In domains with interdependent data, such as graphs, quantifying the
epistemic uncertainty of a Graph Neural Network (GNN) is challenging as
uncertainty can arise at different structural scales. Existing techniques
neglect this issue or only distinguish between structure-aware and
structure-agnostic uncertainty without combining them into a single measure. We
propose GEBM, an energy-based model (EBM) that provides high-quality
uncertainty estimates by aggregating energy at different structural levels that
naturally arise from graph diffusion. In contrast to logit-based EBMs, we
provably induce an integrable density in the data space by regularizing the
energy function. We introduce an evidential interpretation of our EBM that
significantly improves the predictive robustness of the GNN. Our framework is a
simple and effective post hoc method applicable to any pre-trained GNN that is
sensitive to various distribution shifts. It consistently achieves the best
separation of in-distribution and out-of-distribution data on 6 out of 7
anomaly types while having the best average rank over shifts on \emph{all}
datasets.

在具有相互依赖数据的领域中，如图形数据，量化图神经网络 (GNN) 的认知不确定性是具有挑战性的，因为不确定性可以在不同的结构尺度上产生。我们提出了 GEBM，一种能量模型（EBM），通过聚合来自图扩散引起的不同结构级别上的能量，提供高质量的不确定性估计。与基于逻辑的 EBM 不同，我们通过正则化能量函数来在数据空间中引入可积密度。我们引入了我们的 EBM 的证据解释，极大地提高了 GNN 的预测鲁棒性。我们的框架是一个简单有效的事后方法，适用于任何对各种分布转移敏感的预训练 GNN。在 7 种异常类型中，我们在 6 种上实现了最佳的内部分布和外部分布数据分离，并在所有数据集上具有最佳的平均排名。

基于能量的图神经网络的认知不确定性

Energy-based Epistemic Uncertainty for Graph Neural Networks

We discuss recent work for causal inference and predictive robustness in a
unifying way. The key idea relies on a notion of probabilistic invariance or
stability: it opens up new insights for formulating causality as a certain risk
minimization problem with a corresponding notion of robustness. The invariance
itself can be estimated from general heterogeneous or perturbation data which
frequently occur with nowadays data collection. The novel methodology is
potentially useful in many applications, offering more robustness and better
`causal-oriented' interpretation than machine learning or estimation in
standard regression or classification frameworks.

本论文讨论了概率不变性或稳定性的概念及其如何应用于因果推断与预测鲁棒性问题。同时提出了一种用于风险最小化问题的因果形式化方法，通过估计常常出现在数据收集中的异构性或扰动数据来确定这种不变性。此新方法在许多应用中具有潜在的实用价值，比标准回归或分类框架中的机器学习或估计方法提供了更强的鲁棒性和更好的因果解释。