  We present a principled approach for detecting out-of-distribution (OOD) and
adversarial samples in deep neural networks. Our approach consists in modeling
the outputs of the various layers (deep features) with parametric probability
distributions once training is completed. At inference, the likelihoods of the
deep features w.r.t the previously learnt distributions are calculated and used
to derive uncertainty estimates that can discriminate in-distribution samples
from OOD samples. We explore the use of two classes of multivariate
distributions for modeling the deep features - Gaussian and Gaussian mixture -
and study the trade-off between accuracy and computational complexity. We
demonstrate benefits of our approach on image features by detecting OOD images
and adversarially-generated images, using popular DNN architectures on MNIST
and CIFAR10 datasets. We show that more precise modeling of the feature
distributions result in significantly improved detection of OOD and adversarial
samples; up to 12 percentage points in AUPR and AUROC metrics. We further show
that our approach remains extremely effective when applied to video data and
associated spatio-temporal features by detecting adversarial samples on
activity classification tasks using UCF101 dataset, and the C3D network. To our
knowledge, our methodology is the first one reported for reliably detecting
white-box adversarial framing, a state-of-the-art adversarial attack for video
classifiers.
