arXiv：cs.LG· Ivan De Boi, Marnix Van Soom·· 4 小时前AI 评分25
高斯过程能设计出什么样的检验
What Can a Gaussian Process Design Test
AI 导读
高斯过程模型与数据一致，可能因假设正确，也可能因所选输入根本无法暴露错误，而这一区别可在观测响应前从实验设计检验。对有限特征构建的 GP，模型隐含关系恰为核矩阵的零空间，Gale 对偶给出几何解释：能暴露误差的最小观测组是 circuits。按预测功效选择下一个输入，可将针对局部偏差的检验功效从 0.48 提升至 0.72；二维网格设计包含加性检验，而拉丁超立方则没有。
正文
Abstract:A Gaussian process (GP) model can agree with the data for two reasons: its assumptions are right, or the chosen inputs could never have shown that they are wrong. The distinction can be checked from the design before any responses are observed. Every model implies relations that its noiseless responses must satisfy at the chosen inputs, such as the middle value lies on the line through its two neighbours. For GPs built from finitely many features, these relations are exactly the null space of the kernel matrix. Gale duality gives them a geometric interpretation, in which each observation has a vector and the smallest groups of observations that can expose an error are the circuits. For other kernels the relations become soft: response patterns may be improbable under the prior rather than algebraically impossible. A standard test then combines two kinds of evidence. Structural evidence comes from a violated relation and grows without limit as the noise falls. Prior-based evidence only says that a departure is improbable under the prior. With all inputs at the two ends of an interval, for example, a GP can reject a straight line against a large curvature, but only because the implied intercept is improbable, never because curvature was seen. In simulations the predicted power matched the observed rejection rates. Choosing the next input by predicted power raised the power against a localised discrepancy from 0.48 to 0.72, against 0.51 when choosing by predictive variance, and a grid in two dimensions contained exact tests of additivity that a Latin hypercube lacked. The test itself is classical. The contribution is the prospective reading of that test: before observing the responses, the design already determines what kind of contradiction it can produce.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.10122 [cs.LG] |
| (or arXiv:2610.10122v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.10122 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Ivan De Boi [view email]
[v1]
Wed, 7 Oct 2026 14:05:14 UTC (332 KB)
来源：arXiv：cs.LG · arxiv.org