GPLFR beats PCA-GP for low-data, high-dimensional regression tasks

A team led by Edward T. Stevenson (University of Cambridge / Cornell) and including Miles Cranmer has proposed Gaussian Process Latent Factor Regression (GPLFR), a new approach for regression problems where the output space is high-dimensional but training data is scarce. The method treats each output as a linear-Gaussian decoding of a low-dimensional latent state drawn from a Gaussian process prior. By analytically marginalizing the decoder weights, GPLFR couples compression and prediction into a single objective, scaling efficiently to high-dimensional outputs. This contrasts with the common compress-then-predict pipeline (e.g., PCA-GP), which uses a basis optimized for reconstruction rather than prediction, often leading to suboptimal performance in low-data regimes.

GPLFR's effectiveness is showcased by building the first spatially resolved emulator of global climate models for rocky exoplanets—a domain with extremely limited observational training data. The model emulates high-dimensional climate fields (temperature, pressure, etc.) given stellar and planetary parameters. This opens new possibilities for exoplanet characterization, allowing rapid exploration of climate states without running full general circulation models. The paper (arXiv:2606.06576) includes 9 pages of content plus appendices, with supporting code on GitHub. The work bridges machine learning and astrophysics, offering a general tool for any scientific field facing low-data, high-dimensional regression challenges.