高斯过程在边界附近会因核函数截断导致选点偏差，影响优化效率。
Boundary Variance Inflation Causes Acquisition Bias in Gaussian Processes
- 边界截断使核相关区域失真，引发不确定性估计偏差。
- 不同采集策略分别倾向角落或内部壳层，与目标函数无关。
- 提出无函数依赖的诊断方法，可评估任意核与域形下的偏差。
在有界域上使用平稳核的高斯过程会表现出边界处后验方差被放大。尽管这一现象在地统计学中早已被认识，并是贝叶斯优化中过度探索的根源，但其成因与影响仍缺乏深入研究。我们追溯到一个简单的几何机制：核函数相关邻域在域边界处被截断，产生与观测无关的畸变，且随维度增加而加剧。我们发现该畸变在三类采集策略中表现为不同模式：方差最大化将选择集中于角点，负集成后验方差和期望预测信息增益则将选择推向轴对齐的内部壳层。这些模式不依赖任何目标函数，表明采集行为可能被核函数几何主导而非任务特定不确定性。为此，我们提出一种无需目标函数的选取分布诊断工具，适用于任意采集策略、核函数和有界域几何。
原文摘要 · Abstract (English)
Gaussian processes with stationary kernels on bounded domains exhibit inflated posterior variance near the boundary. Despite being a long-recognized artifact in geostatistics and a source of over-exploration in Bayesian optimization, the causes and effects of boundary-induced acquisition bias are underexplored. We trace the root cause to a simple geometric mechanism: the truncation of the kernel correlation neighborhood at the domain boundary creates an observation-independent distortion that worsens with dimensionality. We show how this distortion manifests across three acquisition classes: variance maximization concentrates selections at the corners, whereas negative integrated posterior variance and expected predictive information gain move selections inward to axis-aligned interior shells. These patterns arise without reference to any objective function, meaning that acquisition behavior can be dominated by kernel geometry rather than the desired task-specific uncertainty. To quantify this, we introduce a function-free selection-profile diagnostic for arbitrary acquisitions, kernels, and bounded-domain geometries.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。