03_logistic_regression.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "03-logistic-regression.ipynb",
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8.5"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/pradeepkc11/mpl_tutorial/blob/master/03_logistic_regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o_xViEWvfTTV"
      },
      "source": [
        "# Imports\n",
        "import torch\n",
        "import torchvision\n",
        "from torchvision.datasets import MNIST"
      ],
      "execution_count": 75,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q1Skz7dlfTTV"
      },
      "source": [
        "# Download training dataset\n",
        "dataset = MNIST(root='data/', download=True)"
      ],
      "execution_count": 76,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Koi-fVbAfTTV"
      },
      "source": [
        "When this statement is executed for the first time, it downloads the data to the `data/` directory next to the notebook and creates a PyTorch `Dataset`. On subsequent executions, the download is skipped as the data is already downloaded. Let's check the size of the dataset."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "W9mWyKqAfTTV",
        "outputId": "2f5859fe-4dde-4500-8aa6-589365e08df8"
      },
      "source": [
        "len(dataset)"
      ],
      "execution_count": 77,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "60000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 77
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6pRKB16NfTTW"
      },
      "source": [
        "The dataset has 60,000 images that we'll use to train the model. There is also an additional test set of 10,000 images used for evaluating models and reporting metrics in papers and reports. We can create the test dataset using the `MNIST` class by passing `train=False` to the constructor."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zLqZQOlWfTTW",
        "outputId": "a390ec06-8aee-454d-e302-fddc69ee5177"
      },
      "source": [
        "test_dataset = MNIST(root='data/', train=False)\n",
        "len(test_dataset)"
      ],
      "execution_count": 78,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10000"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 78
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bgJru-f7fTTW"
      },
      "source": [
        "Let's look at a sample element from the training dataset."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4ZmSZeFGfTTW",
        "outputId": "6340f8b3-8f82-4c9f-bf92-292acd512644"
      },
      "source": [
        "dataset[0]"
      ],
      "execution_count": 79,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(<PIL.Image.Image image mode=L size=28x28 at 0x7F3D173FAED0>, 5)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 79
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2oBdGAc4fTTX"
      },
      "source": [
        "It's a pair, consisting of a 28x28px image and a label. The image is an object of the class `PIL.Image.Image`, which is a part of the Python imaging library [Pillow](https://pillow.readthedocs.io/en/stable/). We can view the image within Jupyter using [`matplotlib`](https://matplotlib.org/), the de-facto plotting and graphing library for data science in Python."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "edyBIgXPfTTX"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline"
      ],
      "execution_count": 80,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TSVQL5vJfTTX"
      },
      "source": [
        ""
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "3cxwpTQLfTTX",
        "outputId": "933221a8-5226-428e-8d01-298a4894d42b"
      },
      "source": [
        "image, label = dataset[0]\n",
        "plt.imshow(image, cmap='gray')\n",
        "print('Label:', label)"
      ],
      "execution_count": 81,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Label: 5\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "35ELPbM7fTTX",
        "outputId": "76ad9262-871b-4117-92ed-716b0dd1f8f5"
      },
      "source": [
        "image, label = dataset[10]\n",
        "plt.imshow(image, cmap='gray')\n",
        "print('Label:', label)"
      ],
      "execution_count": 82,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Label: 3\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5vO2Gh9RfTTX"
      },
      "source": [
        "It's evident that these images are relatively small in size, and recognizing the digits can sometimes be challenging even for the human eye. While it's useful to look at these images, there's just one problem here: PyTorch doesn't know how to work with images. We need to convert the images into tensors. We can do this by specifying a transform while creating our dataset."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FBnad_UDfTTX"
      },
      "source": [
        "import torchvision.transforms as transforms"
      ],
      "execution_count": 83,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "084T0emtfTTX"
      },
      "source": [
        "PyTorch datasets allow us to specify one or more transformation functions that are applied to the images as they are loaded. The `torchvision.transforms` module contains many such predefined functions. We'll use the `ToTensor` transform to convert images into PyTorch tensors."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hYvBQ3LzfTTX"
      },
      "source": [
        "# MNIST dataset (images and labels)\n",
        "dataset = MNIST(root='data/', \n",
        "                train=True,\n",
        "                transform=transforms.ToTensor())"
      ],
      "execution_count": 84,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nCZ4h7jMfTTX",
        "outputId": "8cf07568-2ccd-4ab4-985a-129bc2d46378"
      },
      "source": [
        "img_tensor, label = dataset[0]\n",
        "print(img_tensor.shape, label)"
      ],
      "execution_count": 85,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "torch.Size([1, 28, 28]) 5\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "prZFgdtefTTX",
        "outputId": "8660e295-d458-49b4-85fe-6d774e23d521"
      },
      "source": [
        "print(img_tensor[0,10:15,10:15])\n",
        "print(torch.max(img_tensor), torch.min(img_tensor))"
      ],
      "execution_count": 86,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor([[0.0039, 0.6039, 0.9922, 0.3529, 0.0000],\n",
            "        [0.0000, 0.5451, 0.9922, 0.7451, 0.0078],\n",
            "        [0.0000, 0.0431, 0.7451, 0.9922, 0.2745],\n",
            "        [0.0000, 0.0000, 0.1373, 0.9451, 0.8824],\n",
            "        [0.0000, 0.0000, 0.0000, 0.3176, 0.9412]])\n",
            "tensor(1.) tensor(0.)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "Fw-NvsqpfTTX",
        "outputId": "13fee15a-7ae3-4e25-89f4-908d1058f6f8"
      },
      "source": [
        "# Plot the image by passing in the 28x28 matrix\n",
        "plt.imshow(img_tensor[0,10:15,10:15], cmap='gray');"
      ],
      "execution_count": 87,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1dcE0OPBfTTX",
        "outputId": "9490a0f9-e0a5-40a4-c92c-61636a4cc2c7"
      },
      "source": [
        "from torch.utils.data import random_split\n",
        "\n",
        "train_ds, val_ds = random_split(dataset, [50000, 10000])\n",
        "len(train_ds), len(val_ds)"
      ],
      "execution_count": 88,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(50000, 10000)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 88
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pD_oD7BTfTTX"
      },
      "source": [
        "from torch.utils.data import DataLoader\n",
        "\n",
        "batch_size = 128\n",
        "\n",
        "train_loader = DataLoader(train_ds, batch_size, shuffle=True)\n",
        "val_loader = DataLoader(val_ds, batch_size)"
      ],
      "execution_count": 89,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zzVbD7pifTTY"
      },
      "source": [
        "import torch.nn as nn\n",
        "\n",
        "input_size = 28*28\n",
        "num_classes = 10\n",
        "\n",
        "# Logistic regression model\n",
        "model = nn.Linear(input_size, num_classes)"
      ],
      "execution_count": 90,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2ilamccMfTTY"
      },
      "source": [
        "Of course, this model is a lot larger than our previous model in terms of the number of parameters. Let's take a look at the weights and biases."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HAj8gVdUfTTY",
        "outputId": "813db93a-eb4d-48a4-d29e-17d552fb1be1"
      },
      "source": [
        "print(model.weight.shape)\n",
        "model.weight"
      ],
      "execution_count": 91,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "torch.Size([10, 784])\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Parameter containing:\n",
              "tensor([[ 0.0141, -0.0005, -0.0250,  ...,  0.0219, -0.0077, -0.0287],\n",
              "        [ 0.0227,  0.0072,  0.0148,  ...,  0.0115, -0.0303, -0.0216],\n",
              "        [-0.0319, -0.0038,  0.0022,  ..., -0.0081, -0.0211,  0.0277],\n",
              "        ...,\n",
              "        [ 0.0272,  0.0036, -0.0092,  ...,  0.0141,  0.0061, -0.0005],\n",
              "        [-0.0262, -0.0330, -0.0157,  ...,  0.0024, -0.0317,  0.0324],\n",
              "        [ 0.0005,  0.0183, -0.0258,  ...,  0.0061,  0.0068, -0.0082]],\n",
              "       requires_grad=True)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 91
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fRnviQ34fTTY",
        "outputId": "adf0e76b-18fb-4f1c-b87a-4cbf6fddae50"
      },
      "source": [
        "print(model.bias.shape)\n",
        "model.bias"
      ],
      "execution_count": 92,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "torch.Size([10])\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Parameter containing:\n",
              "tensor([ 0.0253, -0.0211,  0.0345,  0.0356,  0.0011,  0.0329, -0.0063,  0.0015,\n",
              "        -0.0157,  0.0343], requires_grad=True)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 92
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9m-JsBr6lSO8",
        "outputId": "1c76dd12-4dd8-44ff-c744-314f6c1e0dbe"
      },
      "source": [
        "images.shape"
      ],
      "execution_count": 93,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([128, 1, 28, 28])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 93
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "X3_ktSR1lVJQ",
        "outputId": "092c8536-d1c9-4a02-c3e6-ab9c8747070f"
      },
      "source": [
        "images.reshape(128, 784).shape"
      ],
      "execution_count": 94,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([128, 784])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 94
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c2HWol7qfTTY"
      },
      "source": [
        "class MnistModel(nn.Module):\n",
        "    def __init__(self):\n",
        "        super().__init__()\n",
        "        self.linear = nn.Linear(input_size, num_classes)\n",
        "        \n",
        "    def forward(self, xb):\n",
        "        xb = xb.reshape(-1, 784)\n",
        "        out = self.linear(xb)\n",
        "        return out\n",
        "    \n",
        "model = MnistModel()"
      ],
      "execution_count": 95,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "voZF2M_3nVnI",
        "outputId": "bbc3a3fa-6ea2-48d8-dd7a-92ce1ae7ef11"
      },
      "source": [
        "model.linear"
      ],
      "execution_count": 96,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Linear(in_features=784, out_features=10, bias=True)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 96
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JciejPo9fTTY",
        "outputId": "cbb839be-c6a0-49f6-8102-26f5414f27ad"
      },
      "source": [
        "print(model.linear.weight.shape, model.linear.bias.shape)\n",
        "list(model.parameters())"
      ],
      "execution_count": 97,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "torch.Size([10, 784]) torch.Size([10])\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[Parameter containing:\n",
              " tensor([[-0.0323, -0.0045, -0.0056,  ...,  0.0219, -0.0106, -0.0157],\n",
              "         [ 0.0079, -0.0143, -0.0094,  ..., -0.0275,  0.0060,  0.0317],\n",
              "         [ 0.0103, -0.0216,  0.0122,  ...,  0.0231,  0.0155,  0.0282],\n",
              "         ...,\n",
              "         [-0.0003, -0.0340, -0.0190,  ...,  0.0274,  0.0055, -0.0322],\n",
              "         [-0.0187,  0.0329, -0.0179,  ...,  0.0066,  0.0217, -0.0105],\n",
              "         [-0.0020, -0.0197,  0.0331,  ..., -0.0067, -0.0326, -0.0118]],\n",
              "        requires_grad=True), Parameter containing:\n",
              " tensor([ 0.0018,  0.0061,  0.0275,  0.0276, -0.0353,  0.0284, -0.0337,  0.0296,\n",
              "         -0.0146, -0.0058], requires_grad=True)]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 97
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nGvgCQn2fTTY"
      },
      "source": [
        "We can use our new custom model in the same way as before. Let's see if it works."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HJ6FGOvYfTTZ",
        "outputId": "dc345177-a7cf-48c0-a524-14f28235dc83"
      },
      "source": [
        "for images, labels in train_loader:\n",
        "    print(images.shape)\n",
        "    outputs = model(images)\n",
        "    break\n",
        "\n",
        "print('outputs.shape : ', outputs.shape)\n",
        "print('Sample outputs :\\n', outputs[:2].data)"
      ],
      "execution_count": 98,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "torch.Size([128, 1, 28, 28])\n",
            "outputs.shape :  torch.Size([128, 10])\n",
            "Sample outputs :\n",
            " tensor([[ 0.2780,  0.1037,  0.0505, -0.3276,  0.1325,  0.4018,  0.0870,  0.0444,\n",
            "          0.3784,  0.1815],\n",
            "        [ 0.2210, -0.2415, -0.0404, -0.0283,  0.1057,  0.0344, -0.2624,  0.2052,\n",
            "          0.1481,  0.3229]])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Wc7d6WD0fTTZ"
      },
      "source": [
        "import torch.nn.functional as F"
      ],
      "execution_count": 99,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6xvjcBVTo14n",
        "outputId": "487cc40e-ae38-4256-f7e4-904d1d0cde18"
      },
      "source": [
        "outputs[:2]"
      ],
      "execution_count": 100,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 0.2780,  0.1037,  0.0505, -0.3276,  0.1325,  0.4018,  0.0870,  0.0444,\n",
              "          0.3784,  0.1815],\n",
              "        [ 0.2210, -0.2415, -0.0404, -0.0283,  0.1057,  0.0344, -0.2624,  0.2052,\n",
              "          0.1481,  0.3229]], grad_fn=<SliceBackward>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 100
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "C3neZ1YGfTTZ",
        "outputId": "545eb194-779d-4f16-93fd-7bc962b876fa"
      },
      "source": [
        "# Apply softmax for each output row\n",
        "probs = F.softmax(outputs, dim=1)\n",
        "\n",
        "# Look at sample probabilities\n",
        "print(\"Sample probabilities:\\n\", probs[:2].data)\n",
        "\n",
        "# Add up the probabilities of an output row\n",
        "print(\"Sum: \", torch.sum(probs[0]).item())"
      ],
      "execution_count": 101,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Sample probabilities:\n",
            " tensor([[0.1135, 0.0954, 0.0904, 0.0619, 0.0981, 0.1285, 0.0938, 0.0899, 0.1255,\n",
            "         0.1031],\n",
            "        [0.1171, 0.0738, 0.0902, 0.0913, 0.1044, 0.0972, 0.0722, 0.1153, 0.1089,\n",
            "         0.1297]])\n",
            "Sum:  0.9999998807907104\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1o9a4hAufTTZ",
        "outputId": "0d094dce-7929-4050-d44f-b220ac33efd3"
      },
      "source": [
        "max_probs, preds = torch.max(probs, dim=1)\n",
        "print(preds)\n",
        "print(max_probs)"
      ],
      "execution_count": 102,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor([5, 9, 8, 8, 8, 7, 8, 4, 8, 3, 7, 8, 5, 8, 2, 8, 8, 5, 5, 0, 8, 8, 0, 8,\n",
            "        0, 7, 2, 0, 5, 8, 9, 8, 8, 8, 5, 8, 5, 2, 5, 6, 0, 8, 8, 8, 7, 6, 0, 5,\n",
            "        9, 8, 5, 7, 5, 4, 8, 7, 7, 9, 8, 4, 5, 0, 8, 7, 9, 5, 0, 8, 8, 5, 5, 0,\n",
            "        3, 8, 8, 3, 8, 0, 8, 5, 8, 8, 0, 8, 7, 5, 0, 8, 8, 8, 8, 5, 0, 5, 8, 8,\n",
            "        9, 8, 8, 2, 4, 8, 2, 8, 5, 7, 8, 0, 5, 5, 8, 8, 8, 9, 3, 8, 3, 8, 3, 8,\n",
            "        8, 8, 8, 8, 8, 8, 8, 7])\n",
            "tensor([0.1285, 0.1297, 0.1395, 0.1361, 0.1458, 0.1180, 0.1665, 0.1214, 0.1427,\n",
            "        0.1401, 0.1412, 0.1553, 0.1554, 0.1298, 0.1084, 0.1435, 0.1248, 0.1337,\n",
            "        0.1476, 0.1194, 0.1242, 0.1697, 0.1306, 0.1572, 0.1334, 0.1153, 0.1162,\n",
            "        0.1121, 0.1383, 0.1580, 0.1253, 0.1257, 0.1287, 0.1229, 0.1225, 0.1504,\n",
            "        0.1228, 0.1248, 0.1400, 0.1301, 0.1357, 0.1522, 0.1357, 0.1681, 0.1339,\n",
            "        0.1123, 0.1469, 0.1180, 0.1428, 0.1129, 0.1367, 0.1270, 0.1281, 0.1258,\n",
            "        0.1214, 0.1172, 0.1186, 0.1288, 0.1212, 0.1187, 0.1495, 0.1441, 0.1263,\n",
            "        0.1188, 0.1183, 0.1284, 0.1407, 0.1258, 0.1259, 0.1228, 0.1259, 0.1265,\n",
            "        0.1290, 0.1297, 0.1138, 0.1177, 0.1249, 0.1416, 0.1148, 0.1289, 0.1321,\n",
            "        0.1512, 0.1246, 0.1419, 0.1119, 0.1442, 0.1071, 0.1378, 0.1230, 0.1242,\n",
            "        0.1127, 0.1142, 0.1243, 0.1260, 0.1622, 0.1340, 0.1270, 0.1274, 0.1355,\n",
            "        0.1292, 0.1375, 0.1224, 0.1175, 0.1380, 0.1263, 0.1177, 0.1886, 0.1437,\n",
            "        0.1264, 0.1357, 0.1249, 0.1189, 0.1290, 0.1261, 0.1211, 0.1283, 0.1233,\n",
            "        0.1226, 0.1311, 0.1425, 0.1596, 0.1306, 0.1217, 0.1280, 0.1662, 0.1378,\n",
            "        0.1212, 0.1218], grad_fn=<MaxBackward0>)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IGvKME9WfTTZ"
      },
      "source": [
        "The numbers printed above are the predicted labels for the first batch of training images. Let's compare them with the actual labels."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TsT85mhffTTZ",
        "outputId": "7612996a-f7a4-4365-def3-9b71477fa3f7"
      },
      "source": [
        "labels"
      ],
      "execution_count": 103,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([8, 4, 2, 3, 8, 7, 2, 8, 9, 4, 0, 2, 9, 4, 1, 0, 4, 7, 9, 6, 7, 0, 3, 6,\n",
              "        7, 2, 1, 1, 8, 2, 8, 3, 5, 6, 7, 3, 2, 3, 7, 2, 6, 3, 5, 2, 0, 1, 0, 0,\n",
              "        8, 6, 3, 2, 8, 4, 0, 2, 0, 6, 4, 9, 3, 8, 6, 6, 0, 7, 8, 3, 4, 7, 5, 6,\n",
              "        5, 0, 5, 6, 9, 7, 7, 5, 3, 4, 8, 4, 5, 9, 1, 7, 7, 0, 1, 9, 7, 7, 3, 3,\n",
              "        9, 6, 3, 5, 7, 3, 1, 6, 2, 8, 3, 4, 0, 8, 1, 3, 3, 3, 5, 4, 0, 2, 9, 8,\n",
              "        2, 2, 8, 8, 9, 0, 8, 1])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 103
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FegT9vhlfTTZ"
      },
      "source": [
        "## Evaluation Metric and Loss Function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wG0IBPVMp3UE",
        "outputId": "8d0b0dfe-6b2e-4f50-c822-a3943a61e37f"
      },
      "source": [
        "outputs[:2]"
      ],
      "execution_count": 104,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 0.2780,  0.1037,  0.0505, -0.3276,  0.1325,  0.4018,  0.0870,  0.0444,\n",
              "          0.3784,  0.1815],\n",
              "        [ 0.2210, -0.2415, -0.0404, -0.0283,  0.1057,  0.0344, -0.2624,  0.2052,\n",
              "          0.1481,  0.3229]], grad_fn=<SliceBackward>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 104
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hHgMnCL4qGDt",
        "outputId": "f0bdc6ca-7e42-4d55-dfa1-34bad902a415"
      },
      "source": [
        "torch.sum(preds == labels)"
      ],
      "execution_count": 105,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(11)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 105
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "11hDOTR1fTTZ"
      },
      "source": [
        "def accuracy(outputs, labels):\n",
        "    _, preds = torch.max(outputs, dim=1)\n",
        "    return torch.tensor(torch.sum(preds == labels).item() / len(preds))"
      ],
      "execution_count": 106,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HwVAxpZXfTTZ",
        "outputId": "29c20484-2589-4135-da09-858942a5f729"
      },
      "source": [
        "accuracy(outputs, labels)"
      ],
      "execution_count": 107,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(0.0859)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 107
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jEyaxGIBrNFm",
        "outputId": "356018e1-c7e0-4675-cdbc-e1cbbda45a35"
      },
      "source": [
        "probs"
      ],
      "execution_count": 108,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[0.1135, 0.0954, 0.0904,  ..., 0.0899, 0.1255, 0.1031],\n",
              "        [0.1171, 0.0738, 0.0902,  ..., 0.1153, 0.1089, 0.1297],\n",
              "        [0.1291, 0.0611, 0.0776,  ..., 0.1238, 0.1395, 0.0927],\n",
              "        ...,\n",
              "        [0.0984, 0.0913, 0.1045,  ..., 0.1227, 0.1378, 0.0875],\n",
              "        [0.1162, 0.0806, 0.0788,  ..., 0.1078, 0.1212, 0.1019],\n",
              "        [0.0825, 0.0788, 0.1105,  ..., 0.1218, 0.0980, 0.0879]],\n",
              "       grad_fn=<SoftmaxBackward>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 108
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AkkyxKR1r8nm",
        "outputId": "baaeed8f-cc0c-4177-bdd4-a01220985131"
      },
      "source": [
        "outputs"
      ],
      "execution_count": 109,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 0.2780,  0.1037,  0.0505,  ...,  0.0444,  0.3784,  0.1815],\n",
              "        [ 0.2210, -0.2415, -0.0404,  ...,  0.2052,  0.1481,  0.3229],\n",
              "        [ 0.2814, -0.4661, -0.2275,  ...,  0.2401,  0.3590, -0.0499],\n",
              "        ...,\n",
              "        [ 0.0326, -0.0422,  0.0927,  ...,  0.2537,  0.3692, -0.0851],\n",
              "        [ 0.1741, -0.1919, -0.2140,  ...,  0.0995,  0.2166,  0.0433],\n",
              "        [-0.0878, -0.1336,  0.2039,  ...,  0.3011,  0.0842, -0.0253]],\n",
              "       grad_fn=<AddmmBackward>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 109
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OqWUQpANfTTZ"
      },
      "source": [
        "loss_fn = F.cross_entropy"
      ],
      "execution_count": 110,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SuESG0hbfTTZ",
        "outputId": "4daf1e55-f1da-48a8-8c7d-94154cdc7ea3"
      },
      "source": [
        "# Loss for current batch of data\n",
        "loss = loss_fn(outputs, labels)\n",
        "print(loss)"
      ],
      "execution_count": 111,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor(2.3153, grad_fn=<NllLossBackward>)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wFOtpxUqfTTZ"
      },
      "source": [
        "We know that cross-entropy is the negative logarithm of the predicted probability of the correct label averaged over all training samples. Therefore, one way to interpret the resulting number e.g. `2.23` is look at `e^-2.23` which is around `0.1` as the predicted probability of the correct label, on average. *The lower the loss, The better the model.*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1cv7a7ukfTTZ"
      },
      "source": [
        "def fit(epochs, lr, model, train_loader, val_loader, opt_func=torch.optim.SGD):\n",
        "    optimizer = opt_func(model.parameters(), lr)\n",
        "    history = [] # for recording epoch-wise results\n",
        "    \n",
        "    for epoch in range(epochs):\n",
        "        \n",
        "        # Training Phase \n",
        "        for batch in train_loader:\n",
        "            loss = model.training_step(batch)\n",
        "            loss.backward()\n",
        "            optimizer.step()\n",
        "            optimizer.zero_grad()\n",
        "        \n",
        "        # Validation phase\n",
        "        result = evaluate(model, val_loader)\n",
        "        model.epoch_end(epoch, result)\n",
        "        history.append(result)\n",
        "\n",
        "    return history"
      ],
      "execution_count": 112,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TAuhlro7fTTZ"
      },
      "source": [
        "The `fit` function records the validation loss and metric from each epoch. It returns a history of the training, useful for debugging & visualization.\n",
        "\n",
        "Configurations like batch size, learning rate, etc. (called hyperparameters), need to picked in advance while training machine learning models. Choosing the right hyperparameters is critical for training a reasonably accurate model within a reasonable amount of time. It is an active area of research and experimentation in machine learning. Feel free to try different learning rates and see how it affects the training process.\n",
        "\n",
        "\n",
        "Let's define the `evaluate` function, used in the validation phase of `fit`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wgWjXs5mfTTZ"
      },
      "source": [
        "def evaluate(model, val_loader):\n",
        "    outputs = [model.validation_step(batch) for batch in val_loader]\n",
        "    return model.validation_epoch_end(outputs)"
      ],
      "execution_count": 113,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FdcKIXvMfTTZ"
      },
      "source": [
        "\n",
        "Finally, let's redefine the `MnistModel` class to include additional methods `training_step`, `validation_step`, `validation_epoch_end`, and `epoch_end` used by `fit` and `evaluate`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SbJN7ICGfTTZ"
      },
      "source": [
        "class MnistModel(nn.Module):\n",
        "    def __init__(self):\n",
        "        super().__init__()\n",
        "        self.linear = nn.Linear(input_size, num_classes)\n",
        "        \n",
        "    def forward(self, xb):\n",
        "        xb = xb.reshape(-1, 784)\n",
        "        out = self.linear(xb)\n",
        "        return out\n",
        "    \n",
        "    def training_step(self, batch):\n",
        "        images, labels = batch \n",
        "        out = self(images)                  # Generate predictions\n",
        "        loss = F.cross_entropy(out, labels) # Calculate loss\n",
        "        return loss\n",
        "    \n",
        "    def validation_step(self, batch):\n",
        "        images, labels = batch \n",
        "        out = self(images)                    # Generate predictions\n",
        "        loss = F.cross_entropy(out, labels)   # Calculate loss\n",
        "        acc = accuracy(out, labels)           # Calculate accuracy\n",
        "        return {'val_loss': loss, 'val_acc': acc}\n",
        "        \n",
        "    def validation_epoch_end(self, outputs):\n",
        "        batch_losses = [x['val_loss'] for x in outputs]\n",
        "        epoch_loss = torch.stack(batch_losses).mean()   # Combine losses\n",
        "        batch_accs = [x['val_acc'] for x in outputs]\n",
        "        epoch_acc = torch.stack(batch_accs).mean()      # Combine accuracies\n",
        "        return {'val_loss': epoch_loss.item(), 'val_acc': epoch_acc.item()}\n",
        "    \n",
        "    def epoch_end(self, epoch, result):\n",
        "        print(\"Epoch [{}], val_loss: {:.4f}, val_acc: {:.4f}\".format(epoch, result['val_loss'], result['val_acc']))\n",
        "    \n",
        "model = MnistModel()"
      ],
      "execution_count": 114,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y-omw1RBfTTZ"
      },
      "source": [
        "Before we train the model, let's see how the model performs on the validation set with the initial set of randomly initialized weights & biases.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tNUBy9qTfTTZ",
        "outputId": "3c969245-a3b0-40d6-f900-679a8313fadc"
      },
      "source": [
        "result0 = evaluate(model, val_loader)\n",
        "result0"
      ],
      "execution_count": 115,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'val_acc': 0.07594936341047287, 'val_loss': 2.3511734008789062}"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 115
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MQRahsa6fTTZ",
        "outputId": "1e5d93b9-791d-4179-d272-ee1a44a3099a"
      },
      "source": [
        "history1 = fit(5, 0.001, model, train_loader, val_loader)"
      ],
      "execution_count": 116,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch [0], val_loss: 1.9790, val_acc: 0.5771\n",
            "Epoch [1], val_loss: 1.7045, val_acc: 0.7175\n",
            "Epoch [2], val_loss: 1.4993, val_acc: 0.7580\n",
            "Epoch [3], val_loss: 1.3445, val_acc: 0.7799\n",
            "Epoch [4], val_loss: 1.2256, val_acc: 0.7934\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cJvMd9CufTTa",
        "outputId": "71026525-bb26-434d-936e-a8059bb8848c"
      },
      "source": [
        "history2 = fit(10, 0.001, model, train_loader, val_loader)"
      ],
      "execution_count": 117,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch [0], val_loss: 1.1324, val_acc: 0.8028\n",
            "Epoch [1], val_loss: 1.0577, val_acc: 0.8092\n",
            "Epoch [2], val_loss: 0.9968, val_acc: 0.8153\n",
            "Epoch [3], val_loss: 0.9461, val_acc: 0.8198\n",
            "Epoch [4], val_loss: 0.9033, val_acc: 0.8240\n",
            "Epoch [5], val_loss: 0.8667, val_acc: 0.8283\n",
            "Epoch [6], val_loss: 0.8350, val_acc: 0.8304\n",
            "Epoch [7], val_loss: 0.8073, val_acc: 0.8324\n",
            "Epoch [8], val_loss: 0.7828, val_acc: 0.8348\n",
            "Epoch [9], val_loss: 0.7610, val_acc: 0.8376\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hON9V8GBfTTa",
        "outputId": "62dfafae-51bf-4e37-9dff-0cb2fad72aaf"
      },
      "source": [
        "history3 = fit(5, 0.001, model, train_loader, val_loader)"
      ],
      "execution_count": 118,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch [0], val_loss: 0.7415, val_acc: 0.8390\n",
            "Epoch [1], val_loss: 0.7239, val_acc: 0.8404\n",
            "Epoch [2], val_loss: 0.7079, val_acc: 0.8431\n",
            "Epoch [3], val_loss: 0.6934, val_acc: 0.8451\n",
            "Epoch [4], val_loss: 0.6801, val_acc: 0.8461\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "V5ALmwZjfTTa",
        "outputId": "b6654de9-4cdb-40cd-ba21-192b3b56c12d"
      },
      "source": [
        "history4 = fit(5, 0.001, model, train_loader, val_loader)"
      ],
      "execution_count": 119,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch [0], val_loss: 0.6678, val_acc: 0.8477\n",
            "Epoch [1], val_loss: 0.6566, val_acc: 0.8488\n",
            "Epoch [2], val_loss: 0.6461, val_acc: 0.8503\n",
            "Epoch [3], val_loss: 0.6364, val_acc: 0.8513\n",
            "Epoch [4], val_loss: 0.6273, val_acc: 0.8523\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sCm1903IfTTa"
      },
      "source": [
        "While the accuracy does continue to increase as we train for more epochs, the improvements get smaller with every epoch. Let's visualize this using a line graph."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "swNRQSa0fTTa",
        "outputId": "33d8a46a-ba24-49c4-a0a0-b797bf5f4596"
      },
      "source": [
        "history = [result0] + history1 + history2 + history3 + history4\n",
        "accuracies = [result['val_acc'] for result in history]\n",
        "plt.plot(accuracies, '-x')\n",
        "plt.xlabel('epoch')\n",
        "plt.ylabel('accuracy')\n",
        "plt.title('Accuracy vs. No. of epochs');"
      ],
      "execution_count": 120,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HXgOorOIfTTa"
      },
      "source": [
        "## Testing with individual images"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_qUQKIJefTTa"
      },
      "source": [
        "While we have been tracking the overall accuracy of a model so far, it's also a good idea to look at model's results on some sample images. Let's test out our model with some images from the predefined test dataset of 10000 images. We begin by recreating the test dataset with the `ToTensor` transform."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KqcHUQK3fTTa"
      },
      "source": [
        "# Define test dataset\n",
        "test_dataset = MNIST(root='data/', \n",
        "                     train=False,\n",
        "                     transform=transforms.ToTensor())"
      ],
      "execution_count": 121,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Sw9J_viefTTa"
      },
      "source": [
        "Here's a sample image from the dataset."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        },
        "id": "yzEdFHq6fTTa",
        "outputId": "33dd4015-14c6-4e71-8fc5-97a2bf99f94e"
      },
      "source": [
        "img, label = test_dataset[0]\n",
        "plt.imshow(img[0], cmap='gray')\n",
        "print('Shape:', img.shape)\n",
        "print('Label:', label)"
      ],
      "execution_count": 122,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Shape: torch.Size([1, 28, 28])\n",
            "Label: 7\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QgwbsDUjfTTa"
      },
      "source": [
        "Let's define a helper function `predict_image`, which returns the predicted label for a single image tensor."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9FfeYQaOfTTa"
      },
      "source": [
        "def predict_image(img, model):\n",
        "    xb = img.unsqueeze(0)\n",
        "    yb = model(xb)\n",
        "    _, preds = torch.max(yb, dim=1)\n",
        "    return preds[0].item()"
      ],
      "execution_count": 123,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9ppgosBYfTTa"
      },
      "source": [
        "`img.unsqueeze` simply adds another dimension at the begining of the 1x28x28 tensor, making it a 1x1x28x28 tensor, which the model views as a batch containing a single image.\n",
        "\n",
        "Let's try it out with a few images."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "sPNcp52ifTTa",
        "outputId": "f21e84ff-00e6-4243-b47c-cfa0b9430bd9"
      },
      "source": [
        "img, label = test_dataset[0]\n",
        "plt.imshow(img[0], cmap='gray')\n",
        "print('Label:', label, ', Predicted:', predict_image(img, model))"
      ],
      "execution_count": 124,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Label: 7 , Predicted: 7\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "Nrj-w1COfTTa",
        "outputId": "8db5dc2a-7d86-46dc-e3e4-b7968303b408"
      },
      "source": [
        "img, label = test_dataset[10]\n",
        "plt.imshow(img[0], cmap='gray')\n",
        "print('Label:', label, ', Predicted:', predict_image(img, model))"
      ],
      "execution_count": 125,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Label: 0 , Predicted: 0\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "EPrF7gB4fTTb",
        "outputId": "c0a2c551-5030-41d2-a247-10a798d73009"
      },
      "source": [
        "img, label = test_dataset[193]\n",
        "plt.imshow(img[0], cmap='gray')\n",
        "print('Label:', label, ', Predicted:', predict_image(img, model))"
      ],
      "execution_count": 126,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Label: 9 , Predicted: 9\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "eetYJdoFfTTb",
        "outputId": "12f0b3fc-de1a-41bc-9378-27032fb6a855"
      },
      "source": [
        "img, label = test_dataset[1839]\n",
        "plt.imshow(img[0], cmap='gray')\n",
        "print('Label:', label, ', Predicted:', predict_image(img, model))"
      ],
      "execution_count": 127,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Label: 2 , Predicted: 8\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jQ6Wsk4TfTTb"
      },
      "source": [
        "Identifying where our model performs poorly can help us improve the model, by collecting more training data, increasing/decreasing the complexity of the model, and changing the hypeparameters.\n",
        "\n",
        "As a final step, let's also look at the overall loss and accuracy of the model on the test set."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6bdjaeG-fTTb",
        "outputId": "de498dad-8bd8-4da5-b7a7-d418c5f79749"
      },
      "source": [
        "test_loader = DataLoader(test_dataset, batch_size=256)\n",
        "result = evaluate(model, test_loader)\n",
        "result"
      ],
      "execution_count": 128,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'val_acc': 0.8662109375, 'val_loss': 0.5891512036323547}"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 128
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pfe2IzF3fTTb"
      },
      "source": [
        "We expect this to be similar to the accuracy/loss on the validation set. If not, we might need a better validation set that has similar data and distribution as the test set (which often comes from real world data)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TqC3HEZJfTTb"
      },
      "source": [
        "## Saving and loading the model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xESC-106fTTb"
      },
      "source": [
        "torch.save(model.state_dict(), 'mnist-logistic.pth')"
      ],
      "execution_count": 66,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CAHSyFLPfTTb"
      },
      "source": [
        "The `.state_dict` method returns an `OrderedDict` containing all the weights and bias matrices mapped to the right attributes of the model."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "elbp48SCfTTb",
        "outputId": "ccda3e31-9883-45e7-ec85-896bd40c7aa2"
      },
      "source": [
        "model.state_dict()"
      ],
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "OrderedDict([('linear.weight',\n",
              "              tensor([[-0.0151, -0.0113,  0.0045,  ..., -0.0111, -0.0239, -0.0173],\n",
              "                      [-0.0249,  0.0024, -0.0137,  ..., -0.0022, -0.0095,  0.0096],\n",
              "                      [ 0.0267, -0.0046, -0.0131,  ..., -0.0015,  0.0086,  0.0346],\n",
              "                      ...,\n",
              "                      [ 0.0352, -0.0284,  0.0061,  ..., -0.0100,  0.0111,  0.0058],\n",
              "                      [-0.0340,  0.0119, -0.0115,  ..., -0.0250,  0.0044, -0.0219],\n",
              "                      [ 0.0246,  0.0345, -0.0094,  ...,  0.0337, -0.0222, -0.0227]])),\n",
              "             ('linear.bias',\n",
              "              tensor([-0.0695,  0.0783, -0.0144, -0.0165,  0.0357,  0.0714,  0.0074,  0.0647,\n",
              "                      -0.0706, -0.0215]))])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 67
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qc9kRTDpfTTb"
      },
      "source": [
        "To load the model weights, we can instante a new object of the class `MnistModel`, and use the `.load_state_dict` method."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OO666r7_1rbW"
      },
      "source": [
        "model2 = MnistModel()"
      ],
      "execution_count": 68,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aUvYwe4Q1six",
        "outputId": "157a0c92-3c5b-4de8-d178-e0b8816760a7"
      },
      "source": [
        "model2.state_dict()"
      ],
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "OrderedDict([('linear.weight',\n",
              "              tensor([[-2.1938e-02, -1.4049e-02,  1.0097e-02,  ...,  1.6160e-02,\n",
              "                        2.4741e-02,  3.3888e-02],\n",
              "                      [ 3.0977e-02, -1.6397e-02, -2.1092e-02,  ...,  2.9806e-02,\n",
              "                        7.2487e-03,  2.8843e-02],\n",
              "                      [ 1.6792e-04,  1.6043e-02, -1.1966e-02,  ..., -2.1404e-02,\n",
              "                        1.1557e-02, -2.3528e-02],\n",
              "                      ...,\n",
              "                      [ 2.2107e-02,  1.5872e-02, -2.3242e-02,  ..., -3.4945e-02,\n",
              "                        1.6031e-02,  9.6321e-03],\n",
              "                      [-1.7691e-02,  2.8140e-02,  2.8226e-02,  ...,  1.6353e-02,\n",
              "                        2.8904e-03,  7.5238e-04],\n",
              "                      [ 1.3572e-02,  2.1589e-02,  3.0525e-02,  ...,  6.4556e-03,\n",
              "                       -9.1712e-04, -7.4932e-07]])),\n",
              "             ('linear.bias',\n",
              "              tensor([-0.0296, -0.0196, -0.0227,  0.0280, -0.0325,  0.0317, -0.0092,  0.0106,\n",
              "                      -0.0035,  0.0117]))])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 69
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gHac9s6e1vyS",
        "outputId": "9f59cf3f-5980-4b57-a84a-5a8341a85828"
      },
      "source": [
        "evaluate(model2, test_loader)"
      ],
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'val_acc': 0.15966796875, 'val_loss': 2.292834520339966}"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 70
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bvR1g8ggfTTb",
        "outputId": "1c18e393-d6de-45a3-a9c1-9140a61c0e8a"
      },
      "source": [
        "model2.load_state_dict(torch.load('mnist-logistic.pth'))\n",
        "model2.state_dict()"
      ],
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "OrderedDict([('linear.weight',\n",
              "              tensor([[-0.0151, -0.0113,  0.0045,  ..., -0.0111, -0.0239, -0.0173],\n",
              "                      [-0.0249,  0.0024, -0.0137,  ..., -0.0022, -0.0095,  0.0096],\n",
              "                      [ 0.0267, -0.0046, -0.0131,  ..., -0.0015,  0.0086,  0.0346],\n",
              "                      ...,\n",
              "                      [ 0.0352, -0.0284,  0.0061,  ..., -0.0100,  0.0111,  0.0058],\n",
              "                      [-0.0340,  0.0119, -0.0115,  ..., -0.0250,  0.0044, -0.0219],\n",
              "                      [ 0.0246,  0.0345, -0.0094,  ...,  0.0337, -0.0222, -0.0227]])),\n",
              "             ('linear.bias',\n",
              "              tensor([-0.0695,  0.0783, -0.0144, -0.0165,  0.0357,  0.0714,  0.0074,  0.0647,\n",
              "                      -0.0706, -0.0215]))])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 71
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zhjBm4BMfTTb"
      },
      "source": [
        "Just as a sanity check, let's verify that this model has the same loss and accuracy on the test set as before."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UynZ4aSLfTTb",
        "outputId": "2341bcf5-9ef5-47d6-9629-647765ebe95e"
      },
      "source": [
        "test_loader = DataLoader(test_dataset, batch_size=256)\n",
        "result = evaluate(model2, test_loader)\n",
        "result"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'val_acc': 0.861035168170929, 'val_loss': 0.6424325704574585}"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 72
        }
      ]
    }
  ]
}