Gaussian Process Latent Factor Regression for Low-Data, High-Dimensional Output Problems
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Computer Science > Machine Learning
Title:Gaussian Process Latent Factor Regression for Low-Data, High-Dimensional Output Problems
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.
| Comments: | 9 pages content + 22 pages appendix/references. Supporting code at this https URL |
| Subjects: | Machine Learning (cs.LG); Earth and Planetary Astrophysics (astro-ph.EP); Instrumentation and Methods for Astrophysics (astro-ph.IM); Machine Learning (stat.ML) |
| Cite as: | arXiv:2606.06576 [cs.LG] |
| (or arXiv:2606.06576v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.06576
arXiv-issued DOI via DataCite (pending registration)
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Submission history
From: Edward Stevenson [view email][v1] Thu, 4 Jun 2026 18:00:00 UTC (16,424 KB)
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