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

2026-07-08 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Space Science & Astronomy, Health & Medical Research · Depth: Expert, extended

Summary

Gaussian Process Latent Factor Regression (GPLFR) is a new probabilistic model designed for regression tasks with low training data and high-dimensional outputs, common in scientific fields. Unlike traditional compress-then-predict methods like PCA-GP, GPLFR jointly learns latent representations and output reconstruction, biasing the representation towards predictability from inputs. This approach addresses the issue where PCA-GP's basis is optimized for reconstruction rather than prediction, especially when structured, unpredictable variation is present. Experiments show GPLFR achieves the same error as PCA-GP with approximately 4× fewer training data on a synthetic benchmark. It also demonstrates superior sample and representation efficiency in biomedical optics emulation and strongly outperforms alternatives in emulating global climate models for rocky exoplanets, handling D_y ≈ 3 × 10^4 output dimensions.

Key takeaway

For Research Scientists or Machine Learning Engineers developing emulators for complex scientific simulations with limited data and high-dimensional outputs, GPLFR offers a significant advantage over traditional PCA-GP pipelines. You should consider implementing GPLFR to improve sample efficiency and prediction accuracy, especially when dealing with structured output noise. Be prepared for a more challenging optimization landscape, which can be mitigated using likelihood tempering and latent noise regularization.

Key insights

GPLFR couples representation learning and regression to prioritize predictable structure in high-dimensional, low-data output problems.

Principles

• Jointly optimize latent representation and regression.
• Bias representation towards input-predictable structure.
• Analytically marginalize decoder weights.

Method

GPLFR represents outputs as a linear-Gaussian decoding of a low-dimensional latent state from a GP prior. It analytically marginalizes decoder weights, coupling compression and prediction in a single objective. Optimization uses MAP estimation with Adam, stabilized by likelihood tempering and latent noise.

In practice

• Use GPLFR for high-dimensional scientific emulation.
• Apply likelihood tempering for decoder misspecification.
• Consider PCA initialization for noiseless data.

Topics

• Gaussian Process Regression
• Latent Factor Models
• High-Dimensional Regression
• Exoplanet Climate Models
• Scientific Emulation
• Low-Data Learning

Code references

• edstevenson/GPLFR

Best for: AI Scientist, Research Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.