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arXiv · 2605.05133

Transformed Latent Variable Multi-Output Gaussian Processes

Xiaoyu Jiang·Xinxing Shi·Sokratia Georgaka·Magnus Rattray·Mauricio A Álvarez
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Abstract

Multi-Output Gaussian Processes (MOGPs) provide a principled probabilistic framework for modelling correlated outputs but face scalability bottlenecks when applied to datasets with high-dimensional output spaces. To maintain tractability, existing methods typically resort to restrictive assumptions, such as employing low-rank or sum-of-separable kernels, which can limit expressiveness. We propose the Transformed Latent Variable MOGP (T-LVMOGP), a novel framework that scales MOGPs to a massive number of outputs while preserving the capacity to capture meaningful inter-output dependencies. T-LVMOGP constructs a flexible multi-output deep kernel by mapping inputs and output-specific latent variables into an embedding space using a Lipschitz-regularised neural network. Combined with stochastic variational inference, our model effectively scales to high-dimensional output settings. Across diverse benchmarks, including climate modelling with over 10,000 outputs and zero-inflated spatial transcriptomics data, T-LVMOGP outperforms baselines in both predictive accuracy and computational efficiency.

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Xiaoyu Jiang, Xinxing Shi, Sokratia Georgaka, Magnus Rattray, Mauricio A Álvarez. 2026-05-06. Transformed Latent Variable Multi-Output Gaussian Processes. https://arxiv.org/abs/2605.05133

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