arXiv：cs.LG· Thomas Cowperthwaite, Louis Sharrock, Lachlan Astfalck, Henry Moss·· 3 小时前
FlowGP 的 Feature Space Adaptation：无需手动调参的高斯过程流
Feature Space Adaptation for Effortless Gaussian Process Flows
AI 导读
研究者提出 Feature Space Adaptation 方法，缓解 FlowGP 在非线性、非高斯条件下采样的两大缺陷：引入核近似以扩展到高分辨率域，并通过测量将扩散引导至条件语句所需的工作量来获得边际似然。该方法首次在 FlowGP 中实现超参数优化，并在地理区域统计量概率降尺度、不规则域 PDE 解推断和从非高斯卫星观测中恢复海平面异常场三项任务上得到验证。
正文
Abstract: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.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); Methodology (stat.ME) |
| Cite as: | arXiv:2610.11459 [stat.ML] |
| (or arXiv:2610.11459v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.11459 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Thomas Cowperthwaite [view email]
[v1]
Thu, 8 Oct 2026 08:12:13 UTC (1,010 KB)
来源：arXiv：cs.LG · arxiv.org