面向高效高斯过程流的特征空间适配
Feature Space Adaptation for Effortless Gaussian Process Flows
- University of Cambridge（剑桥大学）
- University College London（伦敦大学学院）
- University of New South Wales（新南威尔士大学）
- Lancaster University（兰开斯特大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对FlowGP的缺陷，引入核近似与边际似然获取方法，首次实现其超参数优化，并在三类任务中验证了所提方法的有效性。
AI中文摘要：
在线性-高斯框架之外，从高斯过程（GPs）进行条件采样颇具挑战性。近期的FlowGP（Moss等人，2026）等方法可对任意非线性、非高斯陈述进行条件处理，但代价高昂：需手动指定核超参数的昂贵迭代高维扩散过程。本文针对FlowGP的两大显著缺陷加以改进：（1）引入核近似方法，使其可扩展至高分辨率域；（2）提出通过测量引导扩散至条件陈述所需的工作量来获取边际似然的方法。我们首次在FlowGP中实现了超参数优化，并在以下任务中验证了所提方法：基于区域汇总统计量的概率降尺度、不规则域的偏微分方程（PDE）解推断，以及从非高斯卫星观测中恢复海平面异常场。
英文摘要：
Outside the linear-Gaussian regime, conditional sampling from Gaussian processes (GPs) is challenging. Recent methods such as FlowGP (Moss et al., (2026)) can condition on arbitrary non-linear and non-Gaussian statements, but at considerable cost: an expensive iterative and high-dimensional diffusion that requires hand-specified kernel hyperparameters. In this paper, we alleviate two significant drawbacks of FlowGP by (1) introducing kernel approximations that enable scaling to high-resolution domains and (2) proposing a way to obtain the marginal likelihood by measuring the work needed to steer the diffusion towards conditioning statements. We enable, for the first time, hyperparameter optimisation within FlowGP and demonstrate our approach on probabilistic downscaling from areal summary statistics, PDE solution inference on irregular domains, and recovery of sea level anomaly fields from non-Gaussian satellite observations.
