  This paper presents a principled approach for detecting out-of-distribution
(OOD) samples in deep neural networks (DNN). Modeling probability distributions
on deep features has recently emerged as an effective, yet computationally
cheap method to detect OOD samples in DNN. However, the features produced by a
DNN at any given layer do not fully occupy the corresponding high-dimensional
feature space. We apply linear statistical dimensionality reduction techniques
and nonlinear manifold-learning techniques on the high-dimensional features in
order to capture the true subspace spanned by the features. We hypothesize that
such lower-dimensional feature embeddings can mitigate the curse of
dimensionality, and enhance any feature-based method for more efficient and
effective performance. In the context of uncertainty estimation and OOD, we
show that the log-likelihood score obtained from the distributions learnt on
this lower-dimensional subspace is more discriminative for OOD detection. We
also show that the feature reconstruction error, which is the $L_2$-norm of the
difference between the original feature and the pre-image of its embedding, is
highly effective for OOD detection and in some cases superior to the
log-likelihood scores. The benefits of our approach are demonstrated on image
features by detecting OOD images, using popular DNN architectures on commonly
used image datasets such as CIFAR10, CIFAR100, and SVHN.
