发表机构
Brigham Young University（杨百翰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出贝叶斯残差协方差模型，在协方差不确定性下推导最优线性更新恒等式，并在八个图基准上验证，多数情况下优于残差传播，但密集异质图上表现较差。
AI 中文摘要
在一个节点上观察到预测误差可以帮助纠正其他地方的预测，但收益取决于节点之间的残差依赖性。图暗示了这种依赖性可能发生的位置，但并未确定其符号或强度。我们开发了一个残差协方差的贝叶斯模型，以确定已揭示的误差应如何更新一个固定的基于特征的预测器。对于一组固定的已揭示节点，我们推导了在线性残差传播下期望平方误差变化的精确恒等式。该恒等式刻画了最优线性更新，并将任何其他更新的超额误差表示为精确的二次形式。在协方差不确定性下，贝叶斯最优的固定线性更新使用后验均值协方差。我们对四个正半定协方差族进行平均，分别代表无依赖性、正依赖性、负依赖性以及依赖性符号可随图距离交替变化的族。在八个图基准中，有四个显示后验支持在距离剖面族内，表明邻居之间存在负协方差且符号随距离交替。在评估的方法中，我们的方法在每个图上实现了与最佳方法相比最小的最坏情况召回差距。该方法在八个图中的五个上比残差传播改善了平方误差，但在一个密集异质图上表现明显更差。在这些实验中，选择后验最高的族与模型平均的表现相似。
英文摘要
Observing a prediction error at one node can help correct predictions elsewhere, but the benefit depends on the residual dependence between nodes. A graph suggests where that dependence might occur, yet does not establish its sign or strength. We develop a Bayesian model of residual covariance to determine how revealed errors should update a fixed feature-based predictor. For a fixed set of revealed nodes, we derive an exact identity for the change in expected squared error under linear residual propagation. The identity characterizes the optimal linear update and expresses the excess error of any other update as an exact quadratic. Under covariance uncertainty, the Bayes-optimal fixed linear update uses the posterior mean covariance. We average over four positive-semidefinite covariance families representing no dependence, positive dependence, negative dependence, and dependence whose sign can alternate with graph distance. Across eight graph benchmarks, four show posterior support within the distance-profile family for negative covariance between neighbors and alternating signs with distance. Among the evaluated methods, ours achieves the smallest worst-case recall gap to the best method on each graph. The method improves squared error over residual propagation on five of eight graphs, but performs substantially worse on one dense heterophilous graph. In these experiments, selecting the highest-posterior family performs similarly to model averaging.
