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.

本文提出了一种基于降维增强深度神经网络（DNN）的离群检测方法：通过对高维特征进行线性与非线性降维，得到更真实的特征嵌入子空间，利用其计算分布学习和特征重构误差有效地检测不在分布内的样本，实验结果表明其效果优于一些已有方法。

利用子空间技术和特征的概率建模进行样本外检测