH+ecHGyotWza6PEgVSoPkywwO+sG84xyF9C7ojRwD0TTfxqAAIpKW3EV8K1dGlz13DwbGs6vXZpcDqeJWrdWuK5XJTjQLqzHVwiC6SHOKWsTX3Q3HHhtUrL37bjjqqOD4ww9XrXptIXHUleqe083A8gEOXnuQgeUDCh4NRBmISKXGuoAvt9R5JsPIDhIf/OChx1XMNPJRxiDlUAARKVf2Ar7M2EUlC/ggstR52gvvuud0K2BISVJfSBgHLSSUWMW4gE8L7yQt9bqQUKQ+xLyAD7TwTuqLAohIqaIW8LW0VGUBX0a5C+/i3jNdpBCNgYiUKnvQu6UlWNz3/vdDe3swLlIFpU6j7d/Yz5X/90peeOVQZZ/MnumAurskEcpApPHl1pIai8yg94YNwWK+Awequk3rolmLih7PjJNkB48MdXdJkpSBSOPLXuld6WypjCov4MudcfXS/pciz1vz9JrXHucrN5KhOlOSFGUg0hiisozMoHduLamJE9NrZ5bcwoWDw4ORWQUcHhSKBQjVmZKkKIBIY8itWAv5V3pXYbZUNRTLJLJlB4VCAUJ1piRJCiBS2zKZxRNPRI9jFMoy8q30rsJsqWootaspNyhElRsBmDJxitaLSKIUQKS2ZTKL7u7RGQYUzzIyg94J1ZIqR75MYsrEKcyYPCNvyfTuOd30ndd32Dl3LrmT5z/9vIKHJCr1lejhNrV7gRHgQO5KyHBHwq8Ai4B9wCXuvqHQZ2oleh3JlAX56lfhE584VFcqt1JtruxV35ddFpQBmTAB9u+vfG/whGnVudSSel6J/k53PzVP488FZoW3HiCi3rXUpaEhmDcPfvGL0RlGJrPIHfCeOHH0OEYNZxmFRGUSCh5ST0rKQMzsdOB/A28GJgCtwMvufvSYGxBkIF3u/nye178OPOjud4XPnwLOdve8K7eUgdSBUjKMSy4JMotM+ZDW1mBvjDrJMETqSZwZyNeAC4GngYnAx4Bq1ZZ24H4ze9TMeiJenwY8k/V8R3jsMGbWY2brzWz9nj17qtQ0iUWh4JGdYWQyi7POCvbHOOususowRBpdyQsJ3X2rmbW6+whwu5k9BlxThTac4e47zew/AA+Y2W/c/aFyP8Td+4A+CDKQKrRL4rJtG1x1VTDekV2YsKUFXn01etc9Eak5pQaQfWY2AXjczD4PDFGl8RN33xne7zaze4D5QHYA2QmcmPV8enhM6lVmem2mW2pkBI45Bk47Dd70pqrVlRKReJUaBC4Oz70CeJnggr5krF9uZpPM7KjMY+AcYFPOaauBD1ngdGC40PiHxKSa9aQg6J5atgwefTS4P/tsWLu2qnWlRCRepWYg73P3rwB/AK4DMLMrCabXjsWxwD3BTF3GAd9x95+a2aUA7n4rsIZgCu9Wgmm8Hx7jd0olqllPCqpeU0pEklfqLKwN7v6WnGOPuftpsbVsDDQLq0yF9vbON+Bdhd33RKR2VH0WlpldaGb3AjPNbHXW7efAi2NprNSQq6+Ghx4K7nPVeD0pEUlPsS6sXxEMmE8Fvph1fC/wZFyNkoTkZhd33BHcsrOLGq8nJSLpKZiBuPuguz/o7m9393/Kum1w9wNJNVIqUKwIIQSL8qLkHq/Tld4iEq/UV6LHQWMgBDObvv51ePObYcuW6NXbQ0Nw5pmwdeuhY7NmBd1ZyjBEmkq9rkSXSpWyidLmzfk3Uzr++GBLVggKEULwXMFDREpQ8mJAd98KtLr7iLvfDiyMr1lSkkKbKJVShBCCxXvLlsG//Etwf+qp8be7jvVv7Kfzpk5armuh86ZO+jf2p90kkdSUGkAOW4luZp8s471SbaVsovTqq8Eqbwjus0uEZFu1KliHMXduQy7iq+YFP2oL2otWXcTUz09VIJGmNJaV6O+Pq1FC4ZXfpW6i1ORFCKMu+D339lR8sc+3Be0Lr7wwps8VqVclrUR390Ezaw8fXxdvkwQovPK72NTaBssiKhV1wd/3x32sWLuioj03Cm1BO5bPFalXxRYSmpl91syeB54Cfmtme8zsb5NpXgMbGoLTT4e3v73wIHjU4Ddoam0J8l3wS92LPFe+LWjH+rki9apYF9YngXcAb3X3N7j7McDbgHeE4yBSqRtugEceCQJA1CB4sZXfDT52UQ35LvjFAkE+vQt6aRvfVvb3iTSqYgHkYuBCd3/t6uXu24CLgA/F2bCGlZ1hZEQNgmvl95hFXfDbxrfRu6C3os/LbEE7ZeKUUa+N5XNF6lWxADI+aqtZd98DjI+nSXWonFLn27bB+ecfmiEFweMlS0YPgqt7akzi2HO8e043z3/6ee5ccqf2MpemV3AlelQV3lJeS1viK9Ezq75L3av7ssvg1ltHH9M+3yKSkkpWohebhTXXzH4f9V3AkeV8Ud0qp9T5ypXBrVip8127YOZMeOtbg+fr1inLEJG6UzCAuHtrodfHwsxOBP6BYFMpB/rCTauyzzkb+BGQGYNZ5e7Xk6RC02kze3v/8Iewb18w4H3++XDjjYU/UwPeItIA0lxNfgD4lLvPBk4HLjez2RHn/cLdTw1v8QaP7LGMUqbTasBbRJpYagHE3YfcfUP4eC+wBZiWVnuAw7ONUqfTasBbRJpUSeXcY2+EWSfwEHCKu/8+6/jZwA+AHcCzwFXuvjnPZ/QAPQAdHR3zBgcHS29Avm1bW1uDvTEmTID9+0sfJJdE9W/sZ8XaFWwf3k7H5A56F/RqRpRImeIs5x4bM3sdQZBYnh08QhuAGe4+l2A/kh/m+xx373P3Lnfvam9vL68R+bKNc85RdlHjql3vSkRKl2oAMbPxBMGj391HjSy7++/d/aXw8RpgvJlNrXpD8o1lrFmj1d4xKlYpt5RKuoXqXYlIvFILIGZmwDeBLe7+pTznHBeeh5nNJ2jvC7E0SGMZiSqWOZSaWVS73pWIlC61MRAzOwP4BbAROBge/gzQAeDut5rZFcBlBDO2XgH+xt1/VeyztaVt7eu8qZPB4dHjVDMmz2Bg+UDR10v9HBEpTRwLCWPj7r8kWJBY6JyvEWynKw2mWOZQambRu6CXnnt7DuvGUl0qkWSkPoguzalYpdxSK+nGUe9KREqjACKpKFYpt5xKut1zuhlYPsDBaw8ysHxAwUMkIQogkopimUP26wCt1vra7CpN0RWpDTWxkLDaNIjeODKzsXLHONRNJVJddbmQUKQQrfMQqV0KIFLTtM5DpHYpgEhNq/a+5iJSPQogUtOqva+5iFSPAojUNK3zEKldmoUlIiKahSUiIslRABERkYoogEgqStnrQ0RqmwKIJC5qr4+LV12MXWcKJiJ1RAFEEhe1utwJJnNoS1qR+pH2lrYLzewpM9tqZldHvH6Emd0dvv6ImXUm30qptmKryFWqRKQ+pLmlbStwM3AuMBu40Mxm55z2UeDf3P1PgS8Df5dsKyUOpawiV6kSkdqXZgYyH9jq7tvcfT/wXWBxzjmLgTvCx98HFmT2SJf6FbW6PJdKlYjUvjQDyDTgmaznO8Jjkee4+wFgGJiSSOskNrl7fVjOzsYqVSJSHxpmEN3MesxsvZmt37NnT9rNkSIyuwj6tc63l3xbpUpE6tC4FL97J3Bi1vPp4bGoc3aY2ThgMvBC1Ie5ex/QB0Epk6q3VmLTPadbAUOkDqWZgawDZpnZTDObAFwArM45ZzWwNHz8AeAfvRGLd4mI1KHUAkg4pnEFcB+wBfieu282s+vN7L3had8EppjZVuBvgFFTfSV+WjUuIlFUjbcG9W/sZ8XaFWwf3k7H5A56F/Sm1sWjPclFmoOq8TaAqDIfaa7M1p7kIpKPAkiNqbULtvYkF5F8FEBqTNIX7GU/Wca468dh1xnjrh/Hsp8sO+x17UkuIvkogNSYJC/Yy36yjJXrVzLiIwCM+Agr1688LIhoT3IRyUcBpMYkecHue7Sv6HHtSS4i+aS5kFAiZC7MSczCymQexY5roZ+IRFEAqUFJXbBbrTUyiLRaa+zfLSL1T11YTaxnXk9Zx0VEsikDaWK3/NUtQDDmMeIjtForPfN6XjsuIlKIVqKLiIhWoouISHIUQEREpCIKIA1MVXRFJE4aRG9QuVV0M0UZAa3pEJGqUAbSoGqtKKOINB4FkAbUv7GfweHByNdURVdEqiWVAGJmXzCz35jZk2Z2j5m9Ps95A2a20cweN7NY5+UmOV4Q53dluq7yURVdEamWtDKQB4BT3P3Pgd8C1xQ4953ufmq585PLkeQmTnF/V1TXVYaq6IpINaUSQNz9/nBPdICHgelptCMjyfGCan1XviymUBeVquiKSDXVwiysjwB353nNgfvNzIGvu3t0/XHAzHqAHoCOjvK6aZLcxKka31VohlXH5I7I8Y8Zk2coeIhIVcWWgZjZz8xsU8RtcdY5K4ADQL7+mzPc/S3AucDlZnZmvu9z9z5373L3rvb29rLamuQmTtX4rkJZjDaAEpGkxBZA3P1d7n5KxO1HAGZ2CfAeoNvzFORy953h/W7gHmB+HG1N8qJbje8qlMVoAygRSUoqXVhmthD4NHCWu0eO+JrZJKDF3feGj88Bro+jPUlu4lSN78rXTZXJYrQBlIgkIZVqvGa2FTgCeCE89LC7X2pmJwDfcPdFZvZGgqwDgkD3HXcv6Wd6o1fjzR0DgSCLUaYhIpWqpBpvKhmIu/9pnuPPAovCx9uAuUm2q14kmTGJiOSj/UBERET7gYiISHIUQEREpCIKICIiUhEFEBERqYgCiIiIVEQBREREKqIAIiIiFVEASUmSG1iJiMShFsq5N51C5di1mlxE6oUykBQkuYGViEhcFEBSkOQGViIicVEASUGSG1iJiMRFAaSAuAa6tWugiDQCBZA8MgPdg8ODOP7aQHc1goh2DRSRRpDWhlKfBf4LsCc89Bl3XxNx3kLgK0ArwUZTnyvl86tRzr3zps7IXf9mTJ7BwPKBMX22iEitqZsNpUJfdvcb871oZq3AzcC7gR3AOjNb7e6/TqJxGugWESmslruw5gNb3X2bu+8HvgssTurLNdAtIlJYmgHkCjN70sxuM7NjIl6fBjyT9XxHeCySmfWY2XozW79nz558p5VMA90iIoXFFkDM7GdmtinithhYCfwJcCowBHxxrN/n7n3u3uXuXe3t7WP9OA10i4gUEdsYiLu/q5TzzOzvgR9HvLQTODHr+fTwWGK653QrYIiI5JFKF5aZHZ/19HxgU8Rp64BZZjbTzCYAFwCrk2ifiIgUl9YsrM+b2amAAwPAxwHM7ASC6bqL3P2AmV0B3Ecwjfc2d9+cUntFRCRHKgHE3S/Oc/xZYFHW8zXAqPUhIiKSvlqexlsXtK+HiDQr7QcyBtrXQ0SamTKQMdC+HiLSzBRAxkDlTkSkmSmAjIHKnYhIM1MAGQOVOxGRZqYAMgYqdyIizSyV/UDiVo39QEREmkkl+4EoAxERkYoogIiISEUUQEREpCIKICIiUhEFEBERqUhDzsIysz3AYAVvnQo8X+Xm1BP9/fr79fc3r5Pc/ahy3tCQxRTdvaI9bc1sfbnT2BqJ/n79/fr7m/vvL/c96sISEZGKKICIiEhFFEAO15d2A1Kmv7+56e9vbmX//Q05iC4iIvFTBiIiIhVRABERkYoogABmttDMnjKzrWZ2ddrtSZKZnWhmPzezX5vZZjO7Mu02pcHMWs3sMTP7cdptSZqZvd7Mvm9mvzGzLWb29rTblCQz+2T43/4mM7vLzI5Mu01xM7PbzGy3mW3KOvYGM3vAzJ4O748p9jlNH0DMrBW4GTgXmA1caGaz021Vog4An3L32cDpwOVN9vdnXAlsSbsRKfkK8FN3fxMwlyb652Bm04BPAF3ufgrQClyQbqsS8S1gYc6xq4G17j4LWBs+L6jpAwgwH9jq7tvcfT/wXWBxym1KjLsPufuG8PFegovHtHRblSwzmw78FfCNtNuSNDObDJwJfBPA3fe7+7+n21j2nJEAAAH3SURBVKrEjQMmmtk4oA14NuX2xM7dHwJezDm8GLgjfHwH8L5in6MAElwsn8l6voMmu4BmmFkncBrwSLotSdxNwKeBg2k3JAUzgT3A7WEX3jfMbFLajUqKu+8EbgS2A0PAsLvfn26rUnOsuw+Fj58Dji32BgUQAcDMXgf8AFju7r9Puz1JMbP3ALvd/dG025KSccBbgJXufhrwMiV0XTSKsJ9/MUEgPQGYZGYXpduq9HmwvqPoGg8FENgJnJj1fHp4rGmY2XiC4NHv7qvSbk/C3gG818wGCLov/6OZ3ZlukxK1A9jh7pms8/sEAaVZvAv4nbvvcfc/AquAv0i5TWnZZWbHA4T3u4u9QQEE1gGzzGymmU0gGEBbnXKbEmNmRtD/vcXdv5R2e5Lm7te4+3R37yT4d/+P7t40v0Dd/TngGTM7KTy0APh1ik1K2nbgdDNrC/9fWEATTSLIsRpYGj5eCvyo2BsashpvOdz9gJldAdxHMAPjNnffnHKzkvQO4GJgo5k9Hh77jLuvSbFNkqz/CvSHP6C2AR9OuT2JcfdHzOz7wAaCGYmP0QQlTczsLuBsYKqZ7QCuBT4HfM/MPkqwHcYHi36OSpmIiEgl1IUlIiIVUQAREZGKKICIiEhFFEBERKQiCiAiIlIRBRAREamIAoiIiFTk/wPXp80dMYl67AAAAABJRU5ErkJggg==\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "no of iterations: 20000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "no of iterations: 30000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "no of iterations: 40000\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([0.86019219]), array([2.42543209]))"
            ]
          },
          "metadata": {},
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#c) |x - x̂|⁴, Polynomial Regression"
      ],
      "metadata": {
        "id": "X8QjMgD9EVU0"
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "np.random.seed(42)\n",
        "X = np.random.rand(1000,1)\n",
        "y = 5*((X)**(2)) + np.random.rand(1000,1)\n",
        "\n",
        "#ynew = y[-50:] \n",
        "\n",
        "#print(xlen)\n",
        "#print(ylen)\n",
        "\n",
        "#ynewlen = len(ynew)\n",
        "#print(ynewlen)\n",
        "\n",
        "\n",
        "#print(x)\n",
        "#print(y)\n",
        "\n",
        "#plt.scatter(x, ynew)\n",
        "#plt.show\n",
        "\n",
        "\n",
        "def loss(y, y_hat):\n",
        "    loss = np.mean((y_hat - y)**4)\n",
        "    return loss\n",
        "\n",
        "\n",
        "def gradients(X, y, y_hat):\n",
        "    \n",
        "    # X --> Input.\n",
        "    # y --> true/target value.\n",
        "    # y_hat --> hypothesis\n",
        "    # w --> weights (parameter).\n",
        "    # b --> bias (parameter).\n",
        "    \n",
        "    # m-> number of training examples.\n",
        "    m = X.shape[0]\n",
        "    \n",
        "    # Gradient of loss w.r.t weights.\n",
        "    dw = (1/m)*np.dot(X.T, (y_hat - y))\n",
        "    \n",
        "    # Gradient of loss w.r.t bias.\n",
        "    db = (1/m)*np.sum((y_hat - y)) \n",
        "    \n",
        "    return dw, db\n",
        "\n",
        "def x_transform(X, degrees):\n",
        "    \n",
        "    \n",
        "    # degrees --> A list, We add X^(value) feature to the input\n",
        "    #             where value is one of the values in the list.\n",
        "    \n",
        "    \n",
        "    t = X.copy()\n",
        "    \n",
        "    # Appending columns of higher degrees to X.\n",
        "    for i in degrees:\n",
        "        X = np.append(X, t**i, axis=1)\n",
        "            \n",
        "    return X\n",
        "\n",
        "def train(X, y, bs, degrees, epochs, lr):\n",
        "    \n",
        "   \n",
        "    # bs --> Batch Size.\n",
        "    \n",
        "    # degrees --> A list, We add X^(value) feature to the input\n",
        "    #             where value is one of the values in the list.\n",
        "    \n",
        "    \n",
        "    # Adding features to input X.\n",
        "    x = x_transform(X, degrees)\n",
        "    \n",
        "    # m-> number of training examples\n",
        "    # n-> number of features \n",
        "    m, n = x.shape\n",
        "    \n",
        "    # Initializing weights and bias to zeros.\n",
        "    w = np.zeros((n,1))\n",
        "    b = 0\n",
        "    \n",
        "    \n",
        "    y = y.reshape(m,1)\n",
        "    \n",
        "    \n",
        "    losses = []\n",
        "    \n",
        "    # Training loop.\n",
        "    for epoch in range(epochs):\n",
        "        for i in range((m-1)//bs + 1):\n",
        "            \n",
        "            # Defining batches.\n",
        "            start_i = i*bs\n",
        "            end_i = start_i + bs\n",
        "            xb = x[start_i:end_i]\n",
        "            yb = y[start_i:end_i]\n",
        "            \n",
        "            # Calculating hypothesis\n",
        "            y_hat = np.dot(xb, w) + b\n",
        "            \n",
        "            \n",
        "            dw, db = gradients(xb, yb, y_hat)\n",
        "            \n",
        "            \n",
        "            w -= lr*dw\n",
        "            b -= lr*db\n",
        "        \n",
        "        \n",
        "        l = loss(y, np.dot(x, w) + b)\n",
        "        losses.append(l)\n",
        "        \n",
        "   \n",
        "    return w, b, losses\n",
        "\n",
        "\n",
        "# Predicting function.\n",
        "def predict(X, w, b, degrees):\n",
        "    \n",
        "    \n",
        "    # b --> bias (parameter).\n",
        "    #degrees --> A list, We add X^(value) feature to the input\n",
        "    #             where value is one of the values in the list.\n",
        "    \n",
        "    # Adding degrees to input X.\n",
        "    x1 = x_transform(X, degrees)\n",
        "    \n",
        "    \n",
        "    return np.dot(x1, w) + b\n",
        "\n",
        "\n",
        "w, b, l = train(X, y, bs=100, degrees=[2], epochs=1000,\n",
        "                lr=0.01)\n",
        "# Plotting\n",
        "fig = plt.figure(figsize=(8,6))\n",
        "plt.plot(X, y, 'y.')\n",
        "plt.plot(X, predict(X, w, b, [2]), 'r.')\n",
        "plt.legend([\"Data\", \"Polynomial predictions\"])\n",
        "plt.xlabel('X - Input')\n",
        "plt.ylabel('y - target / true')\n",
        "plt.title('Polynomial Regression')\n",
        "plt.show()\n",
        "\n",
        "\n",
        "plt.plot(l) "
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 669
        },
        "id": "xO7q6JPPEXjt",
        "outputId": "67a043a3-ea11-4fca-fb07-058500ee3254"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fd2d8c04c70>]"
            ]
          },
          "metadata": {},
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "np.random.seed(42)\n",
        "X = np.random.rand(1000,1)\n",
        "y = 5*((X)**(2)) + np.random.rand(1000,1)\n",
        "\n",
        "#ynew = y[-50:] \n",
        "\n",
        "#print(xlen)\n",
        "#print(ylen)\n",
        "\n",
        "#ynewlen = len(ynew)\n",
        "#print(ynewlen)\n",
        "\n",
        "\n",
        "#print(x)\n",
        "#print(y)\n",
        "\n",
        "#plt.scatter(x, ynew)\n",
        "#plt.show\n",
        "\n",
        "\n",
        "def loss(y, y_hat):\n",
        "    loss = np.mean((y_hat - y)**7)\n",
        "    return loss\n",
        "\n",
        "\n",
        "def gradients(X, y, y_hat):\n",
        "    \n",
        "    # X --> Input.\n",
        "    # y --> true/target value.\n",
        "    # y_hat --> hypothesis\n",
        "    # w --> weights (parameter).\n",
        "    # b --> bias (parameter).\n",
        "    \n",
        "    # m-> number of training examples.\n",
        "    m = X.shape[0]\n",
        "    \n",
        "    # Gradient of loss w.r.t weights.\n",
        "    dw = (1/m)*np.dot(X.T, (y_hat - y))\n",
        "    \n",
        "    # Gradient of loss w.r.t bias.\n",
        "    db = (1/m)*np.sum((y_hat - y)) \n",
        "    \n",
        "    return dw, db\n",
        "\n",
        "def x_transform(X, degrees):\n",
        "    \n",
        "    \n",
        "    # degrees --> A list, We add X^(value) feature to the input\n",
        "    #             where value is one of the values in the list.\n",
        "    \n",
        "    \n",
        "    t = X.copy()\n",
        "    \n",
        "    # Appending columns of higher degrees to X.\n",
        "    for i in degrees:\n",
        "        X = np.append(X, t**i, axis=1)\n",
        "            \n",
        "    return X\n",
        "\n",
        "def train(X, y, bs, degrees, epochs, lr):\n",
        "    \n",
        "   \n",
        "    # bs --> Batch Size.\n",
        "    \n",
        "    # degrees --> A list, We add X^(value) feature to the input\n",
        "    #             where value is one of the values in the list.\n",
        "    \n",
        "    \n",
        "    # Adding features to input X.\n",
        "    x = x_transform(X, degrees)\n",
        "    \n",
        "    # m-> number of training examples\n",
        "    # n-> number of features \n",
        "    m, n = x.shape\n",
        "    \n",
        "    # Initializing weights and bias to zeros.\n",
        "    w = np.zeros((n,1))\n",
        "    b = 0\n",
        "    \n",
        "    \n",
        "    y = y.reshape(m,1)\n",
        "    \n",
        "    \n",
        "    losses = []\n",
        "    \n",
        "    # Training loop.\n",
        "    for epoch in range(epochs):\n",
        "        for i in range((m-1)//bs + 1):\n",
        "            \n",
        "            # Defining batches.\n",
        "            start_i = i*bs\n",
        "            end_i = start_i + bs\n",
        "            xb = x[start_i:end_i]\n",
        "            yb = y[start_i:end_i]\n",
        "            \n",
        "            # Calculating hypothesis\n",
        "            y_hat = np.dot(xb, w) + b\n",
        "            \n",
        "            \n",
        "            dw, db = gradients(xb, yb, y_hat)\n",
        "            \n",
        "            \n",
        "            w -= lr*dw\n",
        "            b -= lr*db\n",
        "        \n",
        "        \n",
        "        l = loss(y, np.dot(x, w) + b)\n",
        "        losses.append(l)\n",
        "        \n",
        "   \n",
        "    return w, b, losses\n",
        "\n",
        "\n",
        "# Predicting function.\n",
        "def predict(X, w, b, degrees):\n",
        "    \n",
        "    \n",
        "    # b --> bias (parameter).\n",
        "    #degrees --> A list, We add X^(value) feature to the input\n",
        "    #             where value is one of the values in the list.\n",
        "    \n",
        "    # Adding degrees to input X.\n",
        "    x1 = x_transform(X, degrees)\n",
        "    \n",
        "    \n",
        "    return np.dot(x1, w) + b\n",
        "\n",
        "\n",
        "w, b, l = train(X, y, bs=100, degrees=[2], epochs=1000,\n",
        "                lr=0.01)\n",
        "# Plotting\n",
        "fig = plt.figure(figsize=(8,6))\n",
        "plt.plot(X, y, 'y.')\n",
        "plt.plot(X, predict(X, w, b, [2]), 'r.')\n",
        "plt.legend([\"Data\", \"Polynomial predictions\"])\n",
        "plt.xlabel('X - Input')\n",
        "plt.ylabel('y - target / true')\n",
        "plt.title('Polynomial Regression')\n",
        "plt.show()\n",
        "\n",
        "\n",
        "plt.plot(l)  "
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 669
        },
        "id": "rsfzN2QcEfaz",
        "outputId": "6cc412aa-4005-41c9-ab02-212059928dfe"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fd2d8c51fd0>]"
            ]
          },
          "metadata": {},
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}