Improved Gaussian process flows for easier and faster probabilistic modeling
Feature Space Adaptation for Effortless Gaussian Process Flows
Machine Learning
Summary
Gaussian processes are a way to make predictions about complex data, but they become hard to use when the data is not simple or linear. The authors improve an existing method called FlowGP by making it faster and easier to tune, so it works better with complicated, real-world data. They do this by introducing new math tricks that speed up the process and let the system learn important settings automatically. Their approach helps with tasks like refining coarse geographical data and filling in missing information from satellite images.
What this means in practice
- •For climate modelers: Better reconstruct fine-grained climate data from large-area satellite summaries using more accurate and scalable probabilistic models.
- •For engineering simulation teams: Provide reliable inference tools for solving partial differential equations on complex domain shapes with non-standard data distributions.
Authors
Thomas Cowperthwaite, Louis Sharrock, Lachlan Astfalck, Henry Moss
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.