Gradient_Descent_Intro.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Gradient Descent Intro",
      "provenance": [],
      "authorship_tag": "ABX9TyO8AuipF4B6vPsjyVJ2g0ur",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Lakshaypahuja21/Machine-Learning-Basics/blob/master/Gradient_Descent_Intro.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ndvtRbXs2f65"
      },
      "source": [
        "# Gradient Descent\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2MCYLhlK2a0b"
      },
      "source": [
        "## Self analysis"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e0KnJdNB2j_7"
      },
      "source": [
        "### lets say we have data for x and y. Find co-relation statement between them. (y=mx+c)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "In6IuW0j35IK"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wj3PP_9L4QaF"
      },
      "source": [
        "%matplotlib inline\n",
        "def gradient_descent(x,y):\n",
        "  m = b = 0\n",
        "  lr = 0.01 #learning rate or alpha ,  this will be hit and trial\n",
        "  n = len(x)\n",
        "  plt.scatter(x,y, color = 'red', marker='+', linewidth='5' )\n",
        "  for i in range(100):\n",
        "    yp = m*x + b # yp is y predicted value\n",
        "    plt.plot(x,yp , color = 'green')\n",
        "    cost = (1/n) * sum([val**2 for val in (y-yp)])\n",
        "    md = -(2/n)*sum(x*(y-yp))\n",
        "    yd = -(2/n)*sum(y-yp)\n",
        "    m = m - lr*md\n",
        "    b = b - lr*yd\n",
        "    print(\"m: {}, b: {} , cost: {}, iteration {}\".format(m,b,cost,i))"
      ],
      "execution_count": 70,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jd6AdA239UIY"
      },
      "source": [
        "x = np.array([1,2,3,4,5])\n",
        "y = np.array([5,7,9,11,13])\n",
        "#x = np.array([92,56,88,70,80,49,65,35,66,67])\n",
        "#y = np.array([98,68,81,80,83,52,66,30,68,73])"
      ],
      "execution_count": 71,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6bM8X-k96Cib",
        "outputId": "5ace301f-1971-4f6e-9202-6e3a5c7ef515",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "gradient_descent(x,y) # for learning rate 0.01"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "m: 0.62, b: 0.18 , cost: 89.0, iteration 0\n",
            "m: 1.0928, b: 0.3192 , cost: 52.25039999999999, iteration 1\n",
            "m: 1.453232, b: 0.42724799999999996 , cost: 30.831949440000002, iteration 2\n",
            "m: 1.7278860800000002, b: 0.5115091199999999 , cost: 18.347751350784, iteration 3\n",
            "m: 1.9370605952000002, b: 0.5776057727999999 , cost: 11.070010749324897, iteration 4\n",
            "m: 2.096250917888, b: 0.6298300216319999 , cost: 6.826353152519786, iteration 5\n",
            "m: 2.2172859146547204, b: 0.6714583661260799 , cost: 4.350826141683065, iteration 6\n",
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          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "73EOffkNIBdr",
        "outputId": "cc3fc690-51b0-4e92-818d-f2d54a0ba119",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        }
      },
      "source": [
        "%matplotlib inline\n",
        "def gradient_descent(x,y):\n",
        "  m = b = 0\n",
        "  lr = 0.08 #learning rate or alpha ,  this will be hit and trial\n",
        "  n = len(x)\n",
        "  plt.scatter(x,y, color = 'red', marker='+', linewidth='5' )\n",
        "  for i in range(100):\n",
        "    yp = m*x + b # yp is y predicted value\n",
        "    plt.plot(x,yp , color = 'green')\n",
        "    cost = (1/n) * sum([val**2 for val in (y-yp)])\n",
        "    md = -(2/n)*sum(x*(y-yp))\n",
        "    yd = -(2/n)*sum(y-yp)\n",
        "    m = m - lr*md\n",
        "    b = b - lr*yd\n",
        "    print(\"m: {}, b: {} , cost: {}, iteration {}\".format(m,b,cost,i))\n",
        "x = np.array([1,2,3,4,5])\n",
        "y = np.array([5,7,9,11,13])\n",
        "gradient_descent(x,y)"
      ],
      "execution_count": 94,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "m: 4.96, b: 1.44 , cost: 89.0, iteration 0\n",
            "m: 0.4991999999999983, b: 0.26879999999999993 , cost: 71.10560000000002, iteration 1\n",
            "m: 4.451584000000002, b: 1.426176000000001 , cost: 56.8297702400001, iteration 2\n",
            "m: 0.892231679999997, b: 0.5012275199999995 , cost: 45.43965675929613, iteration 3\n",
            "m: 4.041314713600002, b: 1.432759910400001 , cost: 36.35088701894832, iteration 4\n",
            "m: 1.2008760606719973, b: 0.7036872622079998 , cost: 29.097483330142282, iteration 5\n",
            "m: 3.7095643080294423, b: 1.4546767911321612 , cost: 23.307872849944438, iteration 6\n",
            "m: 1.4424862661541864, b: 0.881337636696883 , cost: 18.685758762535738, iteration 7\n",
            "m: 3.4406683721083144, b: 1.4879302070713722 , cost: 14.994867596913156, iteration 8\n",
            "m: 1.6308855378034224, b: 1.0383405553279617 , cost: 12.046787238456794, iteration 9\n",
            "m: 3.2221235247119777, b: 1.5293810083298451 , cost: 9.691269350698109, iteration 10\n",
            "m: 1.7770832372205707, b: 1.1780607551353204 , cost: 7.8084968312098315, iteration 11\n",
            "m: 3.0439475772474127, b: 1.5765710804477953 , cost: 6.302918117062937, iteration 12\n",
            "m: 1.8898457226770244, b: 1.3032248704973899 , cost: 5.098330841763168, iteration 13\n",
            "m: 2.898169312926714, b: 1.6275829443328358 , cost: 4.133961682056365, iteration 14\n",
            "m: 1.9761515088959358, b: 1.4160484030347593 , cost: 3.361340532576948, iteration 15\n",
            "m: 2.7784216197824048, b: 1.6809279342791488 , cost: 2.741808050753047, iteration 16\n",
            "m: 2.0415541605113807, b: 1.5183370872989306 , cost: 2.244528230107478, iteration 17\n",
            "m: 2.6796170361078637, b: 1.735457156285639 , cost: 1.8449036666988363, iteration 18\n",
            "m: 2.090471617540917, b: 1.611567833948162 , cost: 1.5233119201782324, iteration 19\n",
            "m: 2.5976890103737853, b: 1.790290604096816 , cost: 1.2640979056612756, iteration 20\n",
            "m: 2.1264168621494517, b: 1.6969533824619085 , cost: 1.0547704368105268, iteration 21\n",
            "m: 2.529385561184701, b: 1.8447607474362664 , cost: 0.8853615531285766, iteration 22\n",
            "m: 2.1521818147302194, b: 1.7754939584778073 , cost: 0.7479156468369821, iteration 23\n",
            "m: 2.472104720735685, b: 1.8983676540508527 , cost: 0.6360820885229722, iteration 24\n",
            "m: 2.1699839382964696, b: 1.8480185634495874 , cost: 0.5447903801652151, iteration 25\n",
            "m: 2.423763296438881, b: 1.950743302915348 , cost: 0.4699911136477278, iteration 26\n",
            "m: 2.1815831093070837, b: 1.9152179921582295 , cost: 0.4084494012702221, iteration 27\n",
            "m: 2.3826922006906663, b: 2.0016232209455125 , cost: 0.35758014655339476, iteration 28\n",
            "m: 2.1883747814212473, b: 1.9776712492627107 , cost: 0.31531667795040486, iteration 29\n",
            "m: 2.3475529664737507, b: 2.0508239542984783 , cost: 0.280005985849834, iteration 30\n",
            "m: 2.19146424741668, b: 2.0358666977033213 , cost: 0.2503251729489924, iteration 31\n",
            "m: 2.317271157065729, b: 2.0982251873107836 , cost: 0.2252148202231392, iteration 32\n",
            "m: 2.19172583072087, b: 2.0902190019495084 , cost: 0.2038258415569305, iteration 33\n",
            "m: 2.2909832477163747, b: 2.1437555628915694 , cost: 0.1854770944836773, iteration 34\n",
            "m: 2.1898500615476015, b: 2.1410827139250586 , cost: 0.16962156815305135, iteration 35\n",
            "m: 2.2679942505397945, b: 2.1873814501542004 , cost: 0.15581941113049289, iteration 36\n",
            "m: 2.1863812735157397, b: 2.188763177870427 , cost: 0.14371641365577967, iteration 37\n",
            "m: 2.247743906750233, b: 2.2290980581236037 , cost: 0.13302683968149862, iteration 38\n",
            "m: 2.181747562970493, b: 2.2335252935837153 , cost: 0.1235197278285518, iteration 39\n",
            "m: 2.2297797112222417, b: 2.268922416384484 , cost: 0.11500795886067308, iteration 40\n",
            "m: 2.176284659606544, b: 2.2756005683762908 , cost: 0.1073395295828815, iteration 41\n",
            "m: 2.213735385878407, b: 2.306887840824943 , cost: 0.10039058653754176, iteration 42\n",
            "m: 2.170254943136438, b: 2.315192801071317 , cost: 0.09405986334903649, iteration 43\n",
            "m: 2.1993136987020745, b: 2.3430395801944157 , cost: 0.08826423771269985, iteration 44\n",
            "m: 2.1638625904931037, b: 2.3524826719863134 , cost: 0.08293518155053264, iteration 45\n",
            "m: 2.1862727486718105, b: 2.3774314010318136 , cost: 0.07801592372722821, iteration 46\n",
            "m: 2.1572656385141533, b: 2.3876314575042543 , cost: 0.07345918129710392, iteration 47\n",
            "m: 2.1744150151272015, b: 2.4101229178167802 , cost: 0.06922534441882239, iteration 48\n",
            "m: 2.150585587951272, b: 2.4207840437050385 , cost: 0.06528102333197575, iteration 49\n",
            "m: 2.1635786121786147, b: 2.441177514495622 , cost: 0.06159788433500965, iteration 50\n",
            "m: 2.1439150477863547, b: 2.4520713783305874 , cost: 0.05815171649232756, iteration 51\n",
            "m: 2.153630302083688, b: 2.470660734860243 , cost: 0.054921682590988646, iteration 52\n",
            "m: 2.137323817683481, b: 2.4816124722824338 , cost: 0.05188971727120564, iteration 53\n",
            "m: 2.1444599118649865, b: 2.4986390442291735 , cost: 0.04904004275389065, iteration 54\n",
            "m: 2.1308637257526066, b: 2.509516039457312 , cost: 0.04635877856867898, iteration 55\n",
            "m: 2.1359758694885094, b: 2.525178884782891 , cost: 0.04383362645496491, iteration 56\n",
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            "m: 2.0405161418256377, b: 2.8536001910078013 , cost: 0.004120600119124239, iteration 99\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s2-02Cs8Kct-"
      },
      "source": [
        "## conclusion"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HVPhlGmvKfMl"
      },
      "source": [
        "### learing rate 0.08 is better than 0.01"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X5X5deOKKwqa"
      },
      "source": [
        "### statement -> y = 2.04*x + 2.8 \n",
        "### trial --> put = 5, you'll get y = 13 :)\n",
        "\n"
      ]
    }
  ]
}