{"cells":[{"metadata":{},"cell_type":"markdown","source":"# **Theory or why ResNet?**\n> Although it is not obvious,accuracy of newral network decreases with the increase of number of layers (image from original ResNet article)\n![image.png](attachment:image.png)","attachments":{"image.png":{"image/png":"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"}}},{"metadata":{},"cell_type":"markdown","source":"> It may be thought that increasing number of layers allows to catch all possible features and minimize the error, but the result turns out to be totally contrary. This may be explained by comparing two NNs - one shallow and one deeper.NN\n![image.png](attachment:image.png)\nThere are two scenarios - worst case (early layers may be replaced with shallow network and last two act as identity layers y = G(y) = M(y)) and better case scenario (additional layers help to approximate the mapping and reduces error).  In the worst case scenario, both the shallow network and deeper variant of it should give the same accuracy. In the rewarding scenario case, the deeper model should give better accuracy than it’s shallower counter part. On real experiments it turns out that the error is not reduced. 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"}}},{"metadata":{},"cell_type":"markdown","source":">Solution: instead of learning how to map x->y with some kind of function H(x) (output from stacked non-linear layers), residual function F(x) = H(x) - x is defined, wich results in H(x) = F(x) + x, the composition of output from stacked non-linear layers and identity function (see image below: ResNet block) 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"}}},{"metadata":{},"cell_type":"markdown","source":"> The logic behind the solution of this problem can be seen in the image below, as it is easier to get F(x) = 0 than to get the identity 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"}}},{"metadata":{},"cell_type":"markdown","source":"## Step 1 - importing necessary libraries, dataset and preparing it for further work"},{"metadata":{"_uuid":"8f2839f25d086af736a60e9eeb907d3b93b6e0e5","_cell_guid":"b1076dfc-b9ad-4769-8c92-a6c4dae69d19","trusted":true},"cell_type":"code","source":"# importing necessary libraries\nfrom typing import List # importing type alias\nimport logging #event logging\nfrom typing import Optional # optional data type\nfrom functools import partial # enables partial function application\nfrom typing import Tuple # tuple with specified types of contents\nfrom typing import Union # specifie which types may be used\nimport torch.nn as nn # neural network package\nimport numpy as np #math\nimport os # os functions\nimport pandas as pd # data analysis\nimport torch # ML\nfrom torch.optim import Adam # optimization first-order gradient-based optimization of stochastic objective functions\nfrom torchvision.models.resnet import BasicBlock # Basic ResNet block composed by two layers of 3x3conv/batchnorm/activation\nfrom torchvision.models import resnet18, vgg16 # pre-made models to compare\nfrom torch.utils.data import DataLoader # iterable over dataset\nfrom torch.utils.data import Dataset # abstract class representing dataset\nfrom PIL import Image # image class\nfrom matplotlib import pyplot as plt # graphics\nfrom torchvision.models.resnet import ResNet # deep residual networks pre-trained on ImageNet\nfrom sklearn.metrics import roc_auc_score # get roc auc score\nfrom torch import Tensor # multi-dimensional matrix\nfrom torchvision import transforms # image transformations\nfrom torch.autograd import Variable # Tensor wrapper, represents a node in a computational graph\nimport albumentations as A # image augmentation","execution_count":null,"outputs":[]},{"metadata":{"_uuid":"d629ff2d2480ee46fbb7e2d37f6b5fab8052498a","_cell_guid":"79c7e3d0-c299-4dcb-8224-4455121ee9b0","trusted":true},"cell_type":"code","source":"# import data, check if GPU is on\nDATA_FOLDER = '../input/histopathologic-cancer-detection' #importing data\nLABELS = f'{DATA_FOLDER}/train_labels.csv'\nTRAIN_IMAGES_FOLDER = f'{DATA_FOLDER}/train'\nSAMPLE_SUBMISSION = f'{DATA_FOLDER}/sample_submission.csv'\nUSE_GPU = torch.cuda.is_available()","execution_count":null,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"USE_GPU","execution_count":null,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"# df with assigned image ids to labels\nlabels = pd.read_csv(LABELS)\n# lets see total number of examples of each class\nprint(labels['label'].value_counts())","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"### Substep - perform data augmentation"},{"metadata":{"trusted":true},"cell_type":"markdown","source":"> What actually is image augmentation? this technique helps to artificially expand given dataset if the amount of data given is too small or all images are pretty simmilar. This may be achieved by turning, zooming, blurring images, adding noise, saturations and changing colors."},{"metadata":{"trusted":true},"cell_type":"code","source":"# get full path to images from ladels df\ndef format_path_to_images_for_dataset(labels, path):\n    return [os.path.join(path, f'{f}.tif') for f in labels['id'].values]\n# reformat labels\ndef format_labels_for_data_set(labels):\n    return (labels['label'].values.reshape(-1,1))","execution_count":null,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"# initialize datasets using methods from GPU notebook as example\n# full dataset of images and labels\nclass MainDataset(Dataset):\n    # intialize dataset, x_dataset - images, y_dataset - labels, x_tmfs - transformation\n    def __init__(self, x_dataset, y_dataset, x_tfms):\n        self.x_dataset = x_dataset\n        self.y_dataset = y_dataset\n        self.x_tfms = x_tfms\n    # return length of dataset\n    def __len__(self):\n        return self.x_dataset.__len__() \n    # return item by index\n    def __getitem__(self, index):\n        x = self.x_dataset[index]\n        y = self.y_dataset[index]\n        if x_tfms is not None:\n            x = self.x_tfms(x)\n        return x, y\n\n# class of image dataset\nclass ImageDataset(Dataset):\n    # initialize dataset\n    def __init__(self, path_to_image, aug_pipeline=None):\n        self.path_to_image = path_to_image\n        self.aug_pipeline = aug_pipeline\n    # return length of dataset\n    def __len__(self):\n        return len(self.path_to_image)\n    # return image with albumentations performed \n    def __getitem__(self, index):\n        img = Image.open(self.path_to_image[index])\n        if self.aug_pipeline == None:\n            self.aug_pipeline = A.Compose([A.HorizontalFlip(p = 0)]) # for the test if no image agumentations is not performed\n        image_aug = self.aug_pipeline(image = np.array(img))['image']\n        image = Image.fromarray(image_aug, 'RGB') #return image\n        return image\n    \n#class of labels dataset\nclass LabelDataset(Dataset):\n    # intitialize dataset\n    def __init__(self, labels):\n        self.labels = labels\n    # dataset length\n    def __len__(self):\n        return len(labels)\n    #return item from labels dataset by index\n    def __getitem__(self, index):\n        return self.labels[index]","execution_count":null,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"# perform split to train and validation dataset, take equal numbers of exzmples for each class\ndef split(df, split=0.2, samples=5000):\n    # df - dataframe to get data from, split - validation proportion, samples - number of samples for each class\n    class_0 = df.loc[df['label'] == 0]\n    class_1 = df.loc[df['label'] == 1]\n    class_0 = class_0.sample(n=samples)\n    class_1 = class_1.sample(n=samples)\n    tot_split = int(samples * split)\n    valid = [class_0.iloc[:tot_split], class_1.iloc[:tot_split]]\n    valid = pd.concat(valid)\n    train = [class_0.iloc[tot_split:], class_1.iloc[tot_split:]]\n    train = pd.concat(train)\n    return train, valid","execution_count":null,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"# working on dataset\nsample_submission = pd.read_csv(SAMPLE_SUBMISSION)","execution_count":null,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"# set augmentation for images\n# p - probability\naug_pipeline_real = A.Compose([\n        A.RandomRotate90(p = 0.3), # randomly rotate image by 90 degrees 0, 1, 2... times (p is probability of applying)\n        A.Flip(p = 0.3), #Flip the input either horizontally, vertically or both horizontally and vertically\n        A.Transpose(p = 0.1), # Transpose image\n        A.GaussNoise(p = 0.2),\n        A.OneOf([ # blur image\n            A.MedianBlur(blur_limit=3, p=0.1),\n            A.Blur(blur_limit=3, p=0.1),\n        ], p=0.1),\n        A.ShiftScaleRotate(shift_limit=0.0625, scale_limit=0.2, rotate_limit=45, p=0.2), #perform randomly affine transformations\n        A.OneOf([ # give the image distortion\n            A.OpticalDistortion(p=0.1),\n            A.GridDistortion(p=0.1),\n        ], p=0.1),\n        A.HueSaturationValue(p=0.3),#randomly change hue, saturation and value\n    ], p=0.5) # probability to apply\n","execution_count":null,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"# getting train and validation datasets, getting image datasets and labels dataset\ntrain, valid = split(labels)\ntrain_labels = format_labels_for_data_set(train)\nvalid_labels = format_labels_for_data_set(valid)\ntrain_images = format_path_to_images_for_dataset(train, TRAIN_IMAGES_FOLDER)\nvalid_images = format_path_to_images_for_dataset(valid, TRAIN_IMAGES_FOLDER)\ntrain_images_dataset = ImageDataset(train_images, aug_pipeline_real)\nvalid_images_dataset = ImageDataset(valid_images, aug_pipeline_real)\ntrain_labels_dataset = LabelDataset(train_labels)\nvalid_labels_dataset = LabelDataset(valid_labels)\ntrain_images_dataset_no_aug = ImageDataset(train_images, None)\nvalid_images_dataset_no_aug = ImageDataset(valid_images, None)\n","execution_count":null,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"# modified from GPU notebook\ndef implot(dataset, labels, w=2, h=2, cols=9):\n    # plot how 2 images with label 1 and label 0 of dataset may be trasformed after augmentation\n    idx_1 = np.where(labels == 1)[0][0]\n    idx_0 = np.where(labels == 0)[0][0]\n    rows = 2\n    images = [dataset[idx_1] for i in range(cols)] + [dataset[idx_0] for i in range(cols)]\n    print('First row is cancer, second - no cancer')\n    fig = plt.figure(figsize = (cols * w, rows * h))\n    for chart, img in enumerate(images, 1):\n        ax = plt.subplot(rows, cols, chart)\n        ax.imshow(np.array(img))\n        ax.axis('off')\n    fig.tight_layout()\n    plt.show()\nimplot(train_images_dataset, train_labels)","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"> Althoug standard image mean of each channel and std of image channel may be used, mean and std may be calculated for this case, as it may differ"},{"metadata":{"trusted":true},"cell_type":"code","source":"# find mean and std for each of 3 channels in images\nshuffle = True\nbatch_sz = 100\nx_tfms = transforms.Compose([transforms.ToTensor()])\ntrain_dataset = MainDataset(train_images_dataset, train_labels_dataset, x_tfms)\nloader = DataLoader(train_dataset, batch_size=batch_sz, num_workers=0, shuffle=shuffle)\n# from internet\nmean = 0.0\nfor images, _ in loader:\n    batch_samples = images.size(0) \n    images = images.view(batch_samples, images.size(1), -1)\n    mean += images.mean(2).sum(0)\nmean = mean / len(loader.dataset)\n\nvar = 0.0\nfor images, _ in loader:\n    batch_samples = images.size(0)\n    images = images.view(batch_samples, images.size(1), -1)\n    var += ((images - mean.unsqueeze(1))**2).sum([0,2])\nstd = torch.sqrt(var / (len(loader.dataset)*96*96))\n# image size 96 * 96","execution_count":null,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"# mean and std to list to use in normalize\nmean = [mean[i].item() for i in range(len(mean))]\nstd = [std[i].item() for i in range(len(std))]","execution_count":null,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"# dataloader - main utility to load data in pytorch\nbatch_size = 50\nx_tfms = transforms.Compose([transforms.ToTensor(), \n                             transforms.Normalize(\n                                 mean=mean,\n                                 std=std\n                             )\n                            ])\ntrain_dataset = MainDataset(train_images_dataset, train_labels_dataset, x_tfms)\nvalid_dataset = MainDataset(valid_images_dataset, valid_labels_dataset, x_tfms)\ntrain_loader = DataLoader(train_dataset,\n                         batch_size=batch_sz,\n                         num_workers=0,\n                         shuffle=shuffle)\nvalid_loader = DataLoader(valid_dataset,\n                         batch_size=batch_sz,\n                         num_workers=0,\n                         shuffle=shuffle)","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"> Here and further, optimization algorithm Adam is used. It is Stochastic Optimization algorithm, which is sutable for oprimizing functions with lots of variables, as it randomly chooses the variable to optimize each time.\n> As of loss function, binary cross entropy is used with sigmoid output layer. Cross entropy is defined as \n$H(p, q) = -\\sum_x p(x)\\, \\log q(x)\\!$, \nwhere p is actual distribution, but the q is one we got with the model\n"},{"metadata":{"trusted":true},"cell_type":"code","source":"# pass to gpu\ndef to_gpu(tensor):\n    return tensor.cuda() if USE_GPU else tensor\n# first, lets evaluate resnet from GPU notebook, but change functions slightly\ndef create_resnet9_model(output_dim: int = 1) -> nn.Module:\n    model = ResNet(BasicBlock, [1, 1, 1, 1])\n    # размер входящей картинки\n    in_features = model.fc.in_features\n    # output size = 1X1\n    model.avgpool = nn.AdaptiveAvgPool2d(1)\n    model.fc = nn.Linear(in_features, output_dim)\n    model = to_gpu(model)\n    return model\n # loss combines a Sigmoid layer and the BCELoss in one single class\ndef auc_writer(y_true, y_predicted, iteration): # count roc_auc score\n    try:\n        score = roc_auc_score(np.vstack(y_true), np.vstack(y_predicted))\n    except:\n        score = -1\n    print(f'iteration: {iteration}, roc_auc: {score}')\n    \nloss_writer_train = auc_writer\nloss_writer_valid = auc_writer\n# predict function\ndef predict(model, dataloader):\n    model.eval()\n    y_true, y_hat = [], []\n    \n    for x, y in dataloader:\n        x = Variable(T(x))\n        y = Variable(T(y))\n        output = model(x)\n        \n        y_true.append(to_numpy(y))\n        y_hat.append(to_numpy(output))\n    \n    return y_true, y_hat\n#check if tensor\ndef T(tensor):\n    if not torch.is_tensor(tensor):\n        tensor = torch.FloatTensor(tensor)\n    else:\n        tensor = tensor.type(torch.FloatTensor)\n    if USE_GPU:\n        tensor = to_gpu(tensor)\n    return tensor\n# tensor to numpy\ndef to_numpy(tensor):\n    if type(tensor) == np.array or type(tensor) == np.ndarray:\n        return np.array(tensor)\n    elif type(tensor) == Image.Image:\n        return np.array(tensor)\n    elif type(tensor) == Tensor:\n        return tensor.cpu().detach().numpy()\n    else:\n        raise ValueError(msg)\n# check if printing auc sould be triggered\ndef iteration_trigger(iteration, every_x_iteration):\n    if every_x_iteration == 1:\n        return True\n    elif iteration > 0 and iteration % every_x_iteration == 0:\n        return True\n    else:\n        return False\n    \n# triggering\ndef init_triggers(step = 1, train = 10, valid = 10):\n    do_step_trigger = partial(iteration_trigger, every_x_iteration = step)\n    train_loss_trigger = partial(iteration_trigger, every_x_iteration = train)\n    valid_loss_trigger = partial(iteration_trigger, every_x_iteration = valid)\n    \n    return do_step_trigger, train_loss_trigger, valid_loss_trigger\n\ndo_step_trigger, train_loss_trigger, valid_loss_trigger = init_triggers(1, 10, 20)\n# training\ndef train_with_epoch(n_epochs, model, \n                    train_data_loader, \n                    valid_data_loader, \n                    loss, \n                    optimizer, \n                    loss_writer_train, \n                    loss_writer_valid,\n                    do_step_trigger,\n                    train_loss_trigger,\n                    valid_loss_trigger):\n    \n    y_true_train, y_hat_train = [], []\n    for i in range(n_epochs):\n        print('epoch N', i)\n        for iteration, (x, y) in enumerate(train_data_loader):\n            x_train = Variable(T(x), requires_grad = True)\n            y_train = Variable(T(y), requires_grad = True)\n\n            output = model(x_train)\n            y_true_train.append(to_numpy(y_train))\n            y_hat_train.append(to_numpy(output))\n            loss_values = loss(output, y_train)\n            loss_values.backward()\n            if do_step_trigger(iteration):\n                optimizer.step()\n                optimizer.zero_grad()\n            if train_loss_trigger(iteration):\n                print('train_loss_trigger: ')\n                loss_writer_train(y_true_train, y_hat_train, iteration)\n                y_true_train, y_hat_train = [], []\n            if valid_loss_trigger(iteration):\n                print('valid_loss_trigger:')\n                y_true_valid, y_hat_valid = predict(model, valid_data_loader)\n                loss_writer_valid(y_true_valid, y_hat_valid, iteration)\n    return model\n","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"First, training model from GPU model, but with the increased number of epochs"},{"metadata":{"trusted":true},"cell_type":"code","source":"model = create_resnet9_model()\nlr = 1e-3\noptimizer = Adam(model.parameters(), lr)\nloss = nn.BCEWithLogitsLoss()\nmodel = train_with_epoch(10, model, train_loader, valid_loader, loss, optimizer, loss_writer_train, \n                         loss_writer_valid, do_step_trigger, train_loss_trigger, valid_loss_trigger)","execution_count":null,"outputs":[]},{"metadata":{"trusted":true},"cell_type":"code","source":"TEST_IMAGES_FOLDER = f'{DATA_FOLDER}/test/'\n\n#function from GPU notebook that returns name of files in test\ndef test_image_collection(directory: str) -> List:\n    images_name = []\n    for filename in os.listdir(directory):\n        images_name.append(TEST_IMAGES_FOLDER + filename)\n    return(images_name)\n\ntest_image = test_image_collection(TEST_IMAGES_FOLDER)\ntest_images_dataset = ImageDataset(test_image)    \n\n# format test training\nclass TestDataset(Dataset):\n    def __init__(self, x_dataset: Dataset, x_tfms: Optional = None):\n        self.x_dataset = x_dataset\n        self.x_tfms = x_tfms\n        \n    def __len__(self) -> int:\n        return self.x_dataset.__len__() \n        \n    def __getitem__(self, index: int) -> Tuple:\n        x = self.x_dataset[index]\n        if x_tfms is not None:\n            x = self.x_tfms(x)\n        return x\n# load test dataset \ntest_dataset = TestDataset(test_images_dataset, x_tfms)    \n#predict\nbatch_size = 512\nnum_workers = 0\nshuffle = False\ntest_dataloader = DataLoader(test_dataset, batch_size = batch_size, shuffle = shuffle, num_workers = num_workers)\n# predict function\ndef predict_test(model, dataloader):\n    model.eval()\n    y_hat = []\n    \n    for x in dataloader:\n        x = Variable(T(x))\n        output = model(x)\n        \n        y_hat.append(to_numpy(output))\n    return y_hat\ny_hat_test = predict_test(model, test_dataloader)\npredictions = pd.DataFrame(\n    list(\n        zip(\n            test_image,\n            np.vstack(y_hat_test).reshape(-1)\n        )\n    ), \n     columns=['id', 'label'])\n# to csv\npredictions['id'] = predictions['id'].apply(lambda x: x.split('/')[-1].split('.')[0]) \npredictions.to_csv('submission_orig_resnet9.csv', index=False)","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"Result for the net with increased number of epochs - 0.9068"},{"metadata":{},"cell_type":"markdown","source":"> Let's train and then test same model with no data augmentation. Result - 0.5161. Very, very sad"},{"metadata":{"trusted":true},"cell_type":"code","source":"batch_sz = 500\ntrain_dataset = MainDataset(train_images_dataset_no_aug, train_labels_dataset, x_tfms)\nvalid_dataset = MainDataset(valid_images_dataset_no_aug, valid_labels_dataset, x_tfms)\nloader = DataLoader(train_dataset,\n                         batch_size=batch_sz,\n                         num_workers=0,\n                         shuffle=shuffle)\nmodel = create_resnet9_model()\nlr = 1e-3\noptimizer = Adam(model.parameters(), lr)\nloss = nn.BCEWithLogitsLoss()\nmodel = train_with_epoch(10, model, train_loader, valid_loader, loss, optimizer, loss_writer_train, \n                         loss_writer_valid, do_step_trigger, train_loss_trigger, valid_loss_trigger)\nTEST_IMAGES_FOLDER = f'{DATA_FOLDER}/test/'\n\n#function from GPU notebook that returns name of files in test\ndef test_image_collection(directory: str) -> List:\n    images_name = []\n    for filename in os.listdir(directory):\n        images_name.append(TEST_IMAGES_FOLDER + filename)\n    return(images_name)\n\ntest_image = test_image_collection(TEST_IMAGES_FOLDER)\ntest_images_dataset = ImageDataset(test_image)    \n\n# format test training\nclass TestDataset(Dataset):\n    def __init__(self, x_dataset: Dataset, x_tfms: Optional = None):\n        self.x_dataset = x_dataset\n        self.x_tfms = x_tfms\n        \n    def __len__(self) -> int:\n        return self.x_dataset.__len__() \n        \n    def __getitem__(self, index: int) -> Tuple:\n        x = self.x_dataset[index]\n        if x_tfms is not None:\n            x = self.x_tfms(x)\n        return x\n# load test dataset \ntest_dataset = TestDataset(test_images_dataset, x_tfms)    \n#predict\nbatch_size = 512\nnum_workers = 0\nshuffle = False\ntest_dataloader = DataLoader(test_dataset, batch_size = batch_size, shuffle = shuffle, num_workers = num_workers)\n# predict function\ndef predict_test(model, dataloader):\n    model.eval()\n    y_hat = []\n    \n    for x in dataloader:\n        x = Variable(T(x))\n        output = model(x)\n        \n        y_hat.append(to_numpy(output))\n    return y_hat\ny_hat_test = predict_test(model, test_dataloader)\npredictions = pd.DataFrame(\n    list(\n        zip(\n            test_image,\n            np.vstack(y_hat_test).reshape(-1)\n        )\n    ), \n     columns=['id', 'label'])\n# to csv\npredictions['id'] = predictions['id'].apply(lambda x: x.split('/')[-1].split('.')[0]) \npredictions.to_csv('submission_orig_resnet9_no_aug.csv', index=False)","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"> Let's test how amount of training data influences training. We had 10000 examples in training + validation dataset, training - 8000. let's make whole dataset 2000 and 15000."},{"metadata":{"trusted":true},"cell_type":"code","source":"train, valid = split(labels, samples=2000)\ntrain_labels = format_labels_for_data_set(train)\nvalid_labels = format_labels_for_data_set(valid)\ntrain_images = format_path_to_images_for_dataset(train, TRAIN_IMAGES_FOLDER)\nvalid_images = format_path_to_images_for_dataset(valid, TRAIN_IMAGES_FOLDER)\ntrain_images_dataset = ImageDataset(train_images, aug_pipeline_real)\nvalid_images_dataset = ImageDataset(valid_images, aug_pipeline_real)\ntrain_labels_dataset = LabelDataset(train_labels)\nvalid_labels_dataset = LabelDataset(valid_labels)\ntrain_images_dataset_no_aug = ImageDataset(train_images, None)\nvalid_images_dataset_no_aug = ImageDataset(valid_images, None)\nx_tfms = transforms.Compose([transforms.ToTensor(), \n                             transforms.Normalize(\n                                 mean=mean,\n                                 std=std\n                             )\n                            ])\ntrain_dataset = MainDataset(train_images_dataset, train_labels_dataset, x_tfms)\nvalid_dataset = MainDataset(valid_images_dataset, valid_labels_dataset, x_tfms)\ntrain_loader = DataLoader(train_dataset, batch_size=batch_sz, num_workers=0, shuffle=shuffle)\nvalid_loader = DataLoader(valid_dataset, batch_size=batch_sz, num_workers=0, shuffle=shuffle)\nmodel = create_resnet9_model()\nlr = 1e-3\noptimizer = Adam(model.parameters(), lr)\nloss = nn.BCEWithLogitsLoss()\nmodel = train_with_epoch(10, model, train_loader, valid_loader, loss, optimizer, loss_writer_train, \n                         loss_writer_valid, do_step_trigger, train_loss_trigger, valid_loss_trigger)\nTEST_IMAGES_FOLDER = f'{DATA_FOLDER}/test/'\n\n#function from GPU notebook that returns name of files in test\ndef test_image_collection(directory: str) -> List:\n    images_name = []\n    for filename in os.listdir(directory):\n        images_name.append(TEST_IMAGES_FOLDER + filename)\n    return(images_name)\n\ntest_image = test_image_collection(TEST_IMAGES_FOLDER)\ntest_images_dataset = ImageDataset(test_image)    \n\n# format test training\nclass TestDataset(Dataset):\n    def __init__(self, x_dataset: Dataset, x_tfms: Optional = None):\n        self.x_dataset = x_dataset\n        self.x_tfms = x_tfms\n        \n    def __len__(self) -> int:\n        return self.x_dataset.__len__() \n        \n    def __getitem__(self, index: int) -> Tuple:\n        x = self.x_dataset[index]\n        if x_tfms is not None:\n            x = self.x_tfms(x)\n        return x\n# load test dataset \ntest_dataset = TestDataset(test_images_dataset, x_tfms)    \n#predict\nbatch_size = 512\nnum_workers = 0\nshuffle = False\ntest_dataloader = DataLoader(test_dataset, batch_size = batch_size, shuffle = shuffle, num_workers = num_workers)\n# predict function\ndef predict_test(model, dataloader):\n    model.eval()\n    y_hat = []\n    \n    for x in dataloader:\n        x = Variable(T(x))\n        output = model(x)\n        \n        y_hat.append(to_numpy(output))\n    return y_hat\ny_hat_test = predict_test(model, test_dataloader)\npredictions = pd.DataFrame(\n    list(\n        zip(\n            test_image,\n            np.vstack(y_hat_test).reshape(-1)\n        )\n    ), \n     columns=['id', 'label'])\n# to csv\npredictions['id'] = predictions['id'].apply(lambda x: x.split('/')[-1].split('.')[0]) \n\npredictions.to_csv('submission_2000.csv', index=False)","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"> Not that much examples give very small ROC-AUC score - 0.6182. This should have been waited."},{"metadata":{"trusted":true},"cell_type":"code","source":"train, valid = split(labels, samples=15000)\ntrain_labels = format_labels_for_data_set(train)\nvalid_labels = format_labels_for_data_set(valid)\ntrain_images = format_path_to_images_for_dataset(train, TRAIN_IMAGES_FOLDER)\nvalid_images = format_path_to_images_for_dataset(valid, TRAIN_IMAGES_FOLDER)\ntrain_images_dataset = ImageDataset(train_images, aug_pipeline_real)\nvalid_images_dataset = ImageDataset(valid_images, aug_pipeline_real)\ntrain_labels_dataset = LabelDataset(train_labels)\nvalid_labels_dataset = LabelDataset(valid_labels)\nx_tfms = transforms.Compose([transforms.ToTensor(), \n                             transforms.Normalize(\n                                 mean=mean,\n                                 std=std\n                             )\n                            ])\ntrain_dataset = MainDataset(train_images_dataset, train_labels_dataset, x_tfms)\nvalid_dataset = MainDataset(valid_images_dataset, valid_labels_dataset, x_tfms)\ntrain_loader = DataLoader(train_dataset, batch_size=batch_sz, num_workers=0, shuffle=shuffle)\nvalid_loader = DataLoader(valid_dataset, batch_size=batch_sz, num_workers=0, shuffle=shuffle)\nmodel = create_resnet9_model()\nlr = 1e-3\noptimizer = Adam(model.parameters(), lr)\nloss = nn.BCEWithLogitsLoss()\nmodel = train_with_epoch(10, model, train_loader, valid_loader, loss, optimizer, loss_writer_train, \n                         loss_writer_valid, do_step_trigger, train_loss_trigger, valid_loss_trigger)\nTEST_IMAGES_FOLDER = f'{DATA_FOLDER}/test/'\n\n#function from GPU notebook that returns name of files in test\ndef test_image_collection(directory: str) -> List:\n    images_name = []\n    for filename in os.listdir(directory):\n        images_name.append(TEST_IMAGES_FOLDER + filename)\n    return(images_name)\n\ntest_image = test_image_collection(TEST_IMAGES_FOLDER)\ntest_images_dataset = ImageDataset(test_image)    \n\n# format test training\nclass TestDataset(Dataset):\n    def __init__(self, x_dataset: Dataset, x_tfms: Optional = None):\n        self.x_dataset = x_dataset\n        self.x_tfms = x_tfms\n        \n    def __len__(self) -> int:\n        return self.x_dataset.__len__() \n        \n    def __getitem__(self, index: int) -> Tuple:\n        x = self.x_dataset[index]\n        if x_tfms is not None:\n            x = self.x_tfms(x)\n        return x\n# load test dataset \ntest_dataset = TestDataset(test_images_dataset, x_tfms)    \n#predict\nbatch_size = 512\nnum_workers = 0\nshuffle = False\ntest_dataloader = DataLoader(test_dataset, batch_size = batch_size, shuffle = shuffle, num_workers = num_workers)\n# predict function\ndef predict_test(model, dataloader):\n    model.eval()\n    y_hat = []\n    \n    for x in dataloader:\n        x = Variable(T(x))\n        output = model(x)\n        \n        y_hat.append(to_numpy(output))\n    return y_hat\ny_hat_test = predict_test(model, test_dataloader)\npredictions = pd.DataFrame(\n    list(\n        zip(\n            test_image,\n            np.vstack(y_hat_test).reshape(-1)\n        )\n    ), \n     columns=['id', 'label'])\n# to csv\npredictions['id'] = predictions['id'].apply(lambda x: x.split('/')[-1].split('.')[0]) \n\npredictions.to_csv('submission_15000.csv', index=False)","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"> For 15000 examples score is 0.9142"},{"metadata":{},"cell_type":"markdown","source":"> Return to the dataset 0f 10000 samples. Let's see how learning rate influences result. Learning rate basically is step size in optimizer"},{"metadata":{"trusted":true},"cell_type":"code","source":"train, valid = split(labels, samples=10000)\ntrain_labels = format_labels_for_data_set(train)\nvalid_labels = format_labels_for_data_set(valid)\ntrain_images = format_path_to_images_for_dataset(train, TRAIN_IMAGES_FOLDER)\nvalid_images = format_path_to_images_for_dataset(valid, TRAIN_IMAGES_FOLDER)\ntrain_images_dataset = ImageDataset(train_images, aug_pipeline_real)\nvalid_images_dataset = ImageDataset(valid_images, aug_pipeline_real)\ntrain_labels_dataset = LabelDataset(train_labels)\nvalid_labels_dataset = LabelDataset(valid_labels)\ntrain_images_dataset_no_aug = ImageDataset(train_images, None)\nvalid_images_dataset_no_aug = ImageDataset(valid_images, None)\nx_tfms = transforms.Compose([transforms.ToTensor(), \n                             transforms.Normalize(\n                                 mean=mean,\n                                 std=std\n                             )\n                            ])\ntrain_dataset = MainDataset(train_images_dataset, train_labels_dataset, x_tfms)\nvalid_dataset = MainDataset(valid_images_dataset, valid_labels_dataset, x_tfms)\ntrain_loader = DataLoader(train_dataset, batch_size=batch_sz, num_workers=0, shuffle=shuffle)\nvalid_loader = DataLoader(valid_dataset, batch_size=batch_sz, num_workers=0, shuffle=shuffle)\nmodel = create_resnet9_model()\nlr = 1e-4\noptimizer = Adam(model.parameters(), lr)\nloss = nn.BCEWithLogitsLoss()\nmodel = train_with_epoch(10, model, train_loader, valid_loader, loss, optimizer, loss_writer_train, \n                         loss_writer_valid, do_step_trigger, train_loss_trigger, valid_loss_trigger)\nTEST_IMAGES_FOLDER = f'{DATA_FOLDER}/test/'\n\n#function from GPU notebook that returns name of files in test\ndef test_image_collection(directory: str) -> List:\n    images_name = []\n    for filename in os.listdir(directory):\n        images_name.append(TEST_IMAGES_FOLDER + filename)\n    return(images_name)\n\ntest_image = test_image_collection(TEST_IMAGES_FOLDER)\ntest_images_dataset = ImageDataset(test_image)    \n\n# format test training\nclass TestDataset(Dataset):\n    def __init__(self, x_dataset: Dataset, x_tfms: Optional = None):\n        self.x_dataset = x_dataset\n        self.x_tfms = x_tfms\n        \n    def __len__(self) -> int:\n        return self.x_dataset.__len__() \n        \n    def __getitem__(self, index: int) -> Tuple:\n        x = self.x_dataset[index]\n        if x_tfms is not None:\n            x = self.x_tfms(x)\n        return x\n# load test dataset \ntest_dataset = TestDataset(test_images_dataset, x_tfms)    \n#predict\nbatch_size = 512\nnum_workers = 0\nshuffle = False\ntest_dataloader = DataLoader(test_dataset, batch_size = batch_size, shuffle = shuffle, num_workers = num_workers)\n# predict function\ndef predict_test(model, dataloader):\n    model.eval()\n    y_hat = []\n    \n    for x in dataloader:\n        x = Variable(T(x))\n        output = model(x)\n        \n        y_hat.append(to_numpy(output))\n    return y_hat\ny_hat_test = predict_test(model, test_dataloader)\npredictions = pd.DataFrame(\n    list(\n        zip(\n            test_image,\n            np.vstack(y_hat_test).reshape(-1)\n        )\n    ), \n     columns=['id', 'label'])\n# to csv\npredictions['id'] = predictions['id'].apply(lambda x: x.split('/')[-1].split('.')[0]) \n\npredictions.to_csv('submission_lr_4.csv', index=False)","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"> Score - 0.8883"},{"metadata":{"trusted":true},"cell_type":"code","source":"model = create_resnet9_model()\nlr = 1e-1\noptimizer = Adam(model.parameters(), lr)\nloss = nn.BCEWithLogitsLoss()\nmodel = train_with_epoch(10, model, train_loader, valid_loader, loss, optimizer, loss_writer_train, \n                         loss_writer_valid, do_step_trigger, train_loss_trigger, valid_loss_trigger)\nTEST_IMAGES_FOLDER = f'{DATA_FOLDER}/test/'\n\n#function from GPU notebook that returns name of files in test\ndef test_image_collection(directory: str) -> List:\n    images_name = []\n    for filename in os.listdir(directory):\n        images_name.append(TEST_IMAGES_FOLDER + filename)\n    return(images_name)\n\ntest_image = test_image_collection(TEST_IMAGES_FOLDER)\ntest_images_dataset = ImageDataset(test_image)    \n\n# format test training\nclass TestDataset(Dataset):\n    def __init__(self, x_dataset: Dataset, x_tfms: Optional = None):\n        self.x_dataset = x_dataset\n        self.x_tfms = x_tfms\n        \n    def __len__(self) -> int:\n        return self.x_dataset.__len__() \n        \n    def __getitem__(self, index: int) -> Tuple:\n        x = self.x_dataset[index]\n        if x_tfms is not None:\n            x = self.x_tfms(x)\n        return x\n# load test dataset \ntest_dataset = TestDataset(test_images_dataset, x_tfms)    \n#predict\nbatch_size = 512\nnum_workers = 0\nshuffle = False\ntest_dataloader = DataLoader(test_dataset, batch_size = batch_size, shuffle = shuffle, num_workers = num_workers)\n# predict function\ndef predict_test(model, dataloader):\n    model.eval()\n    y_hat = []\n    \n    for x in dataloader:\n        x = Variable(T(x))\n        output = model(x)\n        \n        y_hat.append(to_numpy(output))\n    return y_hat\ny_hat_test = predict_test(model, test_dataloader)\npredictions = pd.DataFrame(\n    list(\n        zip(\n            test_image,\n            np.vstack(y_hat_test).reshape(-1)\n        )\n    ), \n     columns=['id', 'label'])\n# to csv\npredictions['id'] = predictions['id'].apply(lambda x: x.split('/')[-1].split('.')[0]) \npredictions.to_csv('submission_lr_1.csv', index=False)","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":">Score - 0.8861"},{"metadata":{},"cell_type":"markdown","source":"> Let's try premade PyTorch networks - resnet18 and vgg16"},{"metadata":{"trusted":true},"cell_type":"code","source":"model = resnet18(num_classes=1)\nmodel = to_gpu(model)\nlr = 1e-3\noptimizer = Adam(model.parameters(), lr)\nloss = nn.BCEWithLogitsLoss()\nmodel = train_with_epoch(10, model, train_loader, valid_loader, loss, optimizer, loss_writer_train, \n                         loss_writer_valid, do_step_trigger, train_loss_trigger, valid_loss_trigger)\nTEST_IMAGES_FOLDER = f'{DATA_FOLDER}/test/'\n\n#function from GPU notebook that returns name of files in test\ndef test_image_collection(directory: str) -> List:\n    images_name = []\n    for filename in os.listdir(directory):\n        images_name.append(TEST_IMAGES_FOLDER + filename)\n    return(images_name)\n\ntest_image = test_image_collection(TEST_IMAGES_FOLDER)\ntest_images_dataset = ImageDataset(test_image)    \n\n# format test training\nclass TestDataset(Dataset):\n    def __init__(self, x_dataset: Dataset, x_tfms: Optional = None):\n        self.x_dataset = x_dataset\n        self.x_tfms = x_tfms\n        \n    def __len__(self) -> int:\n        return self.x_dataset.__len__() \n        \n    def __getitem__(self, index: int) -> Tuple:\n        x = self.x_dataset[index]\n        if x_tfms is not None:\n            x = self.x_tfms(x)\n        return x\n# load test dataset \ntest_dataset = TestDataset(test_images_dataset, x_tfms)    \n#predict\nbatch_size = 100\nnum_workers = 0\nshuffle = False\ntest_dataloader = DataLoader(test_dataset, batch_size = batch_size, shuffle = shuffle, num_workers = num_workers)\n# predict function\ndef predict_test(model, dataloader):\n    model.eval()\n    y_hat = []\n    \n    for x in dataloader:\n        x = Variable(T(x))\n        output = model(x)\n        \n        y_hat.append(to_numpy(output))\n    return y_hat\ny_hat_test = predict_test(model, test_dataloader)\npredictions = pd.DataFrame(\n    list(\n        zip(\n            test_image,\n            np.vstack(y_hat_test).reshape(-1)\n        )\n    ), \n     columns=['id', 'label'])\n# to csv\npredictions['id'] = predictions['id'].apply(lambda x: x.split('/')[-1].split('.')[0]) \npredictions.to_csv('submission_resnet18.csv', index=False)","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":">Excellent performance - 0.8955. Probably, more epochs needed to show better performance"},{"metadata":{"trusted":true},"cell_type":"code","source":"model = vgg16(num_classes=1)\nmodel = to_gpu(model)\nlr = 1e-3\noptimizer = Adam(model.parameters(), lr)\nloss = nn.BCEWithLogitsLoss()\nmodel = train_with_epoch(10, model, train_loader, valid_loader, loss, optimizer, loss_writer_train, \n                         loss_writer_valid, do_step_trigger, train_loss_trigger, valid_loss_trigger)\nTEST_IMAGES_FOLDER = f'{DATA_FOLDER}/test/'\n\n#function from GPU notebook that returns name of files in test\ndef test_image_collection(directory: str) -> List:\n    images_name = []\n    for filename in os.listdir(directory):\n        images_name.append(TEST_IMAGES_FOLDER + filename)\n    return(images_name)\n\ntest_image = test_image_collection(TEST_IMAGES_FOLDER)\ntest_images_dataset = ImageDataset(test_image)    \n\n# format test training\nclass TestDataset(Dataset):\n    def __init__(self, x_dataset: Dataset, x_tfms: Optional = None):\n        self.x_dataset = x_dataset\n        self.x_tfms = x_tfms\n        \n    def __len__(self) -> int:\n        return self.x_dataset.__len__() \n        \n    def __getitem__(self, index: int) -> Tuple:\n        x = self.x_dataset[index]\n        if x_tfms is not None:\n            x = self.x_tfms(x)\n        return x\n# load test dataset \ntest_dataset = TestDataset(test_images_dataset, x_tfms)    \n#predict\nbatch_size = 100\nnum_workers = 0\nshuffle = False\ntest_dataloader = DataLoader(test_dataset, batch_size = batch_size, shuffle = shuffle, num_workers = num_workers)\n# predict function\ndef predict_test(model, dataloader):\n    model.eval()\n    y_hat = []\n    \n    for x in dataloader:\n        x = Variable(T(x))\n        output = model(x)\n        \n        y_hat.append(to_numpy(output))\n    return y_hat\ny_hat_test = predict_test(model, test_dataloader)\npredictions = pd.DataFrame(\n    list(\n        zip(\n            test_image,\n            np.vstack(y_hat_test).reshape(-1)\n        )\n    ), \n     columns=['id', 'label'])\n# to csv\npredictions['id'] = predictions['id'].apply(lambda x: x.split('/')[-1].split('.')[0]) \npredictions.to_csv('submission_vgg16.csv', index=False)","execution_count":null,"outputs":[]},{"metadata":{},"cell_type":"markdown","source":"> Result is very bad - 0.5463. Probably, more training needed"},{"metadata":{},"cell_type":"markdown","source":"# Final results\n1) It is clearly seen that more epochs give better result\n2) Also, it is clearly seen that ResNet works much better\n3) learning rate did not change the result a lot, but, probably, for smaller learning rate more epochs are needed\n4) The amount of training data strongly influences the precision, thus bigger dataset giving better score"},{"metadata":{},"cell_type":"markdown","source":"# Note\nThe same code reats over and over for implementing datasets and getting test data, as each cell was ment to run in separate session, otherwise GPU memory error would be raised."}],"metadata":{"kernelspec":{"language":"python","display_name":"Python 3","name":"python3"},"language_info":{"pygments_lexer":"ipython3","nbconvert_exporter":"python","version":"3.6.4","file_extension":".py","codemirror_mode":{"name":"ipython","version":3},"name":"python","mimetype":"text/x-python"}},"nbformat":4,"nbformat_minor":4}