用于时空不规则性的协方差增强高斯过程

中文摘要 AI 辅助

非平稳高斯过程（GP）模型是通过适应观测数据来捕捉输入相关变异性的强大工具。然而，由于采样有限和协方差结构高度参数化，它们往往容易过拟合和不确定性估计过度自信，在安全关键应用中可能导致误导性预测。本文受卫星增强系统（SBAS）电离层建模的启发，提出了一个协方差增强高斯过程（CBGP）框架，该框架以增强协方差先验为中心，以发现用于信号和观测变化的非平稳潜在函数，从而捕捉输入域中的不规则性。对“部分白化”观测的GP建模的附加层指导潜在函数相对误差估计，该估计用于在类似梯度下降的过程中迭代更新弱先验。增强后，对先验协方差施加限制以防止过拟合，同时扩大后验不确定性以防止模型过度自信。通过对模拟和实际应用的样本外测试证明了CBGP模型的有效性和鲁棒性，这些测试符合三个九的完整性标准。对南美洲广泛电离层风暴数据集的建模表明，使用比当前运行的SBAS进行的局部拟合更有信息和响应性的区域模型，可以在最具挑战性的空间天气环境中计算SBAS电离层校正的准确可靠方法。

英文摘要

Nonstationary Gaussian process (GP) models are powerful tools for capturing input-dependent variability by adapting to observed data. However, with limited sampling and highly parameterized covariance structure, they are often prone to overfitting and overconfident uncertainty estimates, potentially leading to misleading predictions in safety-critical applications. Motivated by ionospheric modeling for satellite-based augmentation systems (SBAS), this paper proposes a Covariance-Boosted Gaussian Process (CBGP) framework centered upon boosting covariance priors to discover nonstationary latent functions for signal and observation variation that capture irregularities in the input domain. An additional layer of GP modeling of "partially-whitened" observations guides latent function relative error estimation that is used to iteratively update weak priors in a gradient descent-like procedure. Following boosting, restrictions are imposed upon prior covariances to prevent overfitting while posterior uncertainties are inflated to prevent model overconfidence. CBGP model efficacy and robustness are demonstrated through out-of-sample testing of both simulated and real-world applications that meet a three-nines integrity standard. The modeling of an extensive ionospheric storm dataset over South America suggests accurate and reliable means to compute SBAS ionospheric corrections in the most challenging space weather environment using regional models that are more informed and responsive than local fitting performed by currently-operating SBAS.

发表机构

• Sequoia Research Corporation（红杉研究公司）

机构由 AI 辅助整理，请以论文原文为准。