{
  "cells": [
    {
      "cell_type": "markdown",
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        "<a href=\"https://colab.research.google.com/gist/mattbullen/e6f91c776ab3ffca8f165c98f2de7fba/unit08-ex4-gradient_descent_cost_function.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2nUaq79P2PSd"
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      "source": [
        "## Calculating cost with gradient descent and learning rate\n",
        "- Change the iteration and learning rate vaules and see the impact on cost.\n",
        "- Low iteration values with high learning rate (i.e. big steps) may lead to miss the global minimum\n",
        "- Goal is to reach minimum cost with minimum iteration"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fS49cDDW2PSe"
      },
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      "source": [
        "# code credit:codebasics https://codebasics.io/coming-soon\n",
        "\n",
        "import numpy as np\n",
        "\n",
        "def gradient_descent(x,y):\n",
        "    m_curr = b_curr = 0\n",
        "    iterations = 100       #change value\n",
        "    n = len(x)\n",
        "    learning_rate = 0.08   #change value\n",
        "\n",
        "    for i in range(iterations):\n",
        "        y_predicted = m_curr * x + b_curr\n",
        "        cost = (1/n) * sum([val**2 for val in (y-y_predicted)])\n",
        "        md = -(2/n)*sum(x*(y-y_predicted))\n",
        "        bd = -(2/n)*sum(y-y_predicted)\n",
        "        m_curr = m_curr - learning_rate * md\n",
        "        b_curr = b_curr - learning_rate * bd\n",
        "        print (\"m {}, b {}, cost {} iteration {}\".format(m_curr,b_curr,cost, i))\n",
        "\n",
        "x = np.array([1,2,3,4,5])\n",
        "y = np.array([5,7,9,11,13])\n",
        "\n",
        "gradient_descent(x,y)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZM_oaGzK2PSf"
      },
      "outputs": [],
      "source": []
    }
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