Supervised classification.ipynb

{
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  {
   "cell_type": "markdown",
   "id": "1bba0128",
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   "source": [
    "# Supervised learning with PyTorch\n",
    "\n",
    "This is an example of how to build and optimize neural networks with PyTorch. PyTorch and Tensorflow offer a handy mechanism to provide automatic differentiation, using the chain rule in Calculus to calculate the derivative of a function very fast and with GPU support.\n",
    "\n",
    "Our dataset will consist of images of handwritten digits and the task shall be to classify those handwritten digits in the classes {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.\n",
    "\n",
    "If this was a regression problem, we would often try to minimise the mean-squared-error between the output of the neural network and the correct prediction. As we saw in the presentation, this assumes that the underlying probability distribution of the prediction is a Gaussian, which is certainly not true for the distribution of digit classes: for one, the digit classes are discrete and Gaussians are only defined for continuous outputs. The most general probability distribution for a choice of 10 classes is a Categorical distribution (https://en.wikipedia.org/wiki/Categorical_distribution), which is simply a discrete distribution with a given probability value for each class. How can we then sculpt a function that maps the input image to a given class?\n",
    "\n",
    "Suppose the neural network provides an output $f_k(x)$ in the form of a list of probabilities, informing us of the probability that a given image belongs to a certain class $k$. If we know that a given input image x belongs to class C, then the true probability t for this image x to belong to each class is zero for classes that differ from C and 1 for the class C. The network's objective will be to output such probabilities, so that only the i-th component of the output is 1 if the input belongs to class i. The presentation shows how the Bayes' rule leads us naturally to minimize the cross entropy between the target probabilities and the predicted probabilities: $- \\sum_k t_k \\log f_k(x)$. One can gain intuition on this by reading more on the Information Theory concept of cross-entropy and how it relates to Mutual Information: minimizing the mutual information between the labels distribution and the predicted one moves them closer together:  https://en.wikipedia.org/wiki/Cross_entropy\n",
    "\n",
    "The neural network will therefore model a parametrized function that maps the input image pixels into a vector with 10 components, which refer to the probability that the image correspond to that digit.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d0681795",
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install torchvision torch pandas numpy matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "23feddde",
   "metadata": {},
   "outputs": [],
   "source": [
    "# import standard PyTorch modules\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "\n",
    "# import torchvision module to handle image manipulation\n",
    "import torchvision\n",
    "import torchvision.transforms as transforms\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48433f6f",
   "metadata": {},
   "source": [
    "PyTorch allows you to create a class that outputs a single data entry and use that to feed input to your neural network. An example of how you would write such a class is given below, but for this exercise we shall use something ready-made which loads the standard MNIST handwritten digits dataset, just to simplify things.\n",
    "\n",
    "If you want to load a different dataset (for example your own data!), feel free to copy and modify the example Dataset class below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "30205402",
   "metadata": {},
   "outputs": [],
   "source": [
    "class MyDataset(object):\n",
    "    def __init__(self):\n",
    "        pass\n",
    "    def __len__(self):\n",
    "        return 10 # these are how many samples I have\n",
    "    def __getitem__(self, idx):\n",
    "        # give me item with index idx\n",
    "        # read this from some file, but for the purposes of this example, generate a random image and label\n",
    "        my_image = np.random.randn(10,10, 1)\n",
    "        my_label = np.array(np.random.randint(10))\n",
    "        my_image = torch.from_numpy(my_image)\n",
    "        my_label = torch.from_numpy(my_label)\n",
    "        return {\"data\": my_image, \"label\": my_label}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "cc0b0774",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    }
   ],
   "source": [
    "my_dataset = MyDataset()\n",
    "print(len(my_dataset))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6dccfac6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'data': tensor([[[ 1.5547e+00],\n",
      "         [ 5.5951e-01],\n",
      "         [-4.4580e-01],\n",
      "         [-4.0911e-01],\n",
      "         [-1.9626e+00],\n",
      "         [-1.2957e+00],\n",
      "         [ 1.0107e+00],\n",
      "         [ 8.5706e-01],\n",
      "         [ 8.2698e-02],\n",
      "         [ 1.7445e+00]],\n",
      "\n",
      "        [[-1.1114e+00],\n",
      "         [-1.5847e+00],\n",
      "         [-2.0654e-01],\n",
      "         [-1.0200e+00],\n",
      "         [-1.6865e-01],\n",
      "         [-1.2053e-01],\n",
      "         [ 7.0255e-01],\n",
      "         [-5.0251e-01],\n",
      "         [ 1.0529e+00],\n",
      "         [-2.9051e-01]],\n",
      "\n",
      "        [[-9.3932e-02],\n",
      "         [ 2.6510e+00],\n",
      "         [ 1.4673e+00],\n",
      "         [-1.8302e+00],\n",
      "         [-1.2404e-01],\n",
      "         [ 3.8249e-01],\n",
      "         [-5.5515e-02],\n",
      "         [-1.3505e+00],\n",
      "         [ 1.3203e-01],\n",
      "         [ 9.6623e-02]],\n",
      "\n",
      "        [[-7.8525e-01],\n",
      "         [ 6.6473e-01],\n",
      "         [ 4.6917e-01],\n",
      "         [-1.2006e+00],\n",
      "         [-7.7406e-01],\n",
      "         [-1.3107e+00],\n",
      "         [ 4.2693e-01],\n",
      "         [-8.7382e-01],\n",
      "         [-2.5915e-01],\n",
      "         [ 1.5292e+00]],\n",
      "\n",
      "        [[-6.6223e-01],\n",
      "         [-2.2870e-01],\n",
      "         [-1.1778e-01],\n",
      "         [ 1.1825e+00],\n",
      "         [-1.1801e+00],\n",
      "         [-2.1859e-01],\n",
      "         [-1.6676e+00],\n",
      "         [-1.0415e-01],\n",
      "         [ 8.8033e-01],\n",
      "         [-7.0019e-01]],\n",
      "\n",
      "        [[-1.9371e-01],\n",
      "         [ 5.4381e-01],\n",
      "         [-2.9687e-01],\n",
      "         [ 6.8429e-01],\n",
      "         [ 5.0528e-01],\n",
      "         [-6.3122e-02],\n",
      "         [ 2.4948e-02],\n",
      "         [ 3.4935e-02],\n",
      "         [-5.9903e-01],\n",
      "         [ 2.9530e-01]],\n",
      "\n",
      "        [[-9.3742e-02],\n",
      "         [ 5.5731e-01],\n",
      "         [ 4.4727e-01],\n",
      "         [-1.9633e+00],\n",
      "         [ 7.6218e-01],\n",
      "         [-9.8049e-01],\n",
      "         [ 1.6627e-02],\n",
      "         [ 2.7729e-01],\n",
      "         [ 1.7569e-01],\n",
      "         [ 1.2022e+00]],\n",
      "\n",
      "        [[ 2.4165e-02],\n",
      "         [ 3.4443e-01],\n",
      "         [-1.3817e+00],\n",
      "         [-1.6941e+00],\n",
      "         [ 5.7643e-01],\n",
      "         [-3.3574e-01],\n",
      "         [-8.5208e-04],\n",
      "         [ 6.7266e-01],\n",
      "         [ 2.4279e-01],\n",
      "         [ 1.8059e+00]],\n",
      "\n",
      "        [[ 1.5710e+00],\n",
      "         [ 2.8216e+00],\n",
      "         [-2.3268e-02],\n",
      "         [-1.1153e+00],\n",
      "         [-8.6641e-01],\n",
      "         [ 5.0544e-01],\n",
      "         [-3.7233e-02],\n",
      "         [-2.8511e-01],\n",
      "         [-2.3818e+00],\n",
      "         [ 8.0363e-01]],\n",
      "\n",
      "        [[-2.4681e-01],\n",
      "         [ 1.0006e+00],\n",
      "         [ 1.9276e-01],\n",
      "         [-7.3025e-01],\n",
      "         [-1.0975e+00],\n",
      "         [ 9.3319e-01],\n",
      "         [-5.5379e-01],\n",
      "         [-5.1401e-01],\n",
      "         [-8.8545e-01],\n",
      "         [ 4.6912e-01]]], dtype=torch.float64), 'label': tensor(7)}\n"
     ]
    }
   ],
   "source": [
    "print(my_dataset[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f1c9da9",
   "metadata": {},
   "source": [
    "But let's keep things simple and just focus on the actual neural network, using a standard class to load a standard dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e97239d5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz\n",
      "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz to ./data/MNIST/MNIST/raw/train-images-idx3-ubyte.gz\n"
     ]
    },
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting ./data/MNIST/MNIST/raw/train-images-idx3-ubyte.gz to ./data/MNIST/MNIST/raw\n",
      "\n",
      "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz\n",
      "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz to ./data/MNIST/MNIST/raw/train-labels-idx1-ubyte.gz\n"
     ]
    },
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       "version_minor": 0
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting ./data/MNIST/MNIST/raw/train-labels-idx1-ubyte.gz to ./data/MNIST/MNIST/raw\n",
      "\n",
      "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz\n",
      "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz to ./data/MNIST/MNIST/raw/t10k-images-idx3-ubyte.gz\n"
     ]
    },
    {
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       "version_major": 2,
       "version_minor": 0
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting ./data/MNIST/MNIST/raw/t10k-images-idx3-ubyte.gz to ./data/MNIST/MNIST/raw\n",
      "\n",
      "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz\n",
      "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz to ./data/MNIST/MNIST/raw/t10k-labels-idx1-ubyte.gz\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "9e980b594b1942d68ab90d2255e2f42a",
       "version_major": 2,
       "version_minor": 0
      },
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting ./data/MNIST/MNIST/raw/t10k-labels-idx1-ubyte.gz to ./data/MNIST/MNIST/raw\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Use standard MNIST dataset\n",
    "my_dataset = torchvision.datasets.MNIST(\n",
    "    root = './data/MNIST',\n",
    "    train = True,\n",
    "    download = True,\n",
    "    transform = transforms.Compose([\n",
    "        transforms.ToTensor()                                 \n",
    "    ])\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "527089bd",
   "metadata": {},
   "source": [
    "Plot some of the data with their labels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "067b8105",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x1728 with 25 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(nrows=5, ncols=5, figsize=(20,24))\n",
    "for i in range(5):\n",
    "    for j in range(5):\n",
    "        idx = i*5+j\n",
    "        img = my_dataset[idx][0]\n",
    "        label = my_dataset[idx][1]\n",
    "        ax[i, j].imshow(img[0,...].detach().cpu().numpy())\n",
    "        ax[i, j].set(title=f\"Image {idx}, true label {label}\")\n",
    "        ax[i, j].set_xticklabels([])\n",
    "        ax[i, j].set_yticklabels([])\n",
    "plt.subplots_adjust(hspace=0.2,wspace=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e517975c",
   "metadata": {},
   "source": [
    "And now let us define the neural network. In PyTorch, neural networks always extend `nn.Module`. They define their sub-parts in their constructor, which are convolutional layers and fully connected linear layers in this case, and the method `forward` is expected to receive an input image and output the network target.\n",
    "\n",
    "The network parameters are the weights of the `Conv2d` and `Linear` layers, which are conveniently hidden here, but can be accessed if you try to access their `weights` elements.\n",
    "\n",
    "We will not directly output the label probabilities, since we do not actually need it to optimize the neural network: we need only the logits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "d908ef86",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Network(nn.Module):\n",
    "    \"\"\"\n",
    "        This is our parametrized function.\n",
    "        It stores all the parametrized weights theta inside the conv1, conv2, fc1 and fc2 objects.\n",
    "        The forward function receives an image and outputs a vector.\n",
    "        \n",
    "        The intuition is that the i-th component of the vector represents the probability that\n",
    "        the probability that the image belongs to the i-th class however\n",
    "        we do not normalize the output to be in the range [0,1] and to sum to 1. The reason is\n",
    "        that this normalization is done later, in the training step, where the numerical error in it can be\n",
    "        minimized by calculating directly log(probability) instead of calculating first the probability\n",
    "        and then the log of it. Keep in mind therefore, that to get probabilities\n",
    "        from this object one should do F.softmax(my_network(x), dim=1).\n",
    "        \n",
    "        The code has been written like this, as this is a common optimization done in classification problems.\n",
    "    \"\"\"\n",
    "    def __init__(self):\n",
    "        \"\"\"\n",
    "        Constructor. Here we initialize the weights.\n",
    "        \"\"\"\n",
    "        super().__init__()\n",
    "\n",
    "        # define parameters\n",
    "        \n",
    "        # all these steps are purely linear (affine if one considers the bias)\n",
    "        # the forward function adds a non-linearity through the ReLU to allow this to do more than\n",
    "        # simple linear filters\n",
    "        \n",
    "        self.conv1 = nn.Conv2d(in_channels=1, out_channels=6, kernel_size=5)\n",
    "        self.conv2 = nn.Conv2d(in_channels=6, out_channels=12, kernel_size=5)\n",
    "\n",
    "        self.fc1 = nn.Linear(in_features=12*4*4, out_features=120)\n",
    "        self.fc2 = nn.Linear(in_features=120, out_features=60)\n",
    "        self.out = nn.Linear(in_features=60, out_features=10)\n",
    "\n",
    "    def forward(self, x):\n",
    "        \"\"\"\n",
    "        This function is called when one does my_network(x) and it represents the action\n",
    "        of our parametrized function in the image, outputting the probabilities for that image as\n",
    "        a column vector. The input x has shape (B, C, H, W) (ie: batch dimension, channels, height and width).\n",
    "        The output has shape (B, K), where K is the number of classes.\n",
    "        Each row of the output has the probability for each class as a column vector.\n",
    "        Each column of the output has the probability for a single class for all images B given as an input.\n",
    "        \"\"\"\n",
    "\n",
    "        # first convolution\n",
    "        t = self.conv1(x)\n",
    "        # non-linearity\n",
    "        t = F.relu(t)\n",
    "        # reduce size of the image in width and height by taking the maximum\n",
    "        # pixel value in each 2x2 pixel matrix (kernel_size) and skipping one pixel (stride)\n",
    "        # the convolution receives one channel and outputs more\n",
    "        # the goal of the max_pool layer is to reduce the image size, so we\n",
    "        # can get more images in several channels which are smaller in size\n",
    "        # this is a trade off between memory and compute\n",
    "        t = F.max_pool2d(t, kernel_size=2, stride=2)\n",
    "\n",
    "        # second convolution\n",
    "        t = self.conv2(t)\n",
    "        # non-linearity\n",
    "        t = F.relu(t)\n",
    "        # reduce the size of the image in width and height again\n",
    "        t = F.max_pool2d(t, kernel_size=2, stride=2)\n",
    "\n",
    "        # transform images into a single vector using reshape\n",
    "        # this puts all pixel values in a single vector\n",
    "        t = t.reshape(-1, 12*4*4)\n",
    "        \n",
    "        # apply a linear transformation\n",
    "        t = self.fc1(t)\n",
    "        # add a non-linearity\n",
    "        t = F.relu(t)\n",
    "\n",
    "        # another linear transformation\n",
    "        t = self.fc2(t)\n",
    "        # another non-linearity\n",
    "        t = F.relu(t)\n",
    "\n",
    "        # final linear transformation\n",
    "        # the output of this has been set to 10 features, so the output will have the size\n",
    "        # (B, 10)\n",
    "        t = self.out(t)\n",
    "\n",
    "        # note: while we want the function to output a probability,\n",
    "        # we do not actually do any effort to normalize these numbers so that they are in [0, 1]\n",
    "        # and so that their sum is 1\n",
    "        # this would often be done by applying a transformation called Softmax(t) = exp(t)/sum(exp(t))\n",
    "        # however, this will be done internally by PyTorch in the function F.cross_entropy\n",
    "        # which we will call later on when training\n",
    "\n",
    "        return t"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c5620dc",
   "metadata": {},
   "source": [
    "Let us create one instance of this network. We also create an instance of PyTorch's `DataLoader`, which has the task of taking a given number of data elements and outputing it in a single object. This \"mini-batch\" of data is used during training, so that we do not need to load the entire data in memory during the optimization procedure.\n",
    "\n",
    "We also create an instance of the Adam optimizer, which is used to tune the parameters of the network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "988e1979",
   "metadata": {},
   "outputs": [],
   "source": [
    "network = Network()\n",
    "B = 64\n",
    "loader = torch.utils.data.DataLoader(my_dataset, batch_size=B)\n",
    "optimizer = torch.optim.Adam(network.parameters(), lr=1e-3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ee54520",
   "metadata": {},
   "source": [
    "Now we actually repeatedly try to optimize the network parameters. Each time we go through all the data we have, we go through one \"epoch\". For each epoch, we take several \"mini-batches\" of data (given by the `DataLoader` in `loader`) and use it to make one training step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "d15d655d",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/danilo/miniconda3/envs/mlmkl/lib/python3.7/site-packages/torch/nn/functional.py:718: UserWarning: Named tensors and all their associated APIs are an experimental feature and subject to change. Please do not use them for anything important until they are released as stable. (Triggered internally at  /opt/conda/conda-bld/pytorch_1623448224956/work/c10/core/TensorImpl.h:1156.)\n",
      "  return torch.max_pool2d(input, kernel_size, stride, padding, dilation, ceil_mode)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0/10: average loss 0.36116\n",
      "Epoch 1/10: average loss 0.10886\n",
      "Epoch 2/10: average loss 0.07327\n",
      "Epoch 3/10: average loss 0.05648\n",
      "Epoch 4/10: average loss 0.04617\n",
      "Epoch 5/10: average loss 0.03912\n",
      "Epoch 6/10: average loss 0.03184\n",
      "Epoch 7/10: average loss 0.02736\n",
      "Epoch 8/10: average loss 0.02388\n",
      "Epoch 9/10: average loss 0.02053\n"
     ]
    }
   ],
   "source": [
    "epochs = 10\n",
    "# for each epoch\n",
    "for epoch in range(epochs):\n",
    "    losses = list()\n",
    "    # for each mini-batch given by the loader:\n",
    "    for batch in loader:\n",
    "        # get the images in the mini-batch\n",
    "        # this has size (B, C, H, W)\n",
    "        # where B is the mini-batch size\n",
    "        # C is the number of channels in the image (1 for grayscale)\n",
    "        # H is the height of the image\n",
    "        # W is the width of the image\n",
    "        images = batch[0]\n",
    "        # get the labels in the mini-batch (there shall be B of them)\n",
    "        labels = batch[1]\n",
    "        # get the output of the neural network:\n",
    "        logits = network(images)\n",
    "        \n",
    "        # note: the network does not output probabilities directly: it outputs logits\n",
    "        # to get probabilities from it we would need to do F.softmax(logits, dim=1)\n",
    "        # however, this is done inside F.cross_entropy below and we therefore should\n",
    "        # not do it twice here\n",
    "        # the reason it is done internally, in F.cross_entropy, is that what we really\n",
    "        # need is log(probability) and we can reduce the numerical error\n",
    "        # in its calculation by calculating log(softmax(.)) in one go\n",
    "        # (remember softmax(x) = exp(x)/sum(exp(x)), so log(softmax(x)) = x - log(sum(exp(x))))\n",
    "        \n",
    "        # calculate the loss function being minimized\n",
    "        # in this case, it is the cross-entropy between the logits and the true labels\n",
    "        loss = F.cross_entropy(logits, labels)\n",
    "\n",
    "        # clean the optimizer temporary gradient storage\n",
    "        optimizer.zero_grad()\n",
    "        # calculate the gradient of the loss function as a function of the gradients\n",
    "        loss.backward()\n",
    "        # ask the Adam optimizer to change the parameters in the direction of - gradient\n",
    "        # Adam scales the gradient by a constant which is adaptively tuned\n",
    "        # take a look at the Adam paper for more details: https://arxiv.org/abs/1412.6980\n",
    "        optimizer.step()\n",
    "        losses.append(loss.detach().cpu().item())\n",
    "    avg_loss = np.mean(np.array(losses))\n",
    "    print(f\"Epoch {epoch}/{epochs}: average loss {avg_loss:.5f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4980bf4",
   "metadata": {},
   "source": [
    "Let us check what the network says about some new data it has never seen before (note that we set `train` to `False`, to take a statistically independent part of the dataset)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "09646d29",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_dataset = torchvision.datasets.MNIST(\n",
    "    root = './data/MNIST',\n",
    "    train = False,\n",
    "    download = True,\n",
    "    transform = transforms.Compose([\n",
    "        transforms.ToTensor()                                 \n",
    "    ])\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e315b5dc",
   "metadata": {},
   "source": [
    "And now we can plot again the new images, now showing what the network tells us about it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "7a06a4c0",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x1728 with 25 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(nrows=5, ncols=5, figsize=(20,24))\n",
    "for i in range(5):\n",
    "    for j in range(5):\n",
    "        idx = i*5+j\n",
    "        img = test_dataset[idx][0]\n",
    "        label = test_dataset[idx][1]\n",
    "        logits = network(img[None, ...]) # output\n",
    "        probs = F.softmax(logits, dim=1) # apply softmax to normalize them\n",
    "        predicted = torch.argmax(probs[0, ...]) # index of the highest probability\n",
    "        ax[i, j].imshow(img[0,...].detach().cpu().numpy())\n",
    "        ax[i, j].set(title=f\"Image {idx}, true label {label}, predicted: {predicted}\")\n",
    "        ax[i, j].set_xticklabels([])\n",
    "        ax[i, j].set_yticklabels([])\n",
    "plt.subplots_adjust(hspace=0.2,wspace=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73e79a6d",
   "metadata": {},
   "source": [
    "We can also examine the probability that the network gives for all images in the expected class. That is: what is the predicted probability of the network for all images in the true class 4?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "b447df87",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_loader = torch.utils.data.DataLoader(test_dataset, shuffle=False, batch_size=32)\n",
    "logits = list()\n",
    "label = list()\n",
    "for batch in test_loader:\n",
    "    logits += [network(batch[0])]\n",
    "    label += [batch[1]]\n",
    "logits = torch.cat(logits, dim=0)\n",
    "label = torch.cat(label, dim=0)\n",
    "probs = F.softmax(logits, dim=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "d6df7b33",
   "metadata": {},
   "outputs": [],
   "source": [
    "probs_4 = probs.detach().cpu().numpy()[label.detach().cpu().numpy() == 4]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c850c24a",
   "metadata": {},
   "source": [
    "We can histogram it and see that it did mostly a good job, but sometimes it failed. We can go forward and make a cut in the probability and look at those images to identify which images were incorrectly classified."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "93a5fe94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(10, 10))\n",
    "plt.hist(probs_4[:, 4], bins=20)\n",
    "ax.set(xlabel=r\"Probability that a true 4 belongs to class 4 according to the network (p(C$_4$|data))\",\n",
    "       ylabel=\"Number of occurences\",\n",
    "       title=\"\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bff1f8db",
   "metadata": {},
   "source": [
    "### Contact us at the EuXFEL Data Analysis group at any time if you need help analysing your data!\n",
    "\n",
    "#### Danilo Ferreira de Lima: danilo.enoque.ferreira.de.lima@xfel.eu\n",
    "#### Arman Davtyan: arman.davtyan@xfel.eu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0879d703",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}