Transformed Latent Variable Multi-Output Gaussian Processes
Xiaoyu Jiang, Xinxing Shi, Sokratia Georgaka, Magnus Rattray, Mauricio A Álvarez
TLDR
T-LVMOGP scales Multi-Output Gaussian Processes to massive outputs by using a deep kernel and variational inference, outperforming baselines.
Key contributions
- Scales Multi-Output Gaussian Processes (MOGPs) to over 10,000 outputs, overcoming prior limitations.
- Maintains expressiveness by capturing complex inter-output dependencies without restrictive assumptions.
- Utilizes a Lipschitz-regularised neural network and deep kernel for flexible input-output mappings.
- Achieves superior predictive accuracy and computational efficiency through stochastic variational inference.
Why it matters
Multi-Output Gaussian Processes are powerful but struggle with high-dimensional data. T-LVMOGP provides a scalable and expressive framework to overcome this. This enables accurate modeling of complex datasets, opening new possibilities in fields like climate science and genomics.
Original 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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