论文标题
vecchia approximated的深gaussian流程用于计算机实验
Vecchia-approximated Deep Gaussian Processes for Computer Experiments
论文作者
论文摘要
Deep Gaussian过程（DGPS）通过功能组成升级了普通的GP，其中中间GP层经翘曲原始输入，从而为非平稳动力学提供了灵活性。最近的文献中出现了两个DGP政权。在机器学习中普遍存在的“大数据”制度有利于基于快速，高保真预测的近似，基于优化的推断。用于计算机替代建模的“小数据”制度部署后验积分以增强不确定性定量（UQ）。我们的目的是通过掺入Vecchia近似值来扩大贝叶斯DGP后推断的能力来弥合这一差距，从而允许线性计算缩放而不会损害精度或UQ。我们的动机是由超过100,000次运行的模拟运动的替代建模（对于以前的完全bayesian实施而言太大），并证明了预测和UQ优于“大数据”竞争对手的预测。所有方法均在Cran的“ DEEPGP”软件包中实现。
Deep Gaussian processes (DGPs) upgrade ordinary GPs through functional composition, in which intermediate GP layers warp the original inputs, providing flexibility to model non-stationary dynamics. Two DGP regimes have emerged in recent literature. A "big data" regime, prevalent in machine learning, favors approximate, optimization-based inference for fast, high-fidelity prediction. A "small data" regime, preferred for computer surrogate modeling, deploys posterior integration for enhanced uncertainty quantification (UQ). We aim to bridge this gap by expanding the capabilities of Bayesian DGP posterior inference through the incorporation of the Vecchia approximation, allowing linear computational scaling without compromising accuracy or UQ. We are motivated by surrogate modeling of simulation campaigns with upwards of 100,000 runs - a size too large for previous fully-Bayesian implementations - and demonstrate prediction and UQ superior to that of "big data" competitors. All methods are implemented in the "deepgp" package on CRAN.
