验证高斯过程核函数，让不确定性估计更可信。
Kernel Model Validation: How To Do It, And Why You Should Care
- 基于高斯过程的多变量正态特性，设计核函数验证方法
- 核函数错误会导致优化算法收敛变差
- 适合关注模型不确定性的研究人员
高斯过程（GP）常用于不确定性量化（UQ），因其能提供可解释的函数不确定性估计。然而，这些不确定性的概率意义往往不明确，也缺乏校准依据，导致其价值受限且仅具定性意义。本文通过靶向自适应设计（TAD）优化算法说明：若GP预测未校准，将导致收敛性能下降。文章探讨了如何通过正式的核函数验证程序，基于GP预测的多元正态性质，建立对不确定性区间的可信度。以一维回归为例展示模型误设情况，并讨论高维情形下的适用性。
原文摘要 · Abstract (English)
Gaussian Process (GP) models are popular tools in uncertainty quantification (UQ) because they purport to furnish functional uncertainty estimates that can be used to represent model uncertainty. It is often difficult to state with precision what probabilistic interpretation attaches to such an uncertainty, and in what way is it calibrated. Without such a calibration statement, the value of such uncertainty estimates is quite limited and qualitative. We motivate the importance of proper probabilistic calibration of GP predictions by describing how GP predictive calibration failures can cause degraded convergence properties in a target optimization algorithm called Targeted Adaptive Design (TAD). We discuss the interpretation of GP-generated uncertainty intervals in UQ, and how one may learn to trust them, through a formal procedure for covariance kernel validation that exploits the multivariate normal nature of GP predictions. We give simple examples of GP regression misspecified 1-dimensional models, and discuss the situation with respect to higher-dimensional models.
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