BankNatchapol/onevar-linear-regression.ipynb

## onevar-linear-regression.ipynb
{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "OneVar-Linear-Regression.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyOsM8uirjtv1hqO/WON+DbD",
      "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/gist/BankNatchapol/09de0637460f8abec11af42a6b286bd3/onevar-linear-regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "09a37j0BW3ml",
        "colab_type": "text"
      },
      "source": [
        "#**One Variable Linear Regression**\n",
        "---\n",
        "*One variable linear regression* คือ โมเดลทางสถิติที่สามารถบอกถึงความสัมพันธ์ ของตัวแปลต้น 1 ตัวและตัวแปรตามได้ <br><br> \n",
        "ซึ่ง linear regression สามารถเขียน **hypothesis function** ได้ว่า <br><br>\n",
        "\\begin{equation}\n",
        "h_\\theta (x) = \\theta _0 + \\theta _1x\n",
        "\\end{equation} <br><br> \n",
        "และ **cost function** หรือ loss function ได้ว่า <br><br> \n",
        "\\begin{equation}\n",
        "J(\\theta_0,\\theta_1) = \\frac{1}{2m}\\sum^m_{i=1}(h_\\theta(x^{(i)}) - y^{(i)})^2\n",
        "\\end{equation}<br><br>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-loiVnCEZAYZ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np # For calculation \n",
        "import matplotlib.pyplot as plt # For plot \n",
        "\n",
        "def costFunction(s0,s1,m): # Function that return cost \n",
        "  '''\n",
        "    s0: seta#0\n",
        "    s1: seta#1\n",
        "    m: the number of members in array\n",
        "  '''\n",
        "  diff = s0 + s1*x - y\n",
        "  summa = sum(map(lambda x:x**2,diff))\n",
        "  return (1/(2*m))*summa"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XAMMJhEviJkG",
        "colab_type": "text"
      },
      "source": [
        "##**Hyperparameters**\n",
        "ในส่วนของ parameter ที่เราจำเป็นต้องกำหนดค่านั้นจะมีอยู่ 2 ตัวด้วยกัน <br>\n",
        ">1. initial point หรือค่า $\\theta_j$ เริ่มต้น\n",
        ">2. learning rate หรือค่า $\\alpha$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Uwbvl5hRp6Tl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "s0 = 0\n",
        "s1 = 0\n",
        "alpha = 0.05 # learning rate"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JEItxhZsqs3j",
        "colab_type": "text"
      },
      "source": [
        "ในการที่จะ ปรับค่า $\\theta_j$ ให้เป็นค่าที่ทำให้ hypothesis function สามารถประมาณค่า output ได้ และ ทำให้ cost function มีค่าน้อยที่สุด สามารถทำได้โดยใช้ **Gradient Descent Algorithm**<br>\n",
        ">while (! convergence) {<br>\n",
        "$\\;\\;\\;\\;\\;\\;\\;\\theta_j:=\\theta_j - \\alpha\\frac{\\partial}{\\partial\\theta_j}J(\\theta_0,\\theta_1)$<br>\n",
        "}"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-Dtj_DKJxse1",
        "colab_type": "code",
        "outputId": "e9b7e33a-98e4-48b2-c70b-31801c6394fe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        }
      },
      "source": [
        "x = np.array([3,1,0,4,10,5,3,4,8,7,5,1,5,4,6]) #input array \n",
        "y = np.array([2,2,1,3,6,4,3,4,5,5,4,1,5,3,5]) #result array\n",
        "plt.scatter(x,y)\n",
        "plt.title('x,y')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'x,y')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 50
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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nqmfpB9sjtu+3/TXbj9j+5apnKpvtt7R/X3/F9n22n1P1TEWz/UHbZ2x/5Zy1n7H9Gdv/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\nRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1fUzjXBRgkC2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "m = len(x)\n",
        "dif = s0 + s1*x -  y\n",
        "gradient0 = sum(dif)/m\n",
        "gradient1 = sum(dif*x)/m"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IRCvHqpbusru",
        "colab_type": "text"
      },
      "source": [
        "ซึ่งสามารถเขียนย่อยออกมาเป็นสมการได้ว่า<br>\n",
        ">while (! convergence) {<br>\n",
        "$\\;\\;\\;\\;\\;\\;\\;\\theta_0:=\\theta_0-\\alpha\\frac{1}{m}\\sum^m_{i=1}(\\theta_0+\\theta_1x^{(i)}-y^{(i)})$<br>\n",
        "$\\;\\;\\;\\;\\;\\;\\;\\theta_1:=\\theta_1-\\alpha\\frac{1}{m}\\sum^m_{i=1}(\\theta_0+\\theta_1x^{(i)}-y^{(i)})x^{(i)}$<br>\n",
        "}"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kqph2vKfaTAV",
        "colab_type": "code",
        "outputId": "e814694b-9ac0-4edf-e417-6256e4b4f5a8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "costLog = []\n",
        "for i in range(1000): # Learning\n",
        "   diff = s0 + s1*x - y\n",
        "   gradient0 = sum(diff)/m\n",
        "   gradient1 = sum(diff*x)/m\n",
        "   s0 = s0 - alpha*gradient0\n",
        "   s1 = s1 - alpha*gradient1\n",
        "   costLog.append(costFunction(s0,s1,m))\n",
        "   \n",
        "print(f's0 = {s0}\\ns1 = {s1}')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "s0 = 1.16010175007572\n",
            "s1 = 0.5393706290173826\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fx05IQVlx5JL",
        "colab_type": "text"
      },
      "source": [
        "เมื่อดูค่า cost ในแต่ละการ update จะพบว่า ค่าcost จะลดลงเรื่อยๆจนเข้าใกล้ 0"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XFDia-41jImV",
        "colab_type": "code",
        "outputId": "e25412c3-8b2f-4ea3-bee5-b761de46e38f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "plt.plot(range(len(costLog)),costLog);\n",
        "plt.title('Cost is converging');"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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MyhoKdEnzJa2U1Cvpot2M+11JIal7+Eoc8Bq+y8XMrNKggS6pHbgcOAOYByySNK9i3IHA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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o_YoSxUOhk3-",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "para = np.array([[s0,s1]]).T\n",
        "domain = np.array([[1]*12,range(12)]).T\n",
        "result = np.dot(domain[:12],para)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xefRlPWnxUJI",
        "colab_type": "text"
      },
      "source": [
        "เมื่อนำสัมประสิทธิ์ $\\theta_0$ และ $\\theta_1$ มาแทนใน hypothesis function และ plot ออกมาก็จะได้ผลลัพท์ของ linear regression"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ky3cGiTOfjNb",
        "colab_type": "code",
        "outputId": "a530c313-1838-49de-f14e-1bfbec455f50",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "plt.scatter(x,y)\n",
        "plt.plot(range(12),result)\n",
        "plt.title('Linear Regression');"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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gjhcXMWvRZvp2aM6frh3EwPRWQccSkQhTUceh8nLnyblr+dWsfA6VlfN/I/vy\nzXO6k5RQo/OXRCROqKjjTP7mIibkLOSTdYWc3astU6/MpGubpkHHEpEoUlHHiQMlZfzhrRU8NGcl\nzRsn8puvnsqVA0/s1G8RiS8q6jjw4crtTJqZx+rt+xgzKI3Jo/rTumnDoGOJSC1RUcewXfsOce+r\nS3h2/ga6tmnCEzcP5ezeJzc+h4jEHxV1DHJ3XvzvRu56aTG7i0v47vk9+eHw3hqfQ6SeUlHHmHU7\n9jMpN8R7y7dzWpcUnhiTRb+OLYKOJSIBUlHHiNKych55fzW/fWMZiQ0acOflA7j2jK4kaHwOkXpP\nRR0DFm4oZPzzIRZv2sNF/dtz1xUD6Ngyueoniki9oKIO0L6Dpdz32jIe+3A1bZs14qFrBzMyU+Nz\niMj/UlEH5K2lW/h57iI27i7m2qFdGTcygxYan0NEjkJFXcu2Fh3gzpcW88rCTfRp34znvj2MwV1b\nBx1LRGKYirqWlJc7//jPeqb9awkHS8v56cV9GHtuTxomanwOETk+FXUtWLG1iIk5efx7zU6G9WjD\n1Csz6ZHaLOhYIhInVNRRdLC0jAffXsmf3llJk0YJ/OrLp/CVwZ01PoeI1IiKOkrmrtrBxJkhVm7b\nx+jTOjH5sv60bdYo6FgiEodU1BG2e38Jv5i1hKf/vZ7OrZJ5/KYhnNcnNehYIhLHVNQR4u68vHAT\nd760mF37D3HLuT249Qu9adJQb7GInJwqW8TMugB/A9oDDsxw9weiHSyachcUMH12PhsLi+mUksy4\nERmMHph2wq+3Ydd+fp6bx9v528hKa8lj3zidzLSWEUxcM5FePhEJVnVW90qB29z9EzNrDsw3s9fd\nfXGUs0VF7oICJuSEKC4pA6CgsJgJOSGAGpdZaVk5j324hvteW4YZ3H5Zf244s1ug43NEcvlEJDZU\neRCvu29y90/C3xcBS4C4/Y2fPjv/sxI7rLikjOmz82v0OnkFu7nywQ+555UlDOvZhtd/ch43nd09\n8EGUIrV8IhI7arQB1cy6AQOBuUe5bywwFiA9PT0C0aJjY2FxjaYfaf+hUu5/YzmPvL+aVk0a8oev\nD2RUVseYOeTuZJdPRGJPtYvazJoBzwM/cvc9R97v7jOAGQDZ2dkesYQR1iklmYKjlFanlKpHq3sn\nfyuTc/PYsKuYq4ekM35kX1o2ia3xOU5m+UQkNlXr/GUzS6KipJ9095zoRoqucSMySD7iSinJSQmM\nG5FxzOdsKzrID59ewI2P/odGiQ145pZhTBuTFXMlDSe2fCIS26pz1IcBjwBL3P030Y8UXYd3qFXn\nqAh359l5G5j66hKKD5Xxo3YHUi4AAAfHSURBVC/05jvn96RRYuxeEqsmyyci8cHcj7+VwszOBt4D\nQkB5ePJEd3/1WM/Jzs72efPmRSxkEFZt28vEmSE+XrWTId1ac++YTHq1ax50LBGpo8xsvrtnH+2+\nKteo3f19IDb2lNWCQ6XlPDxnJb9/ewWNEhswbUwWX8vuQgNdEktEAqLT5iqZv3Yn458PsXzrXkad\n0pEpX+xPu+aNg44lIvWcihrYc6CEX81ayhMfr6NTy8Y8ckM2w/u1DzqWiAhQz4va3ZmVt5kpLy5i\n+96D3Hx2d35yUR+aNqrXb4uIxJh620gbC4u5/YVFvLFkC/07tuAvN2RzSueUoGOJiHxOvSvqsnLn\n7x+tYfrsfMrcmXhpX246qzuJCboklojEpnpV1Es27WF8Toj/ri/k3D6pTB2dSZfWTYKOJSJyXPWi\nqA+UlPHAm8v587uraJmcxANXncblp3aKmfE5RESOp84X9fvLtzMpN8TaHfv5yuDOTLy0H62aNgw6\nlohItdXZot6x9yBTX1lCzoICurdtylPfGsqZPdsGHUtEpMbqXFG7OzmfFHDPK4spOlDKDy7sxfcu\n6EXjpNgdn0NE5HjqVFGv2b6PSbkhPlixg0HpKUwbcwoZHTQ+h4jEtzpR1CVl5fz5vVU88MZyGiY0\n4O7RmVwzJF3jc4hInRD3Rb1g3S4m5IRYurmIkQM6cMflA+jQUuNziEjdEbdFXXSghF/PzudvH6+l\nffPGzLhuMBcP6BB0LBGRiIvLon5t0WZuf2ERW4oOcMOwbtx2cR+aN469q62IiERCXBX15t0HuOPF\nRcxatJm+HZrzp2sHMTC9VdCxRESiKi6KurzcefLf6/jVv5ZyqKycn43M4Fvn9CBJ43OISD0Q80W9\nbEsRE3JCzF+7i7N6tWHq6Cy6tW0adCwRkVoTs0V9oKSMP769gofmrKRZo0Tu+8qpjBmUpvE5RKTe\nicmi/nDldibNzGP19n2MGZTG5FH9aa3xOUSknoqpot617xD3vrqEZ+dvIL11E564eShn99b4HCJS\nv8VMUe/eX8JFv53Drv0lfOf8nvzwwt4kN9T4HCIiMVPULZsk8a1zenBun1T6dWwRdBwRkZgRM0UN\ncMt5PYOOICISc6osajP7K3AZsNXdM6MVJHdBAdNn57OxsJhOKcmMG5HB6IFpcT8vEZGTVZ0zRh4D\nRkYzRO6CAibkhCgoLMaBgsJiJuSEyF1QENfzEhGJhCqL2t3fBXZGM8T02fkUl5T9z7TikjKmz86P\n63mJiERCxM7BNrOxZjbPzOZt27atRs/dWFhco+knozbnJSISCREranef4e7Z7p6dmppao+d2Skmu\n0fSTUZvzEhGJhJgY1WjciAySj7imYXJSAuNGZMT1vEREIiEmDs87fMRFbRyJUZvzEhGJBHP34z/A\n7GngfKAtsAWY4u6PHO852dnZPm/evEhlFBGp88xsvrtnH+2+Kteo3f3qyEcSEZHqiolt1CIicmwq\nahGRGKeiFhGJcSpqEZEYV+VRHyf0ombbgLUn+PS2wPYIxoklWrb4VZeXT8sWG7q6+1HPFoxKUZ8M\nM5t3rENU4p2WLX7V5eXTssU+bfoQEYlxKmoRkRgXi0U9I+gAUaRli191efm0bDEu5rZRi4jI/4rF\nNWoREalERS0iEuNipqjNbKSZ5ZvZCjMbH3SeSDKzLmb2tpktNrNFZnZr0JkizcwSzGyBmb0cdJZI\nMrMUM3vOzJaa2RIzGxZ0pkgysx+HfybzzOxpM2scdKYTZWZ/NbOtZpZXaVprM3vdzJaH/20VZMYT\nFRNFbWYJwB+BS4D+wNVm1j/YVBFVCtzm7v2BM4Dv1bHlA7gVWBJ0iCh4AJjl7n2BU6lDy2hmacAP\ngWx3zwQSgKuCTXVSHuPzF+IeD7zp7r2BN8O3405MFDUwBFjh7qvc/RDwD+CKgDNFjLtvcvdPwt8X\nUfHLXmeuVGBmnYFRwF+CzhJJZtYSOBd4BMDdD7l7YbCpIi4RSDazRKAJsDHgPCfsGBfivgJ4PPz9\n48DoWg0VIbFS1GnA+kq3N1CHiqwyM+sGDATmBpskou4HfgaUBx0kwroD24BHw5t1/mJmTYMOFSnu\nXgD8GlgHbAJ2u/trwaaKuPbuvin8/WagfZBhTlSsFHW9YGbNgOeBH7n7nqDzRIKZXQZsdff5QWeJ\ngkRgEPAndx8I7CNO/3Q+mvD22iuo+EDqBDQ1s2uDTRU9XnEsclwejxwrRV0AdKl0u3N4Wp1hZklU\nlPST7p4TdJ4IOgu43MzWULHJ6kIzeyLYSBGzAdjg7of/+nmOiuKuK74ArHb3be5eAuQAZwacKdK2\nmFlHgPC/WwPOc0Jipaj/A/Q2s+5m1pCKHRovBpwpYszMqNjOucTdfxN0nkhy9wnu3tndu1Hx//aW\nu9eJtTJ33wysN7PDl6gfDiwOMFKkrQPOMLMm4Z/R4dShnaVhLwI3hL+/AXghwCwnLCauQu7upWb2\nfWA2FXue/+ruiwKOFUlnAdcBITP7NDxtoru/GmAmqZ4fAE+GVyBWAd8IOE/EuPtcM3sO+ISKI5MW\nEMenXFe+ELeZbQCmAL8AnjGzm6kYevmrwSU8cTqFXEQkxsXKpg8RETkGFbWISIxTUYuIxDgVtYhI\njFNRi4jEOBW1iEiMU1GLiMS4/wfL/OR6OaYrZgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}