Transformed Latent Variable Multi-Output Gaussian Processes
For practitioners needing probabilistic models for high-dimensional correlated outputs, T-LVMOGP offers a scalable and expressive alternative to restrictive low-rank MOGPs.
T-LVMOGP scales multi-output Gaussian processes to high-dimensional outputs (e.g., >10,000) using a deep kernel with Lipschitz-regularized neural networks, achieving better predictive accuracy and efficiency than baselines on climate and spatial transcriptomics benchmarks.
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.