minimizing_cost_linear_regression.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "minimizing-cost-linear-regression.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "Minimizing cost"
      ],
      "metadata": {
        "id": "rRypd2AItMQ1"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "tSKeTn7QtCjU"
      },
      "outputs": [],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "import torch.optim as optim"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x_train = torch.FloatTensor([[1], [2], [3]])\n",
        "y_train = torch.FloatTensor([[1], [2], [3]])\n"
      ],
      "metadata": {
        "id": "U83YKwk2tUpC"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Data\n",
        "plt.scatter(x_train, y_train)\n",
        "# Best-fit line\n",
        "xs = np.linspace(1, 3, 1000)\n",
        "plt.plot(xs, xs)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "loZIGpictsva",
        "outputId": "2794972c-d1f1-4a5b-c61f-b270fa5fe47b"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fd992f3a990>]"
            ]
          },
          "metadata": {},
          "execution_count": 11
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "W_l = np.linspace(-5, 7, 1000)\n",
        "cost_l = []\n",
        "for W in W_l:\n",
        "    hypothesis = W * x_train\n",
        "    cost = torch.mean((hypothesis - y_train) ** 2)\n",
        "\n",
        "    cost_l.append(cost.item())"
      ],
      "metadata": {
        "id": "TWjjAEjzvDoT"
      },
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(W_l, cost_l)\n",
        "plt.xlabel('$W$')\n",
        "plt.ylabel('Cost')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        },
        "id": "ce97_5C5vh2h",
        "outputId": "d2c12ac8-8f74-4912-d836-e149cd0bb91e"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "W = 0\n"
      ],
      "metadata": {
        "id": "wzez-lWYwATZ"
      },
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "gradient = torch.sum((W * x_train - y_train) * x_train)\n",
        "print(gradient)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eQCM1U3rwEDq",
        "outputId": "a8259273-71b9-4194-af4d-8ce23f887910"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor(-14.)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "lr = 0.1\n",
        "W -= lr * gradient\n",
        "print(W)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-vQuW8NCwiFE",
        "outputId": "0910df3a-23a2-4a1f-bdb2-b58b02874cb4"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor(1.4000)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x_train = torch.FloatTensor([[1], [2], [3]])\n",
        "y_train = torch.FloatTensor([[1], [2], [3]])\n",
        "\n",
        "W = torch.zeros(1)\n",
        "lr = 0.1\n",
        "\n",
        "nb_epochs = 10\n",
        "for epoch in range(nb_epochs + 1):\n",
        "    hypothesis = x_train * W\n",
        "    cost = torch.mean((hypothesis - y_train) ** 2)\n",
        "    gradient = torch.sum((W * x_train - y_train) * x_train)\n",
        "\n",
        "    print('Epoch {:4d}/{} W: {:.3f}, Cost: {:.6f}'.format(\n",
        "        epoch, nb_epochs, W.item(), cost.item()\n",
        "    ))\n",
        "\n",
        "    W -= lr * gradient"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8ym8-w5vxSG4",
        "outputId": "468555a6-86e2-4e39-c012-5fcc44003f5b"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch    0/10 W: 0.000, Cost: 4.666667\n",
            "Epoch    1/10 W: 1.400, Cost: 0.746666\n",
            "Epoch    2/10 W: 0.840, Cost: 0.119467\n",
            "Epoch    3/10 W: 1.064, Cost: 0.019115\n",
            "Epoch    4/10 W: 0.974, Cost: 0.003058\n",
            "Epoch    5/10 W: 1.010, Cost: 0.000489\n",
            "Epoch    6/10 W: 0.996, Cost: 0.000078\n",
            "Epoch    7/10 W: 1.002, Cost: 0.000013\n",
            "Epoch    8/10 W: 0.999, Cost: 0.000002\n",
            "Epoch    9/10 W: 1.000, Cost: 0.000000\n",
            "Epoch   10/10 W: 1.000, Cost: 0.000000\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x_train = torch.FloatTensor([[1], [2], [3]])\n",
        "y_train = torch.FloatTensor([[1], [2], [3]])\n",
        "# model initialization\n",
        "W = torch.zeros(1, requires_grad=True)\n",
        "optimizer = optim.SGD([W], lr=0.15)\n",
        "\n",
        "nb_epochs = 10\n",
        "for epoch in range(nb_epochs + 1):\n",
        "    # calculate H(x)\n",
        "    hypothesis = x_train * W\n",
        "\n",
        "    cost = torch.mean((hypothesis - y_train) ** 2)\n",
        "    print('Epoch {:4d}/{} W: {:.3f} Cost: {:.6f}'.format(\n",
        "        epoch, nb_epochs, W.item(), cost.item()\n",
        "    ))\n",
        "\n",
        "    # improve H(x) by cost gradient\n",
        "    optimizer.zero_grad()\n",
        "    cost.backward()\n",
        "    optimizer.step()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ExmD3HOv9C4W",
        "outputId": "c481fd4f-9d8a-420c-9fb1-b161a33e9ccf"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch    0/10 W: 0.000 Cost: 4.666667\n",
            "Epoch    1/10 W: 1.400 Cost: 0.746667\n",
            "Epoch    2/10 W: 0.840 Cost: 0.119467\n",
            "Epoch    3/10 W: 1.064 Cost: 0.019115\n",
            "Epoch    4/10 W: 0.974 Cost: 0.003058\n",
            "Epoch    5/10 W: 1.010 Cost: 0.000489\n",
            "Epoch    6/10 W: 0.996 Cost: 0.000078\n",
            "Epoch    7/10 W: 1.002 Cost: 0.000013\n",
            "Epoch    8/10 W: 0.999 Cost: 0.000002\n",
            "Epoch    9/10 W: 1.000 Cost: 0.000000\n",
            "Epoch   10/10 W: 1.000 Cost: 0.000000\n"
          ]
        }
      ]
    }
  ]
}