Gaussian Process Latent Factor Regression for High-Dimensional Outputs

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 method 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 method as Gaussian process latent factor regression (GPLFR). We demonstrate GPLFR by building a spatially resolved emulator of global climate models for rocky exoplanets. Code: https://anonymous.4open.science/r/GPLFR-2C0B