Notebooks/04-Linear-Regression/linear_regression.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "uw1OnWCzU7JP"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cf11pD41YvE-"
      },
      "source": [
        "infections = [2, 5, 18, 28, 43, 61, 95, 139, 245, 388, 593, 978, 1501, 2336, 2922, 3513, 4747, 5823, 6566]"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AQhkqbkoY1p0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "outputId": "5b09663d-7e75-45fe-a86a-5d875ca64580"
      },
      "source": [
        "x = range(len(infections))\n",
        "t = np.log(infections)\n",
        "plt.plot(x, t, 'o' , color='black')"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7d1fff096770>]"
            ]
          },
          "metadata": {},
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pvq6oXHhw4g6"
      },
      "source": [
        "<p align=\"center\">In order to vectorize the derivation formula, we need to omit the for loop and see 't' and 'x' as a vector.</p>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0i_TkvNPY6i-"
      },
      "source": [
        "def update(x, t, w, b, alpha):\n",
        "  N = len(x)\n",
        "  dedw = 0\n",
        "  dedb = 0\n",
        "  y = np.dot(w, x) + b\n",
        "  dedw = np.sum(np.multiply((y - t), x))\n",
        "  dedb = np.sum(y - t)\n",
        "  w = w - (alpha/float(N)) * dedw;\n",
        "  b = b - (alpha/float(N)) * dedb;\n",
        "  return w, b"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cvqDyiXwY7JG"
      },
      "source": [
        "def train(x, t, w, b, alpha, epochs):\n",
        "  for e in range(epochs):\n",
        "    w, b = update(x, t, w, b, alpha)\n",
        "    if e % 1000 == 0 :\n",
        "      print(\"epoch \", e, \" loss: \", calc_cost(x, t, w, b))\n",
        "  return w, b\n"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1lfCYgMuY_tf"
      },
      "source": [
        "def calc_cost(x, t, w, b):\n",
        "  N = len(x)\n",
        "  err = 0\n",
        "  y = np.dot(w, x) + b\n",
        "  err += np.sum(np.multiply((y - t),(y - t)))#(y - t)**2\n",
        "  return err/float(2*N)"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8V3lQifzZBU-",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "32555e2a-3687-498b-ee43-26242a96143e"
      },
      "source": [
        "w = 10\n",
        "b = 10\n",
        "alpha = 0.01\n",
        "epochs = 100000\n",
        "w, b = train(x, t, w, b, alpha, epochs)\n",
        "print(w, b)"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "epoch  0  loss:  87.45189870677237\n",
            "epoch  1000  loss:  0.12089837954019314\n",
            "epoch  2000  loss:  0.08715608811023937\n",
            "epoch  3000  loss:  0.08700017973204525\n",
            "epoch  4000  loss:  0.08699945934758535\n",
            "epoch  5000  loss:  0.0869994560190037\n",
            "epoch  6000  loss:  0.08699945600362369\n",
            "epoch  7000  loss:  0.08699945600355265\n",
            "epoch  8000  loss:  0.08699945600355233\n",
            "epoch  9000  loss:  0.08699945600355237\n",
            "epoch  10000  loss:  0.08699945600355229\n",
            "epoch  11000  loss:  0.08699945600355226\n",
            "epoch  12000  loss:  0.08699945600355226\n",
            "epoch  13000  loss:  0.08699945600355234\n",
            "epoch  14000  loss:  0.08699945600355234\n",
            "epoch  15000  loss:  0.08699945600355234\n",
            "epoch  16000  loss:  0.08699945600355234\n",
            "epoch  17000  loss:  0.08699945600355234\n",
            "epoch  18000  loss:  0.08699945600355234\n",
            "epoch  19000  loss:  0.08699945600355234\n",
            "epoch  20000  loss:  0.08699945600355234\n",
            "epoch  21000  loss:  0.08699945600355234\n",
            "epoch  22000  loss:  0.08699945600355234\n",
            "epoch  23000  loss:  0.08699945600355234\n",
            "epoch  24000  loss:  0.08699945600355234\n",
            "epoch  25000  loss:  0.08699945600355234\n",
            "epoch  26000  loss:  0.08699945600355234\n",
            "epoch  27000  loss:  0.08699945600355234\n",
            "epoch  28000  loss:  0.08699945600355234\n",
            "epoch  29000  loss:  0.08699945600355234\n",
            "epoch  30000  loss:  0.08699945600355234\n",
            "epoch  31000  loss:  0.08699945600355234\n",
            "epoch  32000  loss:  0.08699945600355234\n",
            "epoch  33000  loss:  0.08699945600355234\n",
            "epoch  34000  loss:  0.08699945600355234\n",
            "epoch  35000  loss:  0.08699945600355234\n",
            "epoch  36000  loss:  0.08699945600355234\n",
            "epoch  37000  loss:  0.08699945600355234\n",
            "epoch  38000  loss:  0.08699945600355234\n",
            "epoch  39000  loss:  0.08699945600355234\n",
            "epoch  40000  loss:  0.08699945600355234\n",
            "epoch  41000  loss:  0.08699945600355234\n",
            "epoch  42000  loss:  0.08699945600355234\n",
            "epoch  43000  loss:  0.08699945600355234\n",
            "epoch  44000  loss:  0.08699945600355234\n",
            "epoch  45000  loss:  0.08699945600355234\n",
            "epoch  46000  loss:  0.08699945600355234\n",
            "epoch  47000  loss:  0.08699945600355234\n",
            "epoch  48000  loss:  0.08699945600355234\n",
            "epoch  49000  loss:  0.08699945600355234\n",
            "epoch  50000  loss:  0.08699945600355234\n",
            "epoch  51000  loss:  0.08699945600355234\n",
            "epoch  52000  loss:  0.08699945600355234\n",
            "epoch  53000  loss:  0.08699945600355234\n",
            "epoch  54000  loss:  0.08699945600355234\n",
            "epoch  55000  loss:  0.08699945600355234\n",
            "epoch  56000  loss:  0.08699945600355234\n",
            "epoch  57000  loss:  0.08699945600355234\n",
            "epoch  58000  loss:  0.08699945600355234\n",
            "epoch  59000  loss:  0.08699945600355234\n",
            "epoch  60000  loss:  0.08699945600355234\n",
            "epoch  61000  loss:  0.08699945600355234\n",
            "epoch  62000  loss:  0.08699945600355234\n",
            "epoch  63000  loss:  0.08699945600355234\n",
            "epoch  64000  loss:  0.08699945600355234\n",
            "epoch  65000  loss:  0.08699945600355234\n",
            "epoch  66000  loss:  0.08699945600355234\n",
            "epoch  67000  loss:  0.08699945600355234\n",
            "epoch  68000  loss:  0.08699945600355234\n",
            "epoch  69000  loss:  0.08699945600355234\n",
            "epoch  70000  loss:  0.08699945600355234\n",
            "epoch  71000  loss:  0.08699945600355234\n",
            "epoch  72000  loss:  0.08699945600355234\n",
            "epoch  73000  loss:  0.08699945600355234\n",
            "epoch  74000  loss:  0.08699945600355234\n",
            "epoch  75000  loss:  0.08699945600355234\n",
            "epoch  76000  loss:  0.08699945600355234\n",
            "epoch  77000  loss:  0.08699945600355234\n",
            "epoch  78000  loss:  0.08699945600355234\n",
            "epoch  79000  loss:  0.08699945600355234\n",
            "epoch  80000  loss:  0.08699945600355234\n",
            "epoch  81000  loss:  0.08699945600355234\n",
            "epoch  82000  loss:  0.08699945600355234\n",
            "epoch  83000  loss:  0.08699945600355234\n",
            "epoch  84000  loss:  0.08699945600355234\n",
            "epoch  85000  loss:  0.08699945600355234\n",
            "epoch  86000  loss:  0.08699945600355234\n",
            "epoch  87000  loss:  0.08699945600355234\n",
            "epoch  88000  loss:  0.08699945600355234\n",
            "epoch  89000  loss:  0.08699945600355234\n",
            "epoch  90000  loss:  0.08699945600355234\n",
            "epoch  91000  loss:  0.08699945600355234\n",
            "epoch  92000  loss:  0.08699945600355234\n",
            "epoch  93000  loss:  0.08699945600355234\n",
            "epoch  94000  loss:  0.08699945600355234\n",
            "epoch  95000  loss:  0.08699945600355234\n",
            "epoch  96000  loss:  0.08699945600355234\n",
            "epoch  97000  loss:  0.08699945600355234\n",
            "epoch  98000  loss:  0.08699945600355234\n",
            "epoch  99000  loss:  0.08699945600355234\n",
            "0.43176758262177384 1.7855330350078404\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JBnaVFjgzzB8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 452
        },
        "outputId": "3154df44-8027-47e7-d9c3-e5f4cc542277"
      },
      "source": [
        "plt.plot(x, t, 'o', color='black')\n",
        "yy = np.dot(x, w) + b\n",
        "plt.plot(x, yy)"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7d1ffcc6a080>]"
            ]
          },
          "metadata": {},
          "execution_count": 27
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S289dp5y0osi"
      },
      "source": [],
      "execution_count": 8,
      "outputs": []
    }
  ]
}