Deep neural networks have achieved significant success in the last decades,
but they are not well-calibrated and often produce unreliable predictions. A
large number of literature relies on uncertainty quantification to evaluate the
reliability of a learning model, which is particularly important for
applications of out-of-distribution (OOD) detection and misclassification
detection. We are interested in uncertainty quantification for interdependent
node-level classification. We start our analysis based on graph posterior
networks (GPNs) that optimize the uncertainty cross-entropy (UCE)-based loss
function. We describe the theoretical limitations of the widely-used UCE loss.
To alleviate the identified drawbacks, we propose a distance-based
regularization that encourages clustered OOD nodes to remain clustered in the
latent space. We conduct extensive comparison experiments on eight standard
datasets and demonstrate that the proposed regularization outperforms the
state-of-the-art in both OOD detection and misclassification detection.

深度神经网络在过去几十年取得了重大成功，但它们没有很好的校准性，经常产生不可靠的预测。本文关注于不确定性量化在依赖节点级分类中的应用，并提出了改进的正则化方法来提高分类模型的可靠性。经过大量实验证明，在超过分布检测和误分类检测的应用场景中，提出的正则化方法优于目前的最新技术。

基于距离的正则化提升节点分类中的不确定性量化

Improvements on Uncertainty Quantification for Node Classification via  Distance-Based Regularization

We propose a novel distance-based regularization method for deep metric
learning called Multi-level Distance Regularization (MDR). MDR explicitly
disturbs a learning procedure by regularizing pairwise distances between
embedding vectors into multiple levels that represents a degree of similarity
between a pair. In the training stage, the model is trained with both MDR and
an existing loss function of deep metric learning, simultaneously; the two
losses interfere with the objective of each other, and it makes the learning
process difficult. Moreover, MDR prevents some examples from being ignored or
overly influenced in the learning process. These allow the parameters of the
embedding network to be settle on a local optima with better generalization.
Without bells and whistles, MDR with simple Triplet loss achieves
the-state-of-the-art performance in various benchmark datasets: CUB-200-2011,
Cars-196, Stanford Online Products, and In-Shop Clothes Retrieval. We
extensively perform ablation studies on its behaviors to show the effectiveness
of MDR. By easily adopting our MDR, the previous approaches can be improved in
performance and generalization ability.

本文介绍了一种用于深度度量学习的新型基于距离的正则化方法，即多级距离正则化，可以使嵌入向量之间的成对距离受到多个级别的限制，并对训练过程进行了详细描述以及性能分析。