Deep One-Class Learning

We train a One-Class model (that is, a model that does not need class labels) on MNIST, using Deep SVDD. SVDD places a single center \(\mu\) in the output space of a model \(f_{\theta}\). During training, the parameters \(\theta\) are adjusted to minimize the (squared) sum of the distances of representations \(f_{\theta}(x)\) to this center. Thus, the model is trained to map the training samples close to the center. The idea is that the model learns to map only ID samples close to the center, and not OOD samples. The distance to the center can be used as outlier score.

We test the model against FashionMNIST.

First, some imports etc.

import torch
from torch import nn
from torch.optim import Adam
from torch.utils.data import DataLoader
from torchvision.datasets import MNIST, FashionMNIST
from torchvision.transforms import ToTensor

from pytorch_ood.loss import DeepSVDDLoss
from pytorch_ood.utils import OODMetrics, ToUnknown, fix_random_seed

fix_random_seed(1234)

device = "cuda:0"

Next, we define a simple model. As described in the original paper of Deep SVDD, this model must not use biases in linear layers or convolutions, since this would lead to a trivial solution for the optimization problem.

class Model(nn.Module):
    """ """

    def __init__(self):
        super().__init__()
        self.c1 = nn.Conv2d(1, 16, 3, padding=1, bias=False)
        self.pool = nn.MaxPool2d(2)
        self.c2 = nn.Conv2d(16, 32, 3, padding=1, bias=False)
        self.c3 = nn.Conv2d(32, 64, 3, padding=1, bias=False)

        self.layer5 = nn.Linear(576, 128, bias=False)
        self.layer6 = nn.Linear(128, 2, bias=False)

    def forward(self, x):
        batch_size = x.shape[0]
        x = self.c1(x).relu()
        x = self.pool(x)
        x = self.c2(x).relu()
        x = self.pool(x)
        x = self.c3(x).relu()
        x = self.pool(x)
        x = x.reshape(batch_size, -1)
        x = self.layer5(x).relu()
        x = self.layer6(x)
        return x

Setup training and test data. Mark FashionMNIST as OOD with ToUnknown()

train_dataset = MNIST(root="data", download=True, train=True, transform=ToTensor())
train_loader = DataLoader(train_dataset, num_workers=5, batch_size=128, shuffle=True)

test_dataset_in = MNIST(root="data", download=True, train=False, transform=ToTensor())
test_dataset_out = FashionMNIST(
    root="data",
    download=True,
    train=False,
    transform=ToTensor(),
    target_transform=ToUnknown(),
)

test_loader = DataLoader(
    test_dataset_out + test_dataset_in, shuffle=False, num_workers=5, batch_size=256
)

Setup model, optimizer and training criterion (SVDD). Initialize the center of SVDD with the mean over the dataset

model = Model().to(device)
opti = Adam(model.parameters(), lr=0.001)

with torch.no_grad():
    d = [model(x.to(device)) for x, y in train_loader]
    center = torch.concat(d).mean(dim=0).cpu()

print(center)

criterion = DeepSVDDLoss(n_dim=2, center=center).to(device)

Define a function to the model and print some metrics

def test():
    """ """
    model.eval()
    metrics = OODMetrics()

    with torch.no_grad():
        for x, y in test_loader:
            z = model(x.to(device))
            # calculate distance of points to the center in output space
            distances = criterion.distance(z)
            metrics.update(distances, y)

    print(metrics.compute())
    model.train()

Train model and test at the end of each epoch

for epoch in range(20):
    print(f"Epoch {epoch}")
    for x, _ in train_loader:
        z = model(x.to(device))
        # since this is a one-class method, we do not have to provide any class labels
        loss = criterion(z)
        opti.zero_grad()
        loss.backward()
        opti.step()

    test()