Gaussian Process Latent Factor Regression for Low-Data, High-Dimensional Output Problems

arXiv:2606.06576 · cs.LG, astro-ph.EP, astro-ph.IM, stat.ML · Submitted 2026-06-04 · Read on arXiv

Edward T. Stevenson, Eric T. Wolf, Mei Ting Mak, N. J. Mayne, Miles Cranmer

cs.LG, astro-ph.EP, astro-ph.IM, stat.ML

Submitted: 2026-06-04

Comments: 9 pages content + 23 pages appendix/references. Supporting code at https://github.com/edstevenson/GPLFR

Code: https://github.com/edstevenson/GPLFR

License: http://creativecommons.org/licenses/by/4.0/

The gist: In the sciences, regression tasks often require predicting high-dimensional outputs from few training examples.

Terminology

Abstract

In the sciences, regression tasks often require predicting high-dimensional outputs from few training examples. Multi-output Gaussian processes excel in low-data regimes but typically struggle with high-dimensional outputs. Compress-then-predict pipelines such as PCA-GP (principal component analysis plus Gaussian process regression) handle high dimensionality, but rely on bases optimized for reconstruction rather than prediction. To address this gap, we propose a model that represents 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, we couple compression and prediction in a single objective that scales to high-dimensional outputs. We refer to this model as Gaussian process latent factor regression (GPLFR). We demonstrate GPLFR by building the first spatially resolved emulator of global climate models for rocky exoplanets.

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